Two-color ‘dancing’ light bullets in the graded-index waveguide

Abstract

The propagation of a spatiotemporal soliton in a focusing quadratic-nonlinear waveguide is theoretically investigated. This soliton is a bound state of localized bunches of light energy at the fundamental frequency and at its second harmonics. It is shown that with anisotropic spatial distribution of the refractive index in the cross section of the waveguide, the soliton trajectory can be a spatial Lissajous figure. Such spatiotemporal solitons are called two-color ‘dancing’ light bullets. Unlike dancing light bullets in a waveguide with Kerr nonlinearity, the stability of the dancing bullets discussed here does not require additional restrictions on their apertures, powers, and temporal durations. In addition, a two-color dancing light bullet can be formed both under anomalous and normal dispersion of group velocity. It also distinguishes a two-color dancing light bullet in a quadratic nonlinear waveguide from a dancing light bullet in a Kerr nonlinear waveguide.