光在非均匀介质中的自旋霍尔效应的数学描述
A mathematical description of the spin Hall effect of light in inhomogeneous media
AI总结：
研究Maxwell方程在各向同性非均匀介质中的高斯波包解，推导描述几何运动修正的常微分方程组，证明光在非均匀介质中的自旋霍尔效应。
摘要：
我们研究Maxwell方程在各向同性非均匀介质中的高斯波包解，并推导出一个常微分方程组，该方程组捕捉到几何运动的主导修正。该系统的动力学量包括能量质心、线性和角动量以及四极矩。此外，该系统在频率倒数的一阶近似下闭合。作为直接结果，具有相反圆极化态的高斯波包的能量质心通常以不同方向传播，从而为光在非均匀介质中的自旋霍尔效应提供了数学证明。
英文摘要：
We study Gaussian wave packet solutions for Maxwell's equations in an isotropic, inhomogeneous medium and derive a system of ordinary differential equations that captures the leading-order correction to geodesic motion. The dynamical quantities in this system are the energy centroid, the linear and angular momentum, and the quadrupole moment. Furthermore, the system is closed to first order in the inverse frequency. As an immediate consequence, the energy centroids of Gaussian wave packets with opposite circular polarisations generally propagate in different directions, thereby providing a mathematical proof of the spin Hall effect of light in an inhomogeneous medium.
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