Propagation of Cosh-Airy and Cos-Airy Beams in Parabolic Potential

Abstract

The analytical expressions of one-dimensional cosh-Airy and cos-Airy beams in the parabolic potential are derived in the general and the phase transition points. The expression in the phase transition point shows a symmetric Gaussian intensity profile and is independent of any Airy features, which is completely different from that in the general point. The intensity, the center of gravity, and the effective beam size of the cosh-Airy and cos-Airy beams in the parabolic potential are periodic and have the same period. The effects of the transverse displacement, the cosh factor, and the cosine factor on these periodic behaviors are also investigated. The direction of self-acceleration reverses every half-period. The phase transition point is also the inversion point of the intensity distribution, which indicates that the intensity distributions before and after the phase transition point are mirror symmetrical. The periodic behaviors of the normalized intensity, the center of gravity, and the effective beam size of the cosh-Airy and cos-Airy beams in the parabolic potential are attractive and well displayed. The results obtained here may have potential applications in particle manipulation, signal processing, and so on.

Comparison of Mainardi, cos-Mainardi and cosh-Mainardi beams with and without optical vortex in FT and FrFT systems

“…The propagation of Cos-AiB and Cosh-AiB [42] have been investigated in different mediums. Optical vortex, which is a natural phenomenon in light propagation, was investigated in AiBs [43][44][45][46][47]. The propagation of AiBs with optical vortex and without optical vortex have also been investigated under the fractional Fourier transform [48,49].…”

Controllable transmission of chirped cosh-Gaussian beams in parabolic potential

“…Meanwhile, the same team studied an anharmonic propagation of two-dimensional beams in a parabolic potential, in which periodic inversion and variable rotation are still there [13]. It should be noted that the parabolic potential has various impacts on the beam propagation, including Fourier transform operator [3,[14][15][16], modulation of a symmetric beam [17] and so on [18,19]. Since self-Fourier transform can be associated with gradient-index (GRIN) media, the propagation of pulses in graded-index bers can be achieved by introducing external parabolic potential in optics.…”

“…Besides, researchers investigated the propagation of the Pearcey Gaussian (PeG) beams in a medium with a parabolic refractive index, in which the parabolic refractive index is responsible for the focusing effect [21]. Subsequently, plenty of special beams in a medium with parabolic refractive index were studied, including cosh-Airy beam [17], Hermite-Gaussian vortex beam [22], chirped Pearcey Gaussian vortex beam [23] and so on [24]. Especially, strongly nonlocal nonlinear model proposed by Snyder and Mitchell [25] can be converted into the linear Schrödinger equation with a parabolic potential, thus we can conveniently simplify the nonlinear problem to a linear problem, which is why more and more related intriguing results were reported one after another [26][27][28][29][30][31].…”