Reflection and refraction of Gaussian beams on the interface of an elliptical hyperboloid

By matching the complex phase along the boundary, we analyze the reflection and refraction of Gaussian beams at the surface of an elliptical hyperboloid between media of different refractive indices. In our work, we extend the interface from a hyperboloid of revolution to an elliptical hyperboloid; and also expand the angle of incidence from the usual case of normal incidence to arbitrary angles of incidence. The analytical results can be expediently applied to design and compute optical or quasioptical systems, containing components with hyperboloidal structures.