The electromagnetic field associated with a generalized beam is analyzed theoretically, where the beam may take on an irradiance cross section described by a gaussian function with arbitrary elliptical symmetry. For this analysis, the field is represented by an expansion into an angular spectrum of plane waves. Expressions for the field components throughout a medium that is free of sources are found by use of an asymptotic approximation that is common in gaussian-beam analysis. In addition, more-precise expressions for these components are found, which are valid outside the neighborhood of focus. Near focus, gaussian beams may have only approximately gaussian cross sections, and in this region the behavior of beams without circular symmetry is greatly complicated. The effects of noncircular symmetry are discussed in some detail, and a method for correcting a beam to produce circular symmetry is described.
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