Large Nonlinearities in Four-Wave Mixing in Photorefractive Crystals and Applications in Passive Optical Phase Conjugation

Author: Cronin-Golomb, Mark

Year: 1983

Degree: Dissertation (Ph.D.)

Advisor: Yariv, Amnon

Committee Member: Unknown, Unknown

Option: Physics

DOI: 10.7907/fvr7-3b28

Abstract

This thesis deals with some aspects of real-time holography, phase conjugation and four-wave mixing in photorefractive materials. These materials are particularly attractive because they can easily support real-time holograms of high diffraction efficiency. The effect which gives rise to these holograms is non-resonant and is operative in many crystals over the entire visible spectrum with low power (milliwatt) continuous wave laser beams. Two interwoven lines of research are pursued in this work.

Firstly, the phase shift between the light interference pattern and the refractive index grating, so characteristic of photorefractive holograms, and the magnitude of the diffraction efficiencies available in these crystals (BaTiO3 and Sr1-xBaxNb2O6) are such that a signal beam writing a hologram with a pumping beam will often experience gain. In a four-wave mixing situation, phase conjugate reflectivities well in excess of unity are possible.

We describe the demonstration of several optical oscillator structures which take advantage of this two- and four-wave mixing gain. These include a unidirectional ring resonator and the linear and ring passive phase conjugate mirrors. The linear mirror consists of a photorefractive crystal in a linear optical cavity. When the crystal is illuminated by a signal beam, oscillation builds up in the linear cavity, automatically providing a pair of counterpropagating beams which pump the crystal as a phase conjugate mirror for the signal beam. The beam coupling dynamics are such that once the oscillation has started it is possible to maintain operation even after removal of one of the linear cavity mirrors. This version of the linear mirror is known as the semilinear mirror. The ring mirror feeds the signal beam transmitted through the crystal back around an optical ring cavity to the crystal again where it becomes one of the pumps. An oscillation beam builds up which serves both as the second pump and the phase conjugate beam. Phase conjugate reflectivities of up to thirty per cent are easily observed in these passive devices. Experiments are described which demonstrate phase conjugation in these devices. Another experiment shows the intracavity distortion correction capability of an argon ion laser with one of its end mirrors replaced by a linear passive phase conjugate mirror.

The second line of work in this thesis is theoretical. The mechanism of the photorefractive effect is discussed. A generalization of the standard rate equation model is described, and the predictions of the rate equation model and a competing theory, the hopping model. are compared.

A coupled wave theory of two- and four- wave mixing in photorefractive crystals is developed, showing the importance of the phase shift between the interference pattern and the refractive index grating. The well known effect of two-beam energy coupling is reviewed and applied to a unidirectional ring resonator. Four-wave mixing is solved in the undepleted pumps approximation which linearizes the theory. The effects of linear absorption are considered, and the identity of the behaviors of the reflection and transmission gratings is pointed out.

Fully nonlinear equations of four-wave mixing via a single grating are solved for the transmission grating and separately for the reflection grating. Bistability in the solutions is discussed, and the boundary conditions for regular phase conjugation, as well as for the linear and ring passive phase conjugate mirrors are fitted. Workable expressions for the reflectivities are presented. The dynamics predicted by these theories explains the observed natures of the passive phase conjugate mirrors including the striking abilities of the semilinear and ring mirrors to function even at all. In addition, boundary conditions are fitted for the two interaction region passive phase conjugate mirror recently demonstrated by Feinberg.

Novel interpretations of photorefractive crystals as double phase conjugate mirrors and distortion correction elements in optical systems and circuits are introduced, and theoretically modelled. An application in ring lasers is suggested.

Finally, the relative merits of the ring, linear, semilinear and two interaction region passive phase conjugate mirrors are discussed with regard to threshold, reflectivity and ease of alignment.

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