Abstract

Raman effect in gases can generate an extremely long-living wave of coherence that can lead to the establishment of an almost perfect temporal periodic variation of the medium refractive index. We show theoretically and numerically that the equations, regulate the pulse propagation in hollow-core photonic crystal fibers filled by Raman-active gas, are exactly identical to a classical problem in quantum condensed matter physics – but with the role of space and time reversed – namely an electron in a periodic potential subject to a constant electric field. We are therefore able to infer the existence of Wannier-Stark ladders, Bloch oscillations, and Zener tunneling, phenomena that are normally associated with condensed matter physics, using purely optical means.

© 2015 Optical Society of America

1. Introduction

Hollow-core photonic crystal fibers (HC-PCFs) continue to demonstrate their enormous potential for developing novel photonic devices for different optical applications [1, 2]. HC-PCFs with Kagome-style cladding structure have granted unprecedented strong interactions between light and gaseous media over relatively-long propagation distances with low transmission losses and pressure-tunable dispersion in the visible region [3, 4]. Within approximately a decade of the invention of the HC-PCF, exceptional nonlinear phenomena and applications have been demonstrated and predicted in these kind of fibers such as Stokes generation with drastical reduction in the Raman threshold [5], high harmonic generation [6], efficient deep-ultraviolet radiation [7], ionization-induced soliton self-frequency blueshift [811], strong asymmetrical self-phase modulation, universal modulational instability [12], and built-in parity-time symmetry [13].

The Raman effect is one of the earliest and most fundamental effects in nonlinear optics. When a pulse propagates inside a nonlinear medium, it excites optical phonons, leading to a plethora of phenomena, such as the generation of Stokes and anti-Stokes sidebands for long input pulses, and to an intense redshift for short pulses. The Raman effect has been successfully used to enhance the bandwidth of the output spectra during the supercontinuum generation, a dramatic spectral broadening due to the interaction of optical solitons, typically observed in solid-core optical fibers, and very recently in gas-filled HC-PCFs [14].

Stimulated Raman scattering processes in gases are characterized by a very long molecular coherence relaxation (dephasing) time, of the order of hundreds of picoseconds or more [14], which should be compared to the short relaxation time of phonon oscillations in silica glass (approx. 32 fs). Within this long relaxation phase, the medium exhibits a highly non-instantaneous response to pulsed excitations. Nonlinear interactions between optical pulses and Raman-active gases have been suggested and exploited mainly in the synthesis of subfemtosecond pulses using different techniques [1519]. In addition, continuous down-shift of the frequency of an ultrashort pulse [20], and optical modulation of a continuous wave laser have been demonstrated [21] due to these interactions. Recently, some of the current authors have used the interaction of an ultrashort pulse with a hydrogen-filled HC-PCF to generate a supercontinuum extending from near infrared (1200 nm) to vacuum ultraviolet (124 nm) [14]. In the impulsive excitation regime, when the temporal pulse width is shorter than the Raman oscillation period of the gas, a sinusoidal temporal modulation of the medium refractive index lagging a pump source has been observed experimentally [18, 20, 22]. This modulation can be detected via launching a delayed weak probe within the dephasing time.

In this paper, we analyze the propagation of two temporally separated pulses in HC-PCFs filled with Raman-active gases. By investigating the effect of the Raman polarization induced by a pump pulse in the impulsive excitation regime, we demonstrate a perfect analogy between the spatiotemporal dynamics of a delayed probe and several phenomena observed in condensed matter physics, such as the Wannier-Stark ladder [23], Bloch oscillations [24] and Zener tunneling [25]. Although these effects have been previously observed in optics using periodic complex microstructures [2629], our system is distinguished by the natural occurrence of a temporal periodic crystal via Raman excitation.

2. Governing equations for Raman media

Let us consider the propagation of an ultrashort pulse in a HC-PCF filled with a Raman-active gas. The medium response is described by its total polarization, which is a sum of the linear, Kerr, and Raman polarizations. Ionization-induced plasma generation is neglected, as we assume that the pulse intensity is smaller than the gas ionization threshold. Assuming that only one Raman mode is excited (either the vibrational or rotational one), the dynamics of the Raman polarization (also called coherence) PR can be determined by solving the Bloch equations for a two-level system [19, 30],

tw+w+1T1=iα12h¯(ρ12ρ12*)E2,[t+1T2iωR]ρ12=i2h¯[α12w+(α11α22)ρ12]E2,
where w = ρ22ρ11 is the population inversion between the excited and ground states, t is the time variable, αij and ρij are the elements of the 2 × 2 polarizability and density matrices, respectively, E is the real electric field, ωR is the Raman frequency of the transition, N0 is the molecular number density, T1 and T2 are the population and polarization relaxation times, respectively, and is the reduced Planck’s constant. Finally we have PR[α12(ρ12+ρ12*)+α11ρ11+α22ρ22]N0E, assuming that initially all the molecules are in the ground state. In the regime where the slowly varying envelope approximation (SVEA) is valid, the electric field can be expressed as E=12[A(z,t)exp(iβ0ziω0t)+c.c.], where ω0 is the pulse central frequency, β0 is the propagation constant calculated at ω0, z is the longitudinal coordinate along the fiber, A is the complex envelope, and c.c. denotes the complex conjugate. We first introduce the following new variables: ξ = z/z0, τ = t/t0, ψ = A/A0, z0=t02/|β2(ω0)|, A02=1/(γz0), γ = 3ω0χ(3)poT/(c2ε0AeffpTo, where β2 is the second-order dispersion coefficient, γ is the nonlinear Kerr coefficient in the unit of W−1m−1, χ(3) is the third-order nonlinearity, p is the pressure, po is atmospheric pressure, T is the temperature, To = 273.15 K, c is the speed of light, ε0 is the vacuum permittivity, Aeff is the effective area of the fundamental mode, and t0 is the pulse duration. By using the SVEA, one can derive the following set of normalized coupled equations,
[iξ+D^(iτ)+|ψ|2+ηRe(ρ12)]ψ=0,τw+(w+1)t0T1=4μwIm(ρ12)|ψ|2,[τ+t0T2iδ]ρ12=iμw|ψ|2,
where D^(iτ)=z0m1βm(iτ)m/t0m/m! is the full dispersion operator, βm is the mth order dispersion coefficient calculated at ω0, η = z0/z1, z1 = 0/ (α12 N0 ω0) is the nonlinear Raman length, μ = P0/P1, P0=A02, P1 = 2h̄cε0Aeff/ (α12 t0), δ = ωRt0, and Re, Im represent the real and imaginary parts. In the derivation of Eq. (2), we have neglected the self-steepening effect, assumed that |w| ≫ |ρ12|, and the population inversion is weak, i.e. ρ11 ≈ 1, and ρ22 ≈ 0. These assumptions are physically realistic in gaseous Raman media under few-μJ input-pulse excitation. By comparing the outcomes of single pulse propagation in HC-PCFs filled by Raman-active gases, using our model and another full model based on the unidirectional pulse propagation equation that is not based on SVEA [14,31], very good qualitative agreements, featured in obtaining the wiggled dispersive waves [32], between the two outputs have been obtained. It is worth also to note that the main condition ω0 t0 ≫ 1 for the use of the SVEA [33] is satisfied in the simulations presented in this paper.

3. Raman response function

For femtosecond pulses, the relaxation times of the population inversion (T1) and the coherence (T2) can be safely neglected, since they are of the order of hundreds of picoseconds or more. For instance, T1 ≈ 20 ns and T2 = 433 ps for excited rotational Raman in hydrogen under gas pressure 7 bar at room temperature [14, 36]. This amazingly long relaxation times are a crucial and quite unique feature of gaseous Raman systems, which we use to the full in the present paper. We have also found that the population inversion is almost unchanged from its initial value for pulses with energies in the order of few μJ, i.e. w(τ) ≈ w(−∞) = −1. Hence, the set of the governing equations Eq. (2) can be reduced to a single generalized nonlinear Schrödinger equation,

iξψ+iβ1z0t0τψ+12τ2ψ+|ψ|2ψ+R(τ)ψ=0,
where R(τ)=κτsin[δ(ττ)]|ψ(τ)|2dτ is the resulting Raman convolution, and κ = ημ is the ratio between the Raman and the Kerr nonlinearities. Pumping in the deep anomalous dispersion regime (β2 < 0) is assumed, hence, higher-order dispersion coefficients βm>2 can be neglected, so that the generation of dispersive waves is strongly reduced. For ultra-short pulses with duration t0 ≪ 1/ωR, sin [δ(ττ′)] can be expanded around the temporal location of the pulse peak by using a Taylor expansion. For instance, a fundamental soliton with amplitude V and centered at τ = 0 will induce a Raman contribution in the form of R(τ) ≈ κV sin(δτ)[1 + tanh()] at the zeroth-order approximation. Hence, this soliton will generate a retarded sinusoidal Raman polarization that can impact the dynamics of the other trailing probe pulse lagging behind the pump pulse, see Fig. 1. On the other hand, for t0 ≫ 1/ωR, R (τ) ≈ γR |ψ(τ)|2 with γR = κ/δ, i.e the Raman nonlinearity is considered to be instantaneous. So, the Raman contribution would induce an effective Kerr nonlinearity that is significant, and can compete directly with the intrinsic Kerr nonlinearity of the gas [14, 37].

 

Fig. 1 Temporal evolution of an accelerated oscillating Raman polarization with period Λ = 56.7 fs induced by a propagating fundamental soliton with an amplitude V1 = 1.33, a central wavelength 1064 nm, and a FWHM 15 fs in a H2-filled HC-PCF with a Kagomelattice cross section, a flat-to-flat core diameter 18 μm, a zero dispersion wavelength 413 nm, a gas pressure 7 bar, and a rotational Raman frequency ωR = 17.6 THz. The dashed yellow line represents the temporal evolution of the soliton that excites the coherence wave. The simulation parameters are γ = 7.07 × 10−6 W−1m−1, β2 = −3425.5 fs2/m, Aeff = 134μm2, α12 = 0.8 × 10−41 C m2/V [14, 34], and t0 = 11.34 fs. The parameter γ is calculated using the nonlinear susceptibility of H2 [35]. For these parameters, we have found that higher-order dispersion and self steepening effects have a weak influence on the soliton dynamics. All subsequent calculations in this paper are based on these values.

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Pump solution—

In the following, we will focus on two different pulses that are not overlapped in time, and separated by a delay ≪ T1, T2 in the deep anomalous dispersion regime. The leading pulse is an ultrashort strong ‘pump’ pulse ψ1 with t0 ≪ 1/ωR, while the trailing pulse is a weak ‘probe’ pulse ψ2 with negligible nonlinearity. In this case, Eq. (3) can be used to determine the pump solution. For weak Raman nonlinearity, the solution of Eq. (3) can be assumed to be a fundamental soliton that is perturbed by the Raman polarization, i.e. ψ1 (ξ, τ) = V1 sech [V1 (τu1ξτ̄1 (ξ))]exp[−iΩ1 (ξ)(τu1ξ)] where u1 = β11z0/t0, β11 is the first-order dispersion coefficient of the pump, V1, Ω1, and τ̄1 are the soliton amplitude, central frequency, and position of its peak, respectively. We will launch this soliton as a pump with τ̄1 (0) = 0. Using the variational perturbation method [33] and zeroth-order Taylor approximation, we have found that this soliton is linearly redshifting in the frequency domain with rate g1=12κπδ2csch(πδ/2V1), and decelerating in the time domain, i.e. Ω1 = −g1 ξ, and τ̄1 = g1 ξ2/2. In the case t0 < 1/ωR, we have found that a factor of 12 might be used to correct the overestimated value of g1, resulting from using the zeroth-order approximation.

4. Governing equation for the probe

When a second weak probe pulse is sent after the leading pump soliton described in the previous section, the probe evolution is ruled by the equation

iξψ2+iu2τψ2+12mτ2ψ2+2κV1sin(δτ˜)ψ2=0,
where u2 = β12z0/t0, m = |β21|/|β22|, β1j and β2j are the first and the second order dispersion coefficients of the jth pulse with j = 1, 2. Going to the reference frame of the leading decelerating soliton, τ̃ = τu1ξg1ξ2/2, and applying a generalized form of the Gagnon-Bélanger phase transformation [38] ψ2 (ξ, τ̃) = ϕ(ξ, τ̃) exp [iτ̃(g1ξ + u1u2) + i (g1ξ + u1u2)3/6g1], Eq. (4) becomes
iξϕ=12mτ˜2ϕ+[2κV1sin(δτ˜)+g1τ˜]ϕ.
This equation is the exact analogue of the time-dependent Schrödinger equation of an electron in a periodic crystal in the presence of an external electric field. In Eq. (5) time and space are swapped with respect to the condensed matter physics system, as usual in optics, and we deal with a spatial-dependent Schrödinger equation of a single particle ‘probe’ with mass m in a temporal crystal with a periodic potential U = −2κV1 sin (δτ̃) in the presence of a constant force −g1 in the positive-delay direction. The ‘artificial electric field’ g1 is not independent from the depth of the periodic potential 2κV1. The leading soliton excites a sinusoidal Raman oscillation that forms a periodic structure in the reference frame of the soliton. Due to soliton acceleration induced by the strong spectral redshift, a constant force is applied on this structure. Substituting ϕ(ξ, τ̃) = f(τ̃) exp (iqξ), Eq. (5) becomes an eigenvalue problem with eigenvectors f, and eigenvalues −q. The modes of this equation are the Wannier functions [23] that can exhibit Bloch oscillations [24], intrawell oscillations [39], and Zener tunneling [25] due to the applied force. Note that here we cannot use the so-called Houston functions [40] for solving Eq. (5), since these functions are valid only for small external electric fields - which is not the case. Hence, we must therefore calculate numerically the full solution of Eq. (5).

Wannier-Stark ladder—

As a practical example, let us consider the propagation of an ultra-short soliton with FWHM 15 fs in a H2-filled HC-PCF with a Kagome lattice. The validity of the SVEA is maintained along the fiber, since the soliton does not suffer pulse compression and tends to preserve its shape during propagation. The assumptions of having weak higher-order dispersion coefficients and self-steepening effects have been checked. Also, the role of the vibrational Raman excitation with an oscillation 7 fs is modifying the Kerr nonlinearity. Exciting the rotational Raman shift frequency in the fiber via this soliton will induce a long-lived trailing temporal periodic crystal with a lattice constant Λ = 56.7 fs, corresponding to the time required by the H2 molecule to complete one cycle of rotation, see Fig. 1. In the absence of the applied force, the solutions are the Bloch modes, while in the presence of the applied force, the periodic potential is tilted, and the eigenstates of the system are the Wannier functions portrayed as a 2D color plot in Fig. 2, where the horizontal axis is the time and the vertical axis is the corresponding eigenvalue. These functions are modified Airy beams that have strong or weak oscillating decaying tails. After an eigenvalue step g1Λ, the eigenstates are repeated, but shifted by Λ, forming the Wannier-Stark ladder. As shown, each potential minimum can allow a single localized state with very weak tails. A large number of delocalized modes with long and strong tails exist between the localized states.

 

Fig. 2 A portion of the absolute eigenstates of a Raman-induced temporal periodic crystals with a lattice constant Λ = 56.7 fs in the presence of a force with magnitude g1 = 0.1408 in the positive-delay direction. The vertical axis represents the corresponding eigenvalues −q. The dotted-dashed line is the potential under the applied force.

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Bloch oscillations and Zener tunneling—

An arbitrary weak probe following the soliton will be decomposed into the Wannier modes of the periodic temporal crystal. Due to beating between similar eigenstates in different potential wells, Bloch oscillations arise with a period δ/g1, while beating between different eigenstates in the same potential minimum can result in intrawell oscillations. In our case we did not observe in the simulations the latter kind of beating, since only a single eigenstate is allowed within each well. Interference between modes lying between different wells are responsible for Zener tunneling that allows transitions between different wells (or bands). In the absence of the applied force (g1 = 0), the band structure of the periodic medium can be constructed by plotting the propagation constants of the Bloch modes over the first Brillouin zone [−δ/2, δ/2], as shown in Fig. 3(a). Zener tunneling occurs when a particle transits from the lowest band to the next-higher band. The evolution of a delayed probe in the form of the first Bloch mode inside a H2-filled HC-PCF under the influence of the pump-induced temporal periodic crystal, is depicted in Fig. 3(b). Portions of the probe are localized in different temporal wells. Bloch oscillations are also shown with period 34.7 cm, which correspond to the beating between localized modes in adjacent wells. After each half of this period, an accelerated radiation to the left due to Zener tunneling is also emitted. The Zener tunneling is dominant, and the Bloch oscillations are weak, because the potential wells are relatively far from each other. Hence, the overlapping between the localized modes are small, consistent with the shallowness of the first band in the periodic limit (absence of the applied force).

 

Fig. 3 (a) Bandstructure of the temporal crystal induced by the leading ultrashort soliton propagating in the H2-filled Kagome-lattice HC-PCF with m = 1 in the absence of the applied force. (b) Temporal evolution of a weak probe in the accelerated periodic temporal crystal. The probe initial temporal profile is a Gaussian pulse with FWHM 133.6 fs superimposed on the first Bloch mode of the periodic crystal in the absence of the applied force. The contour plot is given in a logarithmic scale and truncated at −60 dB.

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5. Conclusions

From the Maxwell-Bloch equations we have derived a model based on the slowly varying approximation that is convenient for investigating pulse propagation in HC-PCFs filled by Raman-active gases. We have specialized the model to study the propagation of two pulses that do not temporally overlap and are separated by a time delay smaller than the Raman polarization dephasing time (∼ 100 ps). The leading pulse is an ultrashort strong soliton acting as a pump that experiences a linear redshift and deceleration due to Raman nonlinearity. Closed forms of the pump temporal and spectral dynamics have been obtained. The induced-Raman excitation creates a temporal crystal susceptible to a constant force due to the soliton acceleration. If the trailing pulse is assumed to be a weak probe, the problem is reduced to the motion of a particle in a periodic crystal subject to an external force. Phenomena such as Wannier-stark ladder, Bloch oscillations, and Zener tunneling have been demonstrated by simulations. Our results open new research pathways between nonlinear photonics and condensed-matter physics that will bear fruits not only for fundamental science but also for the conception of novel devices.

Acknowledgments

The authors would like to acknowledge several useful discussions with Prof. Philip St.J. Russell and Dr. John Travers at Max Planck Institute for the Science of Light, Erlangen. The authors would like also to acknowledge the support of this research by the Royal Society of Edinburgh, Scottish Government, and German Max Planck Society for the Advancement of Science.

References and links

1. P. St.J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003). [CrossRef]   [PubMed]  

2. P. St.J. Russell, “Photonic-crystal fibers,” J. Light. Technol. 24, 4729–4749 (2006). [CrossRef]  

3. J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011). [CrossRef]  

4. P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014). [CrossRef]  

5. F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002). [CrossRef]   [PubMed]  

6. O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009). [CrossRef]  

7. N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011). [CrossRef]  

8. W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011). [CrossRef]   [PubMed]  

9. P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011). [CrossRef]   [PubMed]  

10. M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011). [CrossRef]  

11. W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013). [CrossRef]   [PubMed]  

12. M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012). [CrossRef]   [PubMed]  

13. M. F. Saleh, A. Marini, and F. Biancalana, “Shock-induced 𝒫𝒯 -symmetric potentials in gas-filled photonic crystal fibers,” Phys. Rev. A 89, 023801 (2014). [CrossRef]  

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References

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  1. P. St.J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
    [Crossref] [PubMed]
  2. P. St.J. Russell, “Photonic-crystal fibers,” J. Light. Technol. 24, 4729–4749 (2006).
    [Crossref]
  3. J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
    [Crossref]
  4. P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
    [Crossref]
  5. F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
    [Crossref] [PubMed]
  6. O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
    [Crossref]
  7. N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
    [Crossref]
  8. W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
    [Crossref] [PubMed]
  9. P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
    [Crossref] [PubMed]
  10. M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
    [Crossref]
  11. W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
    [Crossref] [PubMed]
  12. M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
    [Crossref] [PubMed]
  13. M. F. Saleh, A. Marini, and F. Biancalana, “Shock-induced 𝒫𝒯 -symmetric potentials in gas-filled photonic crystal fibers,” Phys. Rev. A 89, 023801 (2014).
    [Crossref]
  14. F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum-ultraviolet to infrared supercontinuum in hydrogen-filled photonic crystal fiber,” Optica 2, 292–300 (2015).
    [Crossref]
  15. S. Yoshikawa and T. Imasaka, “A new approach for the generation of ultrashort optical pulses,” Opt. Comm. 96, 94–98 (1993).
    [Crossref]
  16. A. E. Kaplan, “Subfemtosecond pulses in mode-locked 2π solitons of the cascade stimulated raman scattering,” Phys. Rev. Lett. 73, 1243–1246 (1994).
    [Crossref] [PubMed]
  17. H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave raman mixing in the femtosecond regime,” IEEE. J. Quantum Electron. 34, 260–268 (1998).
    [Crossref]
  18. A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked stokes and anti-stokes components in an impulsively excited raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
    [Crossref]
  19. V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
    [Crossref] [PubMed]
  20. G. Korn, O. Dühr, and A. Nazarkin, “Observation of raman self-conversion of fs-pulse frequency due to impulsive excitation of molecular vibrations,” Phys. Rev. Lett. 81, 1215–1218 (1998).
    [Crossref]
  21. K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
    [Crossref]
  22. M. Wittmann, A. Nazarkin, and G. Korn, “fs-pulse synthesis using phase modulation by impulsively excited molecular vibrations,” Phys. Rev. Lett. 84, 5508–5511 (2000).
    [Crossref] [PubMed]
  23. G. H. Wannier, “Wave functions and effective Hamiltonian for Bloch electrons in an electric field,” Phys. Rev. 117, 432 (1960).
    [Crossref]
  24. F. Bloch, “Über die Quantenmechanik der Electronen in Kristallgittern,” Z. Phys. 52, 555 (1928).
    [Crossref]
  25. C. Zener, “A theory of electrical breakdown of solid dielectrics,” R. Soc. Lond. A 145, 523 (1934).
    [Crossref]
  26. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
    [Crossref]
  27. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
    [Crossref]
  28. M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
    [Crossref] [PubMed]
  29. A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
    [Crossref] [PubMed]
  30. V. S. Butylkin, A. E. Kaplan, Y. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interaction of Light with Matter (Springer-Verlag, 1989), 1st ed.
    [Crossref]
  31. P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010).
    [Crossref]
  32. F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum UV to IR supercontinuum generation by impulsive Raman self-scattering in hydrogen-filled PCF,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), p. paper FW1D.1.
  33. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007), 4th ed.
  34. M. J. Weber, CRC Handbook of Laser Science and Technology Supplement 2: Optical Materials (CRC press, 1994), 1st ed.
  35. V. Mizrahi and D. P. Shelton, “Nonlinear susceptibility of h2 and d2 accurately measured over a wide range of wavelengths,” Phys. Rev. A 32, 3454–3460 (1985).
    [Crossref] [PubMed]
  36. W. K. Bischel and M. J. Dyer, “Temperature dependence of the raman linewidth and line shift for the q(1) and q(0) transitions in normal and para-H2,” Phys. Rev. A 33, 3113–3123 (1986).
    [Crossref] [PubMed]
  37. R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
    [Crossref]
  38. L. Gagnon and P. A. Bélanger, “Soliton self-frequency shift versus Galilean-like symmetry,” Opt. Lett 15, 466–468 (1990).
    [Crossref] [PubMed]
  39. A. M. Bouchard and M. Luban, “Bloch oscillations and other dynamical phenomena of electrons in semiconductor superlattices,” Phys. Rev. B 52, 5105 (1995).
    [Crossref]
  40. G. J. Iafrate, J. P. Reynolds, J. He, and J. B. Krieger, “Bloch electron dynamics in spatially homogeneous electric fields,” Int. J. of High Speed Electr. 9, 223 (1998).
    [Crossref]

2015 (1)

2014 (2)

M. F. Saleh, A. Marini, and F. Biancalana, “Shock-induced 𝒫𝒯 -symmetric potentials in gas-filled photonic crystal fibers,” Phys. Rev. A 89, 023801 (2014).
[Crossref]

P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

2013 (1)

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
[Crossref] [PubMed]

2012 (2)

M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

2011 (5)

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[Crossref]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

2010 (1)

P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010).
[Crossref]

2009 (1)

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

2006 (2)

P. St.J. Russell, “Photonic-crystal fibers,” J. Light. Technol. 24, 4729–4749 (2006).
[Crossref]

K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
[Crossref]

2005 (1)

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref] [PubMed]

2003 (2)

R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
[Crossref]

P. St.J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

2002 (1)

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

2000 (2)

M. Wittmann, A. Nazarkin, and G. Korn, “fs-pulse synthesis using phase modulation by impulsively excited molecular vibrations,” Phys. Rev. Lett. 84, 5508–5511 (2000).
[Crossref] [PubMed]

V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
[Crossref] [PubMed]

1999 (3)

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked stokes and anti-stokes components in an impulsively excited raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[Crossref]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
[Crossref]

1998 (3)

H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave raman mixing in the femtosecond regime,” IEEE. J. Quantum Electron. 34, 260–268 (1998).
[Crossref]

G. Korn, O. Dühr, and A. Nazarkin, “Observation of raman self-conversion of fs-pulse frequency due to impulsive excitation of molecular vibrations,” Phys. Rev. Lett. 81, 1215–1218 (1998).
[Crossref]

G. J. Iafrate, J. P. Reynolds, J. He, and J. B. Krieger, “Bloch electron dynamics in spatially homogeneous electric fields,” Int. J. of High Speed Electr. 9, 223 (1998).
[Crossref]

1995 (1)

A. M. Bouchard and M. Luban, “Bloch oscillations and other dynamical phenomena of electrons in semiconductor superlattices,” Phys. Rev. B 52, 5105 (1995).
[Crossref]

1994 (1)

A. E. Kaplan, “Subfemtosecond pulses in mode-locked 2π solitons of the cascade stimulated raman scattering,” Phys. Rev. Lett. 73, 1243–1246 (1994).
[Crossref] [PubMed]

1993 (1)

S. Yoshikawa and T. Imasaka, “A new approach for the generation of ultrashort optical pulses,” Opt. Comm. 96, 94–98 (1993).
[Crossref]

1990 (1)

L. Gagnon and P. A. Bélanger, “Soliton self-frequency shift versus Galilean-like symmetry,” Opt. Lett 15, 466–468 (1990).
[Crossref] [PubMed]

1986 (1)

W. K. Bischel and M. J. Dyer, “Temperature dependence of the raman linewidth and line shift for the q(1) and q(0) transitions in normal and para-H2,” Phys. Rev. A 33, 3113–3123 (1986).
[Crossref] [PubMed]

1985 (1)

V. Mizrahi and D. P. Shelton, “Nonlinear susceptibility of h2 and d2 accurately measured over a wide range of wavelengths,” Phys. Rev. A 32, 3454–3460 (1985).
[Crossref] [PubMed]

1960 (1)

G. H. Wannier, “Wave functions and effective Hamiltonian for Bloch electrons in an electric field,” Phys. Rev. 117, 432 (1960).
[Crossref]

1934 (1)

C. Zener, “A theory of electrical breakdown of solid dielectrics,” R. Soc. Lond. A 145, 523 (1934).
[Crossref]

1928 (1)

F. Bloch, “Über die Quantenmechanik der Electronen in Kristallgittern,” Z. Phys. 52, 555 (1928).
[Crossref]

Abdolvand, A.

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum-ultraviolet to infrared supercontinuum in hydrogen-filled photonic crystal fiber,” Optica 2, 292–300 (2015).
[Crossref]

P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum UV to IR supercontinuum generation by impulsive Raman self-scattering in hydrogen-filled PCF,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), p. paper FW1D.1.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007), 4th ed.

Aitchison, J. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
[Crossref]

Antonopoulos, G.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

Backus, S.

R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
[Crossref]

Baer, C. R. E.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

Bartels, R. A.

R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
[Crossref]

Bélanger, P. A.

L. Gagnon and P. A. Bélanger, “Soliton self-frequency shift versus Galilean-like symmetry,” Opt. Lett 15, 466–468 (1990).
[Crossref] [PubMed]

Belli, F.

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum-ultraviolet to infrared supercontinuum in hydrogen-filled photonic crystal fiber,” Optica 2, 292–300 (2015).
[Crossref]

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum UV to IR supercontinuum generation by impulsive Raman self-scattering in hydrogen-filled PCF,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), p. paper FW1D.1.

Benabid, F.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

Bersch, C.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Biancalana, F.

M. F. Saleh, A. Marini, and F. Biancalana, “Shock-induced 𝒫𝒯 -symmetric potentials in gas-filled photonic crystal fibers,” Phys. Rev. A 89, 023801 (2014).
[Crossref]

M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
[Crossref] [PubMed]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

Bischel, W. K.

W. K. Bischel and M. J. Dyer, “Temperature dependence of the raman linewidth and line shift for the q(1) and q(0) transitions in normal and para-H2,” Phys. Rev. A 33, 3113–3123 (1986).
[Crossref] [PubMed]

Bloch, F.

F. Bloch, “Über die Quantenmechanik der Electronen in Kristallgittern,” Z. Phys. 52, 555 (1928).
[Crossref]

Bouchard, A. M.

A. M. Bouchard and M. Luban, “Bloch oscillations and other dynamical phenomena of electrons in semiconductor superlattices,” Phys. Rev. B 52, 5105 (1995).
[Crossref]

Bräuer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
[Crossref]

Butylkin, V. S.

V. S. Butylkin, A. E. Kaplan, Y. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interaction of Light with Matter (Springer-Verlag, 1989), 1st ed.
[Crossref]

Chang, W.

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum-ultraviolet to infrared supercontinuum in hydrogen-filled photonic crystal fiber,” Optica 2, 292–300 (2015).
[Crossref]

P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[Crossref]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum UV to IR supercontinuum generation by impulsive Raman self-scattering in hydrogen-filled PCF,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), p. paper FW1D.1.

Christodoulides, D. N.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Couny, F.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
[Crossref]

Dühr, O.

G. Korn, O. Dühr, and A. Nazarkin, “Observation of raman self-conversion of fs-pulse frequency due to impulsive excitation of molecular vibrations,” Phys. Rev. Lett. 81, 1215–1218 (1998).
[Crossref]

Dyer, M. J.

W. K. Bischel and M. J. Dyer, “Temperature dependence of the raman linewidth and line shift for the q(1) and q(0) transitions in normal and para-H2,” Phys. Rev. A 33, 3113–3123 (1986).
[Crossref] [PubMed]

Eisenberg, H. S.

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K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
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M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
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V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
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K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
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Hölzer, P.

P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
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G. J. Iafrate, J. P. Reynolds, J. He, and J. B. Krieger, “Bloch electron dynamics in spatially homogeneous electric fields,” Int. J. of High Speed Electr. 9, 223 (1998).
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K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
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K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
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H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave raman mixing in the femtosecond regime,” IEEE. J. Quantum Electron. 34, 260–268 (1998).
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J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
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N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
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V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
[Crossref] [PubMed]

Kamitomo, S.

K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
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R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
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Kawano, H.

H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave raman mixing in the femtosecond regime,” IEEE. J. Quantum Electron. 34, 260–268 (1998).
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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
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F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
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Korn, G.

M. Wittmann, A. Nazarkin, and G. Korn, “fs-pulse synthesis using phase modulation by impulsively excited molecular vibrations,” Phys. Rev. Lett. 84, 5508–5511 (2000).
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A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked stokes and anti-stokes components in an impulsively excited raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
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G. Korn, O. Dühr, and A. Nazarkin, “Observation of raman self-conversion of fs-pulse frequency due to impulsive excitation of molecular vibrations,” Phys. Rev. Lett. 81, 1215–1218 (1998).
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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
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G. J. Iafrate, J. P. Reynolds, J. He, and J. B. Krieger, “Bloch electron dynamics in spatially homogeneous electric fields,” Int. J. of High Speed Electr. 9, 223 (1998).
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T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
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Light, P.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

Marini, A.

M. F. Saleh, A. Marini, and F. Biancalana, “Shock-induced 𝒫𝒯 -symmetric potentials in gas-filled photonic crystal fibers,” Phys. Rev. A 89, 023801 (2014).
[Crossref]

Miri, M. A.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
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V. Mizrahi and D. P. Shelton, “Nonlinear susceptibility of h2 and d2 accurately measured over a wide range of wavelengths,” Phys. Rev. A 32, 3454–3460 (1985).
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R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
[Crossref]

Murnane, M.

R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
[Crossref]

Nazarkin, A.

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

M. Wittmann, A. Nazarkin, and G. Korn, “fs-pulse synthesis using phase modulation by impulsively excited molecular vibrations,” Phys. Rev. Lett. 84, 5508–5511 (2000).
[Crossref] [PubMed]

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked stokes and anti-stokes components in an impulsively excited raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[Crossref]

G. Korn, O. Dühr, and A. Nazarkin, “Observation of raman self-conversion of fs-pulse frequency due to impulsive excitation of molecular vibrations,” Phys. Rev. Lett. 81, 1215–1218 (1998).
[Crossref]

Nold, J.

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[Crossref]

Onishchukov, G.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Oton, C. J.

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref] [PubMed]

Pavesi, L.

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref] [PubMed]

Pertsch, T.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
[Crossref]

Peschel, U.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
[Crossref]

Regensburger, A.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Reynolds, J. P.

G. J. Iafrate, J. P. Reynolds, J. He, and J. B. Krieger, “Bloch electron dynamics in spatially homogeneous electric fields,” Int. J. of High Speed Electr. 9, 223 (1998).
[Crossref]

Robinson, J. S.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

Russell, P. St.J.

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum-ultraviolet to infrared supercontinuum in hydrogen-filled photonic crystal fiber,” Optica 2, 292–300 (2015).
[Crossref]

P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[Crossref]

P. St.J. Russell, “Photonic-crystal fibers,” J. Light. Technol. 24, 4729–4749 (2006).
[Crossref]

P. St.J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum UV to IR supercontinuum generation by impulsive Raman self-scattering in hydrogen-filled PCF,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), p. paper FW1D.1.

Saleh, M. F.

M. F. Saleh, A. Marini, and F. Biancalana, “Shock-induced 𝒫𝒯 -symmetric potentials in gas-filled photonic crystal fibers,” Phys. Rev. A 89, 023801 (2014).
[Crossref]

M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

Schapper, F.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

Shelton, D. P.

V. Mizrahi and D. P. Shelton, “Nonlinear susceptibility of h2 and d2 accurately measured over a wide range of wavelengths,” Phys. Rev. A 32, 3454–3460 (1985).
[Crossref] [PubMed]

Shinzen, K.

K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
[Crossref]

Silberberg, Y.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
[Crossref]

Südmeyer, T.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

Tisch, J. W. G.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

Toninelli, C.

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
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Travers, J. C.

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W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
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[Crossref]

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Figures (3)

Fig. 1
Fig. 1 Temporal evolution of an accelerated oscillating Raman polarization with period Λ = 56.7 fs induced by a propagating fundamental soliton with an amplitude V1 = 1.33, a central wavelength 1064 nm, and a FWHM 15 fs in a H2-filled HC-PCF with a Kagomelattice cross section, a flat-to-flat core diameter 18 μm, a zero dispersion wavelength 413 nm, a gas pressure 7 bar, and a rotational Raman frequency ωR = 17.6 THz. The dashed yellow line represents the temporal evolution of the soliton that excites the coherence wave. The simulation parameters are γ = 7.07 × 10−6 W−1m−1, β2 = −3425.5 fs2/m, Aeff = 134μm2, α12 = 0.8 × 10−41 C m2/V [14, 34], and t0 = 11.34 fs. The parameter γ is calculated using the nonlinear susceptibility of H2 [35]. For these parameters, we have found that higher-order dispersion and self steepening effects have a weak influence on the soliton dynamics. All subsequent calculations in this paper are based on these values.
Fig. 2
Fig. 2 A portion of the absolute eigenstates of a Raman-induced temporal periodic crystals with a lattice constant Λ = 56.7 fs in the presence of a force with magnitude g1 = 0.1408 in the positive-delay direction. The vertical axis represents the corresponding eigenvalues −q. The dotted-dashed line is the potential under the applied force.
Fig. 3
Fig. 3 (a) Bandstructure of the temporal crystal induced by the leading ultrashort soliton propagating in the H2-filled Kagome-lattice HC-PCF with m = 1 in the absence of the applied force. (b) Temporal evolution of a weak probe in the accelerated periodic temporal crystal. The probe initial temporal profile is a Gaussian pulse with FWHM 133.6 fs superimposed on the first Bloch mode of the periodic crystal in the absence of the applied force. The contour plot is given in a logarithmic scale and truncated at −60 dB.

Equations (5)

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t w + w + 1 T 1 = i α 12 h ¯ ( ρ 12 ρ 12 * ) E 2 , [ t + 1 T 2 i ω R ] ρ 12 = i 2 h ¯ [ α 12 w + ( α 11 α 22 ) ρ 12 ] E 2 ,
[ i ξ + D ^ ( i τ ) + | ψ | 2 + η Re ( ρ 12 ) ] ψ = 0 , τ w + ( w + 1 ) t 0 T 1 = 4 μ w Im ( ρ 12 ) | ψ | 2 , [ τ + t 0 T 2 i δ ] ρ 12 = i μ w | ψ | 2 ,
i ξ ψ + i β 1 z 0 t 0 τ ψ + 1 2 τ 2 ψ + | ψ | 2 ψ + R ( τ ) ψ = 0 ,
i ξ ψ 2 + i u 2 τ ψ 2 + 1 2 m τ 2 ψ 2 + 2 κ V 1 sin ( δ τ ˜ ) ψ 2 = 0 ,
i ξ ϕ = 1 2 m τ ˜ 2 ϕ + [ 2 κ V 1 sin ( δ τ ˜ ) + g 1 τ ˜ ] ϕ .

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