Application of dispersion relations for prediction of frequency response of multilayer metallo-dielectric structures

Abstract

We show applications of our analytical approach to predict the performance of multilayer metallo-dielectric bandpass filters, which also enables estimation of their effective permittivity without relying on homogenization techniques. The approach is based on the one-dimensional dispersion relation for an infinite metallo-dielectric structure that accounts for the complex nature of the permittivities for the metal and dielectric constituents. The dispersion relation clearly reveals the band structure (often comprising multiple passbands), directly provides transmittance characteristics such as center wavelengths and bandwidths and enables the calculation of effective propagation constant and effective attenuation. In this work, we evaluate the dispersion relations for metallo-dielectric structures with complex refractive index data for the metal, viz., Ag, acquired from different sources to show the differences in the center wavelength and the cutoff wavelengths. We verify the accuracy of our method numerically by comparing the transmittance spectrum of finite metallo-dielectric structures using the transfer matrix method. We also plot the dispersion relation using Al as the metal and show the differences in the dispersion relations of the infinite structure and the transmittances of the finite structures relative to Ag. Extension to determination of dispersion relations for other polarizations, viz., transverse magnetic, is discussed, along with corresponding transmittance spectra for oblique incidence.