波在高度不均匀薄膜中的传播：精确可解模型
Wave propagation in highly inhomogeneous thin films : exactly solvable models
摘要：
本文给出了波在具有高度空间依赖性介电常数的非均匀薄膜中传播的精确处理方法。它是基于一种空间变换，即用光路代替物理空间，在新的空间中，色散方程是正常行波的色散方程。我们将表明，这样的薄膜的色散特性是等离子体或波导状的，特征频率被确定的介电常数的变化的空间特性只。该理论是可扩展的，因此它可以应用于任何波长范围：光学，IR，射频等，仅取决于特征空间尺度。几个应用程序将被提出，有关的反射性能，这种薄膜（宽带抗反射，或二向色涂层）或通过薄膜的传播和传输。我们将表明，取决于空间依赖性的类型，入射波可以传播或隧道通过这样的薄膜。我们将调查的行为的光群速度和隧穿时间内或通过这样的薄膜。虽然我们可以重现哈特曼效应所对应的相位-时间饱和，但对隧穿情形中群速度的分析显示没有超光速传播的迹象。在某些情况下可以获得强的频率依赖性，这允许预期宽带激光脉冲的强整形。
英文摘要：
We present an exact treatment of wave propagation in some inhomogeneous thin films with highly space-dependent dielectric constant. It is based on a space transformation which replaces the physical space by the optical path. In the new space, the dispersion equation is that of a normal progressive wave. We will show that the dispersion properties of such films are plasma- or waveguide-like, the characteristic frequency being determined by the spatial characteristics of the dielectric constant's variations only. The theory is scalable, so that it can be applied in any wavelength range : optical, IR, radiofrequency, etc. depending only on the characteristic space scales. Several applications will be presented, concerning the reflection properties of such films (broadband anti-reflection, or dichroic coatings) or to the propagation and transmission through the film. We will show that depending on the type of space dependence, an incident wave can either propagate or tunnel through such films. We will investigate the behaviour of the light group-velocity and tunneling time inside or through such films. Though we can reproduce the phase-time saturation corresponding to the Hartman effect, analysis of the group velocity in the tunneling case shows no sign of superluminal propagation. A strong frequency dependence can be obtained in some situations, which allows to anticipate a strong reshaping of brodband laser pulses.
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