The elliptical Hermite-Gaussian beam and its propagation through paraxial systems

A new kind of light beam called the elliptical Hermite-Gaussian beam (EHGB) is introduced in this paper by using tensor method. The EHGB can be used to describe the generalized higher-order laser beams, such as hollow laser beams and the twisted Hermite-Gaussian beams conveniently. It includes the conventional Hermite-Gaussian beams as special cases. Using the generalized Collins integral, we derive the propagation formula of the EHGB passing through axially non-symmetrical paraxial optical systems. The EHGB allows us to treat the propagation and transformation of some complicated laser beams analytically. As an application example, we treat the elliptical flattened Gaussian beams by expressing it as superposition of a series of EHGBs by using polynomial expansion. (C) 2002 Elsevier Science B.V. All rights reserved.