On the Resonant Frequencies of a Partially Shielded Circular Dielectric Cylinder

• Published in: Mathematical models and computer simulations Vol. 16; no. 2; pp. 186 - 196
• Main Authors: Abgaryan, G. V., Shestopalov, Y. V., Romanov, K. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.04.2024; Springer Nature B.V
• Subjects: Boundary value problems; Electromagnetic fields; Electromagnetic radiation; Helmholtz equations; Hilbert space; Identities; Linear algebra; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Operators (mathematics); Resonant frequencies; Resonators; Simulation and Modeling; Tapes (metallic); Wave diffraction; resonant frequencies; partial domain method; boundary value problem; slot resonator; diffraction problem; truncation method
• ISSN: 2070-0482; 2070-0490
• DOI: 10.1134/S2070048224020042

The problem of the diffraction of a TE-polarized electromagnetic wave on a circular dielectric slot resonator is studied. Using the method of integral-summing identities (ISIs), which is a variation of the partial domain method (PDM), the boundary value problem for the Helmholtz equation is reduced to an infinite system of linear algebraic equations (SLAE-2) with the Fredholm operator acting in the Hilbert space of infinite sequences with weight. In the special case of the problem, which corresponds to the absence of metallic tape on the boundary of the resonator, the explicit Cramer formulas for the calculation of the unknown coefficients of the potential function of the electromagnetic field are derived from the SLAE-2. Based on the computational experiments, the complex resonant frequencies, which are approximate values of the natural frequencies of the slot resonator, are found.