Abstract

Spatiotemporal localization is a subject of broad interest in physics, spanning fields such as plasma physics and Bose-Einstein condensation. In nonlinear optics, although localized structures such as light bullets and vortex solitons have attracted much interest, their existence generally requires a careful balance between dispersion, diffraction and nonlinearity, and they are often highly sensitive to instability [1]. In this context, however, research in guided wave optics has shown that self-similarity can act against instabilities in reduced dimensional systems [2], and we show here that this concept can be generalized to the full three dimensional case. This allows us to introduce a new class of self-similar spatiotemporal solutions of the three dimensional [or (3+l)D] nonlinear Schrödinger equation (NLSE) with gain. These solutions correspond to spatiotemporally expanding self-similar light bullets.

© 2009 IEEE