3D wave-packet propagation in inhomogeneous and nonlinear media of Kerr type

• Stable propagation of 3D Gaussian wave packets in nonlinear inhomogeneous fibers.
• New method: complex geometrical optics.
• Spatio-temporal evolution in ordinary differential equations.
• Collapse limit by longitudinal inhomogeneity of the fiber and initial chirps.

Complex geometrical optics (CGO) is applied to spatiotemporal evolution of 3D Gaussian wave packets in nonlinear media of Kerr type. We propose ordinary differential equations (ODEs) for wave packet parameters, which can be derived immediately from the complex eikonal equation and the complex transport equation. The eikonal equation can be used to derive ordinary differential equations for spatial and temporal widths, omitting the complicated variational process used in nonlinear optics. For the combined effect of diffraction, anomalous dispersion and nonlinear refraction we observe two solutions for temporal and spatial widths of the packet propagating in a nonlinear medium of Kerr type: diffraction/dispersion widening and spatiotemporal collapse. Moreover, we discuss the evolution of a 3D Gaussian wave packet in nonlinear inhomogeneous fiber and we present conditions for stable propagation without the collapse effect. We also discuss the influence of initial spatial and temporal chirps on 3D Gaussian wave packet evolution in nonlinear media of Kerr type and in nonlinear inhomogeneous fibers. We demonstrate the ability of CGO method to describe the evolution of a 3D wave packet in a nonlinear dispersive and strongly nonlocal medium, including the existence of a new type of spatiotemporal Gaussian soliton: an accessible spatiotemporal soliton. Moreover, the CGO method is applied to solve a novel problem of the interaction of a pair of 3D Gaussian wave packets in a nonlinear medium of Kerr type.