Nonlinear frequency response of a moving grating with an applied field in bismuth silicon oxide

A fully nonlinear frequency response of a moving grating in bismuth silicon oxide, including the effects of an applied electric field, is modeled by solution of the time-dependent Kukhtarev equations for photorefractive materials. The numerical results are used to define fully the nonlinear response function F(m)=a(-1)[1-exp(-am)], where m is the modulation index in the intensity pattern, to yield the unknown quantity a over a broad range of detuning frequencies f . For low f, the response is superlinear with a<0, and for relatively large f it is sublinear with a>0 . In the midrange we predict, for the first time to our knowledge, a characteristic frequency f(l) at which a=0 and the response is linear, that is, F(m) approximately m, despite the presence of nonlinearly generated higher harmonics of the fundamental grating wave number. In view of this linear behavior, writing a hologram at the linear-response frequency f(l) might permit a more faithful reproduction of an object than that which is possible by writing at the frequency of maximum response at the resonance.