Filamentation of IR and UV femtosecond laser pulses and ionization of gases under their action

Filamentation of IR and UV femtosecond laser pulses and ionization of gases under their action

The issue of the amplification of ultrashort UV laser pulses in electron-beam KrF amplifiers proved inseparably associated with processes of the nonlinear propagation of high-power (up to 1015 W) laser pulses in the atmosphere, gases and pass-through (transparent) optical elements. Conducted experiments have demonstrated the existence of a nonlinear absorption relative to low-intensity UV radiation. Studies of the multi-photon ionization of pure gases (argon and nitrogen) have shown that  an increase of UV laser radiation intensity (greater than 1012 W/cm2) leads to an increase of the number of photons taking part in the process from three to four. Such a change is, apparently, due to a change of the ionization process itself. Thus, at small intensities (from ~3×1010 to 2×1011 W/cm2) higher electronic states are excited by three quanta, then there occurs the one-quantum ionization. At an increase of intensity as the result of the dynamic Stark effect there occurs a shift of higher levels, and they “move” out of the 3-quantum resonance. As the result, a non-resonance 4-quantum ionization occurs. Localization of laser radiation at the propagation of ultrashort pulses in transparent media with peak powers exceeding the critical power is called filamentation; it occurs in the dynamic balance of Kerr self-focusing and  plasma-defocusing of the light beam. Radiation propagating in the nonlinear regime is self-focused and, because of high field intensity, forms an extended plasma channel with a sufficiently high concentration of electrons. These plasma channels are of interest for a broad range of applications.
We demonstrated, using the method of time-resolved optical microscopy, the existence of a single or multiple short (up to 100 μm) and narrow (up to 5 μm in diameter) mini-filament(s) in the air of strongly focused ultrashort laser pulses in the IR range of the spectrum. The length of the emerging luminous plasma channels exceeded the corresponding focal waist.  Plasma density assessed by various methods proved to be rather high (up to 1018 cm–3). The possibility of the existence of such mini-filaments had been earlier doubted by leading experts in this field, because experimental measurements at mild focusing of ultrashort UV pulses yielded much greater lengths and diameters of the filaments (up to several tens of metres and hundreds of micrometres, respectively). Theoretical numerical calculations for such conditions were carried out at the Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences. The results of numerical modelling confirmed the existence of mini-filaments of ultrashort UV pulses, and also gave a systematic description of the fundamental mechanisms of mini-filament formation at the tight focusing of UV ultrashort pulses and their basic dimensional and energy parameters (maximal intensity and density of plasma in a filament).
A number of works were carried out at the Laboratory to study possible applications of mini-filaments. Thus, experiments on the generation of the third harmonic in air mini-filaments were performed. In particular, the maximal efficiency of the conversion of a strongly focused IR ultrashort pulses into a radiation of UV ultrashort pulses (third harmonic) was shown to reach 0.16%. A very tight focusing (numerical apertures of the focusing optics, up to 0.65) of laser pulses was used to develop an innovative technology for microscale bulk marking of natural diamonds (by recording graphite channels; the work was carried out jointly with the Kristall Production Association, Smolensk) and an import-substituting medical technology of volume microperforation of eye tissues for micro-surgery vision correction issues (cornea) and virtually non-invasive removal of malignant tumours on the sclera (the work was carried out jointly with the Institution of the Russian Academy of Sciences Central Clinical Hospital of the Russian Academy of Sciences). It should be noted that the development of working technologies of micromarking and eye microsurgery were preceded by fundamental studies to elucidate the physical mechanisms of microdamages in materials, features and parameters of microfilamentation in transparent media.
In some cases, the indefiniteness of the starting position and total length of a plasma channel formed in filamentation of laser radiation become a significant problem in the delivery of high-intensity radiation to the receiver or the target. These characteristics of the filament depend on the optical properties of the medium and on the parameters of radiation (wavelength, pulse duration, beam size etc.). The most widespread method of localizing laser radiation is the focusing, at which a plasma formation emerges near the geometric waist of the focusing system.
Another method of controlling the position and length of the plasma channel is to spatially modulate the amplitude of the field by applying aperture diaphragms on the light beam forming it. In this way, the distribution of intensity in the cross-section of the beam sharply changes, which leads to the emergence of additional field amplitude maxima owing to the diffraction and local self-focusing of radiation. The LGL investigated the effect of triangular, circular and segmented diaphragms on the initiation of formation, extent and transverse size of the filament. 
The change of phase of incident radiation can also affect the filament position and length. The wavefront of the phase was controlled using an adaptive mirror and a wavefront sensor at two wavelengths, in UV and IR regions. The adaptive mirror has a number of advantages over the pass optics; for instance, by making it possible to avoid phase self-modulation and self-focusing in optical materials. For IR and UV radiations, an increase of the amplitude of additionally introduced aberrations led to significantly increase the length of the plasma channel. Numerical modelling of the experiment led to similar results.
Use of the self-focusing of the light beam has traditionally solved the problem of increasing the radiation intensity in a given volume of the medium, which enables achieving extreme values of intensity close by the order of magnitude to the intra-atomic value when using ultrashort laser radiation; however, the main obstacle in focusing this radiation and increasing the intensity in atmospheric air is plasma formation. Its negative effect on the focusing of laser radiation can be reduced by decreasing pressure. Studies of laser radiation intensity increase based on numerical modelling and experimental data have found that during the filamentation in rarefied air the rate of plasma formation decreases, which reduces the concentration of free electrons in the medium, decreases the blocking effect of plasma on the rise of intensity of the beam at its rigid focusing and makes it possible to achieve higher values of intensity in the region of the focal waist.

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