Parametric Instability Boundaries for Spatial Subharmonics in Photorefractive Moving Gratings: Theory and Experiments

We have derived a nonlinear spatiotemporal differential equation for spacecharge fields from Kukhtarev's material equations in a moving coordinate system and obtained the spatial subharmonic instability boundaries by using linear stability analysis. It is also found that there is an analogy between the temporal subharmonic and the spatial subharmonc instabilities in the sense that the governing differential equations describing the instability boundaries are formally identical. The experiments for generating spatial subharmonic waves are performed in a photorefractive Bi₁₂SiO₂₀ crystal by using conventional moving grating technique. The threshold detunings are experimentally determined and the results are compared with the theory.