2. Theory of Dielectric Waveguides

Dielectric waveguides are the structures that are used to confine and guide the light in the guided-wave devices and circuits of integrated optics. This chapter is devoted to the theory of these waveguides. Other chapters of this book discuss their fabrication by such techniques as sputtering, diffusion, ion implantation or epitaxial growth. A wellknown dielectric waveguide is, of course, the optical fiber which usually has a circular cross-section. In contrast, the guides of interest to integrated optics are usually planar structures such as planar films or strips. Our discussion will focus on these planar guides even though most of the fundamentals are applicable to all dielectric waveguide types. The simplest dielectric guide is the planar slab guide shown in Fig. 2.1, where a planar film of refractive index nf is sandwiched between a substrate and a cover material with lower refractive indices ns and n c ( n f > n ~ > n c ) . Often the cover material is air, in which case n¢=1. As an illustration, we have listed in Table 2.1 the refractive indices of some dielectric waveguide materials used in integrated optics. Typical differences between the indices of the film and the substrate range from 10 .3 to 10 -1, and a typical film thickness is 1 gm. The light is confined by total internal reflection at the film-substrate and film-cover interfaces.