Sinusoidal-Gaussian Beams in Complex Optical systems
Sinusoidal-Gaussian beam solutions are derived for the propagation
of electromagnetic waves in free space and in media having at most quadratic
transverse variations of the index of refraction and the gain or loss.
The resulting expressions are also valid for propagation through other
real and complex lens elements and systems that can be represented in terms
of complex beam matrices. The solutions are in the form of sinusoidal functions
of complex argument times a conventional Gaussian beam factor. In the limit
of large Gaussian beam size, the sine and cosine factors of the beams are
dominant and reduce to the conventional modes of a rectangular waveguide.
In the opposite limit the beams reduce to the familiar fundamental Gaussian
form. Alternate hyperbolic-sinusoidal-Gaussian beam solutions are also
Date Modified January, 1998
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