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Journal of the Optical Society of America B

Vectorial phase conjugation via four-wave mixing in isotropic saturable-gain media

K. S. Syed, Graham J. Crofts, R.P.M. Green, Michael J. Damzen

Published Aug 1, 1997• 14 citations
Publisher

Abstract

We study theoretically the properties of transient degenerate four-wave mixing in an isotropic, homogeneously saturable gain medium with interacting beams of arbitrary strength and polarization state. In particular we investigate the ability of the interaction to exhibit vectorial phase conjugation when orthogonally circularly polarized pump beams are used. This mechanism allows the correction of both phase and polarization distortions introduced to an optical beam. Numerical simulations are compared with experiments that use a flashlamp-pumped Nd3+:YAG amplifier and demonstrate good vector phase-conjugate fidelity for both weak and strong probe beams of arbitrary polarization state.

DOI
10.1364/josab.14.002067

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We study theoretically the properties of transient degenerate four-wave mixing in an isotropic, homogeneously saturable gain medium with interacting beams of arbitrary strength and polarization state. In particular we investigate the ability of the interaction to exhibit vectorial phase conjugation when orthogonally circularly polarized pump beams are used. This mechanism allows the correction of both phase and polarization distortions introduced to an optical beam. Numerical simulations are compared with experiments that use a flashlamp-pumped Nd3+:YAG amplifier and demonstrate good vector phase-conjugate fidelity for both weak and strong probe beams of arbitrary polarization state.
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.>
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
We present a study of vector phase conjugation based on degenerate four-wave mixing in inverted Nd:YAG. The results demonstrate polarization correction for weak probe strength, with near-unity fidelity for polarization compensation of the returning conjugate. As the probe strength is increased, the fidelity of the polarization state of the conjugate is seen to deteriorate to an average value of 92% when the probe is strongly saturating and is several times stronger than the pump beams. We also show that, for strong probe strengths, an individual transmission grating or reflection grating is more efficient than when both gratings are present.
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.
Rigidly held molecules display nonlinear optical properties which differ substantially from the properties of isotropic absorbers.1 In particular, the absorption of a collection of randomly oriented, rigidly held molecules saturates differently for different polarization states. We show that the polarization properties of degenerate four-wave mixing in such a medium are dramatically modified by this polarization-dependent saturation. We predict theoretically that for linearly polarized pump waves and for an input intensity near the saturation intensity, degenerate four-wave mixing in this material system can lead directly to vector phase conjugation; that is, to the simultaneous reversal of the optical wavefront and conjugation of the polarization state of the incident optical field.2 We confirm these theoretical predictions through phase conjugation experiments using fluorescein doped boric acid glass as the material system, and we find that degenerate four-wave mixing leads to nearly perfect vector phase conjugation when pumped by linearly polarized pump waves for field strengths near the saturation intensity.