Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide

Abstract

The propagation of electromagnetic surface waves along a radially inhomogeneous dielectric waveguide is investigated. The problem is formulated in terms of differential equations to be satisfied by the radially dependent parts of the electromagnetic field vectors. The dielectric waveguide is assumed to consist of a homogeneous cladding of infinite extent and a radially inhomogeneous core of higher permittivity. Numerical solutions of the differential equations in the core are obtained by two different methods, viz. by direct numerical integration and by substitution of an appropriate power series expansion. In the cladding the field is expressed in terms of modified Bessel functions. Imposing the boundary conditions at the interface of core and cladding, an equation for the unknown propagation coefficient is obtained. From this equation the propagation coefficients for the lower order modes are computed numerically. Numerical results are presented for some permittivity profiles of practical interest in single-mode transmission along optical fibres.