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In this paper, we illustrate how the periodically modulated nonlinear parameter induced by the spatial beam oscillation can be used to generate broadband resonant radiations, through a train of dark pulses in normally dispersive graded-index multimode fibers under the efficient quasi-phase-matching schemes. More precisely, we demonstrate that two co-propagating waves with equal intensities and certain temporal delays can induce the formation of a train of dark solitons, with each emitting multiple resonant radiation lines, which can possibly form multiple radiation continuums based on vast amount of excited dark solitons. The nonlinear-interaction-aided excitation of dark pulses and their radiations appear to occur through a deterministic pathway, in sharp contrast to the situation for bright pulses in the anomalous dispersion region. The quasi-phase-matching condition via periodic oscillation of spatial beam in the normal-dispersion regime adds a unique dimension to the physical design of multimode waveguides, allowing the spectrum to be engineered for specific applications.

Based on the extended Huygens-Fresnel principle, we have derived the analytical expression of the average intensity of optical coherence lattices (OCLs) in oceanic turbulence with anisotropy, and then the beam quality parameters including the Strehl ratio (SR) and the power-in-the-bucket (PIB) are obtained. One can find that the OCLs will eventually evolve into Gaussian shape with the periodicity reciprocity gradually breaking down when propagating through the anisotropic ocean water, and that the trend of evolving into Gaussian can be accelerated for increasing the ratio of temperature and salinity contributions to the refractive index spectrum ω, the lattice constant a and the rate of dissipation of mean square temperature χT or decreasing the anisotropic factor ξ and the rate of dissipation of turbulent kinetic energy per unit mass of fluid ε. Further, the SR and PIB in the target plane under the effects of oceanic parameters are discussed in detail, and the SR and PIB can be increased for the larger ξ and ε or the smaller χT and ω, namely, the beam quality becomes better. Our results can find potential application in the future optical communication system in an oceanic environment.

The dynamics of Airy beams modeled by the fractional Schrodinger equation (FSE) with the potential barrier are numerically investigated. Adjusting the Levy index provides a convenient way to control the diffraction of Airy beams which presents the non-diffraction and splitting property. It has been found that the total reflection of beams occurs when the depth of the single potential barrier exceeds the threshold, and that the number of reflected waves is influenced by the Levy index and the location of potential barrier. However, the periodic self-imaging phenomenon of Airy beams is shown under a symmetric potential barrier when the Levy index is equal to one, and the self-imaging period of the asymmetric Airy beams is analytically demonstrated and is as twice as that of symmetric Gaussian beams, moreover, the chaoticon of light field is formed during propagation as the Levy index increases. All the properties of Airy beams modeled by FSE confirm the potential application in optical manipulation.

We show that the group-velocity-led optical event horizon (OEH) in optical fibers provides a convenient way to actively control the propagation property of higher-order solitons by a comparatively weak dispersive wave (DW) pulse. It has been found numerically that clean soliton breakup, a process by which a second-order soliton completely splits into a pair of constituent solitons with vastly different power proportions after interacting with the weak DW pulse, will occur while external DWs become polychromatic. The temporal separation between both constituent solitons can be controlled by adjusting the power of the external DW. The more energetic main soliton is advanced/trailed in time depending on the selected frequency of input DW pulse. We have developed an analytic formalism describing the external acting-force (AF) perturbation. These results provide a fundamental explanation and physical scaling of optical pulse evolution in optical fibers and can find applications in improved supercontinuum sources.

We have numerically investigated the propagation properties of ring Airy beams modeled by a fractional Schrodinger equation (FSE). Beam splitting is exhibited and clarified from the view of group delay. Compared with the case of the condition in free space, the focal intensity is greatly enhanced and presents a trend from increasing to decreasing with the decrement of the Levy index, while the focal length largely increases; in addition, the parabolic trajectory is distorted with the Bessel pattern gradually disappearing. However, both the focal intensity and its length get decreased due to the absence of the initial phase of ring Airy beams; simultaneously, the size of the focal spot decreases for a larger Levy index. The changes of focusing properties are clearly clarified. Moreover, without initial phase, the ratio of focal intensity under the Levy index to the condition in free space is given to show the faster growth of focal intensity when the Levy index is lower than 1.25; otherwise, the trend gets reversed. The autofocusing properties of ring Airy beams modeled by FSE can find applications in optical trapping and manipulation.

The dynamics of finite energy Airy beams modeled by the fractional Schrodinger equation (FSE) with a linear potential are numerically investigated. Different from the propagation properties of Airy beams described by the standard Schrodinger equation, the splitting phenomenon, which is presented under the FSE without potential, is influenced by the quadratic chirp and the Levy index. As the linear potential is considered, the periodic evolution of Airy beams is shown, and the period is inversely proportional to the linear potential coefficient. The beam width can undergo an abrupt decrease or increase depending on the sign of potential coefficient. The beam deviation distance increases with the beam width greatly changed if the Levy index increases. Moreover, the quadratic chirp does not influence the evolution period but the intensity distribution. In addition, the intriguing properties are analytically clarified. All these features confirm the promising applications of Airy beams in optical manipulation and optical switch.

We have numerically studied the effect of mutual interactions between soliton and dispersive waves and the possibility to create a solitonic well consisting of initial twin-solitons moving away from each other to trap the incident dispersive wave. Different from the case of the solitonic cage formed by the velocity-matched twin-solitons, the intense dispersive wave can break up into small pulses, which are almost completely trapped within the solitonic well. Moreover, the corresponding spectrum of the trapped dispersive wave can be narrowed firstly and then expanded, and a new dispersive wave can be generated as the twin-solitons collision occurred. By adjusting either the peak power or temporal width of incident dispersive wave, both the intensity of the collision-induced dispersive wave and the position where it is generated can be controlled.

The controlling optical frequency in the regime of an optical event horizon by the collision between a soliton and a probe pulse is investigated, and the process by which the probe is converted into the generated pulse (idler) with new optical frequency is reversible. For the two cases in which the probe wave interacts with a bright/dark soliton, a unified analytical formula governing the reversible frequency conversion process is derived that can predict the frequency of the idler very well. This reversible frequency-conversion process is validated by cascaded four-wave mixing (FWM) triggered by a set of quasi-CW fields, strongly suggesting that the process arose from cascaded Bragg scattering. It establishes a link between the nonlinear interactions of a soliton with the probe and FWM of monochromatic quasi-CWs.