Based on the Snyder and Mitchell model, a closed-form propagation expression of astigmatic sin-Gaussian beams through strongly nonlocal nonlinear media (SNNM) is derived. The evolutions of the intensity distributions and the corresponding wave front dislocations are discussed analytically and numerically. It is generally proved that the light field distribution varies periodically with the propagation distance. Furthermore, it is demonstrated that the astigmatism and edge dislocation nested in the initial sin-Gaussian beams greatly influence the pattern configurations and phase singularities during propagation. In particular, it is found that, when the beam parameters are properly selected, a vortex beam with perfect doughnut-shaped profile can be obtained for astigmatic sin-Gaussian beams with two-lobe pattern propagating in SNNM.

Propagation Property of an Astigmatic sin–Gaussian Beam in a Strongly Nonlocal Nonlinear Media

Abstract. The controllable self-accelerating and self-decelerating Airy–Ince–Gaussian (CAiIG) wave packets in strongly nonlocal nonlinear media are investigated theoretically and numerically by solving the (3 + 1)D Schrödinger equation in cylindric coordinates. Typical examples of the obtained solutions are based on the ratio of the input power and the critical power as well as the initial velocity and the ellipticity. The CAiIG wave packets are constructed by the Airy pulses with initial velocity in temporal domain and the controllable Ince–Gaussian (IG) beams in spatial domain. Self-decelerating and self-accelerating CAiIG wave packets are obtained by selecting different initial velocities. The CAiIG wave packets keep approximately nondispersion properties in temporal dimension. However, the width of packets periodically oscillate or keep steady in spatial dimension according to the ratio of the input power and the critical power. The transverse field patterns of the CAiIG wave packets are manipulated by the IG wave packets, meanwhile the Airy pulses affect their transverse amplitudes. For the self-accelerating CAiIG wave packets, the transverse intensity decays during the propagation. However, to the self-decelerating CAiIG wave packet, the transverse intensity initially vibrates then decays. The direction of the energy flow of CAiIG wave packets in spatial domain periodically changes from the propagating center if the ratio of the input power and the critical power is not equal to 1, which causes the CAiIG beams periodically oscillating during propagation. Their Poynting vector snapshots at different propagating distances are shown.

Propagation of controllable spatiotemporal Airy–Ince–Gaussian beams propagating in strongly nonlocal nonlinear media

The controllable self-accelerating and self-decelerating Airy–Ince–Gaussian (CAiIG) wave packets in strongly nonlocal nonlinear media are investigated theoretically and numerically by solving the (3 + 1)D Schrödinger equation in cylindric coordinates. Typical examples of the obtained solutions are based on the ratio of the input power and the critical power as well as the initial velocity and the ellipticity. The CAiIG wave packets are constructed by the Airy pulses with initial velocity in temporal domain and the controllable Ince–Gaussian (IG) beams in spatial domain. Self-decelerating and self-accelerating CAiIG wave packets are obtained by selecting different initial velocities. The CAiIG wave packets keep approximately nondispersion properties in temporal dimension. However, the width of packets periodically oscillate or keep steady in spatial dimension according to the ratio of the input power and the critical power. The transverse field patterns of the CAiIG wave packets are manipulated by the IG wave packets, meanwhile the Airy pulses affect their transverse amplitudes. For the self-accelerating CAiIG wave packets, the transverse intensity decays during the propagation. However, to the self-decelerating CAiIG wave packet, the transverse intensity initially vibrates then decays. The direction of the energy flow of CAiIG wave packets in spatial domain periodically changes from the propagating center if the ratio of the input power and the critical power is not equal to 1, which causes the CAiIG beams periodically oscillating during propagation. Their Poynting vector snapshots at different propagating distances are shown. 

The Airy-Gaussian wave packets are the Airy wave packets modulated by the Gaussian wave packets. Basing on the separating variable method, the analytical solution has been accessed according to solving the paraxial beam equation in cylindric coordinates in free space. The Airy-Gaussian wave packets with complex variables are combing the Airy function with the complex variables and the Gaussian beams. The propagation characteristics of the complex variables Airy-Gaussian wave packets are studied. The complex variables Airy-Gaussian wave packets will rotate with the increase of propagating distance. Poynting vector reveals the essence of this phenomenon.

Propagation characteristics of complex variables Airy-Gaussian wave packets within free space

The conversion of high-mode solitons propagating in Strongly Nonlocal Nonlinear Media (SNNM) in three coordinate systems, namely, the elliptic coordinate system, the rectangular coordinate system and the cylindrical coordinate system, based on the Snyder–Mitchell Model that describes the paraxial beam propagating in SNNM, is discussed. Through constituting the trial solution with modulating the Gaussian beam by Ince polynomials, the closed-solution of Gaussian beams in elliptic coordinate is accessed. The Ince–Gaussian (IG) beams constitute the exact and continuous transition modes between Hermite–Gaussian beams and Laguerre–Gaussian (LG) beams, which is controlled by the elliptic parameter. The conditions of conversion in the three types of solitons are given in relation to the Gouy phase invariability in stable propagation. The profiles of the IG breather at a different propagating distance are numerically obtained, and the conversions of a few IG solitons are illustrated. The difference between the IG ...

Xiaping Zhang

Papers

Conversion of the high-mode solitons in strongly nonlocal nonlinear media