Dielectric Clad Cylindrical Waveguides

Abstract

An ordinary optical fiber consists of a cylindrical core of a suitable dielectric material coated by a thin layer of another dielectric material of lower refractive index. Thus the refractive index distribution is of the form

$$\begin{array}{*{20}c} {n = n_1 } & {{\rm{for 0 < }}r{\rm{ < }}a} \\ { = n_2 } & {{\rm{for }}r > a} \\\end{array}$$

((4.1))

where n ₁ and n ₂ are the refractive indices of the core and cladding, respectively (n ₁ >n ₂), and a represents the radius of the core. Actually the cladding extends only up to a finite distance; however, very little error is involved in assuming that the cladding thickness is infinite. This is because of the fact that for guided propagation, the light beam undergoes total internal reflections at the core-cladding interface and the thickness of the cladding plays almost no role in the guided propagation. Therefore, in all subsequent analysis we will assume the cladding thickness to be infinite. It should be pointed out that even if the cladding material were absent the fiber would be able to guide the light beam, because air would then act as the second medium (i.e., n ₂ = 1). However, it is always preferred to have a cladding because of the following reasons.