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Japanese Journal of Applied Physics

Polarization Dependence of Reflectivity of Phase-Conjugate Wave Generated by Degenerate Four-Wave Mixing in Bi_ SiO_ : Waves, Optics and Quantum Electronics

Jun-ichi Sakai

Published Oct 20, 1988• 0 citations
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Stationary four-wave mixing in a shifted photorefractive transmission grating formed in cubic gyrotropic crystals of the 23 symmetry is considered in the case of low contrasts of the original optical interference pattern. Expressions for the transmission and reflection coefficients for the phase conjugation of weak light beams in arbitrarily cut samples are obtained by solving exactly the equations for the coupled waves that include the effects of the natural circular birefringence and the linear birefringence induced by the external field. The conditions for the generation of phase-conjugated waves are determined for the mixing at 633 nm in Bi 12 SiO 20 and Bi 12 SiO 20 samples in the case when the grating vector is parallel to the [110] axis and the incident pump waves propagate in the (001) crystal plane and have arbitrary polarisations.
Polarization dependence of phase-conjugate reflectivity by degenerate four-wave mixing is clarified theoretically and experimentally in a saturable-dye-doped polymer film. 1. _INTRODUCTLON A dyedoped film in which optically anisotropic saturable dye molecules are rigidly fixed and are randomly oriented has been used as a nonlinear material which can generate a phase-conjugate (PC) wave by degenerate four-wave mixing13 (DFWM). Such a film can generate a PC wave which has the same polarization state as the probe wave even for a probe wave orthogonally polarized to two pump waves. Tompkin et. al. 4 showed that in such a phase conjugator the nearly perfect vectorial phase conjugation can be obtained at the pump intensity near the saturation intensity of the phase conjugator. In this work following the analysis of Tompkin et. al. 4 closed-form solutions for the PC reflectivities in the dye-doped film are derived for two states of the polarization: the probe wave is polarized parallel and perpendicular to the pump waves. Some experimental results are also demonstrated in an eosin-Y-doped poly-vinyl alcohol (PVA) film and are compared with the theoretical results. 2. POLARIZATION DEPENDENT PC REFLECTIVITIES Dye molecules are modeled as dipoles which are randomly and uniformly oriented and are rigidly fixed in a solid matrix. We assume that each dye molecule has only one component of transition dipole moments at a wavelength considered5. An induced dipole moment of each dye molecule by
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.