Three-dimensional light bullets in Kerr media are known to be unstable. Different schemes were proposed to overcome this obstacle. One of them is to use a nonlinear parametric interaction. Such a type of interaction can be achieved in anisotropic micro-dispersive media where space dispersion is of importance. These media allow us to reach a simultaneous approximate fulfillment of group and phase matching. To study the general (3+1)D case we apply both an approximate analytical approach and numerical simulations. We suggest that nonlinear refraction manifests itself earlier than diffraction and dispersion. Both the general (3+1)D case and axial-symmetry case are studied. With the help of averaged Lagrangian method analytical solutions are derived provided that the fixed relation between the negative coefficients of the group velocity dispersion on both harmonics holds. We demonstrate that a spatiotemporal light bullet propagates for at least 300 nonlinear lengths in anisotropic media at second harmonic generation.
Sergey V. Sazonov, Aleksandr N. Bugay, Alexey A. Kalinovich, Maria V. Komissarova, and Irina G. Zakharova, "Three-dimensional light bullets in anisotropic microdispersive media," Proc. SPIE 10232, Micro-structured and Specialty Optical Fibres V, 102320H (Presented at SPIE Optics + Optoelectronics: April 27, 2017; Published: 16 May 2017); https://doi.org/10.1117/12.2270478.
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