Passage of an electromagnetic wave through a rectangular waveguide with a section of a semiconductor film

Background. In microwave technology, of great interest is the creation of amplifiers and generators based on thin-layered longitudinal inhomogeneities in rectangular waveguides, which are an integral part of many functional devices in the microwave and EHF ranges. Aim. Therefore, it is of practical interest to calculate one of these inhomogeneities in a rectangular waveguide. Methods. One of the methods for calculating such structures is the diffraction of an electromagnetic wave by a segment of a semiconductor film with negative differential conductivity on a narrow wall of a rectangular waveguide. Based on the boundary conditions, a singular integral equation for the electric component of the electromagnetic field was obtained. By the method of inversion of the integral equation and by means of expansion in terms of Chebyshev polynomials, the integral equation is given in a system of two algebraic equations. The coefficients of the system are calculated according to the theory of residues. Then an equation was obtained for calculating the transmission coefficient, which was calculated in the Matcad environment. Results. Based on the integral equation, the values for calculating the transmission coefficient for the structure under consideration are obtained. Conclusion. From the graphs obtained for the calculated transmission coefficient, it can be concluded that there are frequency zones where an electromagnetic wave is amplified in the structure. So, on the basis of the structure under consideration, it is possible to create amplifiers and generators of the microwave and EHF ranges.