Nonparaxial rogue waves in optical Kerr media

Dipole and quadrupole nonparaxial solitary waves

The cubic nonlinear Helmholtz equation with third and fourth order dispersion and non-Kerr nonlinearity, such as the self steepening and the self frequency shift, is considered. This model describes nonparaxial ultrashort pulse propagation in an optical medium in the presence of spatial dispersion originating from the failure of slowly varying envelope approximation. We show that this system admits periodic (elliptic) solitary waves with a dipole structure within a period and also a transition from a dipole to quadrupole structure within a period depending on the value of the modulus parameter of a Jacobi elliptic function. The parametric conditions to be satisfied for the existence of these solutions are given. The effect of the nonparaxial parameter on physical quantities, such as amplitude, pulse width, and speed of the solitary waves, is examined. It is found that by adjusting the nonparaxial parameter, the speed of solitary waves can be decelerated. The stability and robustness of the solitary waves are discussed numerically.

Rogue-pair and dark-bright-rogue waves of the coupled nonlinear Schrödinger equations from inhomogeneous femtosecond optical fibers

The coupled inhomogeneous Schrödinger equations with a wide range of applications describing a field of pluses with the right and the left polarizations that take into account cross-phase modulations, stimulated Ramani scattering, and absorption effects are investigated. A combination of several different approaches is used in a novel way to obtain the explicit expressions for the rogue-pair and dark-bright-rogue waves. We study the dynamics of these structurally stable rogues and analyze the effects of a parameter that controls the region of stability that intrinsically connects the cross-phase modulation and other Kerr nonlinearity factors. The effects of the right and left polarizations on the shape of the rogue-pair and other solitary rogue waves are graphically analyzed. These rogue-pair waves are studied on periodic and non-periodic settings. We observe that rogue-pair wave from the right and left polarizations has a similar structure while the dark-bright-rogue waves have quite different intensity profiles.

Influence of optical activity on rogue waves propagating in chiral optical fibers

We derive the nonlinear Schrödinger (NLS) equation in chiral optical fiber with right- and left-hand nonlinear polarization. We use the similarity transformation to reduce the generalized chiral NLS equation to the higher-order integrable Hirota equation. We present the first- and second-order rational solutions of the chiral NLS equation with variable and constant coefficients, based on the modified Darboux transformation method. For some specific set of parameters, the features of chiral optical rogue waves are analyzed from analytical results, showing the influence of optical activity on waves. We also generate the exact solutions of the two-component coupled nonlinear Schrödinger equations, which describe optical activity effects on the propagation of rogue waves, and their properties in linear and nonlinear coupling cases are investigated. The condition of modulation instability of the background reveals the existence of vector rogue waves and the number of stable and unstable branches. Controllability of chiral optical rogue waves is examined by numerical simulations and may bring potential applications in optical fibers and in many other physical systems.