Restoring geometrical optics near caustics using sequenced metaplectic transforms
Restoring geometrical optics near caustics using sequenced metaplectic transforms
复制标题
使用顺序元波变换恢复焦散附近的几何光学
DOI：
10.1088/1367-2630/aba91a
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发表时间：
2020
影响因子：
3.3
通讯作者：
I. Dodin
中科院分区：
文献类型：
--
作者：
N. Lopez;I. Dodin;I. Dodin
几何光学 (GO) 通常用于模拟弱非均匀介质中的波传播和半经典极限下的量子粒子运动。然而，GO 预测反射点附近以及更一般地焦散处波场的寄生奇点。我们提出了一种新的 GO 公式，称为元波几何光学 (MGO)，它不受这些奇点的影响，并且可以应用于任何线性波动方程。 MGO 使用波场的顺序元波变换，对应于射线相空间的辛变换，使得焦散在新变量中消失并且 GO 恢复。使用 MGO 进行说明分析描述了艾里问题和量子谐振子。在这两种情况下，MGO 解都非常接近精确解，并且在截止点处保持有限，这与通常的 GO 解不同。
Geometrical optics (GO) is often used to model wave propagation in weakly inhomogeneous media and quantum-particle motion in the semiclassical limit. However, GO predicts spurious singularities of the wavefield near reflection points and, more generally, at caustics. We present a new formulation of GO, called metaplectic geometrical optics (MGO), that is free from these singularities and can be applied to any linear wave equation. MGO uses sequenced metaplectic transforms of the wavefield, corresponding to symplectic transformations of the ray phase space, such that caustics disappear in the new variables and GO is reinstated. The Airy problem and the quantum harmonic oscillator are described analytically using MGO for illustration. In both cases, the MGO solutions are remarkably close to the exact solutions and remain finite at cutoffs, unlike the usual GO solutions.