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.
