Interactive analysis of propagation in optical fibers

We have developed a set of computer codes that compute the propagation constants and field patterns for the propagating modes of cylindrical optical fibers. From a simple set of finite difference equations, solutions of the scalar Helmholtz wave-equation may be computed across a range of normalized frequencies to generate curves describing the dispersion characteristics of the fiber. Accurate cutoff frequencies for any mode can also be computed. We designed the computer codes around α-index profiles since these profiles have been extensively covered in the literature, but our system also supports arbitrary profiles within the limits of the "small index gradient" and "weakly guiding" approximations. The computer codes are accurate and fast. They may be used interactively to explore dispersion in optical fibers and the effects of finite cladding width on dispersion.