A simple and powerful new paraxial ray formalism is shown to provide an alternate method for designing Gaussian Beam Resonators. The theory utilizes the Delano yybar diagram approach and is an extension of the recent work by Shack and Kessler for laser systems. The method is shown to be complementary to the conventional ABCD method and is founded upon J.A. Arnaud's pioneering ideas for complex rays. The thesis develops an analytic formulation of a ray based complex wavefront curvature and yields a clearly generalized description of spherical wave propagation, for which Gaussian beams are considered a special case. The resultant theory unifies the complex q parameter and the ABCD law, with the yybar complex ray components and also suggests that the ABCD law for the complex q parameter has its origin in the yybar complex ray. New fundamental equations for designing stable multi-element resonators using the yybar coordinates are derived, and it is shown that the yybar diagram provides a novel method for defining automatically stable resonators. Various applications for the yybar design technique are also discussed, including the setting of convenient design constraints, the description of M2 beams, generating phase diagrams, and resonator synthesis and analysis.
Harvey, James E
Master of Science (M.S.)
College of Engineering
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Masters Thesis (Open Access)
Menard, Kenneth A., "Gaussian beam resonator formalism using the yy method" (1995). Retrospective Theses and Dissertations. 3269.