{'fraction_non_alphanumeric': 0.022083704363312556, 'fraction_numerical': 0.013357079252003561, 'mean_word_length': 4.672727272727273, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Frequency-angular distribution for terahertz emission of single-color laser filament plasma under electrostatic field

Frequency-angular distributions for THz emission in the range of 0.1 - 3 THz generated in a single-color laser filament plasma situated both under and without electrostatic field are for the first time experimentally studied. The angular distribution for various spectral components of this THz emission is demonstrated to differ significantly. The maximal propagation angles for these components grow up under the electric field, the angular distribution for the low-frequency THz emission depending significantly on the laser pulse energy in contrast to the case of no electric field. An increase in the laser pulse energy leads to a decrease of the propagation angles for low-frequency THz emission and to disappearance of the local minimum in the angular distribution on the propagation axis.

Terahertz emission within the range of 0.1 -10 THz 1,2 is quite promising for various applications in biology 3,4 , diagnostics of drugs and microchips 5 , in security systems 6 , medicine 7 , in the study of art objects 8,9 and other fields. Many books and reviews are devoted to generation of THz emission and its applications (see, for example, Refs. 10 and 11). One of the THz emission sources is air plasma formed during filamentation of ultrashort laser pulses 12 . This method of producing THz emission is attractive and may be used to build a laboratory broadband THz source based on a commercial femtosecond laser. THz emission formed by a single-color laser filament plasma was demonstrated in Refs. 13 and 14 to propagate forward into a cone with a minimum on the optical axis (a hollow cone). There was demonstrated in Refs. 15 and 16 that, if the filament plasma was placed under an external electrostatic field, the THz signal amplitude increased considerably and the angular distribution changed to a cone entirely filled by THz emission with a maximum on the axis. However, to the best of our knowledge, the angular distribution of THz spectrum for the laser filament plasma has never been presented including Refs. 15 and 16. The object of our paper is experimental study of THz emission angular distribution within the millimeter and submillimeter spectral range of 0.1 -3 THz for different spectral components generated in plasma channel of a single-color laser filament both under the external electrostatic field and in its absence.
In the experiments we use 100 fs pulses of Ti:Sa laser system with the central wavelength of 740 nm. The laser beam diameter is 3 mm (FW1/eM). Laser pulse energy reaches 3 mJ and can be varied by diffractive attenuators. Laser pulses are focused by a lens with the focal distance of 30 cm, so that the geometric focus coincides with the back edge of the flat electrodes ( Fig. 1a) to ensure for the plasma channel position to be just within the interelectrode gap. The electrodes length along the propagation axis and the interelectrode gap is 15 mm and 5 mm, respectively, the applied voltage being up to several kilovolts. Figure    we obtain an entirely filled cone of THz emission (empty circles in Fig.2b), that is also in good agreement with the previously observed results in Refs. 15 and 16.
An increase in the laser pulse energy leads to an elongation of the laser filament plasma channel and a slight growth of the linear plasma density, which practically does not affect the total angular distribution of the wide-frequency THz radiation 14 . Fig. 3a  In the presence of the external electric field, the energy of the laser pulse significantly influences the THz emission angular distribution in the low-frequency region (Fig. 3c). In the experiments, while the energy increases from 0.5 mJ to 3 mJ, the maximal propagation angles go down from 50 to 30 degrees. In case of relatively low energy, we observe a clear hollow cone with a pronounced dip on the axis. An increase in laser pulse energy leads to the dip decrease down to the complete absence of a local minimum. Also, the detected THz signal rises by almost two orders of magnitude at the same strength of the electric field. In the high-frequency spectral region (Fig. 3d), with a growth of the laser pulse energy, the type of the distribution shape remains practically unchanged, but, in contrast to the case of no field, the amplitude of THz signals increases.
In conclusion, we for the first time experimentally studied the frequency-angular distribution 5 of THz radiation generated in a single-color laser filament plasma both without and under the external electrostatic field. It is shown that without the electric field the angular distribution of various THz spectral components differs significantly. While for the low-frequency components of 0.1 THz, a 'classical' conical distribution of the THz emission with a minimum on the axis is observed, the high-frequency components of 0.3 -1 THz propagate into a narrower cone, which has practically no minimum on the axis. The high-frequency THz components propagate within the narrower cone, the angle of which does not depend on the laser pulse energy. When the external electric field is applied, the maximal propagation angles for THz spectral components grow up.
Unlike the case of no electric field, the angular distribution of the low-frequency THz emission depends significantly on the laser pulse energy. The laser pulse energy growth leads to a decrease of the propagation angles for low-frequency THz components and to disappearance of the local minimum in the angular distribution on the propagation axis.