The photorefractive effect—a review

Abstract

Photorefractive materials have been assuming ever increasing prominence in the non-linear optics field due to their unique capability for displaying strong non-linear effects at milliwatt power levels. In this review we describe in some detail the two currently accepted models of the photorefractive process. The “band transport” model assumes that photo excited electrons (or holes) are ejected from filled donor (or acceptor) sites to the conduction (or valence) band where they migrate to dark regions in the crystal before recombining into empty traps. The charge separation results in a space charge field which modulates the refractive index via the linear electro-optic effect. The “hopping” model assumes that carrier transport occurs via light induced hopping from a filled donor site to a neighbouring empty trap. In particular, we examine the timeand spatial frequency dependence of grating formation and discuss the validity of the simplified model of a material response linear in modulation ratio (fringe contrast). In addition we show that the “hopping” model although physically distinct from the band transport model is described by equations which can be considered as a special case of the band transport equations. Results of a complete numerical simulation of the band transport model are presented to illustrate the properties of the photorefractive effect and to test the validity of the simplified model. The two models are normally formulated for an isotropic material illuminated by two plane wave beams which are assumed to be unaffected by the material. Photorefractive materials, however, are naturally anisotropic and in applications one is often interested in non-plane wave beams. We present for the first time an extension of the model to non-plane wave beams and explicity take full account of the vectorial nature of light and the crystal anisotropy. Barium titanate is used as an example to illustrate the extended model and graphs are presented which show the dependence of the nonlinearity on beam angles, polarisation and crystal orientation. Finally we discuss some applications is non-linear optics which exploit some of the unique features of the photorefractive effect. The photorefractive effect is illustrated throughout the paper by experimental results performed in our own laboratory.