Accelerating Airy wave packets in the presence of quadratic and cubic dispersion

Abstract

The equation governing quadratic and cubic transparent dispersion within the framework of the slowly varying envelope approximation is shown to admit an infinite-energy uniformly moving Airy wave packet solution, as well as a square-integrable accelerating Airy solution. Some insight is provided regarding the local acceleration dynamics in the latter case and comparisons are made with the "accelerating" beam solution introduced by Siviloglou and Christodoulides and experimentally demonstrated by Siviloglou, Broky, Dogariu, and Christodoulides recently. It is shown, in particular, that under certain parametrizations, the presence of cubic dispersion can increase the "depth of penetration" of a wave packet. In other words, a pulse can propagate for a larger range without sustaining significant dispersive distortion than in the presence of quadratic dispersion alone. Finally, imaging properties of accelerating airy wave packets are discussed.

Introduction of optical Newton cradle model for understanding the N-solitons fission process under the action of higher order dispersion

“…This is explained by the fact that the radiation component of the field generated by the fission tends to form an Airy-like pattern under the action of TOD [23], which plays the role of a potential structure binding the soliton chain. To confirm the universal character of the dynamics of the soliton NC under the action of TOD, Fig.…”

Reflection and refraction of an Airy beam at a dielectric interface

“…The resulting Airy pulses can propagate with acceleration and minimum shape distortion over several dispersion lengths in media with quadratic or cubic dispersion [23]. These unique waveforms have so far found application for generating dispersion-and diffraction-resisting optical bullets [24], optical solitons [25], and supercontinua [26].…”

Propagation of time-truncated Airy-type pulses in media with quadratic and cubic dispersion

“…However, it is possible to obtain a finite-energy version of the ideal Airy pulse by modulating it with a time exponential function on the initial plane z 0 [2,3]. The analysis of a finite-energy Airy pulse considering the effects of second-and third-order dispersion was first made in [3] and subsequently in [4][5][6].…”

“…The latter would be of interest for accelerating waves in fiber-optical waveguides, as well for retaining the integrity of the main lobe for large ranges. Besieris and Shaarawi [3] recognized that an exact accelerating and weakly dispersive Airy wave packet solution was possible for the more general case where both second-and third-order dispersion were taken into account. There exist physical situations where one or the other, as well as both, of these effects predominate.…”