Properties of optical spatial solitons in photorefractive crystals with special emphasis to two-photon photorefractive nonlinearity

•Reviewed recent progress of optical spatial solitons in photorefractive media.•Discussed mechanisms of formation and properties of screening and photovoltaic solitons including their self bending.•Properties of vector solitons highlighted and existence of some missing solitons pointed out.•Incoherent solitons and discrete optical spatial solitons including vortex solitons have been discussed.

We have reviewed recent developments of some aspects of optical spatial solitons in photorefractive media. Underlying principles governing the dynamics of photorefractive nonlinearity have been discussed using band transport model. Nonlinear dynamical equations for propagating solitons have been derived considering single as well as two-photon photorefractive processes. Fundamental properties of screening and photovoltaic solitons have been considered. For each type of solitons, three different configurations i.e., bright, dark and gray varieties have been considered. Mechanisms of formation of these solitons due to single as well as two-photon photorefractive processes have been considered and their self bending discussed. Vector solitons, particularly, incoherently coupled solitons due to single photon and two-photon photorefractive phenomena have been highlighted. Existence of some missing solitons have been also pointed out. In addition, incoherent solitons and discrete spatial solitons in optically-induced photorefractive lattices are also discussed.