Steinberg Ben Zion, Shamir Adi, Boag Amir
School of Electrical Engineering, Tel Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jul;74(1 Pt 2):016608. doi: 10.1103/PhysRevE.74.016608. Epub 2006 Jul 20.
We derive an exact spectral representation for the Green's function of Maxwell equations in a two-dimensional homogeneous and rotating environment. The formulation is developed in the medium (noninertial) rest frame, and it represents the response to a point source, where both the source and observation points rotate together with the medium. The closed form expression for the Green's function is derived for (nonrelativistic) slowly rotating media at finite distances. An approximate expression for the efficient evaluation of the Green's function, that avoids laborious summation of rotating-medium spherical harmonics, is provided and tested against the exact expression. Furthermore, it is shown that our spectral theory can provide a broad view of the optical response of rotating systems, from which the classical Sagnac effect is obtained as a special case.
我们推导了二维均匀旋转环境中麦克斯韦方程组格林函数的精确谱表示。该公式是在介质（非惯性）静止参考系中推导出来的，它表示对一个点源的响应，其中源点和观测点都与介质一起旋转。对于有限距离处（非相对论）缓慢旋转的介质，我们推导了格林函数的封闭形式表达式。我们给出了一个用于高效评估格林函数的近似表达式，该表达式避免了对旋转介质球谐函数进行繁琐的求和，并与精确表达式进行了对比测试。此外，结果表明我们的谱理论可以提供旋转系统光学响应的广泛视角，从中可以得到经典的萨格纳克效应作为一个特殊情况。
