Form birefringence of layered media and volume gratings

We investigate the reflection at the interface between a homogeneous medium and a semi-infinite periodic layered medium. The result provides independent confirmation of the form birefringence of the periodic layered medium. In addition, our result shows a fundamental difference between the reflection at the interface between a homogeneous medium and a semi-infinite periodic layered medium and that of a Bragg reflector that consists of a large number of layers. We analyze the form birefringence induced by volume index gratings in a homogeneous medium. The extension of our analysis to multiple volume index gratings provides an explanation of the relationship between birefringence and crystal symmetry.