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Journal of the Optical Society of America B

Anisotropic properties of pulsed four-wave mixing in Cr^4+:YAG saturable absorbers

A. Brignon

Published Oct 1, 1996• 27 citations
Publisher

Abstract

A model of degenerate four-wave mixing (DFWM) in Cr4+:YAG saturable absorbers is given in the transient regime. Because of the presence of absorbing dipoles oriented along specific directions, the DFWM process exhibits an anisotropic behavior. The effects of pump beam fluences, relative polarization of the beams, crystal orientation, absorbance, excited-state absorption, and nonresonant losses are analyzed. The theoretical results are supported by DFWM experiments in Cr4+:YAG performed at 1.06 µm with nanosecond pulses.

DOI
10.1364/josab.13.002154

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IEEE Journal of Quantum Electronics•Jan 1, 1994•29 citations
A model of degenerate four-wave mixing (DFWM) in Cr4+:YAG saturable absorbers is given in the transient regime. Because of the presence of absorbing dipoles oriented along specific directions, the DFWM process exhibits an anisotropic behavior. The effects of pump beam fluences, relative polarization of the beams, crystal orientation, absorbance, excited-state absorption, and nonresonant losses are analyzed. The theoretical results are supported by DFWM experiments in Cr4+:YAG performed at 1.06 µm with nanosecond pulses.
Degenerate four-wave mixing (DFWM) interaction in saturable media has received considerable attention because of its potential for application to optical phase conjugation and correction of phase distortions through aberrating media. For this purpose, saturable solid-state materials, operating at the classical wavelength of neodymium lasers near λ0 = 1.06 μm, are of great interest. Here, we present DFWM in a tetravalent chromium-doped gadolinium-scandium-gallium-garnet (Cr4+:GSGG) crystal. Indeed, tetravalent chromium (Cr4+) doped crystals were recently shown to be effective solid-state saturable absorbers for neodymium lasers.1,2 Furthermore, in comparison with traditional saturable absorbers such as dyes in solution, polymeric films, and color-center materials, these crystals exhibit chemical stability, high optical damage threshold, compactness, and would enable operation at high repetition rates.
Phase conjugation in a Cr(4+):YAG saturable absorber by degenerate four-wave mixing with nanosecond pulses at lambda = 1.06 mu m is demonstrated for the first time to our knowledge. An experimental phase-conjugate energy ref lectivity of ~2% and an overall eff iciency of ~0.4% are achieved. Because of the presence of absorbing dipoles oriented along specif ic directions, it is shown that the phase-conjugated beam can be made orthogonally polarized relative to the signal beam or to both pump beams with almost no reduction of the energy reflectivity.
The transient behavior of degenerate four-wave mixing (DFWM) in a three-level saturable absorber is analyzed and verified experimentally. A sharp peak of phase-conjugated reflectivity is predicted and observed at high pump intensities for pulsed beams. The influence of the time-dependent behavior of the conjugate wave signal on results of pulsed-beam experiments is studied. It is shown that transient effects could account for discrepancies between previous experimental results and steady-state theory.
A mathematical model describing the dynamic emission of intracavity polarized isotropic Cr 4+ :YAG solid--state saturable absorber was developed.This model considers double pumping laser pulses to simulate the actions of Cr 4+ :YAG as a dual Q-switched crystal (1.06 µm) and lasing medium (1.4 µm).The model describes the time evolution of interaction between the pumping laser pulse, partial polarizer and the polarized saturable absorber.The analysis of the polarization process is based on the assumption that at each moment of lasing evolution, the state of polarization represented by an eigenstate corresponds to the lowest radiation losses state.The model offers a simple mechanism for studying the kinetics of the pulsed lasers and the influence of the variations of the pumping laser power and nonlinear anisotropy parameter on the characteristics of the output laser pulses 1.06 µm and 1.4 µm.The angular rotation of the passive switch Cr 4+ :YAG reveals that the transmission of the polarized 1.06 µm laser radiation is strongly anisotropic in the saturation regime.The suggested model estimates the transmission of pumping laser density of the polarized light 1.06 µm radiation as a function of nonlinear anisotropy parameter, temporal behavior of the relative population inversion of Nd-laser, population inversion of the different polarized levels of Cr 4+ :YAG pulsed laser and the output laser pulse densities under impact of different values of the nonlinear anisotropy which is due to the self-induced anisotropy of its saturated absorption.
We describe a theory of four-wave mixing in the saturable absorber Cr4+:YAG{\mathrm{Cr}}^{4+}:\mathrm{Y}\mathrm{A}\mathrm{G}Cr4+:YAG and compare with experiments performed at 1.064 \ensuremath{\mu}m wavelength. We show that the strong polarization dependence of the saturable absorption along orthogonal crystallographic axes leads to unique polarization properties for wave mixing in Cr4+:YAG{\mathrm{Cr}}^{4+}:\mathrm{Y}\mathrm{A}\mathrm{G}Cr4+:YAG. Also there are a range of conditions that lead to vector phase conjugation of the polarization state of a signal beam. Optimum reflectivity for vector phase conjugation occurs when the pump beams have either orthogonal circular polarizations or parallel linear polarizations at 45\ifmmode^\circ\else\textdegree\fi{} to the crystallographic axes. The latter case is unique to this type of nonlinearity.
Degenerate four-wave mixing with orthogonally polarized pump beams at /spl lambda/=1.06 /spl mu/m in the saturable gain of a flash-lamp-pumped Nd:YAG amplifier is investigated, both experimentally and theoretically, using pulses of duration much less than the population relaxation time. We introduce a new set of coupled-wave equations in this short pulse regime that includes the effect of the four interacting waves and the laser gain experienced by all the beams. The dependence of the efficiency of the process on the small-intensity-gain-length product, beam ratios, and fluences is analyzed. A reflectivity of a weak probe beam of 25 percent and a transmission-gain-grating diffraction efficiency of 32 percent are achieved. Finally, the temporal shape of the conjugate signal is studied for various gain-saturation regimes.>