Abstract

We determine the stability of nonlinear guided waves, including solitons, nonlinear surface waves, and modes of nonlinear waveguides, by simply reading the familiar dispersion diagram without further calculation. The waveguide can be of arbitrary cross section and arbitrary profile shape and can be composed of arbitrary nonlinear materials distributed nonuniformly. This criterion is the first to our knowledge that is universal for the long-standing problem of stability of fundamental nonlinear guided waves, i.e., waves without nodes. We also show that the transverse stability of planar nonlinear guided fundamental waves demands that the material be self-defocusing in at least some portion of space, whereas planar black solitons are unstable in arbitrary self-defocusing material.

© 1993 Optical Society of America

Stability of stationary dark waves guided by nonlinear surfaces and waveguides

H. T. Tran
J. Opt. Soc. Am. B 11(5) 789-797 (1994)

Stability of bright and dark surface waves

Yijiang Chen
J. Opt. Soc. Am. B 10(6) 1077-1080 (1993)

Gaussian-beam excitation and stability of three-dimensional nonlinear guided waves

D. Mihalache, D.-M. Baboiu, D. Mazilu, L. Torner, and J. P. Torres
J. Opt. Soc. Am. B 11(7) 1244-1253 (1994)

Stationary nonlinear waves guided by thin films bounded by nonlinear diffusive media

P. Varatharajah, J. V. Moloney, A. C. Newell, and E. M. Wright
J. Opt. Soc. Am. B 10(1) 46-54 (1993)

Dark spatial solitons constructed from modes of linear waveguides

A. W. Snyder, D. J. Mitchell, and B. Luther-Davies
J. Opt. Soc. Am. B 10(12) 2341-2352 (1993)