论文标题
空间分数schrödinger方程中的自动光束动力学
Self-accelerating beam dynamics in the space fractional Schrödinger equation
论文作者
论文摘要
自加速光束是Schrödinger方程的引人入胜的解决方案。由于其特定的相工工程，它们可以加速而无需外部电势或施加力。这些梁的有限能量近似导致了许多应用，从颗粒操纵到体内成像的稳健成像。最近在分数schrödinger方程的背景下研究了最具研究和象征性的光束，即通风梁。众所周知，随着分数顺序的降低，数据包加速度将减小。在这里，我研究了分数schrödinger方程中一般的n阶自加苛性束的情况。使用Madelung分解与小波变换相结合，我得出了光束加速度的分析表达。我表明，无限相阶或将分数阶降至1时达到了非加速度的极限。这项工作提供了对自动加速苛性束的特性的定量描述。
Self-accelerating beams are fascinating solutions of the Schrödinger 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 Schrödinger 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 Schrödinger 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.
