Abstract

Nonlinear optical waveguides have been receiving increasing attention in recent years because of their potential use as all-optical switching devices. Several different forms of the dispersion equation are currently used to find the modal solutions of these waveguides.^1,2 The most widely used dispersion equation is in the addition form presented by Boardman.² This type of nonlinear dispersion equation is easy to use. However, spurious roots may appear in the calculations. In the addition form dispersion equation, there is a multiplication term of the two electric fields at the two sides of the waveguide boundaries. Because of the quadratic relationship between the two electric fields, it is difficult to determine their signs. We have found the existence of spurious roots even for a single-mode self-defocusing nonlinear waveguide, for which the two boundary fields were assumed to have the same sign. We present a new dispersion equation formed by taking the ratio of two addition form dispersion equations. Thus, the multiplication term of the electric fields is removed. The new dispersion equation is efficient to calculate, has direct physical meaning, and avoids the appearance of spurious roots.

© 1991 Optical Society of America