TIME-DEPENDENT NONLINEAR PHOTOREFRACTIVE RESPONSE TO SINUSOIDAL INTENSITY GRATINGS

The time-dependent, nonlinear Kukhtarev equations are numerically solv ed to determine the temporal and spatial dependence of the space-charg e field for a sinusoidal intensity profile with an arbitrary modulatio n depth m. The intensity profile is spatially bounded simulating two i nterfering laser beams of finite spot size. The numerical solution all ows us to critically examine the validity of analytical theories for l inear and nonlinear photorefractive effects. The parametric dependence of the characteristic time constant tau for writing a grating is stud ied including the effects of quiescent intensity I-o, modulation index m and the thermal ionization rate beta. We find that the Kukhtarev eq uations inherently yield a sublinear dependence of the characteristic time constant tau on I-o even for a single trap (acceptor) species whe n I-o is above a critical value I-c. Expression for I-c is given in te rms of material properties, and the sublinearity index is determined f or BSO. The exact dependence of tau on the modulation index (0 < m les s than or equal to 1) is determined for BSO, and the nonsinusoidal wav eform of the space-charge field for large m is fully characterized bot h analytically and numerically.