Simultaneous elliptically and radially polarized THz from one-color laser-induced plasma filament

THz-based technologies and research applications have seen a rapid increment in recent period together with the development of novel radiation sources based both on relativistic electrons and laser techniques. In this framework, laser-induced plasma filament plays an important role in generating intense and broadband THz radiation. Although many attentions have been paid to THz emission from two-color plasma filaments, one-color plasma emission has been scarcely investigated. In particular, the polarization state of one-color THz emission is still controversial due to the limitations of the existing THz detection techniques, which are incapable of simultaneously detecting elliptically and radially polarized THz radiation. In this manuscript, we develop a novel detection method and unambiguously demonstrate for the first time that one-color laser-induced plasma filament simultaneously emits elliptically and radially polarized THz radiation. These polarization states suggest that the generation mechanism results from electric quadrupole, showing a new route for producing more complex polarization states and THz vortex beams.


Introduction
Laser filamentation [1] has aroused a great interest, becoming a field of intense research activity, thanks to its multidisciplinary applications [2][3][4][5][6]. In particular, THz emission by laser filamentation is extremely competitive to other generation mechanisms [7,8]. Within the framework of filaments as secondary radiation sources, the mechanisms behind the emission of THz pulses attract many attentions due to its capability of generating energetic [9] and broadband [10,11] (corresponding to single-cycle level) THz radiation. These characteristics are of paramount importance for many applications, e.g. remote sensing [12,13], linear [11] and non-linear spectroscopy [14]. Moreover, owing to the plasma environment, the generation can be scaled upward with increasing pump laser intensity without the limitation determined by the medium breakdown [15] as in the case of THz generation by crystals [16]. Two main methodologies for THz emission by laser filamentation are known in literature: one-color and two-color emission. THz generation in two-color filament is ascribed to four-wave (FW) mixing and/or photocurrent [17][18][19][20][21][22][23]. The polarization of THz from two-color filament [24][25][26][27][28][29] and the effect of laser chirp on the yield of THz [30] radiation have been deeply investigated.
Compared with the intensive investigations on THz from two-color filament, reports on one-color THz emission are much fewer. On the other hand, the generation mechanisms of THz from one-color plasma are still under debate. The proposed ones are: FW mixing [31], ponderomotive charge separation [32], transition-Cherenkov radiation [33], quadrupoles [34,35] and so on. Enhancement of THz emission from one-color plasma has been achieved by biasing one-color plasma [36] and applying a double pump-beam [37]. The polarization of THz from one-color plasma [33,35,38,39] is controversial due to the lack of detection methodology capable of simultaneously detecting elliptically and radially polarized THz as stated in reference [39]. Thus, it is desirable to develop a novel detection methodology capable of simultaneously detecting elliptically and radially polarized THz to comprehensively characterize THz from one-color filament, which is the aim of this work.
In this manuscript, we develop a novel detection methodology capable of simultaneously detecting elliptically and radially polarized THz, which is based on electro-optic sampling (EOS) technique [40] and a spatial mask. This methodology allows us to simultaneously detect elliptically and radially polarized THz radiation for the first time, to our knowledge. The characteristics of these polarization states are described and their spatial distribution are discussed. Radially polarized THz radiation [41][42][43][44] finds applications in particle acceleration [45], spectroscopy [46] and THz waveguide [47]. Thus, the generation of this polarization state from one-color filament is very valuable for these applications. The results also shed light on the understanding of the THz generation mechanism in one-color plasma filament. Moreover, our experiments open the road for the production of more complex THz states like vector and vortex beams, which are poorly investigated in the THz spectral range.

Experimental setup
The experimental setup is schematically represented in figure 1. The beam, produced by a regenerative amplifier (Coherent Legend) delivering laser pulses with transform-limit duration of τ = 50 fs, central wavelength of λ 0 = 800 nm and repetition frequency of r.f. = 1 kHz, is split into a pump-line to generate THz and a probe-line to detect THz. The pump pulse is focused by a plano-convex lens with 200 mm focal length to generate the filament. The THz generated from the filament is collimated by an off-axis parabolic mirror (PM) with reflected focal length equal to 6 inches. A silicon wafer is required as a filter to clean the THz from the background radiation (fundamental signal and all the frequencies arising from the non-linear effects appearing during the filamentation process). A metallic mask with an open quadrant is applied onto the THz beam to spatially select a portion of it and then a THz polarizer selects the horizontal or vertical THz electric field component. It is noteworthy that the coincidence of the THz center and the mask center is critical to detect THz in the experiment. Hereby, we use the residual pump as a guide to overlap these centers since the center of THz is the same as that of the pump. To make the center of the residual pump beam overlap the center of the mask, we first center the residual pump beam on an iris and close the iris to its minimum, then we make the mask center coincide with the minimum beam.
Another hole-drilled PM with focal length of 2 inches focuses the THz on a 500 μm-thick 110-cut ZnTe required by the EOS diagnostic module. The intensity of the probe beam can be tuned by a combination of a polarizing beam splitter and a half-wave plate. A delay line is used to change the relative arrival time between the THz and the probe on the ZnTe crystals of the EOS module. A lens focuses the probe through the hole-drilled PM, allowing for the collinear propagation of both the THz and probe beam. It is important to remark that the THz focus spot on the ZnTe crystal is completely covered by the probe-beam one to assure an integrated detection of THz field over its spot size. After the ZnTe crystal, a lens collimates the probe beam through a quarter-wave plate and another lens focuses it again. A Wollaston prism splits the probe into two beams, which are sent to a balanced photodiode. The horizontally polarized pump pulse in the experiment has an energy of 5.7 mJ and FWHM (full width at half maximum) diameter of around 10 mm, creating a single filament with length of around 13 mm. The FWHM diameter of the filament is around 177 μm by measuring its fluorescence. To measure the horizontal and vertical THz field components, the probe polarization is kept horizontal while the 001 ZnTe crystal axis is varied: it is in the horizontal direction to measure the vertical THz component and it is rotated to the vertical direction to measure the horizontal THz component [40]. Inset of figure 1 shows the mask orientation and the direction definition. The horizontal and vertical field components are in the plane perpendicular to THz propagation axis. The horizontal field component is parallel to the experimental table surface (ZX plane) and the vertical field component is perpendicular to the experimental table surface. The mask can be open up (U), down (D), left (L) and right (R). Generally, in the EOS detection, 110-cut or 100-cut ZnTe (or GaP) crystals are respectively used to measure the transverse or longitudinal components of the field.

Elliptically polarized THz
We first measure the transverse (horizontal and vertical) electric field components of the THz beam when the spatial mask is not used. In figure 2, the three-dimensional trajectory of the THz field and its projection on the three different planes are shown. The behavior of THz electric field versus time in the  three-dimensional space directly demonstrates that the THz radiation is elliptically polarized. In particular, the red and blue projections in figure 2(a) are respectively the vertical and horizontal polarization components of the elliptically polarized THz beam. These components are directly compared in figure 2(b) in time and in frequency domain (see inset of figure 2(b)), showing that the waveforms of the horizontal and vertical polarization components have different shapes when exhibiting a prominent time shift between them. Moreover, the vertically polarized component is more intense than the horizontal one.

Radially polarized THz
It is worth noticing that for symmetry reason and in ideal conditions, when an elliptically polarized radiation is focused, it has a zero longitudinal component and a nonzero transverse component at the focus. The opposite happens for radially polarized radiation [48]. Therefore, in order to study the transverse electric field's properties of the emitted THz radiation, we applied a metallic mask on the beam. The mask has a circular shape and it acts as a beam blocker which only transmits through one quadrant over four (blocking the remaining portions of the beam), see figure 3. We therefore measure both the horizontal and vertical components of the field after the mask and for four different positions of the mask-opening obtained by rotating the mask around the propagation axis of the THz field. The transverse THz field measured in each quadrant is the sum of THz fields originating from both the elliptical and radial THz radiation. Figure 3 shows the result. The combination of the mask-opening and the THz polarizer's direction is shown on the right side of each panel. For the sake of simplicity, we define the following symbol to denote the electric fields measured for the different quadrants: where α = Hand V indicate respectively the horizontal and vertical polarization components; β = ellip, radandtot respectively denote the polarization state of the electric field (elliptical or radial) and the total field in one quadrant; γ = U, R, DandL shows the mask opening: up, right, down and left. These The THz field is supposed to be symmetric about the horizontal and vertical axes passing through the THz profile center for both the two different states of polarization [35,49].
Equations (2)- (5) show that the reference curves in figure 3 are only determined by the elliptically polarized THz radiation. Figures 3(a) and (b) figure 4, and which can be deduced from symmetry reasoning: the elliptically polarized THz is the only origin of the reference curves. Thus, the discrepancies observed in figures 3(c)-(f) can only be ascribed to the contribution of the radially polarized THz to the total field represented by the red curves.
In summary, the reference curves in figure 3 are only related to contribution of the elliptical polarization state of the THz radiation, whereas the red curves result from the contributions of both the elliptical and radial polarization states. The good overlaps shown in figures 3(a), (b), (g) and (h) reveal that E H Rad,U , E H Rad,D , Moreover, the fact that blue and red curves have the same waveform shape as the reference curve in figures 4(b) and (d) experimentally verifies that the elliptically polarized THz field is the only origin of the reference curves in figure 3. Another characteristic of figures 4(b) and (d) is that the sums of both the horizontal and vertical THz fields in the upper and lower quadrants are bigger than their counterparts in the left and right quadrants. This amplitude difference is addressed to a non-homogeneous spatial distribution of the THz radiation.
Exploiting the characteristics of E α β,γ shown in    figure 6 shows these results in time domain while the inset in the frequency domain. It can be seen that the waveforms of radial THz in the horizontal and vertical directions are in phase and have the same waveform but with different amplitudes. Moreover, the amplitude of the radial THz in vertical direction is stronger than that in the horizontal direction, which is consistent with the reported quadrupole-type THz radiation pattern [49,50], suggesting that THz from one-color filament may result from quadrupole. The different intensities of the radially polarized THz in the horizontal and vertical directions are determined by the polarization of the pump laser. In order to check the relation between the pump polarization and the intensities of the radially polarized THz in the horizontal and vertical directions, we measured the intensities of the radially polarized THz in the horizontal and vertical directions as a function of the pump polarization. It was found that the strongest intensity of the radially polarized THz in the horizontal direction appears near to the vertical pump polarization. Whereas, the strongest in the vertical direction appears near to the horizontal pump polarization. It is noteworthy that the radial THz in the horizontal and vertical directions are in phase and have the same waveform shape, whereas the horizontal and vertical THz fields of elliptically polarized THz are out of phase and have different waveform shapes as shown in figure 2(b).

Conclusion
In this manuscript, we demonstrate that one-color laser-induced filament simultaneously radiates elliptically and radially polarized THz radiation. We measured the horizontal and vertical components of the elliptically polarized field and extracted the fields of the radially polarized THz radiation through a metallic opaque mask. The results of this paper shade light on THz generation mechanism from one-color filament, indicating that the main generation mechanism is related to quadrupole formation, and suggest that more complex vortex THz beams could be realized in plasma starting from structured pump-laser. The radially polarized (and vortex) THz radiation can be used in spectroscopic applications on exotic quantum matter.