Phase shift formulas in electro-optical crystals with an arbitrary incident direction

摘要： The calculation of the phase shift in electro-optical crystals is related to an extensive range of optical devices. A set of analytical phase shift formulas at arbitrary incidence angle and azimuth angle for a plane-parallel electro-optical crystal plate is derived. This enables us to analyze the phase shift induced by an electro-optical crystal with an arbitrary incident direction. As an example, the derived formulas are used to investigate the influence of incidence angle and azimuth angle on the phase shift in a lithium niobate crystal plate. For the field-free lithium niobate crystal, the phase shift depends only on the incidence angle. In contrast, when an external electric field is applied to the crystal, the phase shift is not only strongly influenced by the incidence angle, but also periodically changes with the azimuth angle. In order to validate the correctness of the derived formulas, the experiments are also conducted. The theoretical results are proved to be in good agreement with the experimental results.