非均匀介质中的光学与拉格朗日几何
Optics in nonuniform media and Lagrange geometry
摘要：
本文考虑了在非均匀运动介质中由相对论光学激发的拉格朗日量所对应的运动方程。该模型描述了非均匀无色散运动介质中的光学效应。当使用限制在Minkowski流形上的光学度规时，我们建立了测地线的Euler-Lagrange方程。对于折射率沿$Z$方向增加的特殊情况，我们已经指定了一般模型。构造了相应的欧拉-拉格朗日方程的精确解析解。解的分析表明，光束弯曲到轴$Z$，沿该轴折射率增加。
英文摘要：
In this paper the equations of motion associated with a Lagrangian inspired by relativistic optics in nonuniform moving media are considered. The model describes optical effects in the nonuniform dispersionless moving medium. When using the optical metric restricted to the Minkowski manifold, we have established the Euler-Lagrange equations for geodesics. We have specified the general model to the special case when the refractive index increases along the direction $Z$. The exact analytical solutions of the corresponding Euler-Lagrange equations have been constructed. Analysis of the solutions shows that the light beams are bending to the axes $Z$ along which the refractive index increases.
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