Abstract
The propagation of decelerating Airy pulses in non-instantaneous cubic medium is investigated both theoretically and numerically. In a Debye model, at variance with the case of accelerating Airy and Gaussian pulses, a decelerating Airy pulse evolves into a single soliton for weak and general non-instantaneous response. Airy pulses can hence be used to control soliton generation by temporal shaping. The effect is critically dependent on the response time, and could be used as a way to measure the Debye type response function. For highly non-instantaneous response, we theoretically find a decelerating Airy pulse is still transformed into Airy wave packet with deceleration. The theoretical predictions are confirmed by numerical simulations.
Highlights
Finite energy Airy beam, solutions to the free-particle Schrödinger equation [1], was first introduced theoretically [2] and later realized experimentally [3] by Christodoulides and associates in 2007
We have studied the impact of finite nonlinear response time of Kerr medium on the decelerating Airy pulse propagation
For weak and general Debye type non-instantaneous response, the non-instantaneous Kerr nonlinearity can be used to control decelerating Airy pulse propagation, leading to trajectory reshaping and enhancement of the main lobe intensity
Summary
Finite energy Airy beam, solutions to the free-particle Schrödinger equation [1], was first introduced theoretically [2] and later realized experimentally [3] by Christodoulides and associates in 2007. Giannini and Joseph derived temporal self-accelerating solutions in nonlinear Kerr media as early as 1989. Bekenstein et al considered self-accelerating beams in highly nonlocal nonlinear optical media, in which boundary conditions strongly affect propagation dynamics [35]. In analogy to spatial nonlocal media, a non-instantaneous response as the Raman effect leads to several interesting phenomena in temporal domain [38, 39]. As shown by Deng et al, Airy-type solitary waves are generated by accelerating Airy pulse in the highly non-instantaneous Kerr media [51]. In the present work we will investigate the propagation dynamics of decelerating Airy pulse in a medium with non-instantaneous Kerr nonlinear response in which the nonlinear contribution to the refractive index is governed by a relaxing Debye type equation. We study the effect of the response time and demonstrate that in critical conditions the retarded nonlinearity and the deceleration develop and change simultaneously as well as generate an accelerated soliton with negative acceleration
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