Multi-hump optical solitons in a saturable medium

Coupled Helmholtz equations: Chirped solitary waves

We investigate the existence and stability properties of chirped gray and anti-dark solitary waves within the framework of a coupled cubic nonlinear Helmholtz equation in the presence of self-steepening and a self-frequency shift. We show that for a particular combination of self-steepening and a self-frequency shift, there is not only chirping but also chirp reversal. Specifically, the associated nontrivial phase has two intensity dependent terms: one varies as the reciprocal of the intensity, while the other, which depends on non-Kerr nonlinearities, is directly proportional to the intensity. This causes chirp reversal across the solitary wave profile. A different combination of non-Kerr terms leads to chirping but no chirp reversal. The influence of a nonparaxial parameter on physical quantities, such as intensity, speed, and pulse width of the solitary waves, is studied as well. It is found that the speed of the solitary waves can be tuned by altering the nonparaxial parameter. Stable propagation of these nonparaxial solitary waves is achieved by an appropriate choice of parameters.

Helmholtz-Manakov solitons

A different spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (HM) equation, for describing the evolution of broad multicomponent self-trapped beams in Kerr-type media. By omitting the slowly varying envelope approximation, the HM equation can describe accurately vector solitons propagating and interacting at arbitrarily large angles with respect to the reference direction. The HM equation is solved using Hirota's method, yielding four different classes of Helmholtz soliton that are vector generalizations of their scalar counterparts. General and particular forms of the three invariants of the HM system are also reported.

Generation of higher-order optical (2+1)-dimensional spatial vector solitons in a nonlinear anisotropic medium

We investigate the generation of higher-order optical vector solitons in two transverse dimensions in anisotropic nonlinear media consisting of an incoherent superposition of a Gaussian beam and a higher-order laser mode with a complex internal modal structure. We demonstrate both numerically and experimentally various examples of these stable self-trapped light structures and show that vortex modes carrying topological charge always decay into multiple-humped structures that remain self trapped during propagation. Furthermore, we demonstrate the mutual stabilization of a triple- and a double-humped transverse light structure leading to the formation of a two-dimensional vector soliton without a stabilizing fundamental Gaussian mode.

Stable bound states of one-dimensional autosolitons in a bistable laser

Differential equations describing the interaction of two weakly overlapping autosolitons in the transverse section of a wide-aperture laser with a saturable absorber are derived and analyzed. The existence of in-phase and out-of-phase stable bound autosoliton states is predicted analytically and confirmed numerically.

Instability of multiple pulses in coupled nonlinear Schrodinger equations

An analytical technique for constructing multiple pulses is presented in this article; with it we uncover a homoclinic bifurcation through which multihumped solitary waves can be generated in systems of coupled nonlinear Schrodinger equations. A method is then developed to determine the (in)stability of multiple pulses produced by this mechanism. The analysis is applied to two models that describe optical phenomena in dispersive quadratic and Kerr media, respectively. It sheds considerable light upon the characteristics that predispose multiple pulses arising in this class of systems to be unstable.