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Physical Review Letters

Wave-Mixing and Vector Phase Conjugation by Polarization-Dependent Saturable Absorption in Cr4+:YAG

Michael J. Damzen, Santiago Camacho-López, R.P.M. Green

Published Apr 15, 1996• 19 citations
Publisher

Abstract

We describe a theory of four-wave mixing in the saturable absorber ${\mathrm{Cr}}^{4+}:\mathrm{Y}\mathrm{A}\mathrm{G}$ 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 ${\mathrm{Cr}}^{4+}:\mathrm{Y}\mathrm{A}\mathrm{G}$. 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.

DOI
10.1103/physrevlett.76.2894

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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.
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.
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.
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.
We studied both experimentally and theoretically the transmission and polarization characteristics of a Cr4+ : YAG saturable absorber crystal as a function of the intensity and polarization state of an incident laser beam. We found that a birefringent absorption behaviour is induced and we show that the experimental results are well described by a full numerical model which includes excited-state absorption as well as a ground-state cross-absorption term. By using pump-probe measurements we show that a finite cross-saturation of the absorption is achieved along the crystal axes orthogonal to the polarization of the optical radiation. No induced refractive index birefringence is observed.
The properties of polarization-dependent phase-conjugate (PC) reflectivities by degenerate four-wave mixing in saturable-dye-doped films are investigated on the basis of a four-level model including an excited-state absorption. Numerical calculations are carried out by taking account of the effect of molecular orientation as well as of pump propagation under the assumption that optically anisotropic dye molecules are rigidly fixed in a solid matrix without any positional and orientational order, in which a PC wave can be generated even in the case of a probe wave perpendicularly polarized to pump waves. Two cases of the polarization state are employed, where the polarization direction of the probe wave is either parallel or perpendicular to that of the parallel linearly polarized pump waves. Numerically calculating the PC reflectivities as a function of the pump intensity, we show how the polarization properties of the PC-reflectivity curves depend on saturation parameters, and clarify the influences of the molecular orientational and the pump propagation effect. The numerical results are compared with the experimental results obtained by using eosin-Y-doped polyvinyl alcohol films as saturable absorbers.
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.