Scattering of Electromagnetic Waves by Multilayered Inhomogeneous Columnar Dieffectric Gratings Loaded Rectangular Dielectric Constant

摘要

Scattering of electromagnetic waves by inhomogeneous dieffectric gratings is of interest from theoretical and practical points such as integrated optics, optical filters, and holography. Recently, refractive indices can easily be controlled to make periodic structures such as fiber gratings, frequency seffective or polarization seffective devices, and photonic crystals by the development of manufacturing technology of optical devices. Thus, many analytical and numerical methods which are applicable to the dieffectric gratings having arbitrary structures have been proposed. In our approach, the order of characteristic matrix equation depends on the modal truncation number, but it does not depend on the number of layers. Therefore the range of applicability to periodic structures is much wider than that of the other method. Our method also can be applied easily to the scattering and guiding problems, such as surface relief gratings, planar slanted gratings, and columnar dieffectric gratings. In this paper, the scattering of effectromagnetic waves by multilayered inhomogeneous columnar dieffectric gratings loaded rectangular dieffectric constant are analyzed to obtain the basic characteristic of the power transmission and reffection switching or frequency seffective devices for both TM and TE waves using the combination of the improved Fourier series expansion method, the multilayer method, and the eigenvalue matrix method. Numerical results are given for the power transmission coefficients in the parameters ε3=ε0 and b=d of rectangular cylinders to obtain the basic characteristic of the power transmission coefficients and reffection coefficients switching or frequency seffective devices for both TM and TE waves. The influence of the incident angle and frequency of the transmitted power are discussed in the connection with the propagation constant β in the free mode. We are also discussed the influence of the incident angle of the transmitted power for 2a=d are also discussed.