The cubic–quintic–septic complex Ginzburg–Landau equation formulation of optical pulse propagation in 3D doped Kerr media with higher-order dispersions

Robust propagation of optical vortex beams, necklace-ring solitons, soliton clusters and uniform-ring beams generated in the frame of the higher-order (3 + 1)-dimensional cubic–quintic–septic complex Ginzburg–Landau equation

“…It has also been revealed numerically that spatiotemporal necklace-ring solitons carrying zero, integer and even fractional angular momentum can be self-trapped over a huge propagation distance in the three-dimensional cubic-quintic complex Ginzburg-Landau equation [51]. To the best of our knowledge, spatiotemporal-localized structures in highly nonlinear doped Kerr media where higher-order nonlinearity, diffraction and dispersion act on similar footing are less reported, although we discussed the propagation and stabilization of dissipative optical light bullets under the combined influence of dispersion, diffraction, gain, loss, spectral filtering, Raman effect and cubic-quintic-septic nonlinearities in doped Kerr media with higher-order dispersion terms, based on the higher-order (3 + 1)D cubic-quintic-septic complex Ginzburg-Landau [(3 + 1)D CQS-CGL] equation, very recently [52][53][54]. We show that new families of spatiotemporal dissipative optical bullets, including self-trapped necklace-ring, ring-vortex solitons, uniform-ring beams, spherical and rhombic distributions of light bullets, and fundamental and cluster solitons, are possible in the following (3 + 1)D CQS-CGL equation with higher-order effects such as stimulated Raman scattering, self-steepening and third-, fourth-, fifthand sixth-order dispersion terms:…”