We investigate the generalized higher-order nonlinear Schrödinger equation with variable coefficients under two sets of parametric conditions. The exact one-soliton solution is presented by the ansatz method for one set of parametric conditions. For the other, exact multisoliton solutions are presented by employing the Darboux transformation based on the Lax pair. As an example, we consider a soliton control system, and the results show that the soliton control system may relax the limitations to parametric conditions. The stability of the solution is discussed numerically; the results reveal that finite initial perturbations, such as amplitude, chirp, or white noise, could not influence the main character of the solution. In addition, the evolution of a quite arbitrary Gaussian pulse and the interaction between neighboring pulses have been studied in detail.

Based on the soliton solution on a continuous wave background for an integrable Hirota equation, the reduction mechanism and the characteristics of the Peregrine rogue wave in the propagation of femtosecond pulses of optical fiber are discussed. The results show that there exist two processes of the formation of the Peregrine rogue wave: one is the localized process of the continuous wave background, and the other is the reduction process of the periodization of the bright soliton. The characteristics of the Peregrine rogue wave are exhibited by strong temporal and spatial localization. Also, various initial excitations of the Peregrine rogue wave are performed and the results show that the Peregrine rogue wave can be excited by a small localized (single peak) perturbation pulse of the continuous wave background, even for the nonintegrable case. The numerical simulations show that the Peregrine rogue wave is unstable. Finally, through a realistic example, the influence of the self-frequency shift to the dynamics of the Peregrine rogue wave is discussed. The results show that in the absence of the self-frequency shift, the Peregrine rogue wave can split into several subpulses; however, when the self-frequency shift is considered, the Peregrine rogue wave no longer splits and exhibits mainly a peak changing and an increasing evolution property of the field amplitude.

A three-dimensional dual-band perfect absorber in the THz range (3-10 THz) is theoretically investigated. The absorber is composed of periodically placed cross-and disk-shaped graphene arrays on the top of a gold layer separated by a thick SiO ₂ dielectric spacer. The simulated results show two absorption peaks with near-unity absorbance (99.923% and 99.601%) at wavelengths 43.747 μm and 69.94 μm, respectively. Also, the absorber is insensitive to the polarization of the incident light and has a good tolerance to the incident angle whether it is TE or TM waves. Moreover, the peak wavelengths of the absorber can be flexibly modulated by varying the Fermi level μ _C of graphene while no need to refabricate the structure. This paper provides a new perspective for the design of graphene-based tunable multiband perfect THz absorbers, but not limited to THz absorbers, and may also be used in other THz graphene-based photonic devices.

The generalized nonlinear Schrödinger model with distributed dispersion, nonlinearity, and gain or loss is considered and the explicit, analytical solutions describing the dynamics of bright solitons on a continuous-wave background are obtained in quadratures. Then, the generation, compression, and propagation of pulse trains are discussed in detail. The numerical results show that solitons can be compressed by choosing the appropriate control fiber system, and pulse trains generated by modulation instability can propagate undistorsted along fibers with distributed parameters by controlling appropriately the energy of each pulse in the pulse train.

In the paper, we investigate the propagation dynamics of the Gaussian beam modeled by the fractional Schrödinger equation (FSE) with a variable coefficient. In the absence of the beam’s chirp, for smaller Lévy index, the Gaussian beam firstly splits into two beams, however under the action of the longitudinal periodic modulation, they exhibit a periodically oscillating behaviour. And with the increasing of the Lévy index, the splitting behaviour gradually diminishes. Until the Lévy index equals to 2, the splitting behaviour is completely replaced by a periodic diffraction behaviour. In the presence of the beam’s chirp, one of the splitting beams is gradually suppressed with the increasing of the chirp, while another beam on the opposite direction becomes stronger and exhibits a periodically oscillating behaviour. Also, the oscillating amplitude and period are investigated and the results show that the former is dependent on the modulation frequency, the Lévy index and the beam’s chirp, the latter depends only on the modulation frequency. Thus, the evolution of the Gaussian beam can be well manipulated to achieve the beam management in the framework of the FSE by controlling the system parameters and the chirp parameter.

We consider the nonlinear Schrödinger equation with variable coefficients that describes beam propagation in inhomogeneous graded-index waveguides. By using the direct transformation of variables and functions, we present the exact general bright and dark spatial self-similar solutions. As an application, we discuss the nonlinear tunneling of optical similaritons. The results show that under an integrable condition, the optical waves can similarly pass through the nonlinear barrier or well, and the interaction between the neighboring waves is elastic collision. Under a nonintegrable condition, when they pass through the nonlinear barrier, the optical beams can effectively be compressed for the relatively small value of height of the nonlinear barrier. However, the beam splits into some filaments when the height of the nonlinear barrier is large enough.