Abstract

We consider solutions to the second-harmonic generation equations in two- and three-dimensional dispersive media, in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. We obtain the general solution in an approximate analytical form by means of a variational approach. Then, we directly simulate the two- and three-dimensional cases, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that stable spatiotemporal solitons indeed exist and are stable. These correspond physically to spatiotemporal solitary waves forming in a two-dimensional waveguide or bulk crystal made of nonlinear material like lithium niobate, in which the mutual interaction of two waves stabilizes each against dispersion and diffraction.

© 1998 Optical Society of America