Abstract

A path integral approach to the treatment of propagation problems in integrated optics is presented. This path integral formulation is obtained by exploiting the formal isomorphism between the scalar optical wave equation and the time-dependent Schroedinger wave equation. The propagation constant for the fundamental mode is obtained using the Feynman-Kac formula and a similar approach is used to obtain the propagation constant of the first-order mode. This path integral treatment of integrated optics is implemented numerically using a simple matrix multiplication method that can accommodate arbitrarily graded refractive-index profiles. Propagation constants obtained by this method are shown to be in good agreement with exact results.

© 1986 Optical Society of America