Gaussian beams - Optics and applications

A first article [E 4 042] introduces the topology of Gaussian beams in both the transverse and longitudinal planes. Experimental techniques for analyzing these beams are discussed in order to deduce their physical characteristics.

The first part of this article, after reviewing a few theoretical formulas from the article [E 4 042] , discusses the modification of the characteristics of a Gaussian beam through a thin biconvex lens via its magnification. Next, linear optics, with the transfer matrix formalism, is briefly recalled, in order to extend this theory to Gaussian beams for a fine biconvex lens, then to optical systems centered via their principal points. The "abcd" law of complex radii of curvature is then discussed and exploited with examples of simple applications using convex lenses. This law is then extended to the design of stable linear resonant cavities.

The second part looks at a number of Gaussian beam applications, such as laser photodynamic therapy, light sheet microscopy and optical tweezers, all of which enable interaction between Gaussian beams and the biological medium.

In the final section, the development of beamlets, the elementary signal associated with a light beam, leads to two main applications after a brief theoretical introduction, one describing the propagation of a light beam through an optical device, used by ray tracing software, and the other proposing an adaptive filtering algorithm based on the coefficients of the Gabor series for image processing.