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.

中文翻译：

---

渐变折射率波导中的两色“跳舞”光子弹

理论上研究了时空孤子在聚焦二次非线性波导中的传播。该孤子是在基频及其二次谐波处的局部束能量的束缚状态。结果表明，在波导截面中具有各向异性的折射率空间分布的情况下，孤子轨迹可以是空间李沙育图形。这种时空孤子被称为两色“跳舞”轻子弹。与具有Kerr非线性的波导中的跳动子弹不同，此处讨论的跳动子弹的稳定性不需要对其孔径，功率和时间持续时间进行额外限制。另外，在群速度的异常和正常色散下都可以形成两种颜色的跳舞光子弹。