Abstract
A new kind of laser beam, called a decentered elliptical Gaussian beam (DEGB), is defined by a tensor method. The propagation formula for a DEGB passing through an axially nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be reduced to the formula for a fundamental elliptical Gaussian beam and a decentered Gaussian beam under certain conditions. As an example application of the derived formula, the propagation characteristics of a DEGB in free space are calculated and discussed. As another example we study the properties of a generalized laser beam array constructed by use of a DEGB as the fundamental mode.
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