Light Propagation in Generalized Lens-Like Media

PROPAGATION 203!) Although a great deal of work has been done to describe electromagnetic wave guidance using a sequence of ideal aberrationless lenses, little has been done with more general lens-like media. The objective of this paper is to provide a beginning understanding of what happens to the important descriptive parameters of a light waveguide--wave phase constant, wave spot size, ray trajectory, stability restrictions--for general lens-like media, either continuous or formed from a sequence of focusing elements. Exact solutions for these parameters are difficult or impossible, a possible reason for little having been done.* A second result presented herein is a series of analytical techniques for obtaining useful approximate solutions representing a broad class of lens-like media; some of these techniques are most clearly presented by giving examples, which unfortunately leads to a rather large number of equations. To aid the reader in finding the section dealing with a particular topic, an outline and brief resume is given below. As pointed out by J. W. Tukey, there is no a prion reason why ideal aberrationless lenses are best for use as a communication medium. We would like to know what does happen to wave guidance as we depart from aberrationless lenses, which is the case studied extensively in earlier work. Gas lenses have nearly constant focal length but their "principal planes" are actually curved surfaces. 1 E. A. Marcatili and D. H. Ring have pointed out that these curved principal planes have effects similar to those expected in plane lenses with spherical aberration.