Abstract

Eight unique mode configurations may occur in a multilayer planar waveguide.¹ A correspondence exists between these modes and zero entries in the composite transfer matrix of the structure.² The modes of such a structure are obtainable by equating transfer matrix entries to zero and solving for the complex propagation constants of individual mode types. Based on this theory to find the bound mode of waveguides with any number of layers, a numerical technique was developed that minimizes the magnitude of the bound entry in the transfer matrix.³ This downhill method can find minima of an arbitrary function, but it only converges with first-order accuracy and requires four evaluations of the transfer matrix at each iteration. A new method that takes advantage of the mathematical properties of the transfer matrix to achieve second-order convergence with a reduced computational stencil is presented. This method is capable of finding the propagation constants and field distributions of structures containing materials with complex permittivities. This new method offers improved accuracy and efficiency, compared to the first-order downhill method. Results accurate to within 0.01 dB/cm are typically obtained with one-seventh the computation of the downhill method.

© 1991 Optical Society of America