引力波对光的影响。部件II。引力波探测器中的电场传播和干涉图样
Influence of gravitational waves upon light. Part II. Electric field propagation and interference pattern in a gravitational wave detector
摘要：
在本系列的第二篇文章中，我们将我们最近导出的电场沿光线传播的方程[arXiv：2004.03496]应用于用于检测平坦背景中的引力波的玩具干涉仪的特殊情况，该方程在电磁几何光学极限上有效。这样的方程表明，假设探测器处于横向无迹坐标系中，由于引力波扰动，它具有局部剪切相对运动，电场不会像闵可夫斯基时空中的惯性参考系那样传播。我们提出了在干涉过程结束时的电场，对于任意臂配置相对于平面引力波包传播方向。然后，对于垂直入射，我们计算干涉图样，除了与光在臂中行进的路径差异相关的通常项之外，我们推导出对最终强度的两个新贡献，其产生于：（i）往返电磁频移和（ii）光束的发散。它们的定量相关性相比，传统的贡献，并显示通常是可以忽略不计的，由于光的几何光学制度。此外，由于引力波的存在，极化矢量通常会发生非平行传输，这是一个可能产生进一步贡献的特征。然而，我们的结论是，对于垂直入射的情况下，这样的矢量是平行传输，防止这种校正。
英文摘要：
In this second article of the series, we apply our recently derived equation for the electric field propagation along light rays [arXiv:2004.03496], valid on the electromagnetic geometrical optics limit, to the special case of a toy interferometer used to detect gravitational waves in a flat background. Such an equation shows that, assuming the detector is in the transverse-traceless frame, which has a local shearing relative motion due to the gravitational wave perturbations, the electric field does not propagate as in an inertial reference frame in Minkowski spacetime. We present the electric field at the end of the interferometric process, for arbitrary arm configurations with respect to the plane gravitational wave packet propagation direction. Then, for normal incidence, we compute the interference pattern and, in addition to the usual term associated with the difference in path traveled by light in the arms, we deduce two new contributions to the final intensity, arising from: (i) the round-trip electromagnetic frequency shift and (ii) the divergence of the light beam. Their quantitative relevance is compared to the traditional contribution and shown to be typically negligible due to the geometrical optics regime of light. Moreover, a non-parallel transport of the polarization vector takes place, in general, because of the gravitational wave, a feature which could generate further contributions. However, we conclude that for the normal incidence case such vector is parallel transported, preventing this kind of correction.
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