Generation of stable “dancing” two-component optical bullets

Abstract

Recently a possibility of the formation of “dancing” light bullets was analytically shown in graded-index waveguides with both Kerr and quadratic nonlinearities. At that, a two-color “dancing” light bullet in a quadratic nonlinear waveguide may form at both anomalous and normal group velocity dispersion at the fundamental frequency. Here and in what follows we refer as “dancing” light (optical) bullets spatiotemporal solitons whose trajectories can be spatial Lissajous figures with anisotropic spatial distribution of the refractive index in the cross section of the waveguide. Stability of a two-color “dancing” light bullet was theoretically demonstrated without additional conditions for its temporal duration, aperture, and power. These results were established with the help of the averaged Lagrangian method in the framework of the quasi-optical approach under the conditions of phase and group matching. The mentioned conditions are known to be hardly achievable in experiment. In the present work we study two- color “dancing” light bullet generation by means of numerical simulation including the cases when only one of the conditions of synchronism is fulfilled. We demonstrate that a pulse at the doubled frequency is generated in the waveguide at second harmonic generation (SHG), followed by the formation of the bound state of both harmonics representing a two-color “dancing” light bullet