Abstract

Truly monolithic integration of optoelectronics requires compromises between the individual component and system performances. Design of integrated systems can benefit from the full power of an optimization algorithm, especially in the presence of competing design requirements. Evaluation of the merit function during optimization requires repeated calculation of waveguide modes. Combing the complex plane for solutions to the dispersion relation is too computation-intensive to be practical, particularly for multi-moded and lossy structures, and there is no guarantee that all solutions will be found. Instead, we have demonstrated a numerical technique, based on Cauchy’s integral equation that allows unambiguous identification of all modes in structures with arbitrarily high losses using very short computation times.¹ Further, by plotting the solutions in the complex plane as a function of the square of the complex propagation constant, we observe that the solutions tend to be highly patterned in such a way as to lend insight into the behavior of a wide variety of waveguides.

© 1991 Optical Society of America