一维带限Weierstrass分形分层介质粗糙面电磁波透射特征

Tramsmission Characteristics of Electromagnetic Wave from 1D Band-limited Weierstrass Fractal Rough Surface of Layered Medium

运用微扰法研究平面波入射分层介质粗糙面的电磁波透射问题,推出了不同极化状态的透射波散射系数公式。采用一维带限Weierstrass分形粗糙面模拟实际的分层介质粗糙面,结合一维带限Weierstrass分形粗糙面的功率谱,导出了平面波入射一维带限Weierstrass分形分层介质粗糙面的透射系数计算公式。通过数值计算,得出了HH极化状态下一维带限Weierstrass分形分层介质粗糙面透射系数的分形特征、基本特征、分区特征、随频率变化特征。结果表明,分维、空间基频、标度区间、底层介质介电常数、中间介质介电常数及厚度、粗糙面参数、入射波频率对透射系数的影响非常复杂。

The transmission of the electromagnetic wave with plane wave incidence on a rough surface of a layered medium is studied and the transmission coefficient for different polarizations is obtained by using the small perturbation method combined with the power spectral density of 1D band-limited Weierstrass fraetal rough surface. A 1D band-limited Weierstrass fractal rough surface is proposed for describing the natural rough surface of the layered medium. The curves of the transmission coefficient of the HH polarization with various scattering angles of the transmission wave, the fractal characteristics, the basic characteristics, the zonal characteristics and the characteristics with various frequencies of the transmission coefficient from 1D band-limited Weierstrass fraetal rough surface for different polarizations are obtained by numerical calculation. The numerical results show that the fractal dimension, special fundamental frequency, scale interval, the permittivity of the substrate medium, the permittivity and the mean layer thickness of the intermediate medium, the rms and the correlation length of the rough surface, and the incident frequency have a very complicated influence on the transmission coefficient.