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IEEE Journal of Quantum Electronics

Transient analysis of degenerate four-wave mixing with orthogonally polarized pump beams in a saturable Nd:YAG amplifier

A. Brignon, Jean‐Pierre Huignard

Published Jan 1, 1994• 29 citations
Publisher

Abstract

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.>

DOI
10.1109/3.309884

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Effect of pump beam propagation on transient degenerate four-wave mixing in saturable Nd:YAG amplifiers

A. Brignon, Jean‐Pierre Huignard

Phase distortion correction of an optical wave propagating in laser media is a crucial problem to be taken into account in most of laser systems. For this purpose, phase conjugation through stimulated Brillouin scattering using the master oscillator-power amplification configuration has shown a very good potential to obtain high beam quality in solid-state lasers that operate at variable repetition rates. Another attractive alternative to generate the phase-conjugate wavefronts is to use a four-wave mixing (DFWM) process in the laser amplifier. In this medium, the interference between the interacting beams leads to a spatial modulation of the complex susceptibility of the medium by gain saturation (amplitude gain grating). This all-solid-state solution presents the advantage of suppressing the external nonlinear medium and would realize the required functions in the laser medium itself. Moreover, due to the amplification experienced by all the interacting beams, associated to the resonant nonlinearity of the gain saturation, high reflectivities already have been achieved in Nd:YAG amplifiers using a multipass geometry.1,2

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 1, 1994•0 citations
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.>
A transient model of degenerate four-wave mixing in saturable amplifiers is developed for calculation of the phase-conjugate reflectivity in the weak-probe-beam limit. Our model takes into account the laser amplification of all the interacting beams together with the wave-mixing process between the two counterpropagating pump waves. Experimental investigations are made in a flash-lamp-pumped Nd:YAG amplifier with nanosecond pulses at 1.06 microm. A reflectivity of 22% is achieved when all the waves interfere within the laser medium.
Two-wave mixing at λ = 1.06 μm in the saturable gain of a flash-lamp-pumped Nd:YAG amplifier was investigated, both experimentally and theoretically, by development of a transient analysis. Despite the local response of the inverted medium, it is shown that energy redistribution can occur, thus leading to the depletion of a low-intensity signal beam. Finally we measured a diffraction efficiency of 20% of the transmission-gain grating by diffracting a probe beam at λ = 1.06 μm under the Bragg condition.
The process of saturable-gain four-wave mixing (DFWM) in a diode-pumped Nd:YVO4 amplifier with interacting beams provided by a Nd:YAG oscillator is investigated. Multipass geometries are employed that arrange for the signal beam to experience an increased interaction length relative to that of the pump beams. DFWM reflectivities up to R = 170% and a diffraction efficiency η = 6% of the volume population hologram written in the Nd:YVO4 amplifier are obtained experimentally. A theoretical analysis of multipass DFWM is presented in the transient (pulsed) regime, including the laser amplification and the mutual interaction of all the interacting beams as well as the spectral mismatch between the beam frequency and the gain line-center frequency of the Nd:YVO4 amplifier. It is shown that because of the close spectral matchup of the Nd:YAG oscillator and the Nd:YVO4 amplifier, the amplitude (gain) grating contribution is predominant compared with that of the phase grating.
Degenerate four-wave mixing in the saturable gain of a flash-lamp-pumped Nd:YAG amplifier has been investigated. Three different geometries are examined in which the probe beam experiences (a) one pass, (b) two passes, and (c) four passes of the four-wave interaction region. It is found that multipassing the gain medium has a dramatic effect on the efficiency of the process, with a phase-conjugate reflectivity of 2500 and a conjugate energy extraction efficiency of greater than 200% demonstrated.
The theory of phase conjugation in laser amplifiers by saturable-gain degenerate four-wave mixing with copolarized beams is developed for pulses of arbitrary temporal shape and duration in the limit of a weak signal beam. The influence of the input pulse’s characteristics (energy, temporal pulse shape, duration) on the phase-conjugate reflectivity and on the conjugate pulse shape is analyzed. A sharp instantaneous peak of phase-conjugate reflectivity is predicted at high intensities of the four-wave mixing beams. This effect is experimentally demonstrated at λ0 = 1064 nm in a Nd:YVO4 amplifier pumped by a cw Ti:sapphire laser. A transient peak reflectivity of R ∼ 50% is thus obtained, corresponding to an enhancement of 1.6× compared with the maximum steady-state reflectivity. The experimental results and the theoretical predictions are in good agreement.
Phase distortion correction of an optical wave propagating in laser media is a crucial problem to be taken into account in most of laser systems. For this purpose, phase conjugation through stimulated Brillouin scattering using the master oscillator-power amplification configuration has shown a very good potential to obtain high beam quality in solid-state lasers that operate at variable repetition rates. Another attractive alternative to generate the phase-conjugate wavefronts is to use a four-wave mixing (DFWM) process in the laser amplifier. In this medium, the interference between the interacting beams leads to a spatial modulation of the complex susceptibility of the medium by gain saturation (amplitude gain grating). This all-solid-state solution presents the advantage of suppressing the external nonlinear medium and would realize the required functions in the laser medium itself. Moreover, due to the amplification experienced by all the interacting beams, associated to the resonant nonlinearity of the gain saturation, high reflectivities already have been achieved in Nd:YAG amplifiers using a multipass geometry.1,2