Contents I. Introduction
The task of this paper is to give a broad perspective with historical emphasis on the theory of lightwave propagation in dielectric waveguides. A dielectric is a nonconductor of electric current. This theory is based on Maxwell's equations. In the spirit of this issue, we should recall that these equations were published 147 years ago [1]. Guides of electromagnetic waves were treated by Lord Rayleigh about 37 years later [2]. For a nonmetallic circular cylindrical dielectric waveguide, what we now call a fiber, solutions for the modal wave propagation were first obtained in 1910 by Hondros and Debye [3]. Early workers in the field were mostly interested in longer wavelengths, such as the propagation of microwaves in dielectric wires and dielectric rod antennas. Examples are the experiments conducted in 1936 by the microwave waveguide pioneer Southworth [4] at Bell Labs in Holmdel, the predecessor of the current Crawford Hill Labs. By the early 1940s, the classical textbooks on electromagnetic wave propagation by Stratton [5] and Schelkunoff [6] contained chapters discussing the detailed solutions for the propagating modes of circular dielectric guides as well as metallic waveguides in terms of Bessel and Hankel functions. Among the papers they cite is the 1938 publication by Brillouin on the same subject [7]. It is interesting that the modal solutions given by Stratton, as well as those by Hondros [8] and Carson et al. [9], are of very general validity, allowing the specification of dielectric constants and of finite conductivities (or laser gain) in both core and cladding. These solutions contain as special cases both the lossless dielectric guides for zero conductivity, and the hollow metallic waveguides of microwave technology for a lossless core and a cladding of infinite conductivity.
