Abstract
We study the paraxial wave equation for a monocromatic light wave with two dimensions transverse to the beam propagation. We develop an average description of the field based on the calculation of the beam intensity moments and explicitly demonstrate that the elliptic Gaussian mode in free space can be derived as a solution of the paraxial wave equation from a variational extime of a proper functional of the field amplitude. The propagation characteristics of such modes are analysed.
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