Coherent reflection of a Gaussian beam at optical frequencies from a large convex mirror

Abstract

In some modern laser-system application and performance evaluations, an accurate formula is needed for the spatial distribution of intensity in the reflected or backscattered field that is produced by a coherent Gaussian beam incident upon an optical-grade convex mirror. This paper presents the development of such an analytical formula. The formula is rigorous within the Fresnel approximation, is easy to evaluate, and consists of only a few terms. However, it requires that the mirror size and distance to satisfy the Fresnel condition and the radius of curvature of the mirror be large compared with the wavelength of radiation. With the Gaussian beam transformed to a plane uniform beam and the mirror approximated to a flat circular disk, the formula reduces to the well-known Airy diffraction-pattern formula when subjected to the Fraunhofer condition. Although the formula presented here is strictly applicable only to spherical mirrors with a small aperture-radius-to-radius-of-curvature ratio, when pushed to the full sphere limit, it yields results that have good order-of-magnitude agreement with the machine-calculated results that use the rigorous Mie theory of scattering from a full sphere.