Abstract

A rotating solid homogeneous isotropic dispersion-free dielectric in an accompanying frame of reference turns out to be an inhomogeneous anisotropic medium due to the action of two competitive physical mechanisms: inhomogeneity of the free space caused by rotation and light dragging by the moving medium. In the rotating dielectric, the eikonal equation and a system of ordinary differential equations corresponding to it in the characteristic form are obtained in the geometrical optics approximation. Solutions of the equations at calculated parameters determined using first integrals of the system are pairs of counterpropagating R-trajectories of rays and f-trajectories of phase fronts. A formula for the intensity of a light pulse propagating along an arbitrary R-trajectory is obtained. Counterpropagating trajectories of both types have no common points and are shifted to the opposite sides from the straight line between the end points. Their structural parameters (the minimum distance to the axis of rotation, arc length, domain with respect to the azimuthal coordinate, optical length, etc.) vary under the action of both physical mechanisms depending on the rotation velocity. Closed optical paths in the rotating reference frame (RRF) for a retransmitting network and for a two-mirror Fabry–Perot resonator in an operating laser can be created using two types of mirrors adapted to the rotation frequency; the normals to the reflecting surfaces of the mirrors must have definite different angles with unit vectors of rays and wavefronts of the radiation arriving at the reflector. The Sagnac effect is a consequence of inhomogeneity (deformation) of the free space with respect to the azimuthal coordinate and its magnitude is the result of the competitive action of both physical mechanisms.

中文翻译：

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旋转电介质中的几何光学

摘要

由于两个竞争性物理机制的作用，旋转的固体均匀均质各向同性无分散介电体被证明是不均匀的各向异性介质：旋转引起的自由空间不均匀以及移动介质的光拖曳。在旋转电介质中，通过几何光学近似，可以获得特征形式的电子方程和与之对应的常微分方程组。在使用系统的第一积分确定的计算参数下，方程的解是成对的射线的R传播轨迹和相前的f传播轨迹。沿任意R传播的光脉冲强度的公式-轨迹被获得。两种类型的反向传播轨迹没有公共点，并且从端点之间的直线移到相反的一侧。它们的结构参数（到旋转轴的最小距离，弧长，相对于方位坐标的域，光学长度等）在两种物理机制的作用下均取决于旋转速度而变化。可以使用两种适合于旋转频率的反射镜在旋转参考系（RRF）中为重传网络和法布里-珀罗共振器的两面反射镜建立闭合的光路。反射镜的反射表面的法线必须与到达反射器的辐射的射线和波阵面的单位矢量具有确定的不同角度。