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.

No abstract

No abstract

No abstract

An analytical approach for the calculation of the dyadic Green's functions inside the rectangular cavity over a broad range of frequency is presented. Both vector potential and electric field dyadic Green's functions are considered. The method is based on the extraction of the Green's function at an imaginary wavenumber from itself to obtain a rapidly convergent eigenfunction expansion of the dyadic Green's function. The extracted term encompasses the singularity of the Green's function and is computed using spatial expansions. Results are illustrated for a rectangular cavity up to 5 wavelengths in size with thousands of cavity modes obtained by the 6th order convergent expansion. It is shown that for an accurate and broadband simulation, the proposed method is many times faster than the Ewald method.