The supercontinuum generation and manipulation of Airy-Gaussian pulses in a photonic crystal fiber with three zero-dispersion points are studied using the split-step Fourier method. Firstly, the spectral evolution of Airy-Gaussian pulses in four photonic crystal fibers with different barrier widths was discussed, and the optimal fiber was determined after considering the factors of width and flatness. By analyzing the mechanism of supercontinuum generation in photonic crystal fibers with single, double and three zero-dispersion points, it is found that the photonic crystal fiber with three zero-dispersion points have a larger spectral width due to the component of tunneling solitons. Then, the effects of four characteristic parameters (truncation factor a, distribution factor χ₀, initial chirp C and central wavelength λ) on forming the supercontinuum spectrum of Airy-Gaussian pulses are analyzed in detail. The results show that the spectral width and energy intensity of the dispersive wave and tunneling soliton generation can be well controlled by adjusting the barrier width and initial parameters of the pulse. These research results provide a theoretical basis for generating and manipulating high-power mid-infrared supercontinuum sources.

The evolution of Cos−Gaussian beams in periodic potential optical lattices is theoretically and numerically investigated. By theoretical analysis, a breathing soliton solution of the Gross–Pitaevskii equation with periodic potential is obtained, and the period of the breathing soliton is solved. In addition, the evolution of Cos−Gaussian beams in periodic potential optical lattices is numerically simulated. It is found that breathing solitons generate by appropriately choosing initial medium and beam parameters. Firstly, the effects of the initial parameters of Cos−Gaussian beams (initial phase and width) on its initial waveform and the propagation characteristics of breathing soliton are discussed in detail. Then, the influence of the initial parameters (modulation intensity and modulation frequency) of a photonic lattice on the propagation characteristics of breathing solitons is investigated. Finally, the effects of modulation intensity and modulation frequency on the width and period of the breathing soliton are analyzed. The results show that the number of breathing solitons is manipulated by controlling the initial parameters of Cos−Gaussian beams. The period and width of a breathing soliton are controlled by manipulating the initial parameters of a periodic photonic lattice. The results provide some theoretical basis for the generation and manipulation of breathing solitons.

We numerically investigate and statistically analyze the impact of medium parameters (modulation depth P, modulation factor ω, and gain/loss strength W ₀) and beam parameters (truncation coefficient a and distribution factor χ ₀) on the propagation characteristics of a cosh-Airy beam in the Gaussian parity-time (PT)-symmetric potential. It is demonstrated that the main lobe of a cosh-Airy beam is captured as a soliton, which varies periodically during propagation. The residual beam self-accelerates along a parabolic trajectory due to the self-healing property. With increment in P, the period of a trapped soliton decreases almost monotonically, while the peak power of a trapped soliton increases monotonically. With the increase in ω or decrease in the absolute value of W ₀, the period and peak power of a trapped soliton decrease rapidly and then almost remain unchanged. Moreover, it is indicated that the period of a trapped soliton remains basically unchanged no matter a and χ ₀ increase or decrease. The peak power of a trapped soliton increases with increment of a, but the peak power of a trapped soliton stays relatively constant irrespective of variation in χ ₀.

The propagation characteristics of Airy beams in an inhomogeneous medium with periodic potential are studied theoretically and numerically. The Gross–Pitaevskii equation was solved with periodic potential using the separating variables method, and a breathing soliton solution and the breathing period were obtained. Further, the propagation properties of an Airy beam, and the interaction between two Airy beams while considering the medium parameters and beam parameters were numerically simulated in detail. First, we discuss the influence of the initial medium parameters (modulation intensity P and modulation frequency ω) on the propagation characteristics. Then, we investigate the effect of the initial beam parameters (initial chirp C and position x₀) on the propagation characteristics. Lastly, the interaction of two Airy beams with opposite spatial positions for different phase φ, amplitude A, and initial interval x₀ is analyzed. The breathing period and central position of the breathing solitons could be controlled by changing the initial medium parameters. By varying the initial beam parameters, the deflection direction and size, and the maximal intensity of the breathing solitons were manipulated. The breathing solitons of different bound states were formed by changing the phase φ, amplitude A, and initial interval x₀ of two Airy beams. The results provide a theoretical basis for the propagation and manipulation of Airy beams.