1. Introduction

Terahertz pulse generation via two-color laser filaments has become more and more popular in the last decade. This can be easily understood as it is one of the most powerful table-top sources with energy per pulse reaching the micro joule level [1,2]. Such powerful sources have already been successfully used in nonlinear THz experiments [3,4]. The advantage of this source is not solely based on its output power. For example, in a recent report we have demonstrated the possibility to optimize the output pulse duration via direct control on the electron density distribution, which consequently allowed to tune the central frequency of the broadband emitted pulse [5]. Also interestingly, it has been demonstrated recently that the polarization of the emitted THz radiation can be controlled through the trajectory of the new born electrons within the two-color plasma field [6,7]. Both reports demonstrate the possibility to achieve a full (2π) rotation of the THz pulse polarization while keeping the amplitude of the THz pulses constant. This interesting result was achieved via the direct control on the phase between the ω and 2ω laser field either through the positioning of the frequency doubling crystal (β-BBO) along the laser propagation axis z [6] or using an accurate attosecond phase controller [7]. This finding considerably remodels the conception of the THz generation through two-color plasma filament which was interpreted to be the result of a microscopic 1dimensional (1D) photocurrent model or a four wave mixing process within the plasma filament. According to [7], the rotation of the THz polarization is only possible when at least one of the laser fields is elliptically polarized. In a classic arrangement like in [6], where there is no possibility to play on each laser beam polarization, the ellipticity is gained by the fundamental laser beam within the frequency doubling crystal. Furthermore, a recent report demonstrates an alternative way to vary the relative phase between the ω and 2ω field, and thus controlling THz polarization, by playing with the respective delay of two orthogonal filaments [8].

Based on the results of the above studies one could expect to achieve similar THz polarization control when changing the two-color filament medium gas pressure. The change of pressure will induce a wavelength dependent change of the refractive index, which in turn will affect the phase of the synthesized laser field and consequently offer coherent control on the emitted THz pulse polarization. In the past, some studies have been performed exploring the effect that different gas species, at various pressures, have on the THz emission [1,9–11]. Though, till now no one has studied in detail the possible control this can offer on the THz polarization properties.

In this letter, we demonstrate the direct control the THz pulse polarization through accurate control of the surrounding gas pressure of a two-color plasma filament at relatively low input laser energy. Furthermore, and for the first time to our knowledge, we report the measurement of a circularly polarized THz light from Xenon gas. This result is of major importance for spectroscopic applications and THz applications in biology.

2. Experiment

For the experiments reported here, we used an amplified kHz Ti:Sa laser system delivering 35 fs pulses at 800 nm central wavelength and maximum energy of 2.3 mJ per pulse, with Gaussian profile and a full width half maximum (FWHM) diameter of 6.6 mm. The laser beam is focused within a gas cell using a 200 mm positive lens. A type-I β-BBO crystal (100 μm thick) is housed within the pressure chamber in order to partially double in frequency the fundamental laser pulse and form a dual-color plasma filament. Its front window is made of a fused silica plate of 2 mm thickness; the rear window consists of a 3mm thick polyethylene (measured cut-off frequency at 20 THz). The emitted THz radiation is collected and refocused onto a broadband (0.1 to 30 THz) thermal pyroelectric detector, with a pair of parabolic mirrors through non purged air. An extra silicon wafer with 1 mm thickness was placed between the two parabolas to cut the small fraction of remaining optical light. A broadband THz polarizer is used to conduct the polarization analysis with constant degree of polarization (>99.5%) over the whole frequency range under study (0.1-20 THz).

3. Results and discussion

With the above described experimental arrangement we performed a systematic study for nitrogen over a pressure range spanning from 10 mbar to 1 bar and for input laser energy of 240 μJ. At this level of laser energy, the plasma string remains relatively short and the phase walk-off occurring in the plasma channel can be neglected. The results are presented in Fig. 1 .

 

Fig. 1 Detected THz power as function of nitrogen gas pressure (Dots and black curve) and THz pulse polarization states at different pressure levels. The upper axis (blue colored) represents the calculated phase variation.

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First, one can notice that the emission of THz pulses can be divided in two distinct regimes. There is a first regime for pressures below 100 mbar where the THz emission increases linearly with the air density. In this low pressure regime, as it was already reported in [9], the gas medium is fully ionized while the degree of plasma defocusing is relatively low. On the other hand, at gas pressures higher than 100 mbar, the plasma defocusing becomes dominant [9] and the total emission of THz is relatively constant over the whole pressure range. At the same time and more importantly, the polarization measurements of the emitted THz pulse shows a π/2 polarization rotation over 650 mbar of the gas medium pressure with quasi constant THz power and linear pulse polarization. As mentioned above the change of the surrounding gas pressure systematically leads to a change of the relative dispersion between the two laser fields. In turn, this change in refractive index leads to a change in the relative phase between the ω and 2ω, $\mathrm{\Delta }\text{φ = ω d}\cdot {\text{(n}}_{\text{ω}}{\text{-n}}_{\text{2ω}}\text{)/c}$. One can accurately predict the change in the dispersion using the pressure dependent Sellmeier equation [12]:

The Sellmeier coefficients used for the calculations can be found in Ref [13]. Knowing the phase variation induced by the pressure change, we related it with the state of polarization of the THz pulse at different pressures. As one can see from Fig. 1, the estimated phase variation (blue figures) is in good agreement with the rotation angle of the THz pulse. Furthermore, one could expect that the phase variation varies with the gas species, and consequently expect a bigger phase variation over the same pressure range as the atomic number of the gas increases.

For the experiment described above the emitted THz power was relatively low since the filament plasma string was short. To obtain higher THz powers one needs to create longer filaments and this can be done by increasing the input laser energy. In Fig. 2(a) , we present the yielded THz power as a function of the gas pressure for different input laser pulse energies. One can clearly see that as the input laser pulse energy is increased, which automatically leads to a longer filamentary structure, an oscillatory behavior is becoming more prominent. This experimental observation let us presume that the nature of the oscillatory behavior is directly linked with the plasma length and consequently as it was reported in [14], with the appearance of Maker fringes due to the phase walk-off in the extended plasma filament. In addition, when the THz power exhibits oscillatory behavior we systematically observed that the polarization rotates unpredictably and not in accordance with the estimated relative phase difference variation as in the case of low laser energy power. We interpret this phenomenon as a result of the destructive interferences occurring along the plasma string between the different THz emission points. Another consequence of the plasma length extension is the appearance of ellipticity in the polarization of the emitted THz pulses. Ellipticity has already been observed in [15] and will be discussed at the end of this paper.

 

Fig. 2 (a) Detected THz power as function of nitrogen gas pressure for various laser input energies. (b) Detected THz power as function of nitrogen gas pressure for various BBO tilting angles. For these measurements the BBO crystal is moved from the focusing point, in order to resolve one full oscillation. (c) CCD pictures of plasma fluorescence for a BBO tilt angle of 7 degrees and a non-tilted BBO crystal (pictures were taken with identical scales and camera exposure). (d) On-axis fluorescence intensity profile for a BBO tilt angle of 7 degrees and a non-tilted BBO crystal.

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The oscillatory feature appears to be also dependent on the tilt of the BBO crystal as one can see in Fig. 2(b). A similar observation was reported in [6] and was attributed to the variation in the 800 nm beam ellipticity as the birefringent BBO crystal is tilted. We propose here a different explanation of the effect, which is related to the length of the filament and not on the increased ellipticity, which we measured and found it to be negligible. In our experiments measurements were made for different tilt angles of the BBO crystal, recording at the same time the THz emission, as well as CCD pictures of the filaments’ plasma fluorescence. Figure 2(c) shows the plasma fluorescence for the case of 7 degrees tilt of the crystal compared to the non tilted one. As the on-axis intensity profiles of the CCD pictures attest (Fig. 2(d)), the fluorescence of the plasma string formed after tilting the BBO crystal is twice shorter (7 mm vs. 14 mm). This shortening is the result of the smaller amount of second harmonic when the BBO is tilted. Actually, the presence of the second harmonic increases the total length of the filament as we have seen also performing numerical simulations of the nonlinear propagation of the two-color beam. A detailed study of this phenomenon will be presented elsewhere. Thus, practically, as the tilt reduces the length of the plasma channel it provides an easy way to obtain a rotation of the THz pulse polarization with quasi constant and relatively high THz power.

Furthermore, in order to fully relate the oscillatory behavior of the THz output with the length of the plasma string, we conducted a pressure study with a non tilted BBO crystal for different rare gases. First, as one can see in Fig. 3 , the number of oscillations, over the same pressure range, increases for gases exhibiting higher atomic dispersion. Experimentally, we observed that the plasma formed within helium gas, which shows no oscillatory behavior, was the shortest of all the filaments formed in the other gases. We also observed that for high input laser pulse energy, it is not possible to avoid this oscillatory behavior with gases having a low ionization potential, such as Krypton (14 eV) and Xenon (12.13 eV) as shown in Fig. 3. Even the BBO tilting approach described above is not enough to circumvent the oscillations for Krypton and Xenon gases. For such gases, the saturation intensities within the filament are much lower than for gases with higher ionization potential (e.g. N₂ (15.58 eV) or Ar (15.76 eV), He (24.58 eV)) and the excess of input laser energy leads to an extension of the plasma length as was shown with numerical simulations in [16]. Consequently the effect of phase walk-off cannot be avoided for extended plasma length, whereas it does not exist for very short filamentary structures.

 

Fig. 3 THz power emitted from a double color filament produced in different gas mediums (He, N₂, Ar, Kr, Xe) and at pressures ranging from 10 mbar up to 1 Atm (1013 mbar).

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The disadvantage linked to extended plasma length for the control of the THz pulse polarization rotation can be useful to generate other polarization states than purely linear. As mentioned above, the increase of the input laser energy leads to the appearance of ellipticity on the polarization of the THz pulses. This has already been reported in the literature [15] and was also attributed to an extension of the filament length due to higher input laser pulse energy. The same group demonstrated that a filament can act as a polarization separator for a co-propagating beam [17]. Consequently as the plasma is getting elongated for higher laser pulse energies, the local THz radiation generated along the filament will experience a stronger birefringence, which in turn results to an increased THz ellipticity.

Triggered by this experimental evidence, we investigated the effect induced by the pressure variation for a gas producing longer filamentary structures. Hence, a systematic study of the THz generation in Xenon over one bar of pressure range was performed and the THz polarization state at various pressure levels was analyzed. The results are presented in Fig. 4(a) . As expected, the polarization of the THz pulse is rotating as the pressure of the gas medium is changing. The rotation is much more important than in nitrogen over the same range of pressure, which is due to the bigger atomic dispersion of the xenon gas. Beyond the rotation of the THz pulses polarization, we have been able to obtain elliptically polarized THz pulses at different states and up to fully circular polarized THz pulses, as one can also see in Fig. 4(a). We interpret this interesting result as the result of two joint effects occurring on the plasma filament. It is well known in the literature that the filament radius decreases with an increase of the surrounding gas pressure, see for instance [18]. Also, the length of the filament is known to extend as the gas pressure increases [19].

 

Fig. 4 (a) Detected THz power as function of xenon gas pressure and THz pulse polarization states at different pressure levels of Xenon gas and (b) the linear polarization (red curve) state of THz pulse at low pressure compared to the circular polarized THz (black curve) as recorded at 880 mbar.

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The decrease of the filament radius inevitably leads to a decrease of the generated THz power as one can see in Fig. 4(a). In parallel to the decrease of the main THz component, an increase of the orthogonal THz component is observed until it reaches values equivalent to the main component and results to a circularly polarized THz pulse (Fig. 4(b)). This can be related to the increasing birefringence induced by the extended filament. The combination of both effects induces more and more ellipticity in the polarization of the THz beam up to the point where the polarization becomes fully circular.

5. Conclusions

In conclusion, we have demonstrated experimentally the possibility to control the polarization of THz pulses emitted from two color filaments in gases. We also reported a way to circumvent the disadvantage caused by the phase walk-off between the two laser fields within an extended plasma string. Finally, we have shown the possibility to obtain circularly polarized THz pulses using longer plasma filaments. The later is an elegant and easy way for producing circularly polarized THz light, opening new opportunities in THz TDS.