Optimization of the Shape of Gaussian Beams of a Fixed Length

The procedure of choosing the shape of Gaussian beams in order to minimize a given object function of a certain kind is proposed. The general form of the object function enables both the average square of the quadratic variation of the phase and the average square of the beamwidth to be minimized along the central ray. The error of the transformation of the Gaussian beams at the structural interfaces may also be taken into account. Most of the hitherto published suggestions of how to chose the shape of Gaussian beams are special cases of the described procedure. The aim of this paper is not to propose the object function to be minimized, but only to describe the minimization of a given object function. The minimization assumes the a priori known lengths of the central rays of the Gaussian beams (i.e. the lengths of the beams are not free parameters in the minimization procedure).

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