Four-Wave Mixing and Phase Conjugation in Photorefractive Crystals

Citation

White, Jeffrey Owen (1984) Four-Wave Mixing and Phase Conjugation in Photorefractive Crystals. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/f9ef-m894. https://resolver.caltech.edu/CaltechETD:etd-01192007-152414

Abstract

This thesis is an experimental and theoretical investigation of nonlinear optics in photo-refractive crystals, and applications thereof. Coherent light is used to induce nonlinear, optical frequency polarizations proportional to the cube of the total optical field within these materials. Equivalently, dynamic holography performed wherein the incident light simultaneously writes, reads and erases index of refraction gratings.

The first part of this thesis is a description of the physics of the photo-refractive effect in such crystals as Bi₁₂SiO₂₀, LiNbO₃, KTaO₃, and BaTiO₃. Previous microscopic rate equation models are extended to include the dynamics of a second photo-refractive center with the aim of explaining several discrepancies with experimental data.

The second part reviews the coupled wave theory of fixed gratings and dynamic gratings formed in photo-refractive media. Coupled nonlinear ordinary differential equations describe the interaction between two optical waves; which is caused by the grating that they create. The analysis is extended to the reflection geometry and the ring resonator geometry. The coupling constant is measured in the reflection geometry. Holographic gain is combined with mirror feedback to demonstrate a unidirectional ring oscillator, wherein a optically pumped photo-refractive crystal functions as a directional gain element.

The third part extends the analysis to the holographic formulation of four-wave mixing, wherein four waves and up to four gratings exist in the crystal. The equations are solved in the single grating approximation. The object of much of the analysis is to calculate the reflectivity of a four-wave mixing photo-refractive phase conjugate mirror. The invention of a passive self-pumped phase conjugate mirror is described.

The last part describes three applications of four-wave mixing. We demonstrate the compensation of intracavity laser distortions by replacing an ordinary mirror in a laser with a passive phase conjugate mirror. We propose and demonstrate a phase conjugate window for one-way transmission of an information bearing optical field through a thin phase distortion. Finally, the multiplicative properties of four-wave mixing are combined with the transforming properties of lenses to construct a coherent optical processor capable of convolving and correlating three input fields containing arbitrary spatial phase and amplitude information.

Thesis Files