Abstract

It is often difficult to understand nonlinear guided wave effects because our intuition is built upon linear phenomena. We wish here to show that nonlinear phenomena can be approached from a linear perspective. This is not a new technique for solving nonlinear equations. Rather, we show that the linear perspective (1) anticipates the possible classes of nonlinear waves and their characteristics. It thus predicts novel phenomena, such as solitons with internal dynamics, and it facilitates previously unforeseen generalizations, such as those necessary for the universal criterion for stability. By imparting physical insight, it (2) offers a powerful predictive tool, for example one which foreshadows the phase shift and the radiation free nature of soliton collisions. Further, it (3) shows how the mathematical foundation for nonlinear waves is borrowed from the literature of linear waves. Finally, it (4) allows for closed form solutions of illustrative examples to be lifted directly from the pages of linear physics. This powerful approach is demonstrated here through the vehicle of spatial guided wave optics, embracing such phenomena as guiding and manipulating light by light itself^1-7.

© 1995 Optical Society of America