Modes of dielectric waveguides of arbitrary cross sectional shape

A technique is presented for determining the modal propagation properties of a homogeneous cylindrical dielectric waveguide of arbitrary cross sectional shape and index n1 embedded in a medium of index n2. Both the weakly guiding case in which n1 ≈ n2 and the general case of arbitrary index difference are discussed theoretically. In both cases the approach is to derive integral representations for appropriate components of E and B. These satisfy the appropriate Helmholtz equations inside and outside the guide and also guarantee that the boundary conditions are satisfied. On expansion of the components in certain sets of basis functions, the representations become a set of linear equations. The vanishing of the determinant of this set yields the propagation constants of the various modes. Numerical results are given for weakly guiding fibers of various shapes. Among these are rectangles and ellipses, which make comparisons with previous work possible.