Abstract

We develop a one-dimensional model of THz emissions induced by laser-driven, time-asymmetric ionization and current oscillations in a hydrogen gas. Our model highlights complex scalings of the THz fields with respect to the laser and gas parameters, in particular, a non-monotonic behavior against the laser parameters. Analytical expressions of the transmitted and reflected fields are presented, explaining the THz spectra observed in particle-in-cell and forward-pulse propagation codes. The backward-propagating THz wave is mainly driven by the electron current oscillations at the plasma frequency, and its resulting spectrum operates below the plasma frequency. The transmitted THz wave is emitted from both plasma current oscillations and photo-ionization. Their respective signal presents a contribution below and around the plasma frequency, plus a contribution at higher frequencies associated to the photo-induced current. The interplay between these two mechanisms relies on the ratio between the propagation length and the plasma skin depth.

© 2014 Optical Society of America

1. Introduction

Laser-gas interaction is an elegant way of energy conversion to higher frequencies through up-conversion mechanisms [1], as well as to lower frequencies through down-conversion processes [2]. The reasonable size and high-repetition rates of the latest laser-based frequency converters make them highly promising for next-generation THz pulse devices [3, 4]. Spanning from the infrared to microwaves, the THz radiation spectrum is attractive for many applications in various fields of physics [5], biology and medicine [6], industry [7], security, communication, remote sensing [8] and basic science with, for instance, molecular dynamic spectroscopy [9, 10].

Initially attributed to optical rectification and four-wave mixing via a third-order nonlinearity [11, 12], THz emission has been widely discussed in the optics and plasma literature [1316]. Recently, a consensus has been reached on the so-called two-color scheme, which allows to noticeably increase, by around two orders of magnitude, the THz conversion efficiency in laser-gas interaction above the ionization threshold [17]. The principle of this scheme is to combine a fundamental frequency carried by an ultrashort (femtosecond) pulse with its second harmonic within a highly nonlinear plasma spot. As a result of the subtraction of broad optical bandwidths, new electromagnetic components are generated with spectra centered around THz frequencies. Remarkably, similar THz emissions over large distances have also been reported from long-range filamentation of femtosecond pulses in air or in noble gases (e.g., argon) [1822]. Recent works also pinpoint local plasma-induced photocurrents as key players for THz generation in the filamentation regime [23, 24]. THz pulses are then emitted during and after the gas ionization. Firstly, bursts of attosecond currents are produced around each ionization event. For a specific dephasing between the two laser beams, these bursts interfere constructively to generate THz pulses of the order of the ionization duration [25]. Moreover, transverse current oscillations are driven at the plasma frequency, which prolongs the THz emission after the laser interaction [26]. The resulting THz field reaches amplitudes of the order of several MV/cm, much higher than those produced by four-wave mixing and comparable to those usually attained in tightly-focused geometries. In two-color filamentation experiments, the pulse intensity is currently limited to 50 – 100TW/cm2. Under these conditions, the THz yield appears to increase with respect to the pump energy, up to some saturation [18, 19]. THz yields up to 100 μJ were recently reported for pump energies at the Joule level [27]. The enhanced THz conversion efficiency (∼ 10−4) was attributed to meter-range filaments that maintain long plasma channels.

Out of a filamentation scenario, Particle-In-Cell (PIC) simulations [26, 28], solving Vlasov-Maxwell equations by means of macro-particles, have shown that rising the laser intensity beyond the previous values does not necessarily increase the THz amplitude. While essentially driven by ionization currents, the THz signal also depends on the noble gas serving as the interaction medium and on the pulse duration and carrier-envelope phase, which impose a saturation value for the ionization current. For instance, the large ionization potential in helium was exploited to obtain THz field amplitudes as high as 1.28 GV/m with moderate laser energies. A careful choice of the plasma and laser parameters is thus required to achieve efficient THz production. When computed inside a plasma of constant density, the radiated field is dominated by ionization currents [28]. By contrast, the contribution of the plasma current oscillations seems to prevail outside the plasma region and/or at high pump intensities [29, 30].

In this regard, the THz spectral signature attributed to photocurrents may be different from that produced by plasma current oscillations along the propagation direction. While the former operate over a broad range of low frequencies [16, 31], the latter more specifically operate around and below the plasma frequency [30], that spans the THz region for electron densities < 1019 cm−3. Thus, a clear distinction between the potential sources of THz radiation involved in the dynamics of the free electrons still remains to be drawn. Another open issue concerns the THz energy partition between the transmitted and reflected waves. Several studies have assumed that the largest fraction of the THz energy in the photocurrent model is carried by the forward wave component [2325,31]. Straightforward comparisons between backward and forward spectra computed from a Unidirectional Pulse Propagation Equation (UPPE) model and two-dimensional (2D) Finite-Difference Time-Domain (FD-TD) Maxwell code have validated the unidirectional approach for an argon gas [32]. For pump intensities less than 100 TW/cm2, 2D FD-TD Maxwell simulations predict mostly forward THz emission. This forward radiation is generated predominantly at the ionization front and is not affected by plasma opacity, unlike the backward spectrum. However, when a single laser pulse of much higher intensity (up to 1017 W/cm2) interacts with a 100 μm-thick hydrogen plasma, a noticeable fraction of the THz energy, produced by the plasma current oscillations, can be conveyed by the backward wave [30]. In this regime, alternative key agents for THz generation may be plasma wakefields and the laser wavelength. In this respect, several studies predict strongly enhanced THz yields in the case of single- or two-color pulses operating at long central wavelengths (e.g., 2μm or 4μm) [23, 26]. Here, several effects superimpose, such as the respective influences of the pump laser wavelength and the effective pulse duration, as well as the interference between the low-frequency tail of the pump spectrum with the inner THz spectrum at long enough pump wavelengths.

All of the previously published models of laser-driven THz sources have failed to clarify the connection between the two main “plasma” mechanisms, i.e., ionization-induced photocurrents and current oscillations, particularly the link between forward and backward waves, and their dependencies upon the laser and plasma parameters. The goal of the present work is thus to propose a unified framework accounting both for photocurrents and current oscillations, in order to extend the existing models to laser intensities ≲ 1017 W/cm2. To this purpose, we shall revisit the well-known photocurrent mechanism [17] by separating the THz component from the laser pump field and by including the plasma current oscillation in a self-consistent way. For the sake of simplicity, we shall introduce two semi-analytical 1D models, either discarding or retaining propagation effects, and restrict our analysis to a hydrogen gas. Section 2 introduces our analytical model, which assumes decoupled THz and laser fields. In section 3, we derive scalings of the THz emission against the laser and plasma parameters within the assumption of negligible propapagation effects. Despite this approximation, our scalings perfectly reproduce the tendencies observed in PIC simulations [26]. The choice of optimal parameters for THz emissions is demonstrated in the case of one and two laser colors. In section 4, propagation effects are included. Analytical formulas for the reflected and transmitted THz waves are derived. We demonstrate that the forward wave carries most of the THz energy, provided that the plasma length exceeds the plasma skin depth. Besides, the dependence of the THz amplitude upon the photocurrent amplitude is clearly evidenced and its limitations are discussed. The competition between photocurrents and plasma current oscillations is analyzed, and shown to depend on the ratio between the propagation length inside the gas and the plasma skin depth. In section 5, the backward and forward spectra inferred from our general model are found in remarkable agreement with both PIC and UPPE simulation results.

2. 1D model for laser-driven THz pulses

In this section, we present a simple semi-analytical model predicting the THz emission in gases for a large set of parameters. Drawing upon Refs. [30, 31], it involves two mechanisms, both attributed to the transverse electron current oscillations induced during and after gas ionization by one- or two-color laser pulses. For the laser intensity range scanned in the present article (∼ 1014 − 1017 W/cm2), both the nonlinear polarization (bound electron response) of the medium and the relativistic effects are neglected. Instead, we focus on the interplay of laser-driven photoionization [4, 17, 31] and transverse current oscillations [26, 30].

In the following, the time and space coordinates, (t, x), are normalized to 1/ω0 and λ0/2π, respectively, where ω0 is the pump laser frequency and λ0 is the pump central wavelength. Let us consider a semi-infinite gas of neutral density na, filling the positive x-region and a transverse electric field, EyL, composed of one- or two-color laser pulses propagating toward the gas. The gas density and the laser electric field are normalized to the critical density nc=meω02ε0/e2 and the Compton field meω0c/e, respectively. For low gas densities, na ≪ 1, we can neglect the laser dispersion and energy loss during the ionization processes. We hence assume the laser electric field, generally embedding two colors, to maintain a constant shape as

EyL=a0sin2[(β++2πτ)/2τ][sin(β++2πτ+ϕ)+rsin[2(β++2πτ)+ϕ2]]H(β++2πτ)H(β+).
Here, H is the Heaviside function, β+ = xt, τ is the number of laser cycles in the pulse, a0 is the laser potential vector normalized to mec2/e (the physical laser intensity is evaluated as I0=1.38a02λ02[μm]), r is the ratio of the second harmonic amplitude to the fundamental, and ϕ and ϕ2 are the phase shifts of the ω0 and 2ω0 components, respectively. Various experimental setups are nowadays available and they allow to fix rather freely the second harmonic duration and its relative delay compared to the fundamental pulse length [2, 12, 27]. Therefore, for technical convenience, we shall use equal pulse durations as in Refs. [28, 30] in our theoretical analysis. Second harmonic pulse lengths being twice smaller than the pump duration will instead be employed in section 5, when confronting theoretical predictions to direct numerical simulations. Initially, the finite laser pulse is located in front of the gas, between x = −2πτ and 0. Writing the full electric field as
Ey=EyLtδay,
we propose to calculate the vector potential δay, and the induced electric field, −tδay, containing the THz signal. Given the weak fields considered, the ions can be assumed motionless. In the non-relativistic limit (tvxx), the 1D cold-fluid model reduces to the electron continuity equation, the transverse electron current equation and the wave equation:
tne=νE(EyL)(nane)
tJy+νJy=ne(EyLtδay)
x2δayt2δay=Jy,
where Jy is the transverse electron current, ν is the total (electron-ion plus electron-atom) collision rate, ne is the electron density, and νE [ EyL] is the normalized Ammosov-Delone-Krainov ionization rate of an atom by an oscillating field in linear polarization [3335]. For hydrogen, the latter is defined as
νE(EyL)=4ωaω0|Ea.u.EyL|exp(23|Ea.u.EyL|).
Here, ωa = eEa.u.aB/h̄ is the characteristic atomic frequency, Ea.u.=e2/4πε0aB2meω0c is the atomic field normalized to the Compton field, and aB = 4πε02/mee2 is the Bohr radius. Equations (4) and (5) recast as
(ν+t)(x2t2)δaynetδay=neEyL.
Equations (3) and (7) are solved numerically and approximated analytically in the next sections.

3. Non-propagating THz pulses

In this section, we wish to obtain scaling laws for the THz emissions in terms of the plasma and laser parameters. For simplicity, we first neglect the wave propagation ( x2δay0), which reduces the above equation to an ordinary differential equation:

t2δEy+νtδEy+neδEy=neEyL,
where δEy = −tδay. The assumption xt can be justified in some regions of the (x, t) plane (see next section). The laser field is here a function of time: EyL(xt)EyL(t).

Equations (3) and (8), with the initial condition

ne(0)=δEy(0)=tδEy(0)=0
can be readily solved numerically. A solution δEy(t) (black line) is presented in Fig. 1(a) for a single-color laser pulse (a0 = 0.02, τ = 10, λ0 = 1μm) and negligible collisions (ν = 0). During the ionization process (t < 2πτ), the newborn electrons oscillate in the laser pulse, producing the field at frequency ω0. In contrast to Refs. [4, 17, 31], the remaining current oscillates at the plasma frequency ωpe=ne (normalized to ω0), as described in [30] (note the absence of damping mainly due to the absence of propagation). This is illustrated in the field spectrum (black line) displayed in Fig. 1(b). For the selected gas density, na = 0.0011, complete ionization takes place, so that the main mode emerges at the plasma frequency ωpe ≃ 0.033. We have applied a low-frequency filter, ω < 0.3, to calculate the THz field amplitude. As an example, the filtered field and its spectrum are plotted in red dotted line in Fig. 1(a) and (b), respectively. This methodology has been used to explore the dependencies of the THz field maximum upon the laser and/or gas parameters.

 

Fig. 1 (a) Unfiltered (black line) and filtered (red dotted line) electric field δEy for the parameters ν = 0, a0 = 0.02, τ = 10, λ0 = 1μm (one pump pulse), na = 1.1×10−3, r = 0, and ϕ = 0. (b) Electric field spectrum (black line), and the filtered spectrum (red dotted line) of panel (a) for ω < 0.3 (normalized to ω0). Note the pump’s trace left in the evaluation of δEy and its spectrum.

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The maximum of the THz field normalized to naa0, versus the laser intensity and for different set of parameters is presented in Fig. 2. On panel (a), the THz field maximum is plotted for different laser wavelengths, keeping constant the number of laser cycles in the pulse. For small laser intensities, the gas is weakly ionized, yielding negligible THz emission. When the laser field is strong enough to fully ionize the gas (I > 2×1014 Wcm2), the THz field increases. At very high intensities, ionization occurs at the very beginning of the pulse and thus, due to weakened photocurrents, the THz field amplitude drops. At leading order, the normalized THz amplitude appears weakly sensitive to the laser wavelength, obeying the scaling

δEy~naa0,
in agreement with former predictions [28,30]. In physical units the THz field energy is proportional to ngasI0λ02, where ngas is the gas density. As already reported in Ref. [26], the THz field amplitude, proportional to a0, “oscillates” when increasing the laser intensity. A similar plot is presented in Fig. 2(b) for other parameters. The black solid line corresponds to a reference case (λ0 = 1μm, τ = 10, na = 0.0011). For a fixed number of laser cycles, the normalized THz field is weakly changed when increasing the gas density by a factor 4 (red dashed line) or when doubling the laser frequency (dashed-dotted blue line). This trend confirms Eq. (10).

 

Fig. 2 (a) Maximum of the filtered electric field versus laser intensity in unit of 1018 W/cm2 for a single pulse. Parameters are displayed in the inset, while all others remain equal to those of Fig. 1. (b) Same figure for another set of parameters.

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In addition, the THz field amplitude is substantially reduced when increasing the number of laser cycles in the pulse, as observed for τ = 40 (green solid line). This suggests (at least) a linear decrease in the THz amplitude with the number of optical cycles τ. To further illustrate this dependency, the THz field amplitude is plotted for the case λ0 = 2μm, τ = 5, and na = 0.0044. This situation corresponds to doubling the laser wavelength, while keeping constant the gas density and the laser pulse duration. The resulting pattern (cyan solid curve) does differ from the reference case (black solid line). The number of oscillations noticeably decreases and their amplitude grows from smaller laser intensities, whereas the peak values of δEy/a0na is multiplied by about a factor 2. This result suggests a strong sensitivity of the THz amplitude to the effective number of optical cycles, more pronounced in the case of few-cycle pulses owing to strengthened time-asymmetry and net ionization currents, in agreement with Ref. [26]. Therefore, when considering a single color, we can propose from the previous behaviors a scaling of the THz amplitude as

δEy~naa0/τ.

Apart from this leading-order scaling, the oscillations seen in Fig. 2 introduce a margin of uncertainty of 2 to 4 when doubling the central laser wavelength. This additional refinement completes the above scaling by a factor > 2, which then renders it comparable to the variations reported in Ref. [26]. Here, the THz field amplitudes were seen to drop by a factor ∼10 when passing from 2 μm to 1 μm wavelength using a pump pulse of constant (50 fs) duration and intensity. Similar variations are also compatible with the 14-fold growth in the THz yield reported in Ref. [23] when comparing two-color filaments with 0.8μm and 2μm pumps of same duration but for different atomic densities (local pressure = 6.44 bars resulting in a net scaling rate of about 15.9).

We have also examined the THz field behavior with the phase shifts ϕ and ϕ2. For one laser color (Fig. 3), the THz field amplitude (black solid line) is obviously π-periodic as EyL(t,ϕ+π)=EyL(t,ϕ). However, a more complex behavior arises when using two colors (red dashed line). The THz field amplitude is now 2π-periodic, with a maximum value reached for ϕ2 ≈ 4.1 rad in hydrogen with r2 = 0.2. Importantly, the THz field amplitude is strongly enhanced when using two colors, as illustrated in Fig. 4(a), where, typically, an order of magnitude increase in intensity is found compared to Fig. 2(a). The optimum THz intensity is obtained for the laser intensity I0 ∼ 3 × 1014 W/cm−2 for τ = 10 and ϕ2 = 0. By comparison with Fig. 2(b), the THz intensity attained with one color at similar pump intensity is at least 100 times weaker, thereby confirming the two orders of magnitude often mentioned in gases [1820]. Note that the two-color configuration also gives rise to an oscillatory intensity dependence of the THz field. This dependence is sensitive to the phase ϕ2, as illustrated by the red dashed line (ϕ2 = 0.5) and the cyan solid line (ϕ2 = 1.5). By increasing the number of optical cycles to 40, the oscillations relax (see the dashed-dotted green line), while the optimum laser intensity is shifted. Although a scaling in 1/τ may not apply, the THz field still remains sensitive to the number of laser cycles. The interplay between the harmonic amplitude ratio r and the phase ϕ2 is shown in Fig. 4(b). Here again, the THz field amplitude exhibits non-monotonic variations with r. The maximum THz field is obtained for r ≃ 0.85 and ϕ2 ≃ 4.7.

 

Fig. 3 Maximum of the filtered electric field versus the phase shift ϕ for one laser color (black solid curve) with I = 1016 W/cm−2, τ = 10, λ0 = 1 μm and na = 0.0011, and for two colors (red dashed curve) versus ϕ2 with r2 = 0.2 and ϕ = 0.

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Fig. 4 (a) Maximum of the filtered electric field for a two-color pulse versus laser intensity in unit of 1018 W/cm2 for different phases ϕ2, and r2 = 0.2. (b) Maximum of the filtered electric field versus phase ϕ2 and amplitude field ratio r for I = 1016 W/cm2. The other parameters are ν = 0, τ = 10, λ0 = 1μm, na = 1.1 × 10−3, and ϕ = 0.

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The non-monotonic behavior of the THz field and the previous scalings can be explained with a qualitative analysis of Eqs. (3) and (8). In the short-pulse limit, 2πτ1/na, the solution of Eq. (8) is approximated as

δEyexp(νt/2)nefν2/4sin(nefν2/4t)0min(2πτ,t)neEyLdt,
where nef is the final electron density after gas ionization. For weak collisions ( ν2nef), it is then straightforward that the THz field oscillates at plasma frequency and scales as naa0.

The oscillatory dependence of the THz field upon the laser intensity, and its sensitivity to the laser duration then follows from estimating the source term

G(2πτ)=02πτneEyLdt.
According to [31], the electron density evolution can be calculated knowing that the ionization events are localized around the electric field extrema. The electron density is then approximated as
nef=i=1Nfδne,iH(tti),
where Nf is the number of ionization events occurring at time ti and δne,i is the increase in the electron density following each ionization event. Around an extrema Em,i, the laser electric field expresses as EyLEm,i[1gi2(tti)2], with gi=1Em,id2EyLdt2|ti>0. Using this expression in Eq. (3), we obtain the recurrence relation
δne,i=νE(Em,i)(nak=0i1δne,k)πgi3,
where i > 1 and δne,0 = 0.

As the laser electric field derives from a potential EyL=tAyL with a mean value equal to 0 [ EyLdt=AyL(0)AyL(+)=0], the THz source term becomes

G=i=1Nfδne,iAy,iL,
where Ay,iL=AyL(ti). The scaling of the source term G depends on the time-symmetry of the ionization events.

For one laser color, Eq. (1) recasts as EyL(t)=a0g(t/τ)sin(tϕ). As τ ≫ 1, the laser envelope derivative is small g′/g ∼ 1/τ ≪ 1, and the field extrema are reached at ti=π2+ϕ+kπ, kN. Since g(0) = 0, the vector potential is Ay,ia00tig(u)cos[uϕ]dua0/τ, and the THz source term is thus proportional to Gnaa0/τ, thereby yielding Eq. (11). For one laser color, the higher the number of laser cycles, the weaker the THz field amplitude. The THz amplitude behavior against laser intensity can be explained as follows. For small laser intensities, such as νE [Em,k] ≪ 1, ionization occurs around the laser pulse maximum. As the laser field is anti-symmetric around the maximum, the source term is exactly equal to 0. At higher intensities, there exists a time, tk < πτ, such that νE [Em,k] > 1. In this case, ionization occurs stepwise at several field extrema.

For simplicity, let us assume a two-step ionization: G=δne,k1Ay,k1Lδne,kAy,k. We look for the periodic zeroes of the THz source. The THz field vanishes if G = 0. As δne,k−1 + δne,k = na and δne,k=πgk/3νE[Em,k]na, one finds the relation

4πgk3ωaω0|Ea.u.Em,k|exp(23|Ea.u.Em,k|)=Ay,kAy,kAy,k1.
As the field extremum is |Em,k| = a0g[(π/2 + + ϕ)/τ], we obtain
2k+12π+ϕ=τg1[2Ea.u.3a0W1(K)],
where W−1 (x) is the Lambert function W [36] and
K=3/πgkω04ωaAy,kAy,kAy,k11/λ0.
Hence, for a given kN, there exists a laser amplitude, a0,k, such that the above relation is fulfilled. As W−1(K) ∼ log(K), the condition (18) is weakly sensitive to the laser wavelength, consistently with Fig. 2(a), but depends on g−1 ( 1/I) (we remind that Ea.u.λ0). This variation with the inverse function of the laser envelope for, e.g., a Gaussian or sin2 profile, accounts for the increase of the oscillation wavelength with the laser intensity seen in Fig. 2. For stronger laser intensities, the ionization events shift from the extremum k to the extremum k − 1 until reaching the first extremum (k = 1). Hence, the number of oscillations is proportional to the number of extrema included in half of the laser duration, as observed in Fig. 2(b) (green solid line) where the number of oscillations has increased by a factor ∼ 4.

When the ionization process is asymmetric, as in the two-color configuration, the scaling of the source term G changes. Assuming ϕ = 0, one has

EyL(t)=a0g(t/τ)[sint+rsin(2tϕ2)],
the electric field extrema are located around the times ti solutions of costi + 2r cos[2tiϕ2] = 0. Using the previous relation, the potential vector recasts as Ay,i ≈ −a0g(ti)3costi/4 ∝ a0. The THz emission reaches its maximum when the gas is fully ionized during the whole laser duration. In Fig. 4(a), this event corresponds to I ∼ 5 × 1014 W/cm2 for τ = 10. Maximum THz emission varies with the number of laser cycles: for τ = 40, it is shifted down to the value I ∼ 2 × 1014 W/cm2. Reversely, at fixed intensity (e.g., I = 1014 W/cm2) and wavelength, a 4-fold increase in the pulse duration raises the THz intensity by a minimum factor of ∼36. Up to propagation and multidimensional aspects discarded here, such impressive growths are comparable with those reported in Refs. [18, 23].

In conclusion to this section, our simplified 1D model predicts that the ionization-induced THz emission is utterly defined by the electron current amplitude left after the ionization process, JyG. As already known, the stronger the ionization asymmetry, the higher the THz field amplitude. However, the origin of the asymmetry and its influence change between the one- and two-color configurations. Besides, as we neglect the THz field propagation, the THz spectrum is mainly located around the plasma frequency. This anomalous result is corrected in the next section, where propagation aspects are taken into account.

4. Propagating THz pulses

This section is devoted to the forward and backward THz emissions, and related modifications of the spectrum. For that purpose, we analytically and numerically solve the interaction of a laser pulse with a semi-infinite gas assuming that the laser pulse remains unperturbed while propagating.

The laser pulse defined by Eq. (1), initially located in the vacuum region, x ∈ [−2πτ, 0], interacts with a semi-infinite gas of density profile na(x) = naH[x]. The THz field equation is given in Eq. (7), with the electron density ne described by the continuity equation, Eq. (3). The latter equation is numerically integrated using a 4th-order Runge Kutta method, while the THz wave equation is solved using a 2nd-order explicit centered scheme. A solution is presented in Fig. 5 in black solid line in the panels (a) and (b) for a single color. The THz field presents a small reflected wave, visible in panel (b) at the distance x ∼ −900, with an amplitude ∼ 10−4 for the chosen parameters, and an intense forward wave of amplitude ∼ 10−2 centered around x = 900 [panel (a)]. The reflected wave is similar to that observed in PIC simulations [26, 30]. Basically, the laser field ionizes the gas, hence producing a net transverse current. As discussed in section 3, this current oscillates at the plasma frequency, which maintains the THz emission during several plasma periods. Inside the gas, the laser propagates and pursues the ionization process. The resulting field δEy propagates also forward and increases quasi-linearly with the distance.

 

Fig. 5 δEy for a two-color pulse vs x at time t = 780, (a) zoomed around the laser position and (b) full solution. The numerical solution is shown in black solid line, the numerical solution without dispersion between xt ∈ [−2πτ, 0] is represented in black dashed line, and the analytical solution is plotted in red solid line. The parameters are a0 = 0.02, λ0 = 1μm, ν = 0, τ = 10, r2 = 0.2, ϕ2 = 0.5 and na = 0.0011.

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For a more quantitative description, we now derive an approximate formula for the propagating field δEy. Without collisions (ν → 0), the wave equation, Eq. (7), recasts as:

x2δEyt2δEy=(EyL+δEy)neH(x).
With our unperturbed laser field, function of β+ = xt only, the solution of Eq. (3) expresses as
ne(β+)=[1exp(0max(β+,2πτ)νE(EyL)dβ+)]na.
Introducing the new variables, s = t and β+ = xt, which we find convenient to clearly separate backwarded and forwarded THz components, the wave equation becomes
2β+s2δEys2δEy=(EyL+δEy)neH(β++s).
In the case of a constant electron density, this equation can be solved exactly as in Refs. [28,37]. In the opposite case, to include the ionization effect, we choose to solve Eq. (22) in two distinct domains. In the beam head, β+ ∈ [−2πτ, 0], we neglect the THz field compared to the laser field δEyEyL. This approximation is valid for pulse duration and time such that (2πτ,s)1/na, i.e., such that the THz dispersion is negligible during the ionization process and the propagation distance. In the second region, behind the laser pulse, the electron plasma density is constant and Eq. (22) is solved using the Laplace transform.

In the beam head, the wave equation is approximated as

2β+s2δEys2δEy=neEyLH(β++s).
After some algebra detailed in Appendix A, we find the solution
δEy=14F(xt)+x2G(xt),
for x > 0 and xt > −2πτ, with F(xt)=0xtG(β+)dβ+ and G(β+)=0xtneEyLdβ+. In Eq. (24), F is the current integral while G is related to the current density. As F ∼ 2πτG, the second quantity, affected by a linear growth factor in x, prevails in the forward component for x ≫ 2πτ.

Behind the laser pulse ( EyL=0), Eq. (22) reduces to

2β+s2δEys2δEy=nefδEyH[β++s].
To simplify our analysis, we look for a solution inside the plasma, β+ + s = x > 0. As the laser is fully inside the gas at time t = 2πτ, we introduce the Laplace transform δf^=2πτf(s)epsds. Using the initial conditions δEy(s = 2πτ, β+) = sδEy(s = 2πτ, β+) = 0, Eq. (25) becomes
β+δEy^=(p2+nef2p)δEy^.
To solve the above equation, we apply the field continuity at the position β+ = −2πτ. In the Laplace space, formula (24) becomes δEy^(β+=2πτ)=12p2G(πτG+F/4)1p. The solution is thus
δEy^=[12p2G(πτG+F/4)1p]exp[(p2+nef2p)(β++2πτ)].
From Ref. [36], the Bromwitch inversion gives
δEy=G2nef[t+x+2πτtx2πτ]1/2J1[nef(t2(x+2πτ)2)](πτG+F4)J0[nef(t2(x+2πτ)2)],
for t > 2πτ and 0 < x < t − 2πτ.

Expression (28) reproduces the main functional dependencies derived earlier in Ref. [28], but without the F-function. Here, we go one step beyond. Knowing the solution δEy(x, t) inside the plasma, the reflected wave δEyref, satisfying the equation xδEyreftδEyref=0, is deduced following the characteristic x + t = t0, i.e., δEy(x=0,t0)=δEy(0,x+t)=δEyref(x,t), where δEy(x, t) is given by Eqs. (24) and (28). For 0 < x + t < 2πτ and x < 0, the reflected wave is

δEyref=F(xt)4.
For x < 0 and x + t > 2πτ, we find
δEyref=G2nef[t+x+2πτt+x2πτ]1/2J1[nef((x+t)24π2τ2)](πτG+F4)J0[nef((x+t)24π2τ2)].

Comparing this expression with Ref. [37], we can infer that Eq. (30) describes the backward propagation of a distortionless wave oscillating at the plasma frequency with an electron density fixed by nef. Owing to the bi-directional character of the 1D propagator, the THz backward emission solely follows from the current oscillations over the plasma skin depth. At large time t, the backscattered solution behaves as 1/tsin(neft); its spectrum should convey a dominant mode at plasma frequency accompanied by damped, thus smaller frequencies. In the limit 2πτna1, the first right-hand side term of Eq. (30) is dominant, hence confirming the scaling δEy~G/nef suggested in section 3. Moreover, at late times tx + 2πτ and near the plasma border for x > 0, the field simplifies to

δEy2π1nef1/4t[2Gnef(1+x+2πτt)sin(neftπ4)(4πτG+F)cos(neftπ4)],
which exhibits the expected oscillation at ω=nef. According to Eq. (24), in the ionization region, the amplitude of the forward-propagating wave is proportional to the source term G and increases linearly with the distance. As we neglect the field dispersion in the beam head, this linear increase is valid for x1/na. Behind the laser pulse, where the dispersion is included, the electric field scaling, at a given distance β+ from the beam head, turns into
δEyGt1/4/(nefβ+)3/4
in the limit t ≫ max(1/2nefβ+, β+) and β+ ≫ 2πτ (see Appendix B). As a result, THz scalings can vary with respect to the location of the propagated THz wave.

To validate our analytical formulae, we plot the solution in Fig. 5 in red solid line. The agreement in the plasma region is remarkable, especially in the beam head [Fig. 5(a)], where the small difference is ascribed to the THz wave dispersion, i.e., the neδEy term in Eq. (20). To illustrate this effect, we have numerically solved Eq. (7) neglecting the term tδayne in the laser region xt ∈ [−2πτ, 0]. The resulting curve (dashed black line) fairly agrees with the analytical solution both in the beam head and in the plasma region far from x = 0. Although capturing the right oscillation frequency, the analytical expression of the reflected field yields small discrepancies in the amplitude values, which we attribute to the fact that Eq. (28) is valid for an infinite plasma only.

As for the reflected wave, the forward wave oscillates at the plasma frequency behind the beam head. Yet, far from the laser pulse, the wavelength of the emitted field increases. This effect is illustrated in Fig. 6 where the numerical solution is plotted against x and t. In vacuum, the reflected wave propagates at the velocity −1, while in the plasma, the emitted wave propagates at the velocity +1 right behind the laser pulse. Far from the pulse, the longitudinal wave number relaxes to kx = 0. Indeed, according to Eq. (31) and since xt, the space derivative is xδEyO(1/t), hence supporting the approximation xt used in section 2.

 

Fig. 6 Numerical solution of the field δEy(x, t) saturated to the value ±10−4, for the same parameters as in Fig. 5.

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To visualize the propagation effect on the THz spectra compared with the “ideal” spectrum of Fig. 1(b), we have run a similar case to Fig. 5 but with a finite rescaled plasma length of 40π. The spectra of the reflected and transmitted waves are plotted in Fig. 7 in red and black solid lines, respectively. The intensity spectrum of the reflected wave is approximately a step function with a cut located at the plasma frequency na. Below this frequency, photocurrents weakly contribute to THz emission. Given the plasma thickness, the source term, Eq. (24), mainly depends on xG(xt) ≫ F(xt) inside the plasma. As the reflected wave is driven by F(x + t) outside the plasma, the energy carried by the transmitted wave is higher and mainly determined by the ampitude ratio 2xG/F. Besides, its spectrum now extends above the plasma frequency. This THz field is attributed to both the constructive interferences during the ionization process and the plasma current oscillation. The electron current during ionization presents frequencies around 2/τ, which broadens the THz spectrum above the plasma frequency. The spectra deduced from the analytical expressions Eqs. (24), (28) and (30) are plotted in red and black dashed lines for the transmitted and reflected waves, respectively. A good agreement is obtained with the numerical solution, especially concerning the transmitted wave. The reflected wave presents a plateau between 0 and na, with a peak pronounced around the plasma frequency. Above this frequency, the spectrum dramatically decreases by many orders of magnitude. The intensity spectrum of the transmitted wave, in black dashed line, presents similar features to the numerical solution. In particular, the contribution of the frequencies higher than ωpe, typical of ionization-induced THz emission, has increased. However, for the gas thickness of 40π, the electron current oscillation at the plasma frequency is the dominant process. Indeed, the spectrum above na, mainly depends on the source term xG(xt), while the low-frequency spectrum depends on the plasma current oscillations, driven by the term ~G(2πτ)x1/4/nef.

 

Fig. 7 Intensity spectra of the transmitted field (black lines) and the reflected field (red lines) calculated numerically (solid lines) and according to formula (24), (28) and (30) (dashed lines). The parameters are similar to Fig. 5, but the plasma length is limited to L = 40π. The green dashed line and green solid line correspond to the transmitted field calculated numerically and according to Eqs. (24) and (28) for a plasma length of L = 100π.

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Hence, for propagation length much larger than 1/nef, the photocurrent mechanism becomes dominant, whereas for propagation length comparable to, or smaller than the plasma wavelength, as in Fig. 7, the main mechanism is the plasma current oscillation. To confirm this behavior, we have calculated the transmitted spectrum for a thicker gas of L = 100π. The numerical and semi-analytical solutions are plotted in green dashed line and green solid line, respectively. In this regime, the propagation length is such that L1/na, which leads to a spectrum contribution higher for ω>na, as a result of dominant photocurrents. This tendency is reproduced by the semi-analytical model.

In summary, we have demonstrated within a unified formalism that laser-driven THz radiation can originate from different sources, namely, photoionization [23, 31] and residual current oscillations [26,30]. Our model establishes the missing link between the extreme nonlinear optics and plasma physics communities. The nontrivial interplay between these two mechanisms appears to be highly sensitive to the laser and medium parameters. For a propagation length shorter than the plasma wavelength, THz emission mainly results from plasma current oscillations. For longer gases, THz emission mostly originates from the constructive interferences during gas ionization.

5. Simulations

To further validate our model, we have run 1D PIC simulations using the code calder [38]. The code resolves the wave propagation inside the plasma, the particle trajectories including relativistic effects and field ionization [39]. To reproduce the conditions used in Ref. [26], collisions are neglected. The initial density profile of the hydrogen gas is trapezoidal, with a 90 μm (700c/ω0)-long plateau bordered by 5 μm-long linear ramps. The maximum atomic density is na = 0.0044, yielding an electron density of ne = 1.2 × 1018 cm−3. The initial ion temperature is set to 1 eV. The laser beam has a Gaussian intensity profile with a 35 fs FWHM duration. The laser wavelength is λ0 = 2μm and the maximum intensity is 1017W/cm2. The simulation box is discretized in 9000 cells, each one containing 1000 electrons and 1000 atoms of hydrogen. The numerical resolution is Δx = 16 nm and Δt = 0.048 fs. Calculations have been performed using 3rd-order weight factors, with absorbing conditions for the fields.

The spectra of the transmitted and reflected waves are shown in Fig. 8(a) and compared to those obtained by the simplified wave equation, Eq. (7), assuming an unperturbed laser pulse. At the intensity of 1017W/cm2, both reflected spectra present a plateau at frequencies < ωpe (fω/2π < ωpe/2π ≃ 10THz), due to the dominant contribution of the plasma current oscillations. In contrast, the transmitted wave presents a broadband spectrum in the range [ωpe, ω0] (10 ≤ f ≤ 150THz). Despite the single-color setup considered, the ionization occurring at the beginning of the pulse is asymmetric and produces a net transverse current. As discussed previously, this photoinduced current contributes to the spectrum well above the plasma frequency. Since the gas length (∼ 180π, corresponding to 90μm) exceeds the plasma skin depth (15, corresponding to 5μm), this radiation mechanism prevails, so that the THz energy is mainly contained at frequencies >na. Figure 8(b) compares the resulting THz fields computed below ω = 0.2 (f = 30 THz) from the transmitted and reflected THz waves obtained from the 1D calder code and from our simplified wave equation. This figure displays an excellent agreement between PIC simulations and our theoretical approach.

 

Fig. 8 (a) Spectra of the reflected (solid lines) and transmitted (dashed lines) electric field, normalized to the total energy Utot, produced by a single pump wave in hydrogen (I = 1017 W/cm2, λ0 = 2μm). The red curves correspond to PIC simulations and black lines to δEy calculated numerically according to Eq. (7). (b) Resulting THz fields for the frequency window < 0.2 (f < 30 THz), using the same plotstyle as in (a).

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We have also compared our reduced numerical model to PIC and uppe1d simulations [40] in a two-color configuration for much weaker intensities. The numerical code solving the Unidirectional Pulse Propagation Equation model in one-dimensional (1D) geometry, uppe1d, is generally used to simulate the forward propagation of ultrashort laser pulses through gas-filled capillaries, accounting for Kerr optical effect and gas ionization. This code neglects relativistic and diffraction effects, but it includes the transverse current oscillation at the plasma frequency. In our simulations the laser intensity is set to 1014 W/cm2 or 1015 W/cm2 with r2 = 0.1, ϕ2 = 0 and λ0 = 1μm. The fundamental and frequency-doubled pulses have Gaussian intensity profiles with ~30 fs and ~15 fs FWHM durations, respectively. A 100 μm-long gas is considered. The other parameters are those used in the one-color case. Here, the Kerr polarisation, having a small impact in 1D geometry, is switched off in uppe1d. The transmitted wave spectra are presented in Figs. 9(a) and 9(b) from weak to strong pump intensity. Albeit overestimated by the simple model, which neglects laser dispersion, the agreement is satisfying. The contributions of both the current oscillation ( ω<na) and the non-symmetric ionization ( na<ω<1) are correctly reproduced. A striking feature is the increase of the THz spectrum at high intensities reproducing a spectral pattern comparable with that of Fig. 8(a), i.e., THz emission induced through photocurrents assures the merging with the pump field spectrum.

 

Fig. 9 Intensity spectra of the transmitted electric field, normalized to the total energy Utot, produced by a two-color pulse in hydrogen for (a) I = 1014 W/cm2, λ0 = 1μm and (b) I = 1015 W/cm2, λ0 = 1μm. The red and green curves correspond to PIC and uppe1d simulations, respectively, while the black lines refer to δEy calculated numerically according to Eq. (7). The blue curves show the on-axis intensity spectra obtained from the uppe3d model under similar conditions.

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To end with, we have tested the robustness of our theoretical model by performing three-dimensional (3D) simulations that now include transverse diffraction and Kerr self-focusing. The blue dashed-dotted curves in Figs. 9(a) and 9(b) show the spectra computed at 1014 W/cm2 or 1015 W/cm2 pump intensities, respectively, using the uppe3d model of Ref. [23]. Under similar initial conditions, the two-color field propagates over 100μm with a Gaussian transverse amplitude profile of 20μm radius (1/e2). We can observe that the 3D spectra remain close to their 1D counterparts and, thereby, they still remain strongly connected to the physics captured by our simplified model. With a 1014 W/cm2 pump, the laser field slowly diffracts and, in turn, the THz spectrum decreases in intensity. With a 1015 W/cm2 pump, the laser field starts to experience Kerr self-focusing, which contributes to enhance the THz spectrum to some extent.

6. Conclusions and perspectives

In conclusion, we have developed two models of THz emissions induced by laser-gas interaction. The simplest model describes the plasma current oscillation induced during gas ionization. Some scaling laws for the THz emission in terms of the main laser and gas parameters have been derived and found in good agreement with previous numerical studies [26,31]. A more sophisticated model has been developed, which demonstrates that the previous scalings still mostly hold when accounting for propagation effects. This model is able to reproduce the reflected and transmitted wave spectra obtained by self-consistent numerical simulations. Whereas the reflected spectrum is mainly determined by the current oscillation at plasma frequency, the transmitted spectrum is a subtle mix between plasma current oscillation- and ionization-induced THz emissions. For plasma lengths shorter than the plasma skin depth, the former contribution is dominant, while the latter becomes significant in the opposite case. At leading order, the THz field scaling is ngasIλ0/τ for one laser color and ngasIλ0 for two colors, for which the number of optical cycles in the overall pulse matters in a seemingly more complex dependency. Therefore, because the actual THz emission amplitude is oscillating and therefore not monotonic against laser intensity and the number of laser cycles, a simple, systematic dependence of the THz emission upon the laser wavelength may not be achievable. The present analysis is valid in the non-relativistic regime, upon 1D symmetry assumption. A more detailed model is, however, required to prospect the effect of the J × B force and the induced plasma wave on the THz emissions. Furthermore, one should explore different gases from hydrogen, as the THz field strength and related spectra are expected to vary with the ionization (binding) energy and occurence of multiple ionization.

Appendix

A. Computing Eq. (24)

We look for a solution δEy, in the region β+ ∈ [−2πτ, 0]. Introducing B = sδEy, Eq. (23) becomes

2β+BsB=neEyLH[β++s].
The initial conditions are B(s = 0, β+) = δEy(s = 0, β+) = 0 and B(s, β+ = 0) = δEy(s, β+ = 0) = 0. Starting from s0 = 0, the characteristic is β+β0+=2s, along which the solution reads
B(s,β+)=β0+β+neEyL2H[β++β0+]dβ+.
The resulting electric field is written as
δEy(s,β+)=0sdsβmin+βmax+neEyL2dβ+,
where βmin+=max(β0+,β0+) and βmax+=max(β+,β0+). In the plasma, s > −β+, we split the above integral in three intervals: 0β+/2ds, β+/2β+ds, and β+sds. As β0+β0+ for s ≥ −β+/2, the first term is equal to zero, and the solution becomes:
δEy=β+/2β+ds0β0+neEy2dβ++β+sds0β+neEy2dβ+.
After simple algebra, the solution expresses as Eq. (24).

B. Asymptotic behavior Eq. (32)

Behind the beam head, the scaling for the THz amplitude with the crossed thickness can be obtained in the limit t(= s) ≫ β+ ≫ 2πτ, with β+ = cste. As G2neft+x+2πτtx2πτπτG+F/4, Eq. (28) recasts as

δEyG2nef2t+β+β+J1[nefβ+(β++2t)].
In the limit z ≫ 1, the Bessel function turns into J1[z]~2πzcos[z3π4] [36]. Hence, the THz field amplitude at given distance β+ from the laser pulse scales as
δEy~Gt1/421/4π(nefβ+)3/4.

Acknowledgments

This work was granted access to the HPC resources of TGCC and CINES under the allocation 2013-x2013052707 made by GENCI (Grand Equipement National de Calcul Intensif).

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14. M. Kress, T. Löffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett 29, 1120–1122 (2004). [CrossRef]   [PubMed]  

15. C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical Forward THz Emission from Femtosecond-Laser-Beam Filamentation in Air,” Phys. Rev. Lett. 98, 235002 (2007). [CrossRef]  

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References

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  1. F. Brunel, “Harmonic generation due to plasma effects in a gas undergoing multiphoton ionization in the high-intensity limit,” J. Opt. Soc.Am. B 7, 512–526 (1990).
  2. K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Phys. 2, 605–609 (2008).
  3. K. Reimann, “Table-top sources of ultrashort THz pulses,” Rep. Prog. Phys. 70, 1597–1632 (2007).
    [Crossref]
  4. H. Roskos, M. Thomson, M. Kreß, and T. Löffler, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Las. Phot. Rev. 1, 349–368 (2007).
    [Crossref]
  5. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
    [Crossref]
  6. R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Bio. 47, 3853–3863 (2002).
    [Crossref]
  7. N. Nagai, M. Sumitomo, M. Imaizumi, and R. Fukasawa, “Characterization of electron- or proton-irradiated Si space solar cells by THz spectroscopy,” Semicond. Sci. Technol. 21, 201–209 (2006).
    [Crossref]
  8. J. Liu, J. Dai, S. L. Chin, and X.-C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photonics 4, 627–631 (2010).
    [Crossref]
  9. R. M. Saykally and G. A. Blake, “Molecular Interactions and Hydrogen Bond Tunneling Dynamics: Some New Perspectives,” Science 259, 1570–1575 (1993).
    [Crossref] [PubMed]
  10. B. M. Fischer, M. Walther, and P. Uhd Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Bio. 47, 3807–3814 (2002).
    [Crossref]
  11. D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett 25, 1210–1212 (2000).
    [Crossref]
  12. X. Xie, J. Dai, and X.-C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett. 96, 075005 (2006).
    [Crossref] [PubMed]
  13. T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett 30, 2805–2807 (2005).
    [Crossref] [PubMed]
  14. M. Kress, T. Löffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett 29, 1120–1122 (2004).
    [Crossref] [PubMed]
  15. C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical Forward THz Emission from Femtosecond-Laser-Beam Filamentation in Air,” Phys. Rev. Lett. 98, 235002 (2007).
    [Crossref]
  16. J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, “Terahertz generation in plasmas using two-color laser pulses,” Phys. Rev. E 81, 026407 (2010).
    [Crossref]
  17. K.-Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
    [Crossref] [PubMed]
  18. T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
    [Crossref]
  19. T.-J. Wang, S. Yuan, Y. Chen, J.-F. Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Toward remote high energy terahertz generation,” Appl. Phys. Lett. 97, 111108 (2010).
    [Crossref]
  20. T.-J. Wang, J.-F. Daigle, S. Yuan, F. Théberge, M. Châteauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A 83, 053801 (2011).
    [Crossref]
  21. J.-F. Daigle, F. Théberge, M. Henriksson, T.-J. Wang, S. Yuan, M. Châteauneuf, J. Dubois, M. Piché, and S. L. Chin, “Remote THz generation from two-color filamentation: long distance dependence,” Opt. Express 20, 6825–6834 (2012).
    [Crossref] [PubMed]
  22. O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
    [Crossref]
  23. L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D Numerical Simulations of THz Generation by Two-Color Laser Filaments,” Phys. Rev. Lett. 110, 073901 (2013).
    [Crossref]
  24. A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett 38, 1906–1908 (2013).
    [Crossref] [PubMed]
  25. I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
    [Crossref]
  26. W.-M. Wang, S. Kawata, Z.-M. Sheng, Y.-T. Li, L.-M. Chen, L.-J. Qian, and J. Zhang, “Efficient terahertz emission by mid-infrared laser pulses from gas targets,” Opt. Lett 36, 2608–2610 (2011).
    [Crossref] [PubMed]
  27. T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
    [Crossref]
  28. M. Chen, A. Pukhov, X.-Y. Peng, and O. Willi, “Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases,” Phys. Rev. E 78, 046406 (2008).
    [Crossref]
  29. V. B. Gildenburg and N. V. Vvedenskii, “Optical-to-THz Wave Conversion via Excitation of Plasma Oscillations in the Tunneling-Ionization Process,” Phys. Rev. Lett. 98, 245002 (2007).
    [Crossref] [PubMed]
  30. W.-M. Wang, Z.-M. Sheng, H.-C. Wu, M. Chen, C. Li, J. Zhang, and K. Mima, “Strong terahertz pulse generation by chirped laser pulses in tenuous gases,” Opt. Express 16, 16999–17006 (2008).
    [Crossref] [PubMed]
  31. I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast Spatiotemporal Dynamics of Terahertz Generation by Ionizing Two-Color Femtosecond Pulses in Gases,” Phys. Rev. Lett. 105, 053903 (2010).
    [Crossref] [PubMed]
  32. C. Köhler, E. Cabrera-Granado, I. Babushkin, L. Bergé, J. Herrmann, and S. Skupin, “Directionality of terahertz emission from photoinduced gas plasmas,” Opt. Lett 36, 3166–3168 (2011).
    [Crossref] [PubMed]
  33. A. Perelomov, V. Popov, and M. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).
  34. M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).
  35. G. L. Yudin and M. Y. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).
    [Crossref]
  36. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1964).
  37. B. Nodland and C. J. McKinstrie, “Propagation of a short laser pulse in a plasma,” Phys. Rev. E 56, 7174 (1997).
    [Crossref]
  38. E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
    [Crossref]
  39. R. Nuter, L. Gremillet, E. Lefebvre, A. Lévy, T. Ceccotti, and P. Martin, “Field ionization model implemented in Particle In Cell code and applied to laser-accelerated carbon ions,” Phys. Plasmas 18, 033107 (2011).
    [Crossref]
  40. I. Babushkin, S. Skupin, and J. Herrmann, “Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides,” Opt. Express 18, 9658–9663 (2010).
    [Crossref] [PubMed]

2013 (3)

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D Numerical Simulations of THz Generation by Two-Color Laser Filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[Crossref]

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett 38, 1906–1908 (2013).
[Crossref] [PubMed]

T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
[Crossref]

2012 (1)

2011 (6)

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
[Crossref]

T.-J. Wang, J.-F. Daigle, S. Yuan, F. Théberge, M. Châteauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A 83, 053801 (2011).
[Crossref]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

W.-M. Wang, S. Kawata, Z.-M. Sheng, Y.-T. Li, L.-M. Chen, L.-J. Qian, and J. Zhang, “Efficient terahertz emission by mid-infrared laser pulses from gas targets,” Opt. Lett 36, 2608–2610 (2011).
[Crossref] [PubMed]

C. Köhler, E. Cabrera-Granado, I. Babushkin, L. Bergé, J. Herrmann, and S. Skupin, “Directionality of terahertz emission from photoinduced gas plasmas,” Opt. Lett 36, 3166–3168 (2011).
[Crossref] [PubMed]

R. Nuter, L. Gremillet, E. Lefebvre, A. Lévy, T. Ceccotti, and P. Martin, “Field ionization model implemented in Particle In Cell code and applied to laser-accelerated carbon ions,” Phys. Plasmas 18, 033107 (2011).
[Crossref]

2010 (5)

I. Babushkin, S. Skupin, and J. Herrmann, “Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides,” Opt. Express 18, 9658–9663 (2010).
[Crossref] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast Spatiotemporal Dynamics of Terahertz Generation by Ionizing Two-Color Femtosecond Pulses in Gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

T.-J. Wang, S. Yuan, Y. Chen, J.-F. Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Toward remote high energy terahertz generation,” Appl. Phys. Lett. 97, 111108 (2010).
[Crossref]

J. Liu, J. Dai, S. L. Chin, and X.-C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photonics 4, 627–631 (2010).
[Crossref]

J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, “Terahertz generation in plasmas using two-color laser pulses,” Phys. Rev. E 81, 026407 (2010).
[Crossref]

2009 (1)

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

2008 (3)

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Phys. 2, 605–609 (2008).

W.-M. Wang, Z.-M. Sheng, H.-C. Wu, M. Chen, C. Li, J. Zhang, and K. Mima, “Strong terahertz pulse generation by chirped laser pulses in tenuous gases,” Opt. Express 16, 16999–17006 (2008).
[Crossref] [PubMed]

M. Chen, A. Pukhov, X.-Y. Peng, and O. Willi, “Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases,” Phys. Rev. E 78, 046406 (2008).
[Crossref]

2007 (6)

V. B. Gildenburg and N. V. Vvedenskii, “Optical-to-THz Wave Conversion via Excitation of Plasma Oscillations in the Tunneling-Ionization Process,” Phys. Rev. Lett. 98, 245002 (2007).
[Crossref] [PubMed]

K. Reimann, “Table-top sources of ultrashort THz pulses,” Rep. Prog. Phys. 70, 1597–1632 (2007).
[Crossref]

H. Roskos, M. Thomson, M. Kreß, and T. Löffler, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Las. Phot. Rev. 1, 349–368 (2007).
[Crossref]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical Forward THz Emission from Femtosecond-Laser-Beam Filamentation in Air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

K.-Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
[Crossref] [PubMed]

2006 (2)

X. Xie, J. Dai, and X.-C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett. 96, 075005 (2006).
[Crossref] [PubMed]

N. Nagai, M. Sumitomo, M. Imaizumi, and R. Fukasawa, “Characterization of electron- or proton-irradiated Si space solar cells by THz spectroscopy,” Semicond. Sci. Technol. 21, 201–209 (2006).
[Crossref]

2005 (1)

T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett 30, 2805–2807 (2005).
[Crossref] [PubMed]

2004 (1)

M. Kress, T. Löffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett 29, 1120–1122 (2004).
[Crossref] [PubMed]

2003 (1)

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

2002 (2)

B. M. Fischer, M. Walther, and P. Uhd Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Bio. 47, 3807–3814 (2002).
[Crossref]

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Bio. 47, 3853–3863 (2002).
[Crossref]

2001 (1)

G. L. Yudin and M. Y. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).
[Crossref]

2000 (1)

D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett 25, 1210–1212 (2000).
[Crossref]

1997 (1)

B. Nodland and C. J. McKinstrie, “Propagation of a short laser pulse in a plasma,” Phys. Rev. E 56, 7174 (1997).
[Crossref]

1993 (1)

R. M. Saykally and G. A. Blake, “Molecular Interactions and Hydrogen Bond Tunneling Dynamics: Some New Perspectives,” Science 259, 1570–1575 (1993).
[Crossref] [PubMed]

1990 (1)

F. Brunel, “Harmonic generation due to plasma effects in a gas undergoing multiphoton ionization in the high-intensity limit,” J. Opt. Soc.Am. B 7, 512–526 (1990).

1986 (1)

M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

1966 (1)

A. Perelomov, V. Popov, and M. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1964).

Aléonard, M.-M.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Ammosov, M.

M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Andreeva, V. A.

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett 38, 1906–1908 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
[Crossref]

Arnone, D. D.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Bio. 47, 3853–3863 (2002).
[Crossref]

Audebert, P.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Babushkin, I.

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D Numerical Simulations of THz Generation by Two-Color Laser Filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[Crossref]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

C. Köhler, E. Cabrera-Granado, I. Babushkin, L. Bergé, J. Herrmann, and S. Skupin, “Directionality of terahertz emission from photoinduced gas plasmas,” Opt. Lett 36, 3166–3168 (2011).
[Crossref] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast Spatiotemporal Dynamics of Terahertz Generation by Ionizing Two-Color Femtosecond Pulses in Gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

I. Babushkin, S. Skupin, and J. Herrmann, “Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides,” Opt. Express 18, 9658–9663 (2010).
[Crossref] [PubMed]

Bartel, T.

T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett 30, 2805–2807 (2005).
[Crossref] [PubMed]

Bergé, L.

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D Numerical Simulations of THz Generation by Two-Color Laser Filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[Crossref]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

C. Köhler, E. Cabrera-Granado, I. Babushkin, L. Bergé, J. Herrmann, and S. Skupin, “Directionality of terahertz emission from photoinduced gas plasmas,” Opt. Lett 36, 3166–3168 (2011).
[Crossref] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast Spatiotemporal Dynamics of Terahertz Generation by Ionizing Two-Color Femtosecond Pulses in Gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Blake, G. A.

R. M. Saykally and G. A. Blake, “Molecular Interactions and Hydrogen Bond Tunneling Dynamics: Some New Perspectives,” Science 259, 1570–1575 (1993).
[Crossref] [PubMed]

Borodin, A. V.

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett 38, 1906–1908 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
[Crossref]

Brunel, F.

F. Brunel, “Harmonic generation due to plasma effects in a gas undergoing multiphoton ionization in the high-intensity limit,” J. Opt. Soc.Am. B 7, 512–526 (1990).

Cabrera-Granado, E.

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

C. Köhler, E. Cabrera-Granado, I. Babushkin, L. Bergé, J. Herrmann, and S. Skupin, “Directionality of terahertz emission from photoinduced gas plasmas,” Opt. Lett 36, 3166–3168 (2011).
[Crossref] [PubMed]

Ceccotti, T.

R. Nuter, L. Gremillet, E. Lefebvre, A. Lévy, T. Ceccotti, and P. Martin, “Field ionization model implemented in Particle In Cell code and applied to laser-accelerated carbon ions,” Phys. Plasmas 18, 033107 (2011).
[Crossref]

Châteauneuf, M.

J.-F. Daigle, F. Théberge, M. Henriksson, T.-J. Wang, S. Yuan, M. Châteauneuf, J. Dubois, M. Piché, and S. L. Chin, “Remote THz generation from two-color filamentation: long distance dependence,” Opt. Express 20, 6825–6834 (2012).
[Crossref] [PubMed]

T.-J. Wang, J.-F. Daigle, S. Yuan, F. Théberge, M. Châteauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A 83, 053801 (2011).
[Crossref]

T.-J. Wang, S. Yuan, Y. Chen, J.-F. Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Toward remote high energy terahertz generation,” Appl. Phys. Lett. 97, 111108 (2010).
[Crossref]

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

Chemin, J.-F.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Chen, L.-M.

W.-M. Wang, S. Kawata, Z.-M. Sheng, Y.-T. Li, L.-M. Chen, L.-J. Qian, and J. Zhang, “Efficient terahertz emission by mid-infrared laser pulses from gas targets,” Opt. Lett 36, 2608–2610 (2011).
[Crossref] [PubMed]

Chen, M.

W.-M. Wang, Z.-M. Sheng, H.-C. Wu, M. Chen, C. Li, J. Zhang, and K. Mima, “Strong terahertz pulse generation by chirped laser pulses in tenuous gases,” Opt. Express 16, 16999–17006 (2008).
[Crossref] [PubMed]

M. Chen, A. Pukhov, X.-Y. Peng, and O. Willi, “Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases,” Phys. Rev. E 78, 046406 (2008).
[Crossref]

Chen, Y.

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
[Crossref]

T.-J. Wang, S. Yuan, Y. Chen, J.-F. Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Toward remote high energy terahertz generation,” Appl. Phys. Lett. 97, 111108 (2010).
[Crossref]

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

Chin, S. L.

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett 38, 1906–1908 (2013).
[Crossref] [PubMed]

J.-F. Daigle, F. Théberge, M. Henriksson, T.-J. Wang, S. Yuan, M. Châteauneuf, J. Dubois, M. Piché, and S. L. Chin, “Remote THz generation from two-color filamentation: long distance dependence,” Opt. Express 20, 6825–6834 (2012).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
[Crossref]

T.-J. Wang, J.-F. Daigle, S. Yuan, F. Théberge, M. Châteauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A 83, 053801 (2011).
[Crossref]

T.-J. Wang, S. Yuan, Y. Chen, J.-F. Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Toward remote high energy terahertz generation,” Appl. Phys. Lett. 97, 111108 (2010).
[Crossref]

J. Liu, J. Dai, S. L. Chin, and X.-C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photonics 4, 627–631 (2010).
[Crossref]

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

Cochet, N.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Cole, B. E.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Bio. 47, 3853–3863 (2002).
[Crossref]

Cook, D. J.

D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett 25, 1210–1212 (2000).
[Crossref]

Couairon, A.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical Forward THz Emission from Femtosecond-Laser-Beam Filamentation in Air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

D’Amico, C.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical Forward THz Emission from Femtosecond-Laser-Beam Filamentation in Air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Dai, J.

J. Liu, J. Dai, S. L. Chin, and X.-C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photonics 4, 627–631 (2010).
[Crossref]

X. Xie, J. Dai, and X.-C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett. 96, 075005 (2006).
[Crossref] [PubMed]

Daigle, J.-F.

J.-F. Daigle, F. Théberge, M. Henriksson, T.-J. Wang, S. Yuan, M. Châteauneuf, J. Dubois, M. Piché, and S. L. Chin, “Remote THz generation from two-color filamentation: long distance dependence,” Opt. Express 20, 6825–6834 (2012).
[Crossref] [PubMed]

T.-J. Wang, J.-F. Daigle, S. Yuan, F. Théberge, M. Châteauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A 83, 053801 (2011).
[Crossref]

T.-J. Wang, S. Yuan, Y. Chen, J.-F. Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Toward remote high energy terahertz generation,” Appl. Phys. Lett. 97, 111108 (2010).
[Crossref]

Darbon, S.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Delone, N.

M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Disdier, L.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Dubois, J.

J.-F. Daigle, F. Théberge, M. Henriksson, T.-J. Wang, S. Yuan, M. Châteauneuf, J. Dubois, M. Piché, and S. L. Chin, “Remote THz generation from two-color filamentation: long distance dependence,” Opt. Express 20, 6825–6834 (2012).
[Crossref] [PubMed]

T.-J. Wang, J.-F. Daigle, S. Yuan, F. Théberge, M. Châteauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A 83, 053801 (2011).
[Crossref]

T.-J. Wang, S. Yuan, Y. Chen, J.-F. Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Toward remote high energy terahertz generation,” Appl. Phys. Lett. 97, 111108 (2010).
[Crossref]

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

Eden, S.

M. Kress, T. Löffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett 29, 1120–1122 (2004).
[Crossref] [PubMed]

Elsaesser, T.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast Spatiotemporal Dynamics of Terahertz Generation by Ionizing Two-Color Femtosecond Pulses in Gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett 30, 2805–2807 (2005).
[Crossref] [PubMed]

Esaulkov, M. N.

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett 38, 1906–1908 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
[Crossref]

Faure, J.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Fedotoff, A.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Fischer, B. M.

B. M. Fischer, M. Walther, and P. Uhd Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Bio. 47, 3807–3814 (2002).
[Crossref]

Franco, M.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical Forward THz Emission from Femtosecond-Laser-Beam Filamentation in Air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Fritzler, S.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Fukasawa, R.

N. Nagai, M. Sumitomo, M. Imaizumi, and R. Fukasawa, “Characterization of electron- or proton-irradiated Si space solar cells by THz spectroscopy,” Semicond. Sci. Technol. 21, 201–209 (2006).
[Crossref]

Gaal, P.

T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett 30, 2805–2807 (2005).
[Crossref] [PubMed]

Gildenburg, V. B.

V. B. Gildenburg and N. V. Vvedenskii, “Optical-to-THz Wave Conversion via Excitation of Plasma Oscillations in the Tunneling-Ionization Process,” Phys. Rev. Lett. 98, 245002 (2007).
[Crossref] [PubMed]

Glownia, J. H.

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Phys. 2, 605–609 (2008).

K.-Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
[Crossref] [PubMed]

Gordon, D.

J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, “Terahertz generation in plasmas using two-color laser pulses,” Phys. Rev. E 81, 026407 (2010).
[Crossref]

Gremillet, L.

R. Nuter, L. Gremillet, E. Lefebvre, A. Lévy, T. Ceccotti, and P. Martin, “Field ionization model implemented in Particle In Cell code and applied to laser-accelerated carbon ions,” Phys. Plasmas 18, 033107 (2011).
[Crossref]

Hafizi, B.

J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, “Terahertz generation in plasmas using two-color laser pulses,” Phys. Rev. E 81, 026407 (2010).
[Crossref]

Henriksson, M.

Herrmann, J.

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D Numerical Simulations of THz Generation by Two-Color Laser Filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[Crossref]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

C. Köhler, E. Cabrera-Granado, I. Babushkin, L. Bergé, J. Herrmann, and S. Skupin, “Directionality of terahertz emission from photoinduced gas plasmas,” Opt. Lett 36, 3166–3168 (2011).
[Crossref] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast Spatiotemporal Dynamics of Terahertz Generation by Ionizing Two-Color Femtosecond Pulses in Gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

I. Babushkin, S. Skupin, and J. Herrmann, “Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides,” Opt. Express 18, 9658–9663 (2010).
[Crossref] [PubMed]

Hochstrasser, R. M.

D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett 25, 1210–1212 (2000).
[Crossref]

Houard, A.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical Forward THz Emission from Femtosecond-Laser-Beam Filamentation in Air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Husakou, A.

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

Imaizumi, M.

N. Nagai, M. Sumitomo, M. Imaizumi, and R. Fukasawa, “Characterization of electron- or proton-irradiated Si space solar cells by THz spectroscopy,” Semicond. Sci. Technol. 21, 201–209 (2006).
[Crossref]

Ivanov, M. Y.

G. L. Yudin and M. Y. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).
[Crossref]

Jhajj, N.

T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
[Crossref]

Kawata, S.

W.-M. Wang, S. Kawata, Z.-M. Sheng, Y.-T. Li, L.-M. Chen, L.-J. Qian, and J. Zhang, “Efficient terahertz emission by mid-infrared laser pulses from gas targets,” Opt. Lett 36, 2608–2610 (2011).
[Crossref] [PubMed]

Kim, K. Y.

T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
[Crossref]

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Phys. 2, 605–609 (2008).

Kim, K.-Y.

Köhler, C.

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D Numerical Simulations of THz Generation by Two-Color Laser Filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[Crossref]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

C. Köhler, E. Cabrera-Granado, I. Babushkin, L. Bergé, J. Herrmann, and S. Skupin, “Directionality of terahertz emission from photoinduced gas plasmas,” Opt. Lett 36, 3166–3168 (2011).
[Crossref] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast Spatiotemporal Dynamics of Terahertz Generation by Ionizing Two-Color Femtosecond Pulses in Gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Kosareva, O. G.

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett 38, 1906–1908 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
[Crossref]

Krainov, V.

M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Kreß, M.

H. Roskos, M. Thomson, M. Kreß, and T. Löffler, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Las. Phot. Rev. 1, 349–368 (2007).
[Crossref]

Kress, M.

M. Kress, T. Löffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett 29, 1120–1122 (2004).
[Crossref] [PubMed]

Kuehn, W.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast Spatiotemporal Dynamics of Terahertz Generation by Ionizing Two-Color Femtosecond Pulses in Gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Landoas, O.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Lefebvre, E.

R. Nuter, L. Gremillet, E. Lefebvre, A. Lévy, T. Ceccotti, and P. Martin, “Field ionization model implemented in Particle In Cell code and applied to laser-accelerated carbon ions,” Phys. Plasmas 18, 033107 (2011).
[Crossref]

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Lévy, A.

R. Nuter, L. Gremillet, E. Lefebvre, A. Lévy, T. Ceccotti, and P. Martin, “Field ionization model implemented in Particle In Cell code and applied to laser-accelerated carbon ions,” Phys. Plasmas 18, 033107 (2011).
[Crossref]

Li, C.

Li, Y.-T.

W.-M. Wang, S. Kawata, Z.-M. Sheng, Y.-T. Li, L.-M. Chen, L.-J. Qian, and J. Zhang, “Efficient terahertz emission by mid-infrared laser pulses from gas targets,” Opt. Lett 36, 2608–2610 (2011).
[Crossref] [PubMed]

Linfield, E. H.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Bio. 47, 3853–3863 (2002).
[Crossref]

Liu, J.

J. Liu, J. Dai, S. L. Chin, and X.-C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photonics 4, 627–631 (2010).
[Crossref]

Löffler, T.

H. Roskos, M. Thomson, M. Kreß, and T. Löffler, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Las. Phot. Rev. 1, 349–368 (2007).
[Crossref]

M. Kress, T. Löffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett 29, 1120–1122 (2004).
[Crossref] [PubMed]

Makarov, V. A.

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett 38, 1906–1908 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
[Crossref]

Malka, G.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Malka, V.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Marceau, C.

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
[Crossref]

T.-J. Wang, S. Yuan, Y. Chen, J.-F. Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Toward remote high energy terahertz generation,” Appl. Phys. Lett. 97, 111108 (2010).
[Crossref]

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

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R. Nuter, L. Gremillet, E. Lefebvre, A. Lévy, T. Ceccotti, and P. Martin, “Field ionization model implemented in Particle In Cell code and applied to laser-accelerated carbon ions,” Phys. Plasmas 18, 033107 (2011).
[Crossref]

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B. Nodland and C. J. McKinstrie, “Propagation of a short laser pulse in a plasma,” Phys. Rev. E 56, 7174 (1997).
[Crossref]

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E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

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T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
[Crossref]

Mima, K.

Morel, P.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

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C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical Forward THz Emission from Femtosecond-Laser-Beam Filamentation in Air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Nagai, N.

N. Nagai, M. Sumitomo, M. Imaizumi, and R. Fukasawa, “Characterization of electron- or proton-irradiated Si space solar cells by THz spectroscopy,” Semicond. Sci. Technol. 21, 201–209 (2006).
[Crossref]

Nodland, B.

B. Nodland and C. J. McKinstrie, “Propagation of a short laser pulse in a plasma,” Phys. Rev. E 56, 7174 (1997).
[Crossref]

Nuter, R.

R. Nuter, L. Gremillet, E. Lefebvre, A. Lévy, T. Ceccotti, and P. Martin, “Field ionization model implemented in Particle In Cell code and applied to laser-accelerated carbon ions,” Phys. Plasmas 18, 033107 (2011).
[Crossref]

Oh, T. I.

T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
[Crossref]

Panov, N. A.

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett 38, 1906–1908 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
[Crossref]

Peñano, J.

J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, “Terahertz generation in plasmas using two-color laser pulses,” Phys. Rev. E 81, 026407 (2010).
[Crossref]

Peng, X.-Y.

M. Chen, A. Pukhov, X.-Y. Peng, and O. Willi, “Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases,” Phys. Rev. E 78, 046406 (2008).
[Crossref]

Pepper, M.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Bio. 47, 3853–3863 (2002).
[Crossref]

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A. Perelomov, V. Popov, and M. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Piché, M.

Popov, V.

A. Perelomov, V. Popov, and M. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Prade, B.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical Forward THz Emission from Femtosecond-Laser-Beam Filamentation in Air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Pukhov, A.

M. Chen, A. Pukhov, X.-Y. Peng, and O. Willi, “Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases,” Phys. Rev. E 78, 046406 (2008).
[Crossref]

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R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Bio. 47, 3853–3863 (2002).
[Crossref]

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W.-M. Wang, S. Kawata, Z.-M. Sheng, Y.-T. Li, L.-M. Chen, L.-J. Qian, and J. Zhang, “Efficient terahertz emission by mid-infrared laser pulses from gas targets,” Opt. Lett 36, 2608–2610 (2011).
[Crossref] [PubMed]

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E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

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I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast Spatiotemporal Dynamics of Terahertz Generation by Ionizing Two-Color Femtosecond Pulses in Gases,” Phys. Rev. Lett. 105, 053903 (2010).
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K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Phys. 2, 605–609 (2008).

K.-Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
[Crossref] [PubMed]

Rosenthal, E. W.

T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
[Crossref]

Roskos, H.

H. Roskos, M. Thomson, M. Kreß, and T. Löffler, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Las. Phot. Rev. 1, 349–368 (2007).
[Crossref]

Roskos, H. G.

M. Kress, T. Löffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett 29, 1120–1122 (2004).
[Crossref] [PubMed]

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E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
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E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
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T.-J. Wang, J.-F. Daigle, S. Yuan, F. Théberge, M. Châteauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A 83, 053801 (2011).
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E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
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O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
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J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, “Terahertz generation in plasmas using two-color laser pulses,” Phys. Rev. E 81, 026407 (2010).
[Crossref]

Sheng, Z.-M.

W.-M. Wang, S. Kawata, Z.-M. Sheng, Y.-T. Li, L.-M. Chen, L.-J. Qian, and J. Zhang, “Efficient terahertz emission by mid-infrared laser pulses from gas targets,” Opt. Lett 36, 2608–2610 (2011).
[Crossref] [PubMed]

W.-M. Wang, Z.-M. Sheng, H.-C. Wu, M. Chen, C. Li, J. Zhang, and K. Mima, “Strong terahertz pulse generation by chirped laser pulses in tenuous gases,” Opt. Express 16, 16999–17006 (2008).
[Crossref] [PubMed]

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A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett 38, 1906–1908 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
[Crossref]

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L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D Numerical Simulations of THz Generation by Two-Color Laser Filaments,” Phys. Rev. Lett. 110, 073901 (2013).
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I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
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C. Köhler, E. Cabrera-Granado, I. Babushkin, L. Bergé, J. Herrmann, and S. Skupin, “Directionality of terahertz emission from photoinduced gas plasmas,” Opt. Lett 36, 3166–3168 (2011).
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I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast Spatiotemporal Dynamics of Terahertz Generation by Ionizing Two-Color Femtosecond Pulses in Gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

I. Babushkin, S. Skupin, and J. Herrmann, “Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides,” Opt. Express 18, 9658–9663 (2010).
[Crossref] [PubMed]

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J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, “Terahertz generation in plasmas using two-color laser pulses,” Phys. Rev. E 81, 026407 (2010).
[Crossref]

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M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1964).

Sumitomo, M.

N. Nagai, M. Sumitomo, M. Imaizumi, and R. Fukasawa, “Characterization of electron- or proton-irradiated Si space solar cells by THz spectroscopy,” Semicond. Sci. Technol. 21, 201–209 (2006).
[Crossref]

Taylor, A. J.

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Phys. 2, 605–609 (2008).

K.-Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
[Crossref] [PubMed]

Terent’ev, M.

A. Perelomov, V. Popov, and M. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Théberge, F.

J.-F. Daigle, F. Théberge, M. Henriksson, T.-J. Wang, S. Yuan, M. Châteauneuf, J. Dubois, M. Piché, and S. L. Chin, “Remote THz generation from two-color filamentation: long distance dependence,” Opt. Express 20, 6825–6834 (2012).
[Crossref] [PubMed]

T.-J. Wang, J.-F. Daigle, S. Yuan, F. Théberge, M. Châteauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A 83, 053801 (2011).
[Crossref]

T.-J. Wang, S. Yuan, Y. Chen, J.-F. Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Toward remote high energy terahertz generation,” Appl. Phys. Lett. 97, 111108 (2010).
[Crossref]

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

Thomson, M.

H. Roskos, M. Thomson, M. Kreß, and T. Löffler, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Las. Phot. Rev. 1, 349–368 (2007).
[Crossref]

M. Kress, T. Löffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett 29, 1120–1122 (2004).
[Crossref] [PubMed]

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E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

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C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical Forward THz Emission from Femtosecond-Laser-Beam Filamentation in Air,” Phys. Rev. Lett. 98, 235002 (2007).
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B. M. Fischer, M. Walther, and P. Uhd Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Bio. 47, 3807–3814 (2002).
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Volkov, R. V.

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of Dual Frequency Interaction in the Filament with the Purpose of Efficiency Control of THz Pulse Generation,” J. Infrared Milli Terahz Waves 32, 1157–1167 (2011).
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R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Bio. 47, 3853–3863 (2002).
[Crossref]

Walther, M.

B. M. Fischer, M. Walther, and P. Uhd Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Bio. 47, 3807–3814 (2002).
[Crossref]

Wang, T.-J.

J.-F. Daigle, F. Théberge, M. Henriksson, T.-J. Wang, S. Yuan, M. Châteauneuf, J. Dubois, M. Piché, and S. L. Chin, “Remote THz generation from two-color filamentation: long distance dependence,” Opt. Express 20, 6825–6834 (2012).
[Crossref] [PubMed]

T.-J. Wang, J.-F. Daigle, S. Yuan, F. Théberge, M. Châteauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A 83, 053801 (2011).
[Crossref]

T.-J. Wang, S. Yuan, Y. Chen, J.-F. Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Toward remote high energy terahertz generation,” Appl. Phys. Lett. 97, 111108 (2010).
[Crossref]

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

Wang, W.-M.

W.-M. Wang, S. Kawata, Z.-M. Sheng, Y.-T. Li, L.-M. Chen, L.-J. Qian, and J. Zhang, “Efficient terahertz emission by mid-infrared laser pulses from gas targets,” Opt. Lett 36, 2608–2610 (2011).
[Crossref] [PubMed]

W.-M. Wang, Z.-M. Sheng, H.-C. Wu, M. Chen, C. Li, J. Zhang, and K. Mima, “Strong terahertz pulse generation by chirped laser pulses in tenuous gases,” Opt. Express 16, 16999–17006 (2008).
[Crossref] [PubMed]

Willi, O.

M. Chen, A. Pukhov, X.-Y. Peng, and O. Willi, “Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases,” Phys. Rev. E 78, 046406 (2008).
[Crossref]

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[Crossref] [PubMed]

T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett 30, 2805–2807 (2005).
[Crossref] [PubMed]

Woodward, R. M.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Bio. 47, 3853–3863 (2002).
[Crossref]

Wrobel, R.

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
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X. Xie, J. Dai, and X.-C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett. 96, 075005 (2006).
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J.-F. Daigle, F. Théberge, M. Henriksson, T.-J. Wang, S. Yuan, M. Châteauneuf, J. Dubois, M. Piché, and S. L. Chin, “Remote THz generation from two-color filamentation: long distance dependence,” Opt. Express 20, 6825–6834 (2012).
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T.-J. Wang, S. Yuan, Y. Chen, J.-F. Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Toward remote high energy terahertz generation,” Appl. Phys. Lett. 97, 111108 (2010).
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T.-J. Wang, J.-F. Daigle, S. Yuan, F. Théberge, M. Châteauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A 83, 053801 (2011).
[Crossref]

Zhang, J.

W.-M. Wang, S. Kawata, Z.-M. Sheng, Y.-T. Li, L.-M. Chen, L.-J. Qian, and J. Zhang, “Efficient terahertz emission by mid-infrared laser pulses from gas targets,” Opt. Lett 36, 2608–2610 (2011).
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T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
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T.-J. Wang, S. Yuan, Y. Chen, J.-F. Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Toward remote high energy terahertz generation,” Appl. Phys. Lett. 97, 111108 (2010).
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T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
[Crossref]

Nucl. Fusion (1)

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M.-M. Aléonard, J.-F. Chemin, S. Darbon, L. Disdier, J. Faure, A. Fedotoff, O. Landoas, G. Malka, V. Méot, P. Morel, M. Rabec LeGloahec, A. Rouyer, C. Rubbelynck, V. Tikhonchuk, R. Wrobel, P. Audebert, and C. Rousseaux, “Electron and photon production from relativistic laser plasma interactions,” Nucl. Fusion 43, 629–633 (2003).
[Crossref]

Opt. Express (4)

Opt. Lett (6)

C. Köhler, E. Cabrera-Granado, I. Babushkin, L. Bergé, J. Herrmann, and S. Skupin, “Directionality of terahertz emission from photoinduced gas plasmas,” Opt. Lett 36, 3166–3168 (2011).
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A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett 38, 1906–1908 (2013).
[Crossref] [PubMed]

W.-M. Wang, S. Kawata, Z.-M. Sheng, Y.-T. Li, L.-M. Chen, L.-J. Qian, and J. Zhang, “Efficient terahertz emission by mid-infrared laser pulses from gas targets,” Opt. Lett 36, 2608–2610 (2011).
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[Crossref]

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[Crossref] [PubMed]

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Phys. Med. Bio. (2)

B. M. Fischer, M. Walther, and P. Uhd Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Bio. 47, 3807–3814 (2002).
[Crossref]

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Bio. 47, 3853–3863 (2002).
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T.-J. Wang, J.-F. Daigle, S. Yuan, F. Théberge, M. Châteauneuf, J. Dubois, G. Roy, H. Zeng, and S. L. Chin, “Remote generation of high-energy terahertz pulses from two-color femtosecond laser filamentation in air,” Phys. Rev. A 83, 053801 (2011).
[Crossref]

G. L. Yudin and M. Y. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).
[Crossref]

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[Crossref]

X. Xie, J. Dai, and X.-C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett. 96, 075005 (2006).
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[Crossref]

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Figures (9)

Fig. 1
Fig. 1

(a) Unfiltered (black line) and filtered (red dotted line) electric field δEy for the parameters ν = 0, a0 = 0.02, τ = 10, λ0 = 1μm (one pump pulse), na = 1.1×10−3, r = 0, and ϕ = 0. (b) Electric field spectrum (black line), and the filtered spectrum (red dotted line) of panel (a) for ω < 0.3 (normalized to ω0). Note the pump’s trace left in the evaluation of δEy and its spectrum.

Fig. 2
Fig. 2

(a) Maximum of the filtered electric field versus laser intensity in unit of 1018 W/cm2 for a single pulse. Parameters are displayed in the inset, while all others remain equal to those of Fig. 1. (b) Same figure for another set of parameters.

Fig. 3
Fig. 3

Maximum of the filtered electric field versus the phase shift ϕ for one laser color (black solid curve) with I = 1016 W/cm−2, τ = 10, λ0 = 1 μm and na = 0.0011, and for two colors (red dashed curve) versus ϕ2 with r2 = 0.2 and ϕ = 0.

Fig. 4
Fig. 4

(a) Maximum of the filtered electric field for a two-color pulse versus laser intensity in unit of 1018 W/cm2 for different phases ϕ2, and r2 = 0.2. (b) Maximum of the filtered electric field versus phase ϕ2 and amplitude field ratio r for I = 1016 W/cm2. The other parameters are ν = 0, τ = 10, λ0 = 1μm, na = 1.1 × 10−3, and ϕ = 0.

Fig. 5
Fig. 5

δEy for a two-color pulse vs x at time t = 780, (a) zoomed around the laser position and (b) full solution. The numerical solution is shown in black solid line, the numerical solution without dispersion between xt ∈ [−2πτ, 0] is represented in black dashed line, and the analytical solution is plotted in red solid line. The parameters are a0 = 0.02, λ0 = 1μm, ν = 0, τ = 10, r2 = 0.2, ϕ2 = 0.5 and na = 0.0011.

Fig. 6
Fig. 6

Numerical solution of the field δEy(x, t) saturated to the value ±10−4, for the same parameters as in Fig. 5.

Fig. 7
Fig. 7

Intensity spectra of the transmitted field (black lines) and the reflected field (red lines) calculated numerically (solid lines) and according to formula (24), (28) and (30) (dashed lines). The parameters are similar to Fig. 5, but the plasma length is limited to L = 40π. The green dashed line and green solid line correspond to the transmitted field calculated numerically and according to Eqs. (24) and (28) for a plasma length of L = 100π.

Fig. 8
Fig. 8

(a) Spectra of the reflected (solid lines) and transmitted (dashed lines) electric field, normalized to the total energy Utot, produced by a single pump wave in hydrogen (I = 1017 W/cm2, λ0 = 2μm). The red curves correspond to PIC simulations and black lines to δEy calculated numerically according to Eq. (7). (b) Resulting THz fields for the frequency window < 0.2 (f < 30 THz), using the same plotstyle as in (a).

Fig. 9
Fig. 9

Intensity spectra of the transmitted electric field, normalized to the total energy Utot, produced by a two-color pulse in hydrogen for (a) I = 1014 W/cm2, λ0 = 1μm and (b) I = 1015 W/cm2, λ0 = 1μm. The red and green curves correspond to PIC and uppe1d simulations, respectively, while the black lines refer to δEy calculated numerically according to Eq. (7). The blue curves show the on-axis intensity spectra obtained from the uppe3d model under similar conditions.

Equations (39)

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E y L = a 0 sin 2 [ ( β + + 2 π τ ) / 2 τ ] [ sin ( β + + 2 π τ + ϕ ) + r sin [ 2 ( β + + 2 π τ ) + ϕ 2 ] ] H ( β + + 2 π τ ) H ( β + ) .
E y = E y L t δ a y ,
t n e = ν E ( E y L ) ( n a n e )
t J y + ν J y = n e ( E y L t δ a y )
x 2 δ a y t 2 δ a y = J y ,
ν E ( E y L ) = 4 ω a ω 0 | E a . u . E y L | exp ( 2 3 | E a . u . E y L | ) .
( ν + t ) ( x 2 t 2 ) δ a y n e t δ a y = n e E y L .
t 2 δ E y + ν t δ E y + n e δ E y = n e E y L ,
n e ( 0 ) = δ E y ( 0 ) = t δ E y ( 0 ) = 0
δ E y ~ n a a 0 ,
δ E y ~ n a a 0 / τ .
δ E y exp ( ν t / 2 ) n ef ν 2 / 4 sin ( n ef ν 2 / 4 t ) 0 min ( 2 π τ , t ) n e E y L d t ,
G ( 2 π τ ) = 0 2 π τ n e E y L d t .
n ef = i = 1 N f δ n e , i H ( t t i ) ,
δ n e , i = ν E ( E m , i ) ( n a k = 0 i 1 δ n e , k ) π g i 3 ,
G = i = 1 N f δ n e , i A y , i L ,
4 π g k 3 ω a ω 0 | E a . u . E m , k | exp ( 2 3 | E a . u . E m , k | ) = A y , k A y , k A y , k 1 .
2 k + 1 2 π + ϕ = τ g 1 [ 2 E a . u . 3 a 0 W 1 ( K ) ] ,
K = 3 / π g k ω 0 4 ω a A y , k A y , k A y , k 1 1 / λ 0 .
E y L ( t ) = a 0 g ( t / τ ) [ sin t + r sin ( 2 t ϕ 2 ) ] ,
x 2 δ E y t 2 δ E y = ( E y L + δ E y ) n e H ( x ) .
n e ( β + ) = [ 1 exp ( 0 max ( β + , 2 π τ ) ν E ( E y L ) d β + ) ] n a .
2 β + s 2 δ E y s 2 δ E y = ( E y L + δ E y ) n e H ( β + + s ) .
2 β + s 2 δ E y s 2 δ E y = n e E y L H ( β + + s ) .
δ E y = 1 4 F ( x t ) + x 2 G ( x t ) ,
2 β + s 2 δ E y s 2 δ E y = n ef δ E y H [ β + + s ] .
β + δ E y ^ = ( p 2 + n ef 2 p ) δ E y ^ .
δ E y ^ = [ 1 2 p 2 G ( π τ G + F / 4 ) 1 p ] exp [ ( p 2 + n ef 2 p ) ( β + + 2 π τ ) ] .
δ E y = G 2 n ef [ t + x + 2 π τ t x 2 π τ ] 1 / 2 J 1 [ n ef ( t 2 ( x + 2 π τ ) 2 ) ] ( π τ G + F 4 ) J 0 [ n ef ( t 2 ( x + 2 π τ ) 2 ) ] ,
δ E y ref = F ( x t ) 4 .
δ E y ref = G 2 n ef [ t + x + 2 π τ t + x 2 π τ ] 1 / 2 J 1 [ n ef ( ( x + t ) 2 4 π 2 τ 2 ) ] ( π τ G + F 4 ) J 0 [ n ef ( ( x + t ) 2 4 π 2 τ 2 ) ] .
δ E y 2 π 1 n ef 1 / 4 t [ 2 G n ef ( 1 + x + 2 π τ t ) sin ( n ef t π 4 ) ( 4 π τ G + F ) cos ( n ef t π 4 ) ] ,
δ E y Gt 1 / 4 / ( n ef β + ) 3 / 4
2 β + B s B = n e E y L H [ β + + s ] .
B ( s , β + ) = β 0 + β + n e E y L 2 H [ β + + β 0 + ] d β + .
δ E y ( s , β + ) = 0 s d s β min + β max + n e E y L 2 d β + ,
δ E y = β + / 2 β + d s 0 β 0 + n e E y 2 d β + + β + s d s 0 β + n e E y 2 d β + .
δ E y G 2 n ef 2 t + β + β + J 1 [ n ef β + ( β + + 2 t ) ] .
δ E y ~ Gt 1 / 4 2 1 / 4 π ( n ef β + ) 3 / 4 .

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