Abstract

The propagation of Helmholtz–Gauss beams in media exhibiting loss or gain is studied. The general expressions for the field propagation, the time-averaged power on propagation, the trajectory of the beam centroid, the beam spreading, the nondiffracting distance, and the far field are derived and discussed. Explicit expressions of these parameters for Bessel–Gauss and cosine-Gauss beams are included. The general expressions can be applied straightforwardly to describe the propagation of Mathieu–Gauss and parabolic-Gauss beams in complex media as well.

© 2006 Optical Society of America

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