Spatiotemporal instabilities in nonlinear Kerr media with arbitrary higher-order dispersions are studied by use of standard linear-stability analysis. A generic expression for instability growth rate that unifies and expands on previous results for temporal, spatial, and spatiotemporal instabilities is obtained. It is shown that all odd-order dispersions contribute nothing to instability, whereas all even-order dispersions not only affect the conventional instability regions but may also lead to the appearance of new instability regions. The role of fourth-order dispersion in spatiotemporal instabilities is studied exemplificatively to demonstrate the generic results. Numerical simulations confirm the obtained analytic results.
© 2002 Optical Society of America
(190.0190) Nonlinear optics : Nonlinear optics
(190.3100) Nonlinear optics : Instabilities and chaos
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(260.2030) Physical optics : Dispersion
Shuangchun Wen and Dianyuan Fan, "Spatiotemporal instabilities in nonlinear Kerr media in the presence of arbitrary higher-order dispersions," J. Opt. Soc. Am. B 19, 1653-1659 (2002)