Solutions for planar optical waveguide equations by selecting zero elements in a characteristic matrix

The propagation properties of optical planar waveguides with multilayer index profiles are analyzed by the transfer matrix of transmitted and reflected beam amplitudes in multilayers. The propagation wave number for guided-wave modes is obtained from the condition that certain elements in the transfer matrix must be zero. This numerical technique requires much shorter computer times compared with the usual method of solving the eigenvalue equations, obtained by setting the characteristic determinant to zero. The analysis is also applicable either to waveguides that have losses or to certain cases of uniaxial dielectric anisotropy. All waveguides are assumed to be magnetically isotropic. Some examples of the analysis of graded-index profiles and calculations of the effect of metal claddings and prism perturbations on guided modes are given.