Reflection of plane electromagnetic waves at a planar surface separating two media is typically discussed at length in undergraduate texts. However, a similar analysis for the case of evanescent electromagnetic waves, although illustrative and interesting, is rarely discussed. In this paper, we present such an analysis for the reflection of an evanescent wave at a plane dielectric surface and highlight the important conceptual difference in the energy flow for this case compared to that of a plane wave. It is generally emphasized that an evanescent wave does not propagate energy away from the surface emanating these waves. We show that in the case of an evanescent wave, the pair of incident and reflected waves together propagates energy if the imaginary part of the reflectivity is non-zero. Further, the real part of the reflectivity can be greater than unity in the case of an evanescent wave without violating energy conservation. Connection of these properties to the existence of surface modes, Čerenkov radiation, and a quantum analogue are elucidated in the paper.

中文翻译：

---

了解瞬逝电磁波反射期间的能量传播

平面电磁波在分隔两种介质的平面上的反射通常在本科课本中详细讨论。然而，对倏逝电磁波情况的类似分析，尽管具有说明性和趣味性，却很少被讨论。在本文中，我们对平面电介质表面的倏逝波的反射进行了这样的分析，并强调了这种情况下能量流与平面波相比的重要概念差异。通常强调渐逝波不会从发出这些波的表面传播能量。我们表明，在倏逝波的情况下，如果反射率的虚部不为零，则这对入射波和反射波一起传播能量。更远，在不违反能量守恒的情况下，在倏逝波的情况下，反射率的实部可以大于 1。论文中阐明了这些特性与表面模式、Čerenkov 辐射和量子类似物的存在之间的联系。