Abstract
A new solution of the paraxially approximated wave equation in free space is presented. It has the form of a Hermite-Gaussian function, where the argument of the Hermite polynomial is generally complex. The usual Gaussian beams where such argument is real and those recently described by Siegman where it is complex but coinciding with that of the Gaussian function are particular cases of the general solution presented here. The application of these generalized Gaussian beams to the analysis of the beam emerging from a complex graded-index medium is discussed in detail.
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