ABCD matrix for reflection and refraction of Gaussian beams at the surface of a parabola of revolution.

We report the formulation of an ABCD matrix for reflection and refraction of Gaussian light beams at the surface of a parabola of revolution that separate media of different refractive indices based on optical phase matching. The equations for the spot sizes and wave-front radii of the beams are also obtained by using theABCD matrix. With these matrices, we can more conveniently design and evaluate some special optical systems, including these kinds of elements.