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Engineering Electromagnetics For Optical Fiber
Optical fiber works on the same principle as the dielectric slab waveguide, except of course for the round cross section. A step index fiber is shown in Figure in which a high index core of radius a is surrounded by a lower-index cladding of radius b. Light is confined to the core through the mechanism of total reflection, but again some fraction of the power resides in the cladding as well. As we found in the slab waveguide, the cladding power again moves in toward the core as frequency is raised. Additionally, as is true in the slab waveguide, the fiber supports a mode that has no cutoff. Analysis of the optical fiber is complicated. This is mainly because of the round cross section, along with the fact that it is generally a three-dimensional problem; the slab waveguide had only two dimensions to be concerned about. It is possible to analyze the fiber using rays within the core that reflect from the cladding boundary as light progresses down the fiber. We did this with the slab waveguide and obtained results fairly quickly. The method is difficult in fiber, however, because ray paths are complicated. There are two types of rays in the core: (1) those that pass through the fiber axis (z axis), known as meridional rays, and (2) those that avoid the axis but progress in a spiral-like path as they propagate down the guide. These are known as skew rays; their analysis, although possible, is tedious. Fiber modes are developed that can beassociated with the individual ray types, or with combinations thereof, but it is easier to obtain these by solving the wave equation directly. Our purpose in this section is to provide a first exposure to the optical fiber problem (and to avoid an excessively long treatment). To accomplish this, we will solve the simplest case in the quickest way. The simplest fiber configuration is that of a step index, but with the core and cladding indices of values that are very close, that is n1.
