Abstract

Electrons in atoms and molecules are versatile physical systems allowing a vast range of light–matter interactions. Spontaneous emission, which appears in a wide variety of applications, depends crucially on the bound electron energy levels. The discrete nature of these electron energy levels and the ionization threshold constrain the energy scale of all light–matter interactions involving bound electrons. To bypass these constraints, we take ideas from optical and electronic beam shaping and propose creating new electron states as superpositions of extended states above the ionization threshold. We show that such superpositions enable the control of spontaneous emission with tunable spectra in the eV–keV range. We find that the specific shaping lengthens the diffraction and radiative lifetimes of the wavepackets in exchange for increasing their spatial spreads. Our approach could have applications toward developing novel kinds of light emitters at hard-to-access spectral ranges.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

The rich physics of bound electrons in atoms and molecules is typically limited by the discrete nature of the energy spectrum and by the ionization energy threshold. This is why many phenomena considered in atomic physics are usually confined to the IR–UV spectral range. The upper limit is set by the typical ionization threshold of the outer valence electrons. Going beyond these energy ranges usually involves free electrons that can be manipulated with a strong electromagnetic field [1,2]. Another promising approach to access light–matter interactions at the UV frequencies and above is by high-harmonic generation, also using strong fields, yet applied on initially bound electrons [38]. In either case, the interaction has to involve extended electron states out of equilibrium, manipulated by the strong fields. It seems inevitable then that accessing light–matter interactions at such high frequencies always involves states that are not bound in space and are therefore not considered relevant for atomic physics phenomena.

One could conceive of a completely different way to deal with this problem by engineering the potential to allow for the existence of bound states in the continuum (BICs) [9]. Von Neumann and Wigner were the first to introduce such a construction, defying the conventional wisdom that bound states must be spectrally separated from the extended states [10]. However, the kinds of potentials that support BICs have to be specially designed, while the potentials of atoms and molecules generally cannot be designed [1114].

We will consider another approach by which electron states in the continuum can behave as bound states: shaping the electron as a superposition of extended states to create a localized wavepacket. For example, in 1979, Berry and Balázs proposed a solution of the free-space Schrödinger equation that appears to be localized in 1D and whose shape remains time invariant as with bound electron states (while it also exhibits self-acceleration) [15]. In recent years, this idea has been extensively explored in the optics community, with paraxial and non-paraxial optical beams [1619].

More generally, these kinds of optical beams, such as Bessel [2023] and Airy [16,17] beams, are propagation-invariant wave functions and have the intriguing property of self-healing—restoring their original shape after encountering an obstacle [24]. Such beams can also remain propagation invariant in curved spaces [25,26] and in nonlinear media [27,28]. While the above wavepackets are localized mostly only in 2D, the concept of optical beam shaping can also be applied to create “light-bullets,” which are localized in 3D [29,30]. Importantly, due to the mathematical analogies between optical wavepackets and electron wavepackets, similar concepts are applicable to electrons [3137].

However, the well-known problem with all of the above time-invariant or propagation-invariant wavepackets is that their probability density is not square integrable (hence, without a physical interpretation as a probability density). To circumvent this, one can truncate the wavepackets at a finite distance. In this case, there is no exact time invariance or propagation invariance, but the non-diffracting properties are still present for a finite time and distance, which can be long enough for the desired interaction in experiments [17,32,3840]. Another approach that makes the wavepacket square integrable is shaping a superposition of a range of energies/frequencies, which can create a localized wavepacket, in exchange for limiting its range/duration for which it is non-diffracting [30]. Therefore, wavepacket shaping in space and time offers localized and long-lived electron wavepackets in the continuum of energy levels, created from superpositions of extended states.

With the above wavepackets in mind, we now ask: can shaped electron wavepackets mimic optical phenomena of conventional bound electron states in atoms, such as electron transitions by light emission/absorption? Can shaped electrons give us access to light–matter interactions beyond the ionization threshold that limits bound electron systems? For example, can one create engineered spontaneous emission dynamics (engineered rates, engineered optical spectra, etc.) by shaping a superposition of extended states in the energy continuum to have a tailored spatial profile and energy spectrum?

Here, we propose shape-invariant wavepackets in the presence of a general potential (e.g., the Coulomb potential) that simultaneously suppress their own diffraction, while enabling access to a customizable spectrum of transitions, ranging from the visible to the hard x-ray, via radiative decay to bound states. We develop the analytic tools to maintain the shape invariance of wavepackets and the analytic tools to calculate the radiative transitions of such states into bound states of the potential. Our methods can be extended to a variety of potentials, including the transitions of free electrons illuminated by general time-dependent fields. Specifically for the Coulomb potential, we derive the shape-invariant electron wavepackets and study their dynamics. For example, we find that a shape-invariant wavepacket also affects the behavior of the electron in the Coulomb potential. We show that the presence of a Coulomb potential changes the physics of the system drastically relative to free electrons by allowing shaped wavepackets to decay to bound states through radiative capture. We monitor the “competition” between spontaneous emission and diffraction by developing a quantum electrodynamics (QED) formalism that quantifies the rate of decay by the excited wavepacket, studying specifically how the wavepacket shape alters the emitted radiation into the far field. We find that in all these cases, the wavepacket’s lifetime is limited by the diffraction dynamics of its wavepacket. Even though, in general, the electron wavepackets we consider are diffracting and subject to spontaneous emission, we find parameters that can suppress both effects significantly. Hence, we concisely refer to the shaped wavepackets, which are almost propagation invariant and time invariant, as being quasi-shape invariant.

2. RESULTS

A. Constructing Quasi-Shape-Invariant Wavepackets

To illustrate the concept of quasi-shape-invariant quantum wavepackets above the ionization threshold, we begin from the textbook example of the hydrogen atom, consisting of the Schrödinger equation with the Coulomb potential V(r)=e2/4πϵ0r. The hydrogen atom is one of the most famous problems in quantum mechanics; its electron bound states are well studied, and analytic expressions for the extended states exist in the literature [41]. We introduce a dimensionless parameter x, defined by x=(2/a0)r with spherical radius r and the Bohr radius a0. Likewise, let κ=ka0 be the dimensionless parameter from momentum k.

Figure 1 presents the shaping of the electron wavepacket that is created from superpositions of extended eigenstates, which are called the Whittaker functions wκ(x,t) and can be found in [42]. These eigenstates are of the form

wκ(x,0)=4iκ2eiκxπcsch(π/2κ)01e2iκxs(s1s)i2κds,
and wκ(x,t)=wκ(x,0)exp(iωtκ2), where the time evolution frequency is given by ωκ2 with ω=e2/2πϵ0a082fs1. We focus on a spherically symmetric wavepacket with a Gaussian weighting over momentum space ΨE,ΔE given as follows:
ΨE,ΔE(r,t)=Ne(κμ)2/2σ2wκ(x,t)dκ,
where N is a normalization constant, and μ and σ are the mean and spread (standard deviation) of momentum. In SI units, the energy E is parameterized as E(κ)=(2e2/4πϵ0a0)κx2 via the dimensionless κ. We denote E=E(μ) and ΔE for the spread (standard deviation). As opposed to the bound states, the electron states (1) in the continuum of the energy spectrum are described by Whittaker functions; thus, we call our wavepackets (2) “Whittaker wavepackets.” This wavepacket is customizable because in principle, we can choose arbitrary E and ΔE within the energy continuum. We note that in principle, a Gaussian spread in energy may be realized by exciting the electron with a source that has a coherent distribution of excitation energies of finite bandwidth, such as a laser, where the distribution can be approximated as a Gaussian. In any case, similar results should be obtained for other energy distributions of the electron wavepacket.

 

Fig. 1. Shaping of electron states in the continuum of energy levels of the hydrogen atom creates localized and quasi-shape-invariant high-energy wavepackets, unlimited in energy. The possibility of decay from the continuum to bound states enables a photon emission with energy higher than the ionization threshold. Color, r2|Ψ|2/max{r2|Ψ|2}.

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B. Spatial and Temporal Dynamics

Having shaped the wavepackets, we now characterize their spatial and temporal dynamics. We do this by defining a spatial spread Δr, given by a standard deviation,

Δr=var(envelope(ΨE,ΔE(r,0))),
and a diffraction lifetime Δt, also defined as a standard deviation,
Δt=var(O(t))
of an overlap function
O(t)=|0Ψ*(r,0)Ψ(r,t)r2dr|2.
The overlap function is essentially the degree of first-order temporal coherence, and the diffraction lifetime is essentially the coherence time. Figure 2(a) confirms that as we decrease the energy spread ΔE, then Δr increases. Thus, there is less probability to find the electron near the origin. Manifestly, this should hold true, as a narrower ΔE yields a wavepacket approaching an extended state. From the analytic form of the Whittaker wavepacket (2), we find a functional form for the spatial spread, which we will use later to determine optimal parameters for long-lived bound-like free-electron wavepackets in a potential. We find that the spatial spread is given by
Δr2.471a0(ΔE)/eV.
Furthermore, the overlap O(t) resembles a Gaussian function, as shown in Fig. 2(b). In a similar fashion, as we decrease ΔE, the diffraction lifetime increases, because we approach an extended state that does not diffract (has infinite diffraction lifetime). The diffraction lifetime goes as
Δt0.136eV·fs(ΔE)E.
Further discussion on the determination of formulas (6) and (7) is deferred to Supplement 1, Section II. In Supplement 1, Section IV, we comment on our numerical fits. (See Code 1, Ref. [43] for the files used in our experiment.) Figure 2(c) shows how Δt increases when ΔE is taken to be smaller. In the figure we observe the quasi-shape-invariant nature of the Whittaker wavepackets, i.e., the flexibility to tune large Δt by customizing the parameters E and ΔE and thus obtaining shape-invariant dynamics and slow diffraction over tens of nanoseconds. We view the large Δt as the quasi-shape-invariant evolution of the long-lived Whittaker electrons.

 

Fig. 2. By shaping the (Whittaker) electron wavepacket, we can prolong the lifetime to a desired duration in exchange for increasing the spatial spread. (a) As we decrease the energy spread ΔE, the probability density r2|Ψ|2 spreads out farther in space according to (6). (b) The benefit of making the energy spread small, however, is that the lifetime grows according to (7). Here, Δt=19.14ns and the colors match the Whittaker wavepackets in (a). (c) Envelope of the wavepacket at three points in time: A, B, C [also marked in (b)].

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C. Profile of the Quasi-Shape-Invariant Wavepackets

We now study the profile of the Whittaker wavepacket and how it evolves in time in a quasi-shape-invariant manner. Just as wavepacket shaping is known to extend the lifetime of Dirac fermions [44], wavepacket shaping extends both the diffraction and radiative lifetimes of a Schrödinger electron wavepacket, as the Whittaker wavepacket considered here. For example, Fig. 3(a) presents the Whittaker wavepacket’s radial wavefunction at time zero, marking its nodal structure that highlights the shape-invariant properties, in a fashion similar to the shaped packets in related works [1518,20,21,24,44].

 

Fig. 3. Dynamics of the Whittaker wavepacket. (a) The wavepacket begins at t=0, with a set of nodes marked by dots. The dotted lines trace the nodes, and the cross signals a vanished node. Time frames and overlap points linked in color. (b) A larger range in space that includes more oscillations (only the envelope is plotted) and has a longer lifetime Δt. (c) The geometry of the Whittaker wavepacket is roughly the same as that of the free particle with Bessel functions as modes. Baseline ΔE0/E0 set in (a).

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In particular, as time evolves, the nodes vanish sequentially, which happens via “lifting” of the wavepacket profile due to continuity. The amplitude of the spatial oscillations decreases in time until the nodes vanish and the wavepacket starts to spread out in space. Originally, the Whittaker modes wκ are in phase. Their closely spaced zeros define the nodal structure of the Whittaker wavepacket (see Supplement 1). As we vary time t, the factors exp(iωtκ2) put the modes wκ out of phase; thus, the zeros of the Whittaker wavepacket continuously disappear. In this way, the diffraction eventually destroys the original nodal structure, and having no nodes means that the wavepacket is free to spread in space like a free wavepacket, as shown in Fig. 3(b). In Fig. 3(b), the upper and lower envelopes converge, which destroys the nodal structure. This process of “node lifting” bottlenecks the diffraction of the wavepacket and enables the quasi-shape-invariant property. Notice the similarity between the dynamics of the envelopes in (a) and (b). Finally, in Fig. 3(c), we show that free-particle wavepackets also have a similar nodal structure at time zero, which yields approximately the same overlap function as that of Whittaker wavepackets. A way to see why this holds true is to look at the limiting behavior of the extended mode (1) for large r (x1) [45]: wκ(x,0)exp(iκx)exp(i(1/2κ)ln(x))/x. The logarithmic dependence on x is due to the Coulomb potential. Thus, the electron wavepacket does not approximate a free-particle wave exactly; however, at large values of x, the oscillations from exp(iκx) are dominant and form the free-particle modes. This means that the Whittaker wavepacket at large radii is similar to that of a free particle; hence their time evolutions should be similar. This similarity shows that our methods and conclusions also apply for free electron wavepackets (possibly with a time-dependent perturbation, such as pulsed laser excitation).

D. Radiative Decay

Importantly, however, the physics of free particles is different from that of electrons in a potential. The potential may cause scattering processes between the proton and electron, which in turn could lower the energy of the electron through radiative decay, and thus reduce its stability. We now quantitatively evaluate the competition between diffraction and radiative decay by quantifying the radiative decay. We further show how the shape (specifically spatial extent) of the wavepacket changes the rate of photon emission. Moreover, the spectrum of decay by the electronic wavepacket can be controlled by controlling the mean energy of the wavepacket, and thus the spectral peaks can be continuously tuned if the excitation energy of the electron wavepacket is so tuned.

To show this, we calculate the probability of decay Pn(t)to a bound state |n at a given time t; we develop a formalism (described in Section 4 Methods) through the S-matrix approach [41]. The total decay probability is simply the sum P(t)=n=1Pn(t). Having the total probability, we define the average rate of decay over the time of two diffraction lifetimes Δt via the formula

Γ˜=P(2(Δt))2(Δt)
and analyze it in Fig. 4. In (a) we observe that the probability saturates within a time on the order of Δt. As time evolves, the electron is farther away from the origin; thus, the effect of the Coulomb potential is reduced, and the instantaneous rate of decay converges to zero. The profile of decay rates to individual bound states follows an oscillatory pattern, with the highest decay rate to n=2. Moreover, in both cases, (a) and (b), we find that the dynamics and lifetime of the electron wavepacket are dominated by the diffraction and not by the radiative decay, as the diffraction lifetime is generally shorter than the radiative lifetime. In particular, if we hypothesize a lifetime 1/Γ˜ due to spontaneous emission, then we see that in general Δt1/Γ˜. For example, if E=1eV and ΔE=5.44×105eV, then Γ˜=6.58×106Hz. This yields a hypothetical lifetime of 1/6.58×106Hz=152ns. As a comparison, for the same case, Δt=1.91fs. We also observe the pattern that Γ˜ grows with an increase in ΔE. Many other such examples where Γ˜Δt are given in Supplement 1, Section IV.

 

Fig. 4. Radiative decay of the Whittaker wavepackets to bound states. (a) The decay probability reaches a saturation line for infrared energy E=1eV. The average rate approximates a slope. (b) The profiles of the decay rates (small panels) for the soft-x-ray energy E=217.6eV are monotonously decreasing in comparison to the profiles in (a). Baseline ΔE0/E0 set in (a). Note that (b) may have quantitative corrections due to beyond-dipole corrections arising from the short wavelength of the electromagnetic field, since for our spontaneous emission calculations, we use the dipole approximation.

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Since the radiative lifetime is much longer than the diffraction lifetime, we conclude that formulas (6) and (7) give a good parameterization of the stability and the large Δt versus large Δr trade-off of the Whittaker wavepackets, and show how those properties can be customized.

E. Quantitative Examples

We now present quantitative examples of parameters achievable with Whittaker wavepackets, summarized in Table 1. For a quasi-shape-invariant wavepacket to be considered stable enough for optical transitions, its diffraction lifetime Δt should be longer than the period of the optical cycle of light emitted in the transition. For wavepackets designed to have transitions in the x-ray frequencies, the shortest lifetime we consider in Table 1 is 53 as (comparable to the shortest x-ray pulse duration measured [46] with high-harmonic generation [4749]). For the largest Δr, considered in Table 1, we take 143 nm (comparable to the recently observed [50] Rydberg state at the n=52 state). We note that by shaping electrons in transmission electron microscopes, coherent wavepackets over spatial extents of tens of micrometers have been observed [51]; hence, one can consider much wider electron wavepackets as well. To give specific examples from Table 1, if we fix Δt=53as, then according to formulas (6) and (7) a soft x-ray Whittaker wavepacket (E=200eV) has an energy spread ΔE=0.033eV and a spatial spread Δr=0.72nm, which all fit within the limits established here. If we consider a hard x-ray Whittaker wavepacket (E=10keV), then the energy spread has to shrink to ΔE=660μeV; for the same lifetime, however, Δr gets to 5.1 nm, much smaller than 143 nm. We also studied Whittaker wavepackets with lifetimes on the order of nanoseconds, which require spread Δr on the order of micrometers.

Tables Icon

Table 1. Spread-Lifetime Trade-Off of Whittaker Wavepacketsa

3. DISCUSSION

We have proposed shaping quasi-shape-invariant wavepackets in the continuum of the hydrogen atom. By studying the dynamics of the wavepackets, we utilize the large lifetime versus large spatial spread trade-off of the wavepackets to extend the transition lifetime (both radiative and diffraction lifetimes). These wavepackets exhibit unique phenomena in their decay dynamics, such as a stark change from radiative decay similar to bound states at short times, to saturation at long times (once the electron’s probability density spreads away).

Our approach involves the reduction of the Scrödinger equation to a confluent hypergeometric equation above the ionization threshold, which is known in the literature to lead to the non-singular Whittaker solutions [52,53]. To the best of our knowledge, the quasi-shape-invariant applications of Whittaker wavepackets have been previously unexplored. More importantly, the methods utilized here can be extended directly to other potentials to design additional long-lived wavepackets.

As a proof of concept, we demonstrate our method for the one-electron case. In principle, we could extend our work to many-electron wavepackets: consider the joint wavefunction of a multiple-electron system. With some mean-field techniques, such a possibility has been considered before [54], and it could be an interesting idea for future research to see whether it can alter the light–matter interactions of the many-electron system as in our current paper. Many of the concepts from our paper will still apply in the many-electron case. Altogether, it is clear that the hydrogen atom does not capture all of the physics in any possible system, as, for example, there are no additional electrons. Nevertheless, some competing decay mechanisms could be captured phenomenologically by a master equation approach, to take into account decoherence induced by electron–electron interaction.

It would also be interesting to consider whether or not the energy bandwidth of the shaped electron would be converted into the spectral bandwidth of the emitted radiation. Similarly, the coherence of the radiation could be related to the coherence function of the electron. For example, a partially mixed electron state would probably result in a partially mixed radiation state.

We believe that a promising approach for generating quasi-shape-invariant wavepackets is to use quantum optimal control to generate our wavepackets [55]. For example, [56] demonstrates directed electron XUV emission for hydrogen and argon through an optimization process that targets particular photoelectron spectra and angular distributions of the emission in photoionization. Moreover, [57] proposes a gradient-free quantum control method to derive pulses that create tailored superpositions of hole states for argon with predefined properties. In a similar fashion, we could design the optical pulses by solving an optimization problem that aims to match the overlap function and radiative decay of quasi-shape-invariant wavepackets ( [57] even proposes what the target overlap function and radiative decay should be). The vector potential that describes the excitation pulse can be added as a classical potential to the Schrödinger equation, which we can solve by following the same approach and quantified with the same formulas (probably requiring some numerical work).

Other directions toward the design of the quasi-shape-invariant electron wavepacket include: shaping the light excitation with special nanostructures to enable control of the interference between free-electron superposition states [58], control of bound electrons [59,60], and programmable Rydberg wave packets [61]. Our theoretical work in combination with advances in coherent control could navigate research on generation of target electron wavepackets in the future. It may also be of interest to consider how laser-based shaping of an excited electron in the ionization continuum impacts the radiation emission in high-harmonic generation, where propagation of and radiation by an electron in the ionization continuum is a key step in the process.

Our methods, and specifically the time-dependent QED formalism, can be applied to a variety of other systems. For instance, a good candidate is the system of shaped free electrons that interact with time-dependent potentials [58,6267]. Thus, it will also be interesting to study how more complicated wavepacket shapes (e.g., Airy) alter the spontaneous radiative transition rates.

In most of the above methods, the shaping of the electron is done by fs laser pulses in the visible or infrared spectrum, carrying μJ-mJ pulse energy. This way, we can bring an electron to high energies (EUV, or even soft-x-ray scales) without any need for an x-ray source. For example, the same 1 mJ scale laser pulses that are used in high-harmonic generation [68] and in above-threshold ionization [69], as well as in coherent control in femtochemistry [70], can be used for our purposes. A particularly exciting opportunity for shaping quasi-shape-invariant electron wavepackets could make use of the quantum electron–photon interaction in laser-driven transmission electron microscopes [6367,71]. For example, recent work has shown the possibility to shape electron pulses into attosecond bunches [66,71], which is possible even on the level of the single electron wavepacket [72]. Very recent work also demonstrated the possibility to shape the orbital angular momentum of the electron through laser interaction [7375], as well as using multiple laser harmonics for the complete shaping of the electron in time [76].

Quasi-shape-invariant wavepackets can bring atomic physics phenomena to new energy ranges such as soft and hard x rays. Utilizing these phenomena might introduce new quantum light sources and other applications to a diversity of physical systems, including various Dirac particles and free electrons under strong fields, as well as other wave systems that often describe analogous physics, such as water waves, acoustic waves on membranes, and electromagnetic waves.

4. METHODS

A. Shaping of Quasi-Shape-Invariant Wavepackets

The nature of our analysis (both analytic and numerical) is universal and can be generalized to calculate the transitions of wavepackets under any potential, including time-dependent potentials. Specifically, the derivation of the Whittaker modes, the shaping of the wavepackets, the analytic monitoring of the evolution, and the shaping that enables the quasi-shape-invariant properties of the superpositions (see further details in Supplement 1, Sections I and II) can also be reproduced for electrons in the vicinity of other potentials. However, most cases would require finding the extended states numerically or working with arbitrary wavepackets, without finding the eigenstates at all. Furthermore, to obtain an analytic expression for the probability of transition decay from wavepackets in the continuum to bound states, we use time-dependent spontaneous emission calculations that, in theory, can be applied for any interaction potential.

B. QED Formalism for Radiative Decay

Our formalism is based on QED and the S-matrix approach [41], for which the probability of transition from the initial state |i to the final state |f, through the emission of a photon with momentum k and polarization λ, is given by

dPfi(k,λ)=Vd3k(2π)3|Sfi(k,λ)|2
for a finite volume V; here,
Sfi=f|Tei0tH^intdt|i
is the matrix element of the time-ordered unitary evolution operator of the EM interaction Hamiltonian
H^int[ψ]=iemed3xψ*A^(x,t)·ψ,
which for the wavepacket ψ is defined via the vector potential A^ and the mass of the electron me. Up to first order, we derive the universal expression
Sfi(k,λ)=eme2ϵ0ωkV0tdteiωktε^kλ·d3xψf*(x,t)eik·x·ψi(x,t)
for the photon’s frequency ωk and its polarization direction ε^kλ, the initial state ψi(x,t), the final state ψf(x,t) and its time-dependence eiωft (being an energy eigenstate). In this paper, we use |i as the Whittaker wavepacket and |f as the bound states, but wavepackets of any physical system can be used, either by using their analytic expressions as done here (complete derivations in Supplement 1, Section III), or going through a fully numerical approach.

Funding

Marie Curie (328853-MC-BSiCS); Department of Energy Fellowship (DE-FG02-97ER25308); U.S. Department of Energy (DE-SC0001299); Army Research Office (ARO) through the Institute for Soldier Nanotechnologies (W911NF-18-2-0048).

Acknowledgment

We would like to thank Pamela Siska, Thomas Christensen, Josué López, Peter Lu, and Jamison Sloan for useful comments on the paper, as well as Thomas Beck and Maxim Metlitski for useful discussions. I. K. was supported by the Marie Curie Grant and by the Azrieli Faculty Fellowship. N. R. was supported by the Department of Energy Fellowship DE-FG02-97ER25308.

 

See Supplement 1 for supporting content.

REFERENCES

1. L. Sch, Beam-Wave Interaction in Periodic and Quasi-Periodic Structures (Springer, 2011).

2. A. Friedman, A. Gover, G. Kurizki, S. Ruschin, and A. Yariv, “Spontaneous and stimulated emission from quasifree electrons,” Rev. Mod. Phys. 60, 471 (1988). [CrossRef]  

3. N. H. Burnett, H. A. Baldis, M. C. Richardson, and G. D. Enright, “Harmonic generation in CO2 laser target generation,” Appl. Phys. Lett. 31, 172–174 (1977). [CrossRef]  

4. A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987). [CrossRef]  

5. M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988). [CrossRef]  

6. A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998). [CrossRef]  

7. T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012). [CrossRef]  

8. D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018). [CrossRef]  

9. C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 331–335 (2016). [CrossRef]  

10. J. von Neumann and E. P. Wigner, “Über merkwürdige diskrete eigenwerte,” Phys. Z. 30, 465–467 (1929).

11. Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observations of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011). [CrossRef]  

12. C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013). [CrossRef]  

13. B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014). [CrossRef]  

14. N. Rivera, C. W. Hsu, B. Zhen, H. Buljan, J. D. Joannopoulos, and M. Soljačić, “Controlling directionality and dimensionality of radiation by perturbing separable bound states in the continuum,” Sci. Rep. 6, 33394 (2016). [CrossRef]  

15. M. V. Berry and N. L. Balázs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979). [CrossRef]  

16. G. A. Sivlioglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007). [CrossRef]  

17. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901(2007). [CrossRef]  

18. I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012). [CrossRef]  

19. R. Penciu, K. Makris, and N. Efremidis, “Nonparaxial abruptly autofocusing beams,” Opt. Lett. 41, 1042–1045 (2016). [CrossRef]  

20. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A. 4, 651–654 (1987). [CrossRef]  

21. J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987). [CrossRef]  

22. K. Makris and D. Psaltis, “Superoscillatory diffraction-free beams,” Opt. Lett. 36, 4335–4337 (2011). [CrossRef]  

23. K. Makris, D. Papazoglou, and S. Tzortzakis, “Invariant superoscillatory electromagnetic fields in 3D-space,” J. Opt. 19, 014003 (2016). [CrossRef]  

24. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008). [CrossRef]  

25. R. Bekenstein, J. Nemirovsky, I. Kaminer, and M. Segev, “Shape-preserving accelerating electromagnetic wave packets in curved space,” Phys. Rev. X 4, 011038 (2014). [CrossRef]  

26. A. Patsyk, M. A. Bandres, R. Bekenstein, and M. Segev, “Observation of accelerating wave packets in curved space,” Phys. Rev. X 8, 011001 (2018). [CrossRef]  

27. I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self trapped optical beams,” Phys. Rev. Lett. 106, 213902 (2011). [CrossRef]  

28. I. Kaminer, J. Nemirovsky, and M. Segev, “Self-accelerating self-trapped nonlinear beams of Maxwell’s equations,” Opt. Express 20, 18827–18835 (2012). [CrossRef]  

29. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010). [CrossRef]  

30. J. L. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017). [CrossRef]  

31. K. Y. Bliokh, M. R. Dennis, and F. Nori, “Relativistic electron vortex beams: angular momentum and spin-orbit interaction,” Phys. Rev. Lett. 107, 174802 (2011). [CrossRef]  

32. N. Voloch-Block, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013). [CrossRef]  

33. V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014). [CrossRef]  

34. J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, “Structured quantum waves,” Nat. Phys. 11, 629–634 (2015). [CrossRef]  

35. M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464, 737 (2010). [CrossRef]  

36. J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301 (2010). [CrossRef]  

37. B. McMorran, A. Agrawal, I. Anderson, A. Herzing, H. Lezec, J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011). [CrossRef]  

38. A. Mathis, F. Courvoisiera, L. Froehly, L. Fufaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012). [CrossRef]  

39. E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. Makris, and M. Segev, “Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams,” Opt. Express 21, 13425–13435 (2013). [CrossRef]  

40. R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014). [CrossRef]  

41. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Elsevier, 1981).

42. E. T. Whittaker and G. N. Watson, A Course in Modern Analysis, 4th ed. (Cambridge University, 1995), p. 340.

43. R. Dangovski, “WhittakerWavepackets,” https://drive.google.com/drive/folders/0B4FK9pSy4zn4NG8wZ1BOME0tb2c

44. I. Kaminer, J. Nemirovsky, M. Rechtsman, R. Bekenstein, and M. Segev, “Self-accelerating dirac particles and prolonging the lifetime of relativistic fermions,” Nat. Phys. 11, 261–267 (2015). [CrossRef]  

45. D. Zwillinger, Handbook of Differential Equations (Academic, 1997).

46. J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017). [CrossRef]  

47. B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65, 011804 (2001). [CrossRef]  

48. N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses,” Nat. Commun. 5, 3331 (2014). [CrossRef]  

49. G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1 μm OPCPA source,” J. Phys. B 49, 155601 (2016). [CrossRef]  

50. J. Palmer and S. D. Hogan, “Experimental demonstration of a Rydberg-atom beam splitter,” Phys. Rev. A 95, 053413 (2017). [CrossRef]  

51. R. Shiloh, Y. Lereah, Y. Lilach, and A. Arie, “Sculpturing the electron wave function using nanoscale phase masks,” Ultramicroscopy 144, 26–31 (2014). [CrossRef]  

52. L. Slater, Confluent Hypergeometric Functions (Cambridge University, 1960).

53. I. Thompson, Coulomb Functions (in NIST Handbook of Mathematical Functions) (Cambridge University, 2010).

54. M. Mutzafi, I. Kaminer, G. Harari, and M. Segev, “Non-diffracting multi-electron vortex beams balancing their electron-electron interactions,” Nat. Commun. 8, 650 (2017). [CrossRef]  

55. J. Werschnik and E. Gross, “Quantum optimal control theory,” J. Phys. B 40, R175 (2007). [CrossRef]  

56. R. E. Goetz, A. Karamatskou, R. Santra, and C. P. Koch, “Quantum optimal control of photoelectron spectra and angular distributions,” Phys. Rev. A 93, 013413 (2016). [CrossRef]  

57. R. E. Goetz, M. Merkel, A. Karamatskou, R. Santra, and C. P. Koch, “Maximizing hole coherence in ultrafast photoionization of argon with an optimization by sequential parametrization update,” Phys. Rev. A 94, 023420 (2016). [CrossRef]  

58. K. E. Echternkamp, A. Feist, S. Schäfer, and C. Ropers, “Ramsey-type phase control of free-electron beams,” Nat. Phys. 12, 1000–1004 (2016). [CrossRef]  

59. C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014). [CrossRef]  

60. M. Wollenhaupt, C. Lux, M. Krug, and T. Baumert, “Tomographic reconstruction of designer free-electron wave packets,” ChemPhysChem 14, 1341–1349 (2013). [CrossRef]  

61. D. W. Schumacher, J. H. Hoogenraad, D. Pinkos, and P. H. Bucksbaum, “Programmable cesium Rydberg wave packets,” Phys. Rev. A 6, 4719–4726 (2016). [CrossRef]  

62. B. Barwick, D. J. Flannigan, and A. H. Zewail, “Photon-induced near-field electron microscopy,” Nature 462, 902–906 (2009). [CrossRef]  

63. A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, and C. Ropers, “Quantum coherent optical phase modulation in an ultrafast transmission electron microscope,” Nat. Phys. 521, 200–203 (2015). [CrossRef]  

64. A. Ryabov and P. Baum, “Electron microscopy of electromagnetic waveforms,” Science 353, 374–377 (2016). [CrossRef]  

65. P. Baum, “Quantum dynamics of attosecond electron pulse compression,” J. Appl. Phys. 122, 223105 (2017). [CrossRef]  

66. Y. Morimoto and P. Baum, “Diffraction and microscopy with attosecond electron pulse trains,” Nat. Phys. 14, 252–256 (2018). [CrossRef]  

67. Q.-C. Ning, U. Saalmann, and J. M. Rost, “Electron dynamics driven by light-pulse derivatives,” Phys. Rev. Lett. 120, 033203 (2018). [CrossRef]  

68. J. J. Macklin, J. D. Kmetec, and C. L. I. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766 (1993). [CrossRef]  

69. W. Nicklich, H. Kumpfmüller, and H. Walther, “Above-threshold ionization of cesium under femtosecond laser pulses: new substructure due to strongly coupled bound states,” Phys. Rev. Lett. 69, 3455–3458 (1992). [CrossRef]  

70. A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998). [CrossRef]  

71. C. Heide, T. Higuchi, H. B. Weber, and P. Hommelhoff, “Coherent electron trajectory control in graphene,” Phys. Rev. Lett. 121, 207401 (2018). [CrossRef]  

72. K. E. Priebe, C. Rathje, S. V. Yalunin, T. Hohage, A. Feist, S. Schäfer, and C. Ropers, “Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy,” Nat. Photonics 11, 793–797 (2017). [CrossRef]  

73. W. Cai, O. Reinhardt, I. Kaminer, and J. G. D. Abajo, “Efficient orbital angular momentum transfer between plasmons and free electrons,” Phys. Rev. B 98, 045424 (2018). [CrossRef]  

74. G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018). [CrossRef]  

75. G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019). [CrossRef]  

76. O. Reinhardt and I. Kaminer, “Revealing the quantum nature of a free electron in an attosecond laser pulse,” in Frontiers in Optics (Optical Society of America, 2018), paper FTh3C-7.

References

  • View by:
  • |
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  • |

  1. L. Sch, Beam-Wave Interaction in Periodic and Quasi-Periodic Structures (Springer, 2011).
  2. A. Friedman, A. Gover, G. Kurizki, S. Ruschin, and A. Yariv, “Spontaneous and stimulated emission from quasifree electrons,” Rev. Mod. Phys. 60, 471 (1988).
    [Crossref]
  3. N. H. Burnett, H. A. Baldis, M. C. Richardson, and G. D. Enright, “Harmonic generation in CO2 laser target generation,” Appl. Phys. Lett. 31, 172–174 (1977).
    [Crossref]
  4. A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987).
    [Crossref]
  5. M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
    [Crossref]
  6. A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
    [Crossref]
  7. T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
    [Crossref]
  8. D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
    [Crossref]
  9. C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 331–335 (2016).
    [Crossref]
  10. J. von Neumann and E. P. Wigner, “Über merkwürdige diskrete eigenwerte,” Phys. Z. 30, 465–467 (1929).
  11. Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observations of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
    [Crossref]
  12. C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
    [Crossref]
  13. B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
    [Crossref]
  14. N. Rivera, C. W. Hsu, B. Zhen, H. Buljan, J. D. Joannopoulos, and M. Soljačić, “Controlling directionality and dimensionality of radiation by perturbing separable bound states in the continuum,” Sci. Rep. 6, 33394 (2016).
    [Crossref]
  15. M. V. Berry and N. L. Balázs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
    [Crossref]
  16. G. A. Sivlioglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
    [Crossref]
  17. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901(2007).
    [Crossref]
  18. I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
    [Crossref]
  19. R. Penciu, K. Makris, and N. Efremidis, “Nonparaxial abruptly autofocusing beams,” Opt. Lett. 41, 1042–1045 (2016).
    [Crossref]
  20. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A. 4, 651–654 (1987).
    [Crossref]
  21. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref]
  22. K. Makris and D. Psaltis, “Superoscillatory diffraction-free beams,” Opt. Lett. 36, 4335–4337 (2011).
    [Crossref]
  23. K. Makris, D. Papazoglou, and S. Tzortzakis, “Invariant superoscillatory electromagnetic fields in 3D-space,” J. Opt. 19, 014003 (2016).
    [Crossref]
  24. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
    [Crossref]
  25. R. Bekenstein, J. Nemirovsky, I. Kaminer, and M. Segev, “Shape-preserving accelerating electromagnetic wave packets in curved space,” Phys. Rev. X 4, 011038 (2014).
    [Crossref]
  26. A. Patsyk, M. A. Bandres, R. Bekenstein, and M. Segev, “Observation of accelerating wave packets in curved space,” Phys. Rev. X 8, 011001 (2018).
    [Crossref]
  27. I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self trapped optical beams,” Phys. Rev. Lett. 106, 213902 (2011).
    [Crossref]
  28. I. Kaminer, J. Nemirovsky, and M. Segev, “Self-accelerating self-trapped nonlinear beams of Maxwell’s equations,” Opt. Express 20, 18827–18835 (2012).
    [Crossref]
  29. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
    [Crossref]
  30. J. L. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).
    [Crossref]
  31. K. Y. Bliokh, M. R. Dennis, and F. Nori, “Relativistic electron vortex beams: angular momentum and spin-orbit interaction,” Phys. Rev. Lett. 107, 174802 (2011).
    [Crossref]
  32. N. Voloch-Block, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
    [Crossref]
  33. V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
    [Crossref]
  34. J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, “Structured quantum waves,” Nat. Phys. 11, 629–634 (2015).
    [Crossref]
  35. M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464, 737 (2010).
    [Crossref]
  36. J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301 (2010).
    [Crossref]
  37. B. McMorran, A. Agrawal, I. Anderson, A. Herzing, H. Lezec, J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
    [Crossref]
  38. A. Mathis, F. Courvoisiera, L. Froehly, L. Fufaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
    [Crossref]
  39. E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. Makris, and M. Segev, “Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams,” Opt. Express 21, 13425–13435 (2013).
    [Crossref]
  40. R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
    [Crossref]
  41. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Elsevier, 1981).
  42. E. T. Whittaker and G. N. Watson, A Course in Modern Analysis, 4th ed. (Cambridge University, 1995), p. 340.
  43. R. Dangovski, “WhittakerWavepackets,” https://drive.google.com/drive/folders/0B4FK9pSy4zn4NG8wZ1BOME0tb2c
  44. I. Kaminer, J. Nemirovsky, M. Rechtsman, R. Bekenstein, and M. Segev, “Self-accelerating dirac particles and prolonging the lifetime of relativistic fermions,” Nat. Phys. 11, 261–267 (2015).
    [Crossref]
  45. D. Zwillinger, Handbook of Differential Equations (Academic, 1997).
  46. J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
    [Crossref]
  47. B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65, 011804 (2001).
    [Crossref]
  48. N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses,” Nat. Commun. 5, 3331 (2014).
    [Crossref]
  49. G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
    [Crossref]
  50. J. Palmer and S. D. Hogan, “Experimental demonstration of a Rydberg-atom beam splitter,” Phys. Rev. A 95, 053413 (2017).
    [Crossref]
  51. R. Shiloh, Y. Lereah, Y. Lilach, and A. Arie, “Sculpturing the electron wave function using nanoscale phase masks,” Ultramicroscopy 144, 26–31 (2014).
    [Crossref]
  52. L. Slater, Confluent Hypergeometric Functions (Cambridge University, 1960).
  53. I. Thompson, Coulomb Functions (in NIST Handbook of Mathematical Functions) (Cambridge University, 2010).
  54. M. Mutzafi, I. Kaminer, G. Harari, and M. Segev, “Non-diffracting multi-electron vortex beams balancing their electron-electron interactions,” Nat. Commun. 8, 650 (2017).
    [Crossref]
  55. J. Werschnik and E. Gross, “Quantum optimal control theory,” J. Phys. B 40, R175 (2007).
    [Crossref]
  56. R. E. Goetz, A. Karamatskou, R. Santra, and C. P. Koch, “Quantum optimal control of photoelectron spectra and angular distributions,” Phys. Rev. A 93, 013413 (2016).
    [Crossref]
  57. R. E. Goetz, M. Merkel, A. Karamatskou, R. Santra, and C. P. Koch, “Maximizing hole coherence in ultrafast photoionization of argon with an optimization by sequential parametrization update,” Phys. Rev. A 94, 023420 (2016).
    [Crossref]
  58. K. E. Echternkamp, A. Feist, S. Schäfer, and C. Ropers, “Ramsey-type phase control of free-electron beams,” Nat. Phys. 12, 1000–1004 (2016).
    [Crossref]
  59. C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
    [Crossref]
  60. M. Wollenhaupt, C. Lux, M. Krug, and T. Baumert, “Tomographic reconstruction of designer free-electron wave packets,” ChemPhysChem 14, 1341–1349 (2013).
    [Crossref]
  61. D. W. Schumacher, J. H. Hoogenraad, D. Pinkos, and P. H. Bucksbaum, “Programmable cesium Rydberg wave packets,” Phys. Rev. A 6, 4719–4726 (2016).
    [Crossref]
  62. B. Barwick, D. J. Flannigan, and A. H. Zewail, “Photon-induced near-field electron microscopy,” Nature 462, 902–906 (2009).
    [Crossref]
  63. A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, and C. Ropers, “Quantum coherent optical phase modulation in an ultrafast transmission electron microscope,” Nat. Phys. 521, 200–203 (2015).
    [Crossref]
  64. A. Ryabov and P. Baum, “Electron microscopy of electromagnetic waveforms,” Science 353, 374–377 (2016).
    [Crossref]
  65. P. Baum, “Quantum dynamics of attosecond electron pulse compression,” J. Appl. Phys. 122, 223105 (2017).
    [Crossref]
  66. Y. Morimoto and P. Baum, “Diffraction and microscopy with attosecond electron pulse trains,” Nat. Phys. 14, 252–256 (2018).
    [Crossref]
  67. Q.-C. Ning, U. Saalmann, and J. M. Rost, “Electron dynamics driven by light-pulse derivatives,” Phys. Rev. Lett. 120, 033203 (2018).
    [Crossref]
  68. J. J. Macklin, J. D. Kmetec, and C. L. I. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766 (1993).
    [Crossref]
  69. W. Nicklich, H. Kumpfmüller, and H. Walther, “Above-threshold ionization of cesium under femtosecond laser pulses: new substructure due to strongly coupled bound states,” Phys. Rev. Lett. 69, 3455–3458 (1992).
    [Crossref]
  70. A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
    [Crossref]
  71. C. Heide, T. Higuchi, H. B. Weber, and P. Hommelhoff, “Coherent electron trajectory control in graphene,” Phys. Rev. Lett. 121, 207401 (2018).
    [Crossref]
  72. K. E. Priebe, C. Rathje, S. V. Yalunin, T. Hohage, A. Feist, S. Schäfer, and C. Ropers, “Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy,” Nat. Photonics 11, 793–797 (2017).
    [Crossref]
  73. W. Cai, O. Reinhardt, I. Kaminer, and J. G. D. Abajo, “Efficient orbital angular momentum transfer between plasmons and free electrons,” Phys. Rev. B 98, 045424 (2018).
    [Crossref]
  74. G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
    [Crossref]
  75. G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
    [Crossref]
  76. O. Reinhardt and I. Kaminer, “Revealing the quantum nature of a free electron in an attosecond laser pulse,” in Frontiers in Optics (Optical Society of America, 2018), paper FTh3C-7.

2019 (1)

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

2018 (7)

W. Cai, O. Reinhardt, I. Kaminer, and J. G. D. Abajo, “Efficient orbital angular momentum transfer between plasmons and free electrons,” Phys. Rev. B 98, 045424 (2018).
[Crossref]

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

C. Heide, T. Higuchi, H. B. Weber, and P. Hommelhoff, “Coherent electron trajectory control in graphene,” Phys. Rev. Lett. 121, 207401 (2018).
[Crossref]

Y. Morimoto and P. Baum, “Diffraction and microscopy with attosecond electron pulse trains,” Nat. Phys. 14, 252–256 (2018).
[Crossref]

Q.-C. Ning, U. Saalmann, and J. M. Rost, “Electron dynamics driven by light-pulse derivatives,” Phys. Rev. Lett. 120, 033203 (2018).
[Crossref]

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

A. Patsyk, M. A. Bandres, R. Bekenstein, and M. Segev, “Observation of accelerating wave packets in curved space,” Phys. Rev. X 8, 011001 (2018).
[Crossref]

2017 (6)

J. L. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).
[Crossref]

K. E. Priebe, C. Rathje, S. V. Yalunin, T. Hohage, A. Feist, S. Schäfer, and C. Ropers, “Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy,” Nat. Photonics 11, 793–797 (2017).
[Crossref]

P. Baum, “Quantum dynamics of attosecond electron pulse compression,” J. Appl. Phys. 122, 223105 (2017).
[Crossref]

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

J. Palmer and S. D. Hogan, “Experimental demonstration of a Rydberg-atom beam splitter,” Phys. Rev. A 95, 053413 (2017).
[Crossref]

M. Mutzafi, I. Kaminer, G. Harari, and M. Segev, “Non-diffracting multi-electron vortex beams balancing their electron-electron interactions,” Nat. Commun. 8, 650 (2017).
[Crossref]

2016 (10)

R. E. Goetz, A. Karamatskou, R. Santra, and C. P. Koch, “Quantum optimal control of photoelectron spectra and angular distributions,” Phys. Rev. A 93, 013413 (2016).
[Crossref]

R. E. Goetz, M. Merkel, A. Karamatskou, R. Santra, and C. P. Koch, “Maximizing hole coherence in ultrafast photoionization of argon with an optimization by sequential parametrization update,” Phys. Rev. A 94, 023420 (2016).
[Crossref]

K. E. Echternkamp, A. Feist, S. Schäfer, and C. Ropers, “Ramsey-type phase control of free-electron beams,” Nat. Phys. 12, 1000–1004 (2016).
[Crossref]

A. Ryabov and P. Baum, “Electron microscopy of electromagnetic waveforms,” Science 353, 374–377 (2016).
[Crossref]

D. W. Schumacher, J. H. Hoogenraad, D. Pinkos, and P. H. Bucksbaum, “Programmable cesium Rydberg wave packets,” Phys. Rev. A 6, 4719–4726 (2016).
[Crossref]

G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
[Crossref]

R. Penciu, K. Makris, and N. Efremidis, “Nonparaxial abruptly autofocusing beams,” Opt. Lett. 41, 1042–1045 (2016).
[Crossref]

K. Makris, D. Papazoglou, and S. Tzortzakis, “Invariant superoscillatory electromagnetic fields in 3D-space,” J. Opt. 19, 014003 (2016).
[Crossref]

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 331–335 (2016).
[Crossref]

N. Rivera, C. W. Hsu, B. Zhen, H. Buljan, J. D. Joannopoulos, and M. Soljačić, “Controlling directionality and dimensionality of radiation by perturbing separable bound states in the continuum,” Sci. Rep. 6, 33394 (2016).
[Crossref]

2015 (3)

J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, “Structured quantum waves,” Nat. Phys. 11, 629–634 (2015).
[Crossref]

A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, and C. Ropers, “Quantum coherent optical phase modulation in an ultrafast transmission electron microscope,” Nat. Phys. 521, 200–203 (2015).
[Crossref]

I. Kaminer, J. Nemirovsky, M. Rechtsman, R. Bekenstein, and M. Segev, “Self-accelerating dirac particles and prolonging the lifetime of relativistic fermions,” Nat. Phys. 11, 261–267 (2015).
[Crossref]

2014 (7)

N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses,” Nat. Commun. 5, 3331 (2014).
[Crossref]

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

R. Shiloh, Y. Lereah, Y. Lilach, and A. Arie, “Sculpturing the electron wave function using nanoscale phase masks,” Ultramicroscopy 144, 26–31 (2014).
[Crossref]

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
[Crossref]

R. Bekenstein, J. Nemirovsky, I. Kaminer, and M. Segev, “Shape-preserving accelerating electromagnetic wave packets in curved space,” Phys. Rev. X 4, 011038 (2014).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

2013 (4)

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

N. Voloch-Block, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

M. Wollenhaupt, C. Lux, M. Krug, and T. Baumert, “Tomographic reconstruction of designer free-electron wave packets,” ChemPhysChem 14, 1341–1349 (2013).
[Crossref]

E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. Makris, and M. Segev, “Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams,” Opt. Express 21, 13425–13435 (2013).
[Crossref]

2012 (4)

A. Mathis, F. Courvoisiera, L. Froehly, L. Fufaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

I. Kaminer, J. Nemirovsky, and M. Segev, “Self-accelerating self-trapped nonlinear beams of Maxwell’s equations,” Opt. Express 20, 18827–18835 (2012).
[Crossref]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

2011 (5)

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observations of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

K. Y. Bliokh, M. R. Dennis, and F. Nori, “Relativistic electron vortex beams: angular momentum and spin-orbit interaction,” Phys. Rev. Lett. 107, 174802 (2011).
[Crossref]

K. Makris and D. Psaltis, “Superoscillatory diffraction-free beams,” Opt. Lett. 36, 4335–4337 (2011).
[Crossref]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self trapped optical beams,” Phys. Rev. Lett. 106, 213902 (2011).
[Crossref]

B. McMorran, A. Agrawal, I. Anderson, A. Herzing, H. Lezec, J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

2010 (3)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464, 737 (2010).
[Crossref]

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301 (2010).
[Crossref]

2009 (1)

B. Barwick, D. J. Flannigan, and A. H. Zewail, “Photon-induced near-field electron microscopy,” Nature 462, 902–906 (2009).
[Crossref]

2008 (1)

2007 (3)

G. A. Sivlioglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901(2007).
[Crossref]

J. Werschnik and E. Gross, “Quantum optimal control theory,” J. Phys. B 40, R175 (2007).
[Crossref]

2001 (1)

B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65, 011804 (2001).
[Crossref]

1998 (2)

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

1993 (1)

J. J. Macklin, J. D. Kmetec, and C. L. I. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766 (1993).
[Crossref]

1992 (1)

W. Nicklich, H. Kumpfmüller, and H. Walther, “Above-threshold ionization of cesium under femtosecond laser pulses: new substructure due to strongly coupled bound states,” Phys. Rev. Lett. 69, 3455–3458 (1992).
[Crossref]

1988 (2)

A. Friedman, A. Gover, G. Kurizki, S. Ruschin, and A. Yariv, “Spontaneous and stimulated emission from quasifree electrons,” Rev. Mod. Phys. 60, 471 (1988).
[Crossref]

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

1987 (3)

A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987).
[Crossref]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A. 4, 651–654 (1987).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

1979 (1)

M. V. Berry and N. L. Balázs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[Crossref]

1977 (1)

N. H. Burnett, H. A. Baldis, M. C. Richardson, and G. D. Enright, “Harmonic generation in CO2 laser target generation,” Appl. Phys. Lett. 31, 172–174 (1977).
[Crossref]

1929 (1)

J. von Neumann and E. P. Wigner, “Über merkwürdige diskrete eigenwerte,” Phys. Z. 30, 465–467 (1929).

Abajo, J. G. D.

W. Cai, O. Reinhardt, I. Kaminer, and J. G. D. Abajo, “Efficient orbital angular momentum transfer between plasmons and free electrons,” Phys. Rev. B 98, 045424 (2018).
[Crossref]

Agrawal, A.

B. McMorran, A. Agrawal, I. Anderson, A. Herzing, H. Lezec, J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

Ališauskas, G.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Ališauskas, S.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Anderson, I.

B. McMorran, A. Agrawal, I. Anderson, A. Herzing, H. Lezec, J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

Andriukaitis, G.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Andriukaitis, S.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Argenti, L.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Arie, A.

R. Shiloh, Y. Lereah, Y. Lilach, and A. Arie, “Sculpturing the electron wave function using nanoscale phase masks,” Ultramicroscopy 144, 26–31 (2014).
[Crossref]

N. Voloch-Block, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

Arpin, P.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Assion, A.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

Backus, S.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

Balázs, N. L.

M. V. Berry and N. L. Balázs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[Crossref]

Balciunas, O. D.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Balciunas, T.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Baldis, H. A.

N. H. Burnett, H. A. Baldis, M. C. Richardson, and G. D. Enright, “Harmonic generation in CO2 laser target generation,” Appl. Phys. Lett. 31, 172–174 (1977).
[Crossref]

Baltuška, A.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Bandres, M. A.

A. Patsyk, M. A. Bandres, R. Bekenstein, and M. Segev, “Observation of accelerating wave packets in curved space,” Phys. Rev. X 8, 011001 (2018).
[Crossref]

Barwick, B.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

B. Barwick, D. J. Flannigan, and A. H. Zewail, “Photon-induced near-field electron microscopy,” Nature 462, 902–906 (2009).
[Crossref]

Baum, P.

Y. Morimoto and P. Baum, “Diffraction and microscopy with attosecond electron pulse trains,” Nat. Phys. 14, 252–256 (2018).
[Crossref]

P. Baum, “Quantum dynamics of attosecond electron pulse compression,” J. Appl. Phys. 122, 223105 (2017).
[Crossref]

A. Ryabov and P. Baum, “Electron microscopy of electromagnetic waveforms,” Science 353, 374–377 (2016).
[Crossref]

Baumert, T.

M. Wollenhaupt, C. Lux, M. Krug, and T. Baumert, “Tomographic reconstruction of designer free-electron wave packets,” ChemPhysChem 14, 1341–1349 (2013).
[Crossref]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

Becker, A.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Bekenstein, R.

A. Patsyk, M. A. Bandres, R. Bekenstein, and M. Segev, “Observation of accelerating wave packets in curved space,” Phys. Rev. X 8, 011001 (2018).
[Crossref]

I. Kaminer, J. Nemirovsky, M. Rechtsman, R. Bekenstein, and M. Segev, “Self-accelerating dirac particles and prolonging the lifetime of relativistic fermions,” Nat. Phys. 11, 261–267 (2015).
[Crossref]

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

R. Bekenstein, J. Nemirovsky, I. Kaminer, and M. Segev, “Shape-preserving accelerating electromagnetic wave packets in curved space,” Phys. Rev. X 4, 011038 (2014).
[Crossref]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

Bergt, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

Berruto, G.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

Berry, M. V.

M. V. Berry and N. L. Balázs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[Crossref]

Biagioni, P.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

Blättermann, A.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh, M. R. Dennis, and F. Nori, “Relativistic electron vortex beams: angular momentum and spin-orbit interaction,” Phys. Rev. Lett. 107, 174802 (2011).
[Crossref]

Boyd, R. W.

J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, “Structured quantum waves,” Nat. Phys. 11, 629–634 (2015).
[Crossref]

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
[Crossref]

Boyer, K.

Brixner, T.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

Broky, J.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901(2007).
[Crossref]

Brown, S.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Bucksbaum, P. H.

D. W. Schumacher, J. H. Hoogenraad, D. Pinkos, and P. H. Bucksbaum, “Programmable cesium Rydberg wave packets,” Phys. Rev. A 6, 4719–4726 (2016).
[Crossref]

Buljan, H.

N. Rivera, C. W. Hsu, B. Zhen, H. Buljan, J. D. Joannopoulos, and M. Soljačić, “Controlling directionality and dimensionality of radiation by perturbing separable bound states in the continuum,” Sci. Rep. 6, 33394 (2016).
[Crossref]

Burnett, N. H.

N. H. Burnett, H. A. Baldis, M. C. Richardson, and G. D. Enright, “Harmonic generation in CO2 laser target generation,” Appl. Phys. Lett. 31, 172–174 (1977).
[Crossref]

Cai, W.

W. Cai, O. Reinhardt, I. Kaminer, and J. G. D. Abajo, “Efficient orbital angular momentum transfer between plasmons and free electrons,” Phys. Rev. B 98, 045424 (2018).
[Crossref]

Carbone, F.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

Chang, C.-L.

G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
[Crossref]

Chang, Z.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65, 011804 (2001).
[Crossref]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

Chen, M.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Cheng, Y.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

Chew, A.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

Chini, M.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

Christodoulides, D. N.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self trapped optical beams,” Phys. Rev. Lett. 106, 213902 (2011).
[Crossref]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901(2007).
[Crossref]

G. A. Sivlioglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[Crossref]

Chua, S.-L.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Courvoisiera, F.

A. Mathis, F. Courvoisiera, L. Froehly, L. Fufaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Cunningham, E.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

Dennis, M. R.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
[Crossref]

K. Y. Bliokh, M. R. Dennis, and F. Nori, “Relativistic electron vortex beams: angular momentum and spin-orbit interaction,” Phys. Rev. Lett. 107, 174802 (2011).
[Crossref]

Ding, T.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Dogariu, A.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901(2007).
[Crossref]

Dollar, F.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Dreisow, F.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observations of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Dudley, J. M.

A. Mathis, F. Courvoisiera, L. Froehly, L. Fufaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Durfee, C. G.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

Durnin, J.

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A. 4, 651–654 (1987).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Echternkamp, K. E.

K. E. Echternkamp, A. Feist, S. Schäfer, and C. Ropers, “Ramsey-type phase control of free-electron beams,” Nat. Phys. 12, 1000–1004 (2016).
[Crossref]

A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, and C. Ropers, “Quantum coherent optical phase modulation in an ultrafast transmission electron microscope,” Nat. Phys. 521, 200–203 (2015).
[Crossref]

Efremidis, N.

Enright, G. D.

N. H. Burnett, H. A. Baldis, M. C. Richardson, and G. D. Enright, “Harmonic generation in CO2 laser target generation,” Appl. Phys. Lett. 31, 172–174 (1977).
[Crossref]

Fan, G.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Feist, A.

K. E. Priebe, C. Rathje, S. V. Yalunin, T. Hohage, A. Feist, S. Schäfer, and C. Ropers, “Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy,” Nat. Photonics 11, 793–797 (2017).
[Crossref]

K. E. Echternkamp, A. Feist, S. Schäfer, and C. Ropers, “Ramsey-type phase control of free-electron beams,” Nat. Phys. 12, 1000–1004 (2016).
[Crossref]

A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, and C. Ropers, “Quantum coherent optical phase modulation in an ultrafast transmission electron microscope,” Nat. Phys. 521, 200–203 (2015).
[Crossref]

Ferray, M.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

Flannigan, D. J.

B. Barwick, D. J. Flannigan, and A. H. Zewail, “Photon-induced near-field electron microscopy,” Nature 462, 902–906 (2009).
[Crossref]

Frabboni, S.

J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, “Structured quantum waves,” Nat. Phys. 11, 629–634 (2015).
[Crossref]

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
[Crossref]

Friedman, A.

A. Friedman, A. Gover, G. Kurizki, S. Ruschin, and A. Yariv, “Spontaneous and stimulated emission from quasifree electrons,” Rev. Mod. Phys. 60, 471 (1988).
[Crossref]

Froehly, L.

A. Mathis, F. Courvoisiera, L. Froehly, L. Fufaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Fufaro, L.

A. Mathis, F. Courvoisiera, L. Froehly, L. Fufaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Gaeta, A.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Galloway, B. R.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

García de Abajo, F. J.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

Gazzadi, G. C.

J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, “Structured quantum waves,” Nat. Phys. 11, 629–634 (2015).
[Crossref]

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
[Crossref]

Gerber, G.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

Gibson, G.

Goetz, R. E.

R. E. Goetz, M. Merkel, A. Karamatskou, R. Santra, and C. P. Koch, “Maximizing hole coherence in ultrafast photoionization of argon with an optimization by sequential parametrization update,” Phys. Rev. A 94, 023420 (2016).
[Crossref]

R. E. Goetz, A. Karamatskou, R. Santra, and C. P. Koch, “Quantum optimal control of photoelectron spectra and angular distributions,” Phys. Rev. A 93, 013413 (2016).
[Crossref]

Gordon, C. L. I.

J. J. Macklin, J. D. Kmetec, and C. L. I. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766 (1993).
[Crossref]

Gover, A.

N. Voloch-Block, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

A. Friedman, A. Gover, G. Kurizki, S. Ruschin, and A. Yariv, “Spontaneous and stimulated emission from quasifree electrons,” Rev. Mod. Phys. 60, 471 (1988).
[Crossref]

Greenfield, E.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. Makris, and M. Segev, “Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams,” Opt. Express 21, 13425–13435 (2013).
[Crossref]

Grillo, V.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, “Structured quantum waves,” Nat. Phys. 11, 629–634 (2015).
[Crossref]

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
[Crossref]

Gross, E.

J. Werschnik and E. Gross, “Quantum optimal control theory,” J. Phys. B 40, R175 (2007).
[Crossref]

Hagstotz, S.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Hankla, A.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Harari, G.

M. Mutzafi, I. Kaminer, G. Harari, and M. Segev, “Non-diffracting multi-electron vortex beams balancing their electron-electron interactions,” Nat. Commun. 8, 650 (2017).
[Crossref]

Harris, J.

J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, “Structured quantum waves,” Nat. Phys. 11, 629–634 (2015).
[Crossref]

Heck, R.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Heide, C.

C. Heide, T. Higuchi, H. B. Weber, and P. Hommelhoff, “Coherent electron trajectory control in graphene,” Phys. Rev. Lett. 121, 207401 (2018).
[Crossref]

Heinrich, M.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observations of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Hernández-García, C.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Herne, C.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

Herzing, A.

B. McMorran, A. Agrawal, I. Anderson, A. Herzing, H. Lezec, J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

Higuchi, T.

C. Heide, T. Higuchi, H. B. Weber, and P. Hommelhoff, “Coherent electron trajectory control in graphene,” Phys. Rev. Lett. 121, 207401 (2018).
[Crossref]

Hogan, S. D.

J. Palmer and S. D. Hogan, “Experimental demonstration of a Rydberg-atom beam splitter,” Phys. Rev. A 95, 053413 (2017).
[Crossref]

Hohage, T.

K. E. Priebe, C. Rathje, S. V. Yalunin, T. Hohage, A. Feist, S. Schäfer, and C. Ropers, “Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy,” Nat. Photonics 11, 793–797 (2017).
[Crossref]

Hommelhoff, P.

C. Heide, T. Higuchi, H. B. Weber, and P. Hommelhoff, “Coherent electron trajectory control in graphene,” Phys. Rev. Lett. 121, 207401 (2018).
[Crossref]

Hong, K.-H.

G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
[Crossref]

Hoogenraad, J. H.

D. W. Schumacher, J. H. Hoogenraad, D. Pinkos, and P. H. Bucksbaum, “Programmable cesium Rydberg wave packets,” Phys. Rev. A 6, 4719–4726 (2016).
[Crossref]

Hsu, C. W.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 331–335 (2016).
[Crossref]

N. Rivera, C. W. Hsu, B. Zhen, H. Buljan, J. D. Joannopoulos, and M. Soljačić, “Controlling directionality and dimensionality of radiation by perturbing separable bound states in the continuum,” Sci. Rep. 6, 33394 (2016).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Hu, S.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

Hurwitz, I.

Ishii, N.

N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses,” Nat. Commun. 5, 3331 (2014).
[Crossref]

Itatani, J.

N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses,” Nat. Commun. 5, 3331 (2014).
[Crossref]

Jacquot, M.

A. Mathis, F. Courvoisiera, L. Froehly, L. Fufaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Jara, H.

Jaron-Becker, A.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Joannopoulos, J. D.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 331–335 (2016).
[Crossref]

N. Rivera, C. W. Hsu, B. Zhen, H. Buljan, J. D. Joannopoulos, and M. Soljačić, “Controlling directionality and dimensionality of radiation by perturbing separable bound states in the continuum,” Sci. Rep. 6, 33394 (2016).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Johann, U.

Johnson, S. G.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Kaldun, A.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Kaminer, I.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

W. Cai, O. Reinhardt, I. Kaminer, and J. G. D. Abajo, “Efficient orbital angular momentum transfer between plasmons and free electrons,” Phys. Rev. B 98, 045424 (2018).
[Crossref]

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

M. Mutzafi, I. Kaminer, G. Harari, and M. Segev, “Non-diffracting multi-electron vortex beams balancing their electron-electron interactions,” Nat. Commun. 8, 650 (2017).
[Crossref]

J. L. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).
[Crossref]

I. Kaminer, J. Nemirovsky, M. Rechtsman, R. Bekenstein, and M. Segev, “Self-accelerating dirac particles and prolonging the lifetime of relativistic fermions,” Nat. Phys. 11, 261–267 (2015).
[Crossref]

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

R. Bekenstein, J. Nemirovsky, I. Kaminer, and M. Segev, “Shape-preserving accelerating electromagnetic wave packets in curved space,” Phys. Rev. X 4, 011038 (2014).
[Crossref]

I. Kaminer, J. Nemirovsky, and M. Segev, “Self-accelerating self-trapped nonlinear beams of Maxwell’s equations,” Opt. Express 20, 18827–18835 (2012).
[Crossref]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self trapped optical beams,” Phys. Rev. Lett. 106, 213902 (2011).
[Crossref]

O. Reinhardt and I. Kaminer, “Revealing the quantum nature of a free electron in an attosecond laser pulse,” in Frontiers in Optics (Optical Society of America, 2018), paper FTh3C-7.

Kanai, T.

N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses,” Nat. Commun. 5, 3331 (2014).
[Crossref]

Kaneshima, K.

N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses,” Nat. Commun. 5, 3331 (2014).
[Crossref]

Kapteyn, H. C.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

Karamatskou, A.

R. E. Goetz, A. Karamatskou, R. Santra, and C. P. Koch, “Quantum optimal control of photoelectron spectra and angular distributions,” Phys. Rev. A 93, 013413 (2016).
[Crossref]

R. E. Goetz, M. Merkel, A. Karamatskou, R. Santra, and C. P. Koch, “Maximizing hole coherence in ultrafast photoionization of argon with an optimization by sequential parametrization update,” Phys. Rev. A 94, 023420 (2016).
[Crossref]

Karimi, E.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, “Structured quantum waves,” Nat. Phys. 11, 629–634 (2015).
[Crossref]

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
[Crossref]

Kärtner, F. X.

G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
[Crossref]

Keathley, P. D.

G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
[Crossref]

Kiefer, B.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

Kitano, K.

N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses,” Nat. Commun. 5, 3331 (2014).
[Crossref]

Kmetec, J. D.

J. J. Macklin, J. D. Kmetec, and C. L. I. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766 (1993).
[Crossref]

Koch, C. P.

R. E. Goetz, A. Karamatskou, R. Santra, and C. P. Koch, “Quantum optimal control of photoelectron spectra and angular distributions,” Phys. Rev. A 93, 013413 (2016).
[Crossref]

R. E. Goetz, M. Merkel, A. Karamatskou, R. Santra, and C. P. Koch, “Maximizing hole coherence in ultrafast photoionization of argon with an optimization by sequential parametrization update,” Phys. Rev. A 94, 023420 (2016).
[Crossref]

Krogen, P.

G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
[Crossref]

Krug, M.

M. Wollenhaupt, C. Lux, M. Krug, and T. Baumert, “Tomographic reconstruction of designer free-electron wave packets,” ChemPhysChem 14, 1341–1349 (2013).
[Crossref]

Kumpfmüller, H.

W. Nicklich, H. Kumpfmüller, and H. Walther, “Above-threshold ionization of cesium under femtosecond laser pulses: new substructure due to strongly coupled bound states,” Phys. Rev. Lett. 69, 3455–3458 (1992).
[Crossref]

Kurizki, G.

A. Friedman, A. Gover, G. Kurizki, S. Ruschin, and A. Yariv, “Spontaneous and stimulated emission from quasifree electrons,” Rev. Mod. Phys. 60, 471 (1988).
[Crossref]

L’Huillier, A.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

Lacourt, P. A.

A. Mathis, F. Courvoisiera, L. Froehly, L. Fufaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

Lai, C.-J.

G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
[Crossref]

Lamb, R. J.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Elsevier, 1981).

Laurent, G. M.

G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
[Crossref]

Laux, M.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Lee, J.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Lereah, Y.

R. Shiloh, Y. Lereah, Y. Lilach, and A. Arie, “Sculpturing the electron wave function using nanoscale phase masks,” Ultramicroscopy 144, 26–31 (2014).
[Crossref]

N. Voloch-Block, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

Lezec, H.

B. McMorran, A. Agrawal, I. Anderson, A. Herzing, H. Lezec, J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

Li, J.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

Li, X. F.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

Liang, H.

G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
[Crossref]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Elsevier, 1981).

Lilach, Y.

R. Shiloh, Y. Lereah, Y. Lilach, and A. Arie, “Sculpturing the electron wave function using nanoscale phase masks,” Ultramicroscopy 144, 26–31 (2014).
[Crossref]

N. Voloch-Block, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

Lompre, L. A.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

Lu, L.

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

Luk, T. S.

Lumer, Y.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

Lux, C.

M. Wollenhaupt, C. Lux, M. Krug, and T. Baumert, “Tomographic reconstruction of designer free-electron wave packets,” ChemPhysChem 14, 1341–1349 (2013).
[Crossref]

Macklin, J. J.

J. J. Macklin, J. D. Kmetec, and C. L. I. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766 (1993).
[Crossref]

Madan, I.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

Madronero, J.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Mafakheri, E.

J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, “Structured quantum waves,” Nat. Phys. 11, 629–634 (2015).
[Crossref]

Mainfray, G.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

Makris, K.

Mancuso, C. A.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Manus, C.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

Martin, F.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Mathis, A.

A. Mathis, F. Courvoisiera, L. Froehly, L. Fufaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

McClelland, J.

B. McMorran, A. Agrawal, I. Anderson, A. Herzing, H. Lezec, J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

McGrouther, D.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

McIntyre, I. A.

McMorran, B.

B. McMorran, A. Agrawal, I. Anderson, A. Herzing, H. Lezec, J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

McPherson, A.

Merkel, M.

R. E. Goetz, M. Merkel, A. Karamatskou, R. Santra, and C. P. Koch, “Maximizing hole coherence in ultrafast photoionization of argon with an optimization by sequential parametrization update,” Phys. Rev. A 94, 023420 (2016).
[Crossref]

Meyer, K.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Miaja-Avila, L.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Morimoto, Y.

Y. Morimoto and P. Baum, “Diffraction and microscopy with attosecond electron pulse trains,” Nat. Phys. 14, 252–256 (2018).
[Crossref]

Mücke, O. D.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Mücke, T.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Murnane, M. M.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

Mutzafi, M.

M. Mutzafi, I. Kaminer, G. Harari, and M. Segev, “Non-diffracting multi-electron vortex beams balancing their electron-electron interactions,” Nat. Commun. 8, 650 (2017).
[Crossref]

Nemirovsky, J.

I. Kaminer, J. Nemirovsky, M. Rechtsman, R. Bekenstein, and M. Segev, “Self-accelerating dirac particles and prolonging the lifetime of relativistic fermions,” Nat. Phys. 11, 261–267 (2015).
[Crossref]

R. Bekenstein, J. Nemirovsky, I. Kaminer, and M. Segev, “Shape-preserving accelerating electromagnetic wave packets in curved space,” Phys. Rev. X 4, 011038 (2014).
[Crossref]

E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. Makris, and M. Segev, “Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams,” Opt. Express 21, 13425–13435 (2013).
[Crossref]

I. Kaminer, J. Nemirovsky, and M. Segev, “Self-accelerating self-trapped nonlinear beams of Maxwell’s equations,” Opt. Express 20, 18827–18835 (2012).
[Crossref]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

Nicklich, W.

W. Nicklich, H. Kumpfmüller, and H. Walther, “Above-threshold ionization of cesium under femtosecond laser pulses: new substructure due to strongly coupled bound states,” Phys. Rev. Lett. 69, 3455–3458 (1992).
[Crossref]

Ning, Q.-C.

Q.-C. Ning, U. Saalmann, and J. M. Rost, “Electron dynamics driven by light-pulse derivatives,” Phys. Rev. Lett. 120, 033203 (2018).
[Crossref]

Nolte, S.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observations of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Nori, F.

K. Y. Bliokh, M. R. Dennis, and F. Nori, “Relativistic electron vortex beams: angular momentum and spin-orbit interaction,” Phys. Rev. Lett. 107, 174802 (2011).
[Crossref]

O’Neil, G.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Ott, C.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Palmer, J.

J. Palmer and S. D. Hogan, “Experimental demonstration of a Rydberg-atom beam splitter,” Phys. Rev. A 95, 053413 (2017).
[Crossref]

Papazoglou, D.

K. Makris, D. Papazoglou, and S. Tzortzakis, “Invariant superoscillatory electromagnetic fields in 3D-space,” J. Opt. 19, 014003 (2016).
[Crossref]

Patsyk, A.

A. Patsyk, M. A. Bandres, R. Bekenstein, and M. Segev, “Observation of accelerating wave packets in curved space,” Phys. Rev. X 8, 011001 (2018).
[Crossref]

Peleg, O.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observations of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Penciu, R.

Pfeifer, T.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Pinkos, D.

D. W. Schumacher, J. H. Hoogenraad, D. Pinkos, and P. H. Bucksbaum, “Programmable cesium Rydberg wave packets,” Phys. Rev. A 6, 4719–4726 (2016).
[Crossref]

Plaja, L.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Plotnik, Y.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observations of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Pomarico, E.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

Popmintchev, D.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Popmintchev, T.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Priebe, K. E.

K. E. Priebe, C. Rathje, S. V. Yalunin, T. Hohage, A. Feist, S. Schäfer, and C. Ropers, “Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy,” Nat. Photonics 11, 793–797 (2017).
[Crossref]

Psaltis, D.

Pugzlys, A.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Raith, P.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Rathje, C.

K. E. Priebe, C. Rathje, S. V. Yalunin, T. Hohage, A. Feist, S. Schäfer, and C. Ropers, “Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy,” Nat. Photonics 11, 793–797 (2017).
[Crossref]

Rechtsman, M.

I. Kaminer, J. Nemirovsky, M. Rechtsman, R. Bekenstein, and M. Segev, “Self-accelerating dirac particles and prolonging the lifetime of relativistic fermions,” Nat. Phys. 11, 261–267 (2015).
[Crossref]

Reinhardt, O.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

W. Cai, O. Reinhardt, I. Kaminer, and J. G. D. Abajo, “Efficient orbital angular momentum transfer between plasmons and free electrons,” Phys. Rev. B 98, 045424 (2018).
[Crossref]

O. Reinhardt and I. Kaminer, “Revealing the quantum nature of a free electron in an attosecond laser pulse,” in Frontiers in Optics (Optical Society of America, 2018), paper FTh3C-7.

Ren, X.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

Rhodes, C. K.

Richardson, M. C.

N. H. Burnett, H. A. Baldis, M. C. Richardson, and G. D. Enright, “Harmonic generation in CO2 laser target generation,” Appl. Phys. Lett. 31, 172–174 (1977).
[Crossref]

Rivera, N.

N. Rivera, C. W. Hsu, B. Zhen, H. Buljan, J. D. Joannopoulos, and M. Soljačić, “Controlling directionality and dimensionality of radiation by perturbing separable bound states in the continuum,” Sci. Rep. 6, 33394 (2016).
[Crossref]

Ropers, C.

K. E. Priebe, C. Rathje, S. V. Yalunin, T. Hohage, A. Feist, S. Schäfer, and C. Ropers, “Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy,” Nat. Photonics 11, 793–797 (2017).
[Crossref]

K. E. Echternkamp, A. Feist, S. Schäfer, and C. Ropers, “Ramsey-type phase control of free-electron beams,” Nat. Phys. 12, 1000–1004 (2016).
[Crossref]

A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, and C. Ropers, “Quantum coherent optical phase modulation in an ultrafast transmission electron microscope,” Nat. Phys. 521, 200–203 (2015).
[Crossref]

Rost, J. M.

Q.-C. Ning, U. Saalmann, and J. M. Rost, “Electron dynamics driven by light-pulse derivatives,” Phys. Rev. Lett. 120, 033203 (2018).
[Crossref]

Rundquist, A.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

Ruschin, S.

A. Friedman, A. Gover, G. Kurizki, S. Ruschin, and A. Yariv, “Spontaneous and stimulated emission from quasifree electrons,” Rev. Mod. Phys. 60, 471 (1988).
[Crossref]

Ryabov, A.

A. Ryabov and P. Baum, “Electron microscopy of electromagnetic waveforms,” Science 353, 374–377 (2016).
[Crossref]

Saalmann, U.

Q.-C. Ning, U. Saalmann, and J. M. Rost, “Electron dynamics driven by light-pulse derivatives,” Phys. Rev. Lett. 120, 033203 (2018).
[Crossref]

Santra, R.

R. E. Goetz, M. Merkel, A. Karamatskou, R. Santra, and C. P. Koch, “Maximizing hole coherence in ultrafast photoionization of argon with an optimization by sequential parametrization update,” Phys. Rev. A 94, 023420 (2016).
[Crossref]

R. E. Goetz, A. Karamatskou, R. Santra, and C. P. Koch, “Quantum optimal control of photoelectron spectra and angular distributions,” Phys. Rev. A 93, 013413 (2016).
[Crossref]

Sch, L.

L. Sch, Beam-Wave Interaction in Periodic and Quasi-Periodic Structures (Springer, 2011).

Schäfer, S.

K. E. Priebe, C. Rathje, S. V. Yalunin, T. Hohage, A. Feist, S. Schäfer, and C. Ropers, “Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy,” Nat. Photonics 11, 793–797 (2017).
[Crossref]

K. E. Echternkamp, A. Feist, S. Schäfer, and C. Ropers, “Ramsey-type phase control of free-electron beams,” Nat. Phys. 12, 1000–1004 (2016).
[Crossref]

A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, and C. Ropers, “Quantum coherent optical phase modulation in an ultrafast transmission electron microscope,” Nat. Phys. 521, 200–203 (2015).
[Crossref]

Schattschneider, P.

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301 (2010).
[Crossref]

Schauss, J.

A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, and C. Ropers, “Quantum coherent optical phase modulation in an ultrafast transmission electron microscope,” Nat. Phys. 521, 200–203 (2015).
[Crossref]

Schley, R.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. Makris, and M. Segev, “Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams,” Opt. Express 21, 13425–13435 (2013).
[Crossref]

Schrauth, S. E.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Schumacher, D. W.

D. W. Schumacher, J. H. Hoogenraad, D. Pinkos, and P. H. Bucksbaum, “Programmable cesium Rydberg wave packets,” Phys. Rev. A 6, 4719–4726 (2016).
[Crossref]

Segev, M.

A. Patsyk, M. A. Bandres, R. Bekenstein, and M. Segev, “Observation of accelerating wave packets in curved space,” Phys. Rev. X 8, 011001 (2018).
[Crossref]

M. Mutzafi, I. Kaminer, G. Harari, and M. Segev, “Non-diffracting multi-electron vortex beams balancing their electron-electron interactions,” Nat. Commun. 8, 650 (2017).
[Crossref]

I. Kaminer, J. Nemirovsky, M. Rechtsman, R. Bekenstein, and M. Segev, “Self-accelerating dirac particles and prolonging the lifetime of relativistic fermions,” Nat. Phys. 11, 261–267 (2015).
[Crossref]

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

R. Bekenstein, J. Nemirovsky, I. Kaminer, and M. Segev, “Shape-preserving accelerating electromagnetic wave packets in curved space,” Phys. Rev. X 4, 011038 (2014).
[Crossref]

E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. Makris, and M. Segev, “Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams,” Opt. Express 21, 13425–13435 (2013).
[Crossref]

I. Kaminer, J. Nemirovsky, and M. Segev, “Self-accelerating self-trapped nonlinear beams of Maxwell’s equations,” Opt. Express 20, 18827–18835 (2012).
[Crossref]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self trapped optical beams,” Phys. Rev. Lett. 106, 213902 (2011).
[Crossref]

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observations of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Seyfried, V.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

Shan, B.

B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65, 011804 (2001).
[Crossref]

Shaw, J. M.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Shiloh, R.

R. Shiloh, Y. Lereah, Y. Lilach, and A. Arie, “Sculpturing the electron wave function using nanoscale phase masks,” Ultramicroscopy 144, 26–31 (2014).
[Crossref]

Shim, B.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Siqueira, J. P.

G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
[Crossref]

Siviloglou, G. A.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901(2007).
[Crossref]

Sivlioglou, G. A.

Slater, L.

L. Slater, Confluent Hypergeometric Functions (Cambridge University, 1960).

Soljacic, M.

N. Rivera, C. W. Hsu, B. Zhen, H. Buljan, J. D. Joannopoulos, and M. Soljačić, “Controlling directionality and dimensionality of radiation by perturbing separable bound states in the continuum,” Sci. Rep. 6, 33394 (2016).
[Crossref]

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 331–335 (2016).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Stein, G. J.

G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
[Crossref]

Stone, A. D.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 331–335 (2016).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

Strehle, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

Szameit, A.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observations of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Thompson, I.

I. Thompson, Coulomb Functions (in NIST Handbook of Mathematical Functions) (Cambridge University, 2010).

Tian, H.

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301 (2010).
[Crossref]

Tonomura, A.

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464, 737 (2010).
[Crossref]

Tzortzakis, S.

K. Makris, D. Papazoglou, and S. Tzortzakis, “Invariant superoscillatory electromagnetic fields in 3D-space,” J. Opt. 19, 014003 (2016).
[Crossref]

Uchida, M.

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464, 737 (2010).
[Crossref]

Unguris, J.

B. McMorran, A. Agrawal, I. Anderson, A. Herzing, H. Lezec, J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

Vanacore, G. M.

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

Verbeeck, J.

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301 (2010).
[Crossref]

Voloch-Block, N.

N. Voloch-Block, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

von Neumann, J.

J. von Neumann and E. P. Wigner, “Über merkwürdige diskrete eigenwerte,” Phys. Z. 30, 465–467 (1929).

Walther, H.

W. Nicklich, H. Kumpfmüller, and H. Walther, “Above-threshold ionization of cesium under femtosecond laser pulses: new substructure due to strongly coupled bound states,” Phys. Rev. Lett. 69, 3455–3458 (1992).
[Crossref]

Wang, K.

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

Wang, Y.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

Watanabe, S.

N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses,” Nat. Commun. 5, 3331 (2014).
[Crossref]

Watson, G. N.

E. T. Whittaker and G. N. Watson, A Course in Modern Analysis, 4th ed. (Cambridge University, 1995), p. 340.

Weber, H. B.

C. Heide, T. Higuchi, H. B. Weber, and P. Hommelhoff, “Coherent electron trajectory control in graphene,” Phys. Rev. Lett. 121, 207401 (2018).
[Crossref]

Werschnik, J.

J. Werschnik and E. Gross, “Quantum optimal control theory,” J. Phys. B 40, R175 (2007).
[Crossref]

Whittaker, E. T.

E. T. Whittaker and G. N. Watson, A Course in Modern Analysis, 4th ed. (Cambridge University, 1995), p. 340.

Wigner, E. P.

J. von Neumann and E. P. Wigner, “Über merkwürdige diskrete eigenwerte,” Phys. Z. 30, 465–467 (1929).

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

Wollenhaupt, M.

M. Wollenhaupt, C. Lux, M. Krug, and T. Baumert, “Tomographic reconstruction of designer free-electron wave packets,” ChemPhysChem 14, 1341–1349 (2013).
[Crossref]

Wong, J. L.

J. L. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).
[Crossref]

Wu, Y.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

Yalunin, S. V.

K. E. Priebe, C. Rathje, S. V. Yalunin, T. Hohage, A. Feist, S. Schäfer, and C. Ropers, “Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy,” Nat. Photonics 11, 793–797 (2017).
[Crossref]

A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, and C. Ropers, “Quantum coherent optical phase modulation in an ultrafast transmission electron microscope,” Nat. Phys. 521, 200–203 (2015).
[Crossref]

Yariv, A.

A. Friedman, A. Gover, G. Kurizki, S. Ruschin, and A. Yariv, “Spontaneous and stimulated emission from quasifree electrons,” Rev. Mod. Phys. 60, 471 (1988).
[Crossref]

Yin, Y.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

Zewail, A. H.

B. Barwick, D. J. Flannigan, and A. H. Zewail, “Photon-induced near-field electron microscopy,” Nature 462, 902–906 (2009).
[Crossref]

Zhang, Y.

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Zhao, K.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

Zhen, B.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 331–335 (2016).
[Crossref]

N. Rivera, C. W. Hsu, B. Zhen, H. Buljan, J. D. Joannopoulos, and M. Soljačić, “Controlling directionality and dimensionality of radiation by perturbing separable bound states in the continuum,” Sci. Rep. 6, 33394 (2016).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Zwillinger, D.

D. Zwillinger, Handbook of Differential Equations (Academic, 1997).

ACS Photon. (1)

J. L. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).
[Crossref]

Am. J. Phys. (1)

M. V. Berry and N. L. Balázs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[Crossref]

Appl. Phys. Lett. (2)

N. H. Burnett, H. A. Baldis, M. C. Richardson, and G. D. Enright, “Harmonic generation in CO2 laser target generation,” Appl. Phys. Lett. 31, 172–174 (1977).
[Crossref]

A. Mathis, F. Courvoisiera, L. Froehly, L. Fufaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

ChemPhysChem (1)

M. Wollenhaupt, C. Lux, M. Krug, and T. Baumert, “Tomographic reconstruction of designer free-electron wave packets,” ChemPhysChem 14, 1341–1349 (2013).
[Crossref]

J. Appl. Phys. (1)

P. Baum, “Quantum dynamics of attosecond electron pulse compression,” J. Appl. Phys. 122, 223105 (2017).
[Crossref]

J. Opt. (1)

K. Makris, D. Papazoglou, and S. Tzortzakis, “Invariant superoscillatory electromagnetic fields in 3D-space,” J. Opt. 19, 014003 (2016).
[Crossref]

J. Opt. Soc. Am. A. (1)

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A. 4, 651–654 (1987).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. B (3)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

J. Werschnik and E. Gross, “Quantum optimal control theory,” J. Phys. B 40, R175 (2007).
[Crossref]

G. J. Stein, P. D. Keathley, P. Krogen, H. Liang, J. P. Siqueira, C.-L. Chang, C.-J. Lai, K.-H. Hong, G. M. Laurent, and F. X. Kärtner, “Water-window soft x-ray high-harmonic generation up to the nitrogen k-edge driven by a kHz, 2.1  μm OPCPA source,” J. Phys. B 49, 155601 (2016).
[Crossref]

Nat. Commun. (5)

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond x-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref]

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses,” Nat. Commun. 5, 3331 (2014).
[Crossref]

M. Mutzafi, I. Kaminer, G. Harari, and M. Segev, “Non-diffracting multi-electron vortex beams balancing their electron-electron interactions,” Nat. Commun. 8, 650 (2017).
[Crossref]

G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Barwick, F. J. García de Abajo, and F. Carbone, “Attosecond coherent control of free-electron wave functions using semi-infinite light fields,” Nat. Commun. 9, 2694 (2018).
[Crossref]

Nat. Mater. (1)

G. M. Vanacore, G. Berruto, I. Madan, E. Pomarico, P. Biagioni, R. J. Lamb, D. McGrouther, O. Reinhardt, I. Kaminer, B. Barwick, V. Grillo, E. Karimi, F. J. García de Abajo, and F. Carbone, “Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields,” Nat. Mater. 18, 573–579 (2019).
[Crossref]

Nat. Photonics (2)

K. E. Priebe, C. Rathje, S. V. Yalunin, T. Hohage, A. Feist, S. Schäfer, and C. Ropers, “Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy,” Nat. Photonics 11, 793–797 (2017).
[Crossref]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

Nat. Phys. (5)

K. E. Echternkamp, A. Feist, S. Schäfer, and C. Ropers, “Ramsey-type phase control of free-electron beams,” Nat. Phys. 12, 1000–1004 (2016).
[Crossref]

A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, and C. Ropers, “Quantum coherent optical phase modulation in an ultrafast transmission electron microscope,” Nat. Phys. 521, 200–203 (2015).
[Crossref]

Y. Morimoto and P. Baum, “Diffraction and microscopy with attosecond electron pulse trains,” Nat. Phys. 14, 252–256 (2018).
[Crossref]

I. Kaminer, J. Nemirovsky, M. Rechtsman, R. Bekenstein, and M. Segev, “Self-accelerating dirac particles and prolonging the lifetime of relativistic fermions,” Nat. Phys. 11, 261–267 (2015).
[Crossref]

J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, “Structured quantum waves,” Nat. Phys. 11, 629–634 (2015).
[Crossref]

Nat. Rev. Mater. (1)

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 331–335 (2016).
[Crossref]

Nature (6)

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464, 737 (2010).
[Crossref]

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301 (2010).
[Crossref]

N. Voloch-Block, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

B. Barwick, D. J. Flannigan, and A. H. Zewail, “Photon-induced near-field electron microscopy,” Nature 462, 902–906 (2009).
[Crossref]

C. Ott, A. Kaldun, L. Argenti, P. Raith, K. Meyer, M. Laux, Y. Zhang, A. Blättermann, S. Hagstotz, T. Ding, R. Heck, J. Madronero, F. Martin, and T. Pfeifer, “Reconstruction and control of a time-dependent two-electron wave packet,” Nature 516, 374–378 (2014).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. A (5)

B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65, 011804 (2001).
[Crossref]

J. Palmer and S. D. Hogan, “Experimental demonstration of a Rydberg-atom beam splitter,” Phys. Rev. A 95, 053413 (2017).
[Crossref]

D. W. Schumacher, J. H. Hoogenraad, D. Pinkos, and P. H. Bucksbaum, “Programmable cesium Rydberg wave packets,” Phys. Rev. A 6, 4719–4726 (2016).
[Crossref]

R. E. Goetz, A. Karamatskou, R. Santra, and C. P. Koch, “Quantum optimal control of photoelectron spectra and angular distributions,” Phys. Rev. A 93, 013413 (2016).
[Crossref]

R. E. Goetz, M. Merkel, A. Karamatskou, R. Santra, and C. P. Koch, “Maximizing hole coherence in ultrafast photoionization of argon with an optimization by sequential parametrization update,” Phys. Rev. A 94, 023420 (2016).
[Crossref]

Phys. Rev. B (1)

W. Cai, O. Reinhardt, I. Kaminer, and J. G. D. Abajo, “Efficient orbital angular momentum transfer between plasmons and free electrons,” Phys. Rev. B 98, 045424 (2018).
[Crossref]

Phys. Rev. Lett. (12)

C. Heide, T. Higuchi, H. B. Weber, and P. Hommelhoff, “Coherent electron trajectory control in graphene,” Phys. Rev. Lett. 121, 207401 (2018).
[Crossref]

Q.-C. Ning, U. Saalmann, and J. M. Rost, “Electron dynamics driven by light-pulse derivatives,” Phys. Rev. Lett. 120, 033203 (2018).
[Crossref]

J. J. Macklin, J. D. Kmetec, and C. L. I. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766 (1993).
[Crossref]

W. Nicklich, H. Kumpfmüller, and H. Walther, “Above-threshold ionization of cesium under femtosecond laser pulses: new substructure due to strongly coupled bound states,” Phys. Rev. Lett. 69, 3455–3458 (1992).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901(2007).
[Crossref]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, O. D. Balčiunas, T. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observations of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self trapped optical beams,” Phys. Rev. Lett. 106, 213902 (2011).
[Crossref]

K. Y. Bliokh, M. R. Dennis, and F. Nori, “Relativistic electron vortex beams: angular momentum and spin-orbit interaction,” Phys. Rev. Lett. 107, 174802 (2011).
[Crossref]

Phys. Rev. X (3)

R. Bekenstein, J. Nemirovsky, I. Kaminer, and M. Segev, “Shape-preserving accelerating electromagnetic wave packets in curved space,” Phys. Rev. X 4, 011038 (2014).
[Crossref]

A. Patsyk, M. A. Bandres, R. Bekenstein, and M. Segev, “Observation of accelerating wave packets in curved space,” Phys. Rev. X 8, 011001 (2018).
[Crossref]

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
[Crossref]

Phys. Z. (1)

J. von Neumann and E. P. Wigner, “Über merkwürdige diskrete eigenwerte,” Phys. Z. 30, 465–467 (1929).

Rev. Mod. Phys. (1)

A. Friedman, A. Gover, G. Kurizki, S. Ruschin, and A. Yariv, “Spontaneous and stimulated emission from quasifree electrons,” Rev. Mod. Phys. 60, 471 (1988).
[Crossref]

Sci. Rep. (1)

N. Rivera, C. W. Hsu, B. Zhen, H. Buljan, J. D. Joannopoulos, and M. Soljačić, “Controlling directionality and dimensionality of radiation by perturbing separable bound states in the continuum,” Sci. Rep. 6, 33394 (2016).
[Crossref]

Science (5)

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, G. Ališauskas, S. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

B. McMorran, A. Agrawal, I. Anderson, A. Herzing, H. Lezec, J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

A. Ryabov and P. Baum, “Electron microscopy of electromagnetic waveforms,” Science 353, 374–377 (2016).
[Crossref]

Ultramicroscopy (1)

R. Shiloh, Y. Lereah, Y. Lilach, and A. Arie, “Sculpturing the electron wave function using nanoscale phase masks,” Ultramicroscopy 144, 26–31 (2014).
[Crossref]

Other (8)

L. Slater, Confluent Hypergeometric Functions (Cambridge University, 1960).

I. Thompson, Coulomb Functions (in NIST Handbook of Mathematical Functions) (Cambridge University, 2010).

D. Zwillinger, Handbook of Differential Equations (Academic, 1997).

L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Elsevier, 1981).

E. T. Whittaker and G. N. Watson, A Course in Modern Analysis, 4th ed. (Cambridge University, 1995), p. 340.

R. Dangovski, “WhittakerWavepackets,” https://drive.google.com/drive/folders/0B4FK9pSy4zn4NG8wZ1BOME0tb2c

L. Sch, Beam-Wave Interaction in Periodic and Quasi-Periodic Structures (Springer, 2011).

O. Reinhardt and I. Kaminer, “Revealing the quantum nature of a free electron in an attosecond laser pulse,” in Frontiers in Optics (Optical Society of America, 2018), paper FTh3C-7.

Supplementary Material (2)

NameDescription
» Code 1       Code for our experiments.
» Supplement 1       Supplemental document

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Figures (4)

Fig. 1.
Fig. 1. Shaping of electron states in the continuum of energy levels of the hydrogen atom creates localized and quasi-shape-invariant high-energy wavepackets, unlimited in energy. The possibility of decay from the continuum to bound states enables a photon emission with energy higher than the ionization threshold. Color, r2|Ψ|2/max{r2|Ψ|2}.
Fig. 2.
Fig. 2. By shaping the (Whittaker) electron wavepacket, we can prolong the lifetime to a desired duration in exchange for increasing the spatial spread. (a) As we decrease the energy spread ΔE, the probability density r2|Ψ|2 spreads out farther in space according to (6). (b) The benefit of making the energy spread small, however, is that the lifetime grows according to (7). Here, Δt=19.14ns and the colors match the Whittaker wavepackets in (a). (c) Envelope of the wavepacket at three points in time: A, B, C [also marked in (b)].
Fig. 3.
Fig. 3. Dynamics of the Whittaker wavepacket. (a) The wavepacket begins at t=0, with a set of nodes marked by dots. The dotted lines trace the nodes, and the cross signals a vanished node. Time frames and overlap points linked in color. (b) A larger range in space that includes more oscillations (only the envelope is plotted) and has a longer lifetime Δt. (c) The geometry of the Whittaker wavepacket is roughly the same as that of the free particle with Bessel functions as modes. Baseline ΔE0/E0 set in (a).
Fig. 4.
Fig. 4. Radiative decay of the Whittaker wavepackets to bound states. (a) The decay probability reaches a saturation line for infrared energy E=1eV. The average rate approximates a slope. (b) The profiles of the decay rates (small panels) for the soft-x-ray energy E=217.6eV are monotonously decreasing in comparison to the profiles in (a). Baseline ΔE0/E0 set in (a). Note that (b) may have quantitative corrections due to beyond-dipole corrections arising from the short wavelength of the electromagnetic field, since for our spontaneous emission calculations, we use the dipole approximation.

Tables (1)

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Table 1. Spread-Lifetime Trade-Off of Whittaker Wavepacketsa

Equations (12)

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wκ(x,0)=4iκ2eiκxπcsch(π/2κ)01e2iκxs(s1s)i2κds,
ΨE,ΔE(r,t)=Ne(κμ)2/2σ2wκ(x,t)dκ,
Δr=var(envelope(ΨE,ΔE(r,0))),
Δt=var(O(t))
O(t)=|0Ψ*(r,0)Ψ(r,t)r2dr|2.
Δr2.471a0(ΔE)/eV.
Δt0.136eV·fs(ΔE)E.
Γ˜=P(2(Δt))2(Δt)
dPfi(k,λ)=Vd3k(2π)3|Sfi(k,λ)|2
Sfi=f|Tei0tH^intdt|i
H^int[ψ]=iemed3xψ*A^(x,t)·ψ,
Sfi(k,λ)=eme2ϵ0ωkV0tdteiωktε^kλ·d3xψf*(x,t)eik·x·ψi(x,t)

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