Self-accelerating beam dynamics in the space fractional Schrödinger equation

D. Colas
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引用次数: 4

Abstract

Self-accelerating beams are fascinating solutions of the Schrodinger equation. Thanks to their particular phase engineering, they can accelerate without the need of external potentials or applied forces. Finite-energy approximations of these beams have led to many applications, spanning from particle manipulation to robust in vivo imaging. The most studied and emblematic beam, the Airy beam, has been recently investigated in the context of the fractional Schrodinger equation. It was notably found that the packet acceleration would decrease with the reduction of the fractional order. Here, I study the case of a general nth-order self-accelerating caustic beam in the fractional Schrodinger equation. Using a Madelung decomposition combined with the wavelet transform, I derive the analytical expression of the beam's acceleration. I show that the non-accelerating limit is reached for infinite phase order or when the fractional order is reduced to 1. This work provides a quantitative description of self-accelerating caustic beams' properties.
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空间分数阶Schrödinger方程中的自加速束流动力学
自加速束是薛定谔方程的迷人解。由于其特殊的相位工程,它们可以在不需要外部电位或施加力的情况下加速。这些光束的有限能量近似已经导致了许多应用,从粒子操纵到健壮的体内成像。研究最多和最具代表性的光束,艾里光束,最近在分数阶薛定谔方程的背景下进行了研究。值得注意的是,数据包的加速度会随着分数阶的减小而减小。在这里,我研究了分数阶薛定谔方程中一般的n阶自加速焦散束的情况。利用马德隆分解与小波变换相结合的方法,导出了光束加速度的解析表达式。我证明了非加速极限是在无限相阶或分数阶降为1时达到的。本文对自加速焦散光束的性质进行了定量描述。
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