Resonance fileds in waveguide transmission problems

Abstract

In this work we study resonant states and fields in waveguide transmission problems for waveguides of rectangular cross section loaded with parallel-plane dielectric diaphragms when determination of the transmission coefficient and fields admit closed-form solutions. In some cases, permittivity of the layered parallel-plane dielectric diaphragms can be determined from the transmission coefficient considered as a one-to-one function of a complex variable. Mathematical methods relevant to this work are examined, including determination of zeros of complex-valued functions related to the transmission coefficient and their calculation in the complex domain. Numerical simulations are performed using specially created Matlab codes (in X-band) including calculation of resonance states and fields in waveguides of rectangular cross section loaded with several parallel-plane dielectric diaphragms. The resonances states are determined as zeros of complex-valued functions found in the closed form. The existence and distribution of the zeros of these functions for one-, two- and three-section diaphragms are proved and properties of the corresponding resonance states are analyzed. In addition to this, we show that the modulus of the transmission coefficient demonstrates a characteristic oscillation behavior and increases considerably when the diaphragms permittivity is approaching a resonance value.