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Quantum Electronics

Phase conjugation upon SBS of a focused laser speckle beam

В. А. Богачев, Кочемасов Геннадий Григорьевич, Стариков Федор Алексеевич

Published Sep 30, 2008• 0 citations
Publisher

Abstract

The phase conjugation (PC) of a focused Gaussian laser beam with a partial spatial coherence of the wave front is studied numerically and theoretically upon SBS within the framework of a three-dimensional nonstationary SBS model, which takes into account transient processes and SBS saturation. The dependences of the PC coefficient h on the laser radiation power are obtained for different excesses of the angular divergence over the diffraction limit ξ . It is found that for the given reflectance of laser radiation from the SBS mirror, the PC coefficient monotonically decreases with increasing the divergence. For example, under the near threshold SBS conditions, h decreases from 70% to 30%, when ξ increases from 1 to 10. For the given divergence, the PC coefficient increases with increasing the reflectance and approaches the ideal one ( h > 90%) upon deep SBS saturation, when the reflectance exceeds 90%—95%.

DOI
10.1070/qe2008v038n09abeh013780

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The phase conjugation (PC) of a focused Gaussian laser beam with a partial spatial coherence of the wave front is studied numerically and theoretically upon SBS within the framework of a three-dimensional nonstationary SBS model, which takes into account transient processes and SBS saturation. The dependences of the PC coefficient h on the laser radiation power are obtained for different excesses of the angular divergence over the diffraction limit ξ . It is found that for the given reflectance of laser radiation from the SBS mirror, the PC coefficient monotonically decreases with increasing the divergence. For example, under the near threshold SBS conditions, h decreases from 70% to 30%, when ξ increases from 1 to 10. For the given divergence, the PC coefficient increases with increasing the reflectance and approaches the ideal one ( h > 90%) upon deep SBS saturation, when the reflectance exceeds 90%—95%.
To the best of our knowledge, a novel self-phase-conjugation technique for laser radiation is proposed, which is based on the self-filtration of the phase-conjugate component in a nonlinear absorbing medium, bleached by a pump wave with the intricate spatial structure in the region of location of its speckles. Similar to the stimulated Brillouin scattering (SBS) case, the mechanism of the phase-conjugate wave discrimination against the noise background is based on the coincidence of the speckles in the pump and conjugate waves throughout the bulk of the medium. To compensate for a drop in the signal power due to total absorption, the amplification in conventional laser gain cells is used. The feasibility of the phase conjugation with reflectivities from unity to tens of percent is demonstrated by analytical estimates and numerical calculations. The technique can find application in the middle and far IR spectral regions, where the implementation of phase conjugation via SBS is either hindered or impossible at all.
Phase conjugation (PC) processes at degenerate four-wave mixing (DFWM) in the active medium of a pulsed e-beam controlled discharge CO2-laser were studied both experimentally and theoretically. The experiment was carried out with the following parameters: laser gas mixture CO2:N2:He=1:2:4, gas pressure 0.3 bar, active medium length 1.2 m, resonator length 12 m (17.7 m for single line laser), interaction angle ~10 mrad at DFWM without optical delay between probe wave and co-propagating pump one. Integral PC reflectivity (PCR) strongly depends on such parameters as: specific input energy (Fig. 1); intensity ratio for probe J3 and co-propagating pump J1 wave (Fig.2); coherency of the laser radiation, that varied by rotation of mutual polarization or with optical delay between probe wave and co-propagating pump one; geometry of DFWM; output mirror reflectance Rout (8-80%) (PCR was maximum with Rout of 8% but best quality of PC signal was observed with Rout =80%); gas mixture composition and pressure, being maximum for a mixture with a low fraction of helium and at higher pressure (up to 0.6 bar). A periodical dependence of PCR on optical delay between probe and co-propagating pump wave with periods 10−3 and 10−5 m was observed. The PCR did not depend on spectral content and a degree of linear polarization of the laser radiation.
It is demonstrated theoretically and experimentally that, in four-wave phase conjugation of a spatially incoherent speckle signal, the reflection coefficient and the phase conjugation fidelity fall on increase in the rate of change of the spatial structure of the speckle beam. The law of decay of both these parameters is the same for media with an exponential grating erasure rate, but in the case of double-exponential relaxation the conjugated fraction of the signal decreases much more slowly than the reflection coefficient. Experimental results show that the standard model of deep trapping levels can describe the kinetics of formation of dynamic gratings in a nominally pure crystal of strontium barium niobate, but the presence of shallow trapping levels has to be taken into account for doped crystals.
An experimental investigation was made of phase conjugation under conditions of degenerate four-wave interaction of CO2 laser radiation in carbon tetrachloride as a function of various parameters of the signal radiation and of the experimental geometry. It was found that the conjugation accuracy for a single-mode signal beam with a divergence of 2 mrad was 87%, but when a phase plate introducing a divergence of 70 mrad was used, the accuracy was 77%. The reflection efficiency and the phase conjugation quality depended strongly on the ratio of the energy density of the signal wave to the energy density of the pump wave. An investigation was made of the dependence of the reflection coefficient on the angular mismatch between the counterpropagating pump waves and on the matching of the optical paths of the interacting waves.
Degenerate four-wave mixing (DFWM) and phase conjugation (PC) of pulsed CO2 laser radiation on transient gratings inside its own laser medium have been studied both experimentally and theoretically. The operational mode of the e-beam controlled discharge CO2 laser has been chosen in such a way (CO2:N2:He equals 1:2:4, p equals 0.28 atm, tin equals 30 microsecond(s) ) that the laser pulse length ((tau) out approximately 10 - 20 microsecond(s) ) is comparable with an effective relaxation time of the upper laser level ((tau) rel approximately 15 - 30 microsecond(s) ). The time-history of the CO2 laser and PC signal pulses, and PC reflectivity have been thoroughly investigated for different cavity Q factors and specific electrical energy inputs. It has been shown, that the formation of the PC signal under the intracavity DFWM on gain (amplitude) and thermal (phase) gratings is characterized by a complicated time history that reflects the main relaxation processes taking place inside the inverted medium. A feature of the transient PC process inside the laser active medium is the dependence of the effective relaxation time of the upper laser level on the intensity of pumping waves. PC reflectivity has been obtained by numerical calculations. A comparison of the theoretical and experimental data confirms the contribution of two different mechanisms of grating formation under DFWM inside the active medium of the CO2 laser.
A study of the influence of the spatial structure and statistics of the pump beams in the phase-conjugation process is made, showing that the reflectivity varies along the phase-conjugation mirror when the phase factor in the coupling equations that describe the process is not constant. The mutual coherence function of the generated field is calculated from the mutual reflectivity of the mirror for two commonly used statistics for the partially coherent pump beams. Finally, the influence of diffractional effects is also analyzed, showing that, in general, the fidelity of the process is degraded.