Sanamzadeh Mohammadreza, Tsang Leung, Johnson Joel T, Burkholder Robert J, Tan Shurun
J Opt Soc Am A Opt Image Sci Vis. 2017 Mar 1;34(3):395-409. doi: 10.1364/JOSAA.34.000395.
A theoretical investigation of energy conservation, reflectivity, and emissivity in the scattering of electromagnetic waves from 3D multilayer media with random rough interfaces using the second-order small perturbation method (SPM2) is presented. The approach is based on the extinction theorem and develops integral equations for surface fields in the spectral domain. Using the SPM2, we calculate the scattered and transmitted coherent fields and incoherent fields. Reflected and transmitted powers are then found in the form of 2D integrations over wavenumber in the spectral domain. In the integrand, there is a summation over the spectral densities of each of the rough interfaces with each weighted by a corresponding kernel function. We show in this paper that there exists a "strong" condition of energy conservation in that the kernel functions multiplying the spectral density of each interface obey energy conservation exactly. This means that energy is conserved independent of the roughness spectral densities of the rough surfaces. Results of this strong condition are illustrated numerically for up to 50 rough interfaces without requiring specification of surface roughness properties. Two examples are illustrated. One is a multilayer configuration having weak contrasts between adjacent layers, random layer thicknesses, and randomly generated permittivity profiles. The second example is a photonic crystal of periodically alternating permittivities of larger dielectric contrast. The methodology is applied to study the effect of roughness on the brightness temperatures of the Antarctic ice sheet, which is characterized by layers of ice with permittivity fluctuations in addition to random rough interfaces. The results show that the influence of roughness can significantly increase horizontally polarized thermal emission while leaving vertically polarized emissions relatively unaffected.
本文提出了一种理论研究，利用二阶小扰动法（SPM2）对具有随机粗糙界面的三维多层介质中电磁波散射的能量守恒、反射率和发射率进行研究。该方法基于消光定理，推导了谱域中表面场的积分方程。利用SPM2，我们计算了散射和透射的相干场以及非相干场。然后，通过在谱域中对波数进行二维积分来求出反射和透射功率。在被积函数中，对每个粗糙界面的谱密度进行求和，每个谱密度都由相应的核函数加权。我们在本文中表明，存在一种“强”能量守恒条件，即乘以每个界面谱密度的核函数精确地遵守能量守恒。这意味着能量守恒与粗糙表面的粗糙度谱密度无关。在不需要指定表面粗糙度特性的情况下，对多达50个粗糙界面的这种强条件结果进行了数值说明。给出了两个例子。一个是多层结构，相邻层之间对比度较弱，层厚度随机，介电常数分布随机生成。第二个例子是具有较大介电对比度的周期性交替介电常数的光子晶体。该方法被应用于研究粗糙度对南极冰盖亮度温度的影响，南极冰盖除了随机粗糙界面外，还具有介电常数波动的冰层特征。结果表明，粗糙度的影响可以显著增加水平极化热发射，而对垂直极化发射的影响相对较小。
