On the resonant frequencies of a partially shielded circular dielectric cylinder

The problem of diffraction of a TE-polarized electromagnetic wave on a circular dielectric slit resonator is investigated. Using the method of integral-summing identities, 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 were are derived from SLAE-2. On the basis of computational experiments, the complex resonant frequencies, which are approximate values of the natural frequencies of the slot resonator, are found.