Quantum mechanics

Trigonometric functions

Gaussian

Beam (structure)

Pure mathematics

Field (mathematics)

Hyperbolic function

Soliton

Classical mechanics

Gaussian beam

Breather

Physics

Nonlinear system

Mathematics

Optics

Invariant (physics)

Mathematical analysis

Geometry

Communications in Nonlinear Science and Numerical Simulation

In this study, the propagation characteristics of complex-valued hyperbolic-cosine-Gaussian (CVHCG) beams were studied based on the nonlocal nonlinear Schrödinger equation in strongly nonlocal nonlinear media (SNNM). The CVHCG beams exhibited some unique propagation characteristics. By adjusting the complex-valued parameters, CVHCG beams can propagate with different forms in SNNM, including Gaussian-like, nearly flat-topped, multi-peak, and four-peak forms. CVHCG beams can form shape-invariant solitons and breathers under certain incident parameters. In addition, CVHCG beams can also form generalized shape-variant high-order spatial solitons and breathers. In general, the beam width and light intensity pattern of the CVHCG beams always change periodically. A complete theoretical model was constructed, and the expressions for the propagation, light intensity, and second-order moment beam width were obtained analytically. Some typical propagation characteristics were demonstrated via numerical simulations. The results of this study can be extended to investigate other complex-valued beams.

Periodic propagation of complex-valued hyperbolic-cosine-Gaussian solitons and breathers with complicated light field structure in strongly nonlocal nonlinear media