Abstract

The scalar wave equation has been used in computer modeling of semiconductor devices such as rib waveguides being designed and fabricated for optoelectronics research. Accurate results of light propagation in structures, having uniform index regions separated by sharp interfaces, have been obtained using a finite difference approach. Device structures that are grown with a continuous variation in semiconductor composition are of increasing interest. For example, aluminum composition varies continuously during the growth of GaAlAs layers of GRINSCH lasers. Since these variations imply a continuous change in the refractive index of the material, the scalar wave equation is no longer applicable in modeling the optical performances of such waveguides. The inclusion of this nonzero variation in refractive index along the depth of the material into the solution of Max well’s equations leads to six wave equations, one for each component of the electromagnetic field. Since these equations share the same propagation constants, the solution can be obtained by any of them and the magnetic components H_x and H_y have been chosen for their simplicity; they are solved with the finite difference computer model used for scalar equations with minimal adaptation.

© 1991 Optical Society of America