Transients due to Two Wave Mixing in Photorefractive Media.

Photorefractive media exhibit photon induced refractive index changes through a unique series of processes. The photoexcitation and subsequent transport of charge carriers give rise to a space charge electric field that, through the linear electro-optic effect, modulates the index of refraction, resulting in a phase grating being recorded in the medium. The nonlocal property of the photorefractive gratings, resulting from charge transport, is responsible for a wide range of interesting phenomena such as beam amplification, fringe bending, phase conjugation and spatial solitons. It is shown in this thesis that another type of soliton--a photoinduced solitary charge wave--is also observable because of unusual nonlinear wave mixing in photorefractive media. This dissertation provides a comprehensive study of the dynamics of grating formation and erasure in photorefractive media. Numerical solutions, and analytic solutions where appropriate, of the field and material equations form the basis for the transient analysis. For the transmission geometry, it is shown that upon readout of the hologram with an appropriate beam, the grating envelope approximates the hyperbolic secant function, and propagates through the medium without changing its shape, much like a bright soliton. In fact, the evolution of the grating envelope is described by the damped sine-Gordon equation. Since the grating is a consequence of charge distribution, the propagating envelope may be regarded as a collection of solitary charge waves. This theoretical investigation predicted the possibility of trapping the grating to substantially prolong the readout, which was subsequently confirmed by experiments. Furthermore, readout with other Bragg matched beams can lead to rapid erasure, and oscillations in the diffraction efficiency with time. Similar extensive analysis was carried out for the reflection geometry. The grating evolution for this case is described by a variant of the tan-Gordon equation which supports a hyperbolic tangent-like traveling wave envelope. The effect of applied field, beam fanning, nonlinear response and non-zero absorption on the evolution of the grating envelope and Bragg selectivity are also discussed. Finally, the validity of the standard thermal fixing model, and the transients due to diffraction from thermally fixed gratings are examined in detail.