Closed form solution for three-dimensional reflection of an arbitrary Gaussian beam by a smooth surface

Abstract

A high-frequency analysis of the reflection of an electromagnetic Gaussian beam (GB) from a metallic parabolic surface is presented for the three-dimensional case. The reflected field is evaluated analytically by use of the physical optics approximation and is expressed in closed form in terms of the incident GB parameters. Similarities with the two-dimensional case and also with ray tracing theory are pointed out. Although the same problem has been investigated in the past by several researchers, this paper presents a physically appealing and intuitive closed form expression for the reflected field in the paraxial zone that does not appear to be available in the literature.