Perturbative analysis of cross-talk of two pieces of photorefractive phase gratings stored in one point by angle multiplexing

In this paper, we have applied a perturbative expanding method to the hopping model, and studied the cross-talk between two pieces of phase gratings stored in one point of photorefractive material by angle multiplexing. The coupling equations and their steady solution have been derived. It has been found that the fundamental harmonic of the first grating is coupled with the second-order harmonic of the second grating and the second-order harmonic of the first gating is coupled with the fundamental harmonic of the second grating. The positions of maximums of the plots about the normalised fundamental and second-order harmonics of the space-charge field vs. the normalised grating vector (k/k0) are at k/k0=1.414 and k/k0=1.01 for delta k/k0=0, respectively, which are at k/k0=1 and k/k0=1/sqrt2 for the case of storing single grating in one point. This kind of deviation has been confirmed by our two-wave coupling experiment with Ce:KNSBN crystal. At the same time, we have found the degree of deviation of the second-order harmonic of the space-charge field strongly depends on the difference of normalised grating vector (k/k0)between the two pieces of gratings, but that of fundamental harmonic weakly depends on it. In addition, it has been found that the degrees of deviation of both harmonics do not depend on the modulation depth.