Effects of inductive waves on multi-band below-cut-off transmission in waveguides loaded with dielectric metamaterials

Unusual backward and forward wave propagation in below cut-off waveguides loaded with dielectric metamaterials comprised of linear arrays of dielectric resonators (DRs) has been investigated by using theoretical, numerical, and experimental methods. Transmission bands were shown to correspond to three lowest resonances in arrays and were analyzed by using the concepts of magneto- and electro-inductive (MI and EI) waves describing the transfer of resonance excitation along the chains of coupled resonators. Equivalent circuit models (ECMs) have been constructed to describe MI and EI wave propagation and to obtain the dispersion diagrams. Good agreement between the obtained data and the results of full-wave simulations, theoretical calculations, and experiments provided an opportunity to determine coupling coefficients characterizing interaction between DRs in arrays at various resonances. It was shown that ripples observed in below cut-off transmission bands are transmission resonances caused by Fabry-Perot oscillations of inductive waves at impedance mismatch at the array ends. Fitting the transmission spectra for MI/EI waves in arrays, calculated by using the Transfer Matrix Method to the spectra obtained by using full-wave simulations/measurements, allowed for determining the ECM parameters to fully characterize the DR array properties.