Objective In 1979, Berry and Balazs provided the first theoretical derivation of Airy wave packets from quantum mechanics. Finite-energy Airy beams (FEABs) are achieved by an exponential aperture in an optical study by Siviloglou and Christodoulides in 2007. FEABs have since proven a valuable research tool and their potential applications are wide-ranging. Examples are light bullets, curved plasma channel generation, optical routing, optical interconnection, vacuum electron acceleration, and laser-assisted guiding of electric discharges. FEAB applications are based on light-field regulation theory. Therefore, controlling the propagation and interaction of FEABs in different nonlinear media has attracted great interest. Thus far, most of this research has focused on the propagation dynamics of a single FEAB and the interaction of two FEABs. It is found that breathing solitons or soliton pairs can be generated during the propagation. However, the interaction of solitons and FEABs has been little investigated. In the present study, we investigate the interaction of solitons and a single FEAB or two FEABs in a saturable nonlinear medium. This novel phenomenon is applicable to beam control and optical information processing.
Methods We first established the theoretical model and considered the one-dimensional case for convenience. A light wave propagating through saturated nonlinear medium satisfies the nonlinear Schr?dinger equation. For different initial incident beams, the beam evolution is simulated in the saturated nonlinear medium using the split-step Fourier method. In addition, the dynamic characteristics of the FEAB-soliton interaction are investigated by changing the model parameters: initial amplitude ratio R, initial interval b, phase shift Q, and saturable nonlinear strength β.
Results and Discussions When a weak-energy FEAB and a soliton interacted with a phase shift of 0 or π, the collision is followed by a breathing soliton (Fig. 2). The peak intensity of the breathing soliton is higher in the in-phase case than in the out-of-phase case (Fig. 4(a)). By adjusting the phase shift in the range -π<Q<0 or 0<Q<π, the tilt angle (angle from the longitudinal axis) is first increased and then decreased, and is maximized at approximately ±3.5° when Q=?π/2 (Fig. 3). This property is a useful reference for the fabrication of optical interconnection devices. In the in-phase case, enlarging the initial amplitude ratio and reducing the initial interval more strongly emphasized the linearly increasing trend of the average peak intensity of the breathing soliton. When the initial interval |b| is enlarged, the average peak intensity of the breathing soliton is almost unchanged in the in-phase case (Fig. 4(b)), but the reverse is true in the out-of-phase case (Fig. 4(c)). Meanwhile, increasing the nonlinear saturation parameter β increased the average peak intensity of the breathing soliton and decreased the breathing period, in both the in-phase and out-of-phase cases (Fig. 6). When two FEABs interacted with the soliton, changing the initial interval b altered the period of the breathing soliton (Fig. 8), and when R is sufficiently large, increasing its initial amplitude ratio gradually increased the peak intensity of the breathing soliton. Coexistence of solitons and soliton pairs is enabled by energy shedding from the Airy main and side lobes (Fig. 9).
Conclusions The interaction of FEABs and solitons is numerically studied in a saturated nonlinear medium, and the effects of a single FEAB and two FEABs on the soliton propagation are analyzed. For weak-energy FEABs, the post-collision propagation mode of the soliton became a damped oscillatory mode. The breathing soliton is tilted rightward at -π<Q<0 and leftward at 0<Q<π. The maximum tilt angle is ±3.5° at Q=?π/2. When the initial amplitude ratio increased and the initial interval decreased, a monotonic increase and decrease in the mean intensity of the breathing soliton is observed in the in-phase and out-of-phase cases, respectively. For strong energy FEABs, the peak position of the breathing soliton moved leftward in the in-phase case, but in the out-of-phase case, two solitons with different intensities are formed with a certain angle. When two FEABs interacted with a soliton for a given initial amplitude ratio, the mean peak intensity of the breathing soliton is linearly related to the initial interval in both the in-phase and out-of-phase cases. Increasing the initial amplitude ratio gradually enhanced the beam interaction, and a single soliton or soliton pair is formed. When the amplitude ratio is sufficiently large, the soliton and soliton pair could co-exist because energy is shed from the Airy main and side lobes.
