复坐标中的波传播
Wave propagation in complex coordinates
摘要：
本文研究波动方程在复位置平面上的解析延拓。对于电磁波的特殊情况下，我们提供了一个物理意义，这样的分析延续的一个家庭密切相关的非均匀介质。对于有界介电常数配置文件，我们发现反射的现象可以与分支切割波起源于在复杂的位置的介电常数的极点。要求这些分支切割消失，我们得到一个大家庭的非均匀介质，是无反射的一个单一的入射角。将这一性质扩展到所有的入射角，使我们得到一个广义形式的Poschl-Teller势。最后，我们分析我们的研究结果内的相位积分（WKB）方法。
英文摘要：
We investigate the analytic continuation of wave equations into the complex position plane. For the particular case of electromagnetic waves we provide a physical meaning for such an analytic continuation in terms of a family of closely related inhomogeneous media. For bounded permittivity profiles we find the phenomenon of reflection can be related to branch cuts in the wave that originate from poles of the permittivity at complex positions. Demanding that these branch cuts disappear, we derive a large family of inhomogeneous media that are reflectionless for a single angle of incidence. Extending this property to all angles of incidence leads us to a generalized form of the Poschl Teller potentials. We conclude by analyzing our findings within the phase integral (WKB) method.
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