Theory of 2×2 switch based on electro-optic and piezoelectric effects in photorefractive LiNbO3 crystal

Based on the electro-optic and piezoelectric effects, the principle of a 2×2 bypass–exchange switch in photorefractive LiNbO3 crystal is discussed. In photorefractive volume grating, the Bragg condition can be changed by applying a field during readout. That is, by applying a specific field Es or zero, the diffraction efficiency will be 0 or 1, respectively and this property can be used to realize the bypass or exchange operation of the switch. In this paper, considering both the piezoelectric and electro-optic effects caused by the applied electric field, we analyzed relations of both the specific field and the incident intensity ratio with respect to the writing angles and polarizations of writing beams.