Reflection of Gaussian beams at the surface of an ellipsoid of revolution

An ellipsoid of revolution is an important focusing element. By matching the complex phase, the formulas are deduced for reflection of Gaussian beams at the surface of an ellipsoid of revolution in this paper. The analysis is extended to an arbitrary angle of incidence, and the derived results are transformed into ABCD ray matrices. By making use of these matrices, we can handily design and estimate some special quasioptical systems, including such elements as cylindrical or ellipsoidal shapes.