Abstract

Basis set techniques commonly used in quantum chemistry to compute the eigenvalues and eigenfunctions of the time-independent Schrodinger equation are applied to the paraxial wave equation to compute the propagation constants and the modal field distributions for dielectric waveguide structures with arbitrarily graded refractive-index profiles. A product basis of quantum mechanical harmonic oscillator eigenfunctions is used to convert the eigenvalue form of the paraxial wave equation into a matrix diagonalization problem. For a typical single (double) channel waveguide structure a basis, i.e., matrix, size of about 100 (200) is sufficient to obtain converged values for the low-order propagation constants and modal field distributions. Consequently, the propagation properties of these structures are easily studied on a VAX minicomputer. The utility of this method in diffused channel waveguide design and analysis is illustrated using examples from Ti:LiNbO₃ integrated optical waveguide technology.

© 1987 Optical Society of America