Self-accelerating Airy-Ince-Gaussian and Airy-Helical-Ince-Gaussian light bullets in free space

Abstract

The evolution of the three-dimensional (3D) self-accelerating Airy-Ince-Gaussian (AiIG) and Airy-Helical-Ince-Gaussian (AiHIG) light bullets is investigated by solving the (3+1)D linear spatiotemporal evolution equation of an optical field analytically. As far as we know, the numerical experimental demonstrations of the Ince-Gaussian (IG) and Helical-Ince-Gaussian (HIG) beams in various modes are first developed to study the evolution characteristics of the different 3D spatiotemporal light bullets. A conclusion can be drawn that the different photoelastics, pulse stacked, boundary, elliptical ring and physically separated in-line vortices can be achieved by adjusting the ellipticity, the evolution distance and the mode-number of light bullets.

Spatiotemporal Airy Ince–Gaussian wave packets in strongly nonlocal nonlinear media

“…Likewise, one can easily obtain the self-accelerating AiIG breathers periodically oscillating when the balance between diffraction and nonlinearity is broken. The phenomenon shows the spatial periodically oscillating (breather state) or steady (soliton state), temporal self-accelerating and approximately non-dispersion properties of AiIG breathers and solitons reported in SNNM are different from other spatiotemporal Airy related wave packets diffracting in spatial dimension while propagating in free space 17 , 18 . Without loss of generality, the relationship of AiIG, Airy Laguerre Gaussian (AiLG), and Airy Hermite Gaussian (AiHG) breathers and solitons will be analysed as follow.…”

“…5(a1–a3) ] to reconstruct the computer-generated holograms [see gray insets display of Fig. 5(c1–c3) ] of the desired beam profiles 18 . The holograms are obtained by computing the interference patterns between the complex amplitude profile of the hIG beams at the Z = 0 plane [see Fig.…”

“…Semifocal separation f ( Z ) = f 0 w ( Z )/ w 0 , f 0 denotes semifocal separation at waist plane Z = 0. ξ and J satisfy continuity in the whole space. ϕ G is the Gaussian solution 5 , 18 where D is a normalization constant.…”

“…Over the past decades, tremendous efforts have been made by researchers to generate the three-dimensional (3D) localized optical solitons 13 – 21 , which also called spatiotemporal light bullets, are localized in both space and time. Among which, Airy wave packets were widely reported in free space 16 – 18 and quadratic index medium 20 , 21 due to the self-accelerating 22 – 26 , self healing 27 and no diffraction 28 features of Airy distribution. It is worth mentioning some pioneer works in Airy related wave packets.…”

“…have studied the 3D localized Airy-Hermite-Gaussian and Airy-Helical-Hermite-Gaussian wave packets 17 , and Peng et al . have obtained the 3D localized Airy-Ince-Gaussian and Airy-Helical-Ince-Gaussian wave packets 18 . Then, the chirped Airy Gaussian vortex wave packets in quadratic index medium 20 and Airy Gaussian and Airy Gaussian vortex light bullets in harmonic potential 21 have been reported.…”