Propagation properties of elegant Hermite-cosh-Gaussian laser beams

So far, the elegant Hermite-Gaussian (EHG) beams and cosh-Gaussian (ChG) beams have been studied in detail, respectively. In this present paper, a more generalized beam containing this two beams is introduced and studied. Just as the more generalized cases for the standard Hermite-Gaussian (SHG) beams and ChG beams are called Hermite-cosh-Gaussian (HChG) beams, the more generalized cases for EHG beams and ChG beams are named elegant Hermite-cosh-Gaussian beams (EHChG). This kind of beam is also another special case in Hermite-sinusoidal-Gaussian (HSG) family as well as the HChG beam. An analytical solution of the EHChG beam propagating through a first-order ABCD system is derived. The closed form of M-2-factor and the power in bucket are presented to characterize the quality of these beams, and correspondingly, the beam width and the curvature radius are expressed in terms of generalized ABCD law. Moreover, the kurtosis is employed to describe the sharpness of the EHChG beams and its variation versus the propagation distance is plotted numerically. (C) 2002 Elsevier Science B.V. All rights reserved.