Enhanced high field terahertz emission from plasma wakefields via pulse sharpening by a foil shutter

High field terahertz (THz) radiation source is of great interest for various applications in physics, chemistry and biology. It provides a powerful tool to manipulate and control the fundamental properties of different systems,¹ since it covers the natural frequency range of many kinds of single-particle and collective excitations. For example, novel quantum phenomena of materials have been explored with the aid of high field THz pulses via coupling with excitations such as intersubband electronic transitions,² phonon resonances,³ magnetic spin resonances,⁴ collective plasmon responses,⁵ local molecular vibrations,⁶ and so on.

Large-scale acceleration facilities can provide high field THz pulses with peak amplitude up to a few tens of MV/cm via mechanisms, for example, coherent transition radiation of ultrashort electron bunches.⁷ Recently, smaller sacle laser-driven sources are also capable of generating THz pulses with field strength of several to several tens of MV/cm, based on different schemes such as two-color laser filamentation in air,⁸ optical rectification in nonlinear organic crystals,⁹ difference frequency mixing¹⁰ and tilted laser front in nonlinear crystals.¹¹ Intense THz emission from plasma has also been proposed,^12–15 since this kind of medium has the advantage of without damage threshold limitations.

In our previous work, we proposed a method to generate high field THz pulses with field strength in the GV/cm regime from plasma wakefields driven by tailored laser pulses with a sharp rising edge.¹⁶ Later, we showed that such a THz generation process can be realized through the self-evolution process of the laser pulses in gaseous density plasmas.¹⁷ By snow plowing electrons forward due to the laser ponderomotive force, an overdense electron spike is formed at the front of the laser pulse, which gradually erodes the laser pulse front via local pump depletion effect.¹⁸ Eventually a quasi-step function like laser shape is formed. This results in a net residual transverse momentum of electrons, and consequently excites net transverse currents which emit the low frequency THz pulses.¹⁷ In this process, a high density electron spike at the laser front is essential for efficient etching of the pulse front. However, this requires a large laser intensity in order to have the strong ponderomotive force.

In this paper, we address how to enhance the THz field strength while reduce the incident laser intensity at the same time. We show that this can be achieved by separating the laser sharpening and wakefield emission into a two-stage process. Firstly, a thin foil target is employed to act as a ultrafast optical shutter, which chops the transmitted laser pulses to have a ultra-sharp front. The underlying mechasnism is known as relativistic transparence.¹⁹ The feasibility of using this method to obtain sharp laser front is also comfirmed by the recent experimental results.²⁰ Then, such a shaped laser pulse propagates through a gaseous density target and generates THz pulses via excitation of residual transverse currents as discussed previously.¹⁷ We demonstrate this scheme via numerical simulations. Results show that THz field strength can be significantly enhanced by one order of magnitude with the aid of the foil shutter. Influences of the foil density and laser polarization on the THz strength are also discussed.

To verify the THz generation process, we firstly carried out two-dimensional (2D) particle-in-cell (PIC) simulations using the relativistic fully electromagnetic code Virtual Laser Plasma Lab (VLPL).²¹ A sketch of the scheme is illustrated in Fig. 1. The simulation box has a size of 250λ₀ × 40λ₀ in the x − y plane, with a grid resolution of λ₀/100 × λ₀/20. Here, λ₀ = 0.8μm is the laser wavelength. A laser pulse propagates along x-direction from the left to the right of the simulation box and is noramlly incident onto the target. The laser field is linearly polarzied in z-direction, with a Gaussian temporal profile $a ( t ) = a 0 exp ( − t 2 / τ 0 2 )$⁠. Here, a₀ = 10 is the peak laser amplitude normalized by eE₀/m_ecω₀, with E₀ the laser electric field amplitude, ω₀ the laser angular frequency, e the elementary charge, m_e the electron mass, and c the light speed in vaccum. This amplitude corresponds to a peak intensity of I₀ ≃ 2 × 10²⁰ W/cm² (⁠$I 0 λ 0 2 =1.37×1 0 18 a 0 2$ Wμm²/cm²). The laser pulse duration τ₀ is about 11 fs full-width at half-maximum (FWHM). The laser pulse has a spot size of 10λ₀ FWHM in the transverse direction.

The target is composed of a nanometer-scale thin foil in the front of a low density gas target. The parameters for the thin foil are chosen closely to the experimental conditions.²⁰ It has a thickness of 4 nm with a peak density of 20n_c, where $n c = m e ω 0 2 /4π e 2 ∼1 0 21$ W/cm² is the critical plasma density. Considering the pre-expansion effect due to laser prepulse, an exponential density profile with a scale length of 50 nm is assumed in front of the foil. Such thin foil targets can be realized experimentally by use of free-standing ultra-thin diamond-like carbon (DLC) foils.²² The gas target has a density of 0.02n_c and is initially located between 60λ₀ ≤ x ≤ 300λ₀ in the x-direction. Supersonic gas jet nozzles capable of producing uniform gases (e.g., hydrogen, helium and nitrogen gases) with such density are commercially available.^23,24 Both targets are taken to be fully ionized plamas and the ions are set to be immobile. In the simulations, a moving window with a velocity of 0.6c in the x-direction is adopted.

Figure 2(a)) shows the on-axis waveform of the transmitted laser electric field E_z (red line) propagating in the gaseous plasma after passing through the foil. It is plotted versus x along the central line y = 0 at time t = 100T₀, where T₀ is the laser period. As a reference, we also plot the laser waveform in the case of without the foil target, as shown in the red line in Fig. 2(b). With the foil target, pulse steepening effect can be clearly seen. The laser pulse has an extremely sharp rising edge, reaching its maximum amplitude in about one optical cycle. In addition, the laser intensity is also enhanced to a peak amplitude of a₀ ≃ 16. This may be attribute to self-focusing effect through the foil target. While in the case of without the foil target, the lase pulse almost remains its initial symmetric Gaussian shape and the initial amplitude of a₀ ≃ 10. This comparison unambiguously demonstrates the thin foil indeed plays an important role in the laser shaping process, which acts as a fast optical “shutter” to chop the incident laser and generate the fast rising edge in the transmitted pulse, due to a sudden onset of relativistic transparency, the dynamic of which is discussed in Ref. [19].

The plasma density at the same time is depicted as the green lines in Fig. 2. In the areas corresponding to the laser pulse front, the peak density in the case of with the foil target is higher due to a larger laser ponderomotive force. But for both cases, the ponderomotive forces are not high enough to snow plough the electrons to form a high density peak. The plasma density remains underdense, which is not favorable to efficient local pump depletion and leading edge erosion, in contrast to the previously studied case where an overdense density spike is formed in front of the laser pulse.¹⁷ This also indicates the sharpened laser shape in Fig. 2(a) is formed mainly with the help of the foil shutter.

Now with the initial Gaussian temporal profile nearly transformed into a quasi-step function pulse, plasma electrons can gain net residual transverse momenta after interaction with the laser pulse, which can be seen from the transverse momentum that can be expressed as the integral of the transverse field:¹⁷ 

with η = t − x/c. For laser pulses with a step-function-like shape, the above integral can be nonzero, i.e., electrons acquire net momenta. As a consequence, net transverse currents are excited in the laser plasma wakefields. Therefore, THz emission can be expected. Figure 3(a) shows a snapshot of the THz field distribution in the x − y plane as it propagates in the vaccum area at time t = 500T₀. To see it more clearly, we present the line-out of the field along the central line y = 0 in the inset of Figure 3(a). It shows the peak electric field strength of the THz pulse reaches several GV/cm. We note that in our previous study where laser pulse self-evolving into a quasi-step function shape is considered, THz with field strength of ∼0.3 GV/cm is generated with a laser amplitude of a₀ = 30.¹⁷ In comparison, here with the help of the foil shutter, THz field strength is multi-GV/cm, i.e., increased by one order of magnitude, while a less intense laser pulse of a₀ = 10 is used. Figure 3(b) shows the Fourier spectra of the THz radiation for the two cases of with and without the foil targets, where a large (about 30-fold) enhancement of THz strength by using the foil shutter is also evident. These results demonstrate the advantage of the present scheme. In the previous single-stage process, laser sharpening is achieved via front etching by the high density spike in the front of the pulse. However, the density and lifetime of the electron peak are limited by multi-dimensional effects like transverse spreading. This drawback is overcomed here by shaping the laser front firstly by the foil shutter. Then the shaped laser pulses can efficiently generate THz emission through interaction with the gaseous plasmas.

Next we performed a series of simualitons to study the parametric dependence of the scheme using 1D simualitions for the sake of faster computation. The THz dependence on laser intensity a₀ and gaseous plasma density n_e has been discussed in the previous study, which shows the THz peak amplitude increases with increasing both a₀ and n_e.¹⁷ Here, we study the influence of the foil target on the THz emission. Figure 4(a) presents the THz spectra for the cases of different foil densities. It shows that THz can be generated for a large range of initial foil densities. With increasing the foil density, the THz pulse energy ∫E_ωdω firstly increases and then decreases. When the foil density is large enough, no THz emission can be observed. These results can be understood from the transmitted laser waveforms after passing through the foil, as shown in Fig. 4(b). For a small foil density, the laser sharpening effect is not evident. Consequently, the THz generation is not efficient. For a large foil density, the transmitted laser pulse has a sharply rising edge. However, more laser energy is lost at the same time due to reflection. When the foil is dense enough, nearly all the laser energy is reflected. Therefore, an optimal foil density exists for efficient THz generation. Radiation spectrum without out the foil is also shown in Fig. 4(a), which manifests itself due to the 1D effect, i.e., electron spike can be maintained in the front of the laser pulse that results in pulse front etching. Nevertheless, the enhancement of THz field strength by using the foil shutter is evident. Besides the amplitude, the spectra shift to higher frequencies with increasing the foil density. This is because the radiation frequency is related to the relativistic plasma frequency $ω p r e l = ( 4 π e 2 n e / γ m e ) 1 / 2$ as discussed before,¹⁷ where γ is the plasma Lorentz factor. With the increase of the foil density, γ is reduced due to less laser energy transmitted. Consequently, the central frequency increases.

Finally, we discuss the influence of laser polarization. Figure 4(c) shows the THz spectra for the cases of using linearly polarized laser (LPL) and circularly polarized laser (CPL) pulses. In contrast to the LPL case, no THz radiation is generated for the CPL case. From the waveforms of the reflected and transmitted laser pusles shown in Fig. 4(d), one can see that the transmitted pulse with sharp rising edge is efficiently generated for the LPL case, while only small laser energy can transmit through the foil target for the CPL case. This is because the transmission effect here is within the relativistic transparency regime.¹⁹ For CPL pulses, the laser ponderomotive force lacks a fast oscillation term, which makes the target heating effect far less efficient compared to the LPL case. As a result, the THz generation process is also less efficient for the CPL pulse case, since it is more difficult to reach the criterion for relativistic transparency.

In conclusion, we present a dual-stage sheme to enhance THz field strength generated from laser-driven plamsa wakefields. This is realized by employing a thin foil target in front of the gaseous plasmas as an optical shutter to shape the driving laser pulse prior to the THz conversion process. Sharp front laser pulse is produced via the mechanism of relativistic transparency. Compared to the case of without the foil shutter, THz field strength is notably enhanced by one order of magnitude, reaching multi-GV/cm while has less requirements of the laser amplitude. The feasibility of laser sharpening by using the thin foil shutter has been demonstrated in recent experiments. The required laser intensity is within reach of current and/or near future laser technologies. This study thus paves the way for high field THz generation in the multi-GV/cm regime. This unprecedented high field can lead to non-perturbative interaction with atoms (characteristic atomic electric field strength $E a t =e/4π ϵ 0 r B 2 ≈5.14$ GV/cm with r_B the Bohr radius of hydrogen atom and ϵ₀ the permittivity of free space), which is of high interest for various applications such as THz extreme nonlinear optics and coherent control of materials.

This work was supported by the Deutsche Forschungsgemeinschaft SFB TR 18 and by EU FP7 project EUCARD-2, and the Science and Technology Fund of the National Key Laboratory of Shock Wave and Detonation Physics (China) with project Nos. 077110 and 077160. Z.-Y. C. also acknowledges financial support from the China Scholarship Council (201404890001).