Spatial harmonics of photorefractive gratings in a barium titanate crystal

Calibrated optical Bragg-scattering measurements of the fundamental steady-state space-charge-field amplitude, and of two higher spatial harmonics, in photorefractive p-type barium titanate excited by a light intensity pattern that is a simple sine function of distance are reported. These measurements are performed over the entire range (0<m<1) of intensity modulation index m when the modulation period is both much larger than, and comparable to, the smallest characteristic (Debye screening) length involved in the photoconduction process. There is no externally applied electric field. The measurements are compared to numerical solutions of the standard single-carrier band-conduction model of photoconductivity, and good agreement is found except for large unexplained differences at high modulation index (∼0.8<m<1). Phenomenological analytic expressions are also given for the fundamental and two higher field-grating harmonics that are useful approximations to the numerical solutions of the standard model equations for all m and for (small, intermediate, and large) grating periods.