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Abstract

**Multi-Gaussian Beams - a Super-Gaussian Alternative**

A top-hat laser beam profile is highly sought in a wide variety of
applications. However, this top-hat profile, represented by a circ
function, destabilizes as it propagates, leading to an undesirable ringing
phenomena. This is well known from the study of diffraction of a
plane wave by a circular hole. The oft-used Gaussian-profiled beam
has the advantage of retaining its smooth shape as it propagates through
free space. The disadvantage of the Gaussian shape is that the low
intensity at the sides of the beam do not make it a good enough approximation
to the desired top-hat shape. For example, the Gaussian shape is
much less efficient at extracting energy from a laser amplifier than the
top-hat. One popular alternative is the super-Gaussian beam. However,
the evaluation of the propagated field cannot be performed in a closed
form.

In this study, a new class of beams, known as multi-Gaussian beams,
are proposed which have the advantages of the super-Gaussian, while having
diffraction characteristics which are analytically soluble. The multi-Gaussian
beams consist of a small sum of finite-width Gaussian beams side-by-side.
Thus, current analytical techniques can be used to traces multi-Gaussian
beams through optical systems represented by an arbitrary complex ABCD
matrix.

*Date Modified January, 1998*

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