Abstract

A beam width measure based on Rényi entropy was introduced by Luis [Opt. Lett 31, 3644 (2006)] . That one-dimensional analysis was limited to beam profiles with rectangular symmetry. In this Letter, we derive a general Rényi beam width measure that accounts for the diffraction properties of beams with profiles of arbitrary symmetry. We also show that the square of this measure has a quadratic dependence as a function of the propagation coordinate, so that it can be applied to propagation through arbitrary ABCD paraxial systems. The Rényi beam propagation factor, here introduced, is discussed in examples where the $M^2$ factor seems to have a limited effectiveness in describing the beam spreading.

© 2008 Optical Society of America

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