Considered are the problems of electromagnetic wave scattering, absorption and emission by several types of twodimensional and three-dimensional dielectric and metallic objects: arbitrary dielectric cylinder, thin material strip and disk, and arbitrary perfectly electrically conducting surface of rotation. In each case, the problem is rigorously formulated and reduced to a set of boundary integral equations with smooth, singular and hyper-singular kernel functions. These equations are further discretized using Nystrom-type quadrature formulas adapted to the type of kernel singularity and the edge behavior of unknown function. Convergence of discrete models to exact solutions is guaranteed by general theorems. Practical accuracy is achieved by inverting the matrices of the size that is only slightly greater than the maximum electrical dimension of corresponding scatterer. Sample numerical results are presented.
Time-harmonic electromagnetic wave diffraction by a perfectly electrically conducting (PEC) finite rotationally symmetric surface located in free space is investigated. The problem is split to independent azimuth orders and reduced to the sets of coupled hypersingular and singular integral equations (IEs) for the surface current components. These IEs are discretized by the Nystrom-type method of discrete singularities using the interpolation type quadrature formulas. From the solutions of corresponding matrix equations the near-and the far-field patterns are obtained. The presented method has guaranteed convergence for arbitrary not axially symmetric primary field.Index Terms-Body of revolution (BOR), focusing, interpolation type quadrature formulas, radar cross-section, scattering, singular and hypersingular integral equations.
The authors consider the electromagnetic field in the presence of a dielectric body of revolution (BOR) in the axially symmetric case. The associated Muller boundary integral equation (IE) is reduced to a set of two IEs, further discretised using the Nystrom method. They derive a determinantal equation for the search of natural modes and present a new approach for the calculation of its roots. Results obtained are compared with known data for a dielectric sphere and a BOR generated by a super-ellipse as an approximation of a finite circular cylinder. The resonant frequencies and the Q-factors of the natural modes of a dielectric spheroid are studied.
The paper presents an analytical method based on the Muller integral equations (IEs) and the Body of Revolution (BOR) approach for the full three dimensional modeling of microwave and optical dielectric resonators. The method is applied to verify the accuracy for resonant frequencies and Q-factors of microwave resonators and compared with published theoretical and experimental results. Keywords: dielectric resonators, Q-factor, interpolation type quadrature formulas.
INTRODUCTIONDielectric disk resonators are used in a variety of microwave and optical applications, including filters, oscillators, frequency meters, nano-antennas, microlasers and biosensing. Whilst in the microwave regime the lower order resonant modes are used in practice, in optical applications it is the high order whispering gallery modes that are practically relevant as they can reach high Q-factors and entail high sensitivity. However, accurate analysis of microwave and optical resonators which fully accounts for their three-dimensional nature still presents a challenge. To date, a range of approximate semi-analytical methods have been used to accurately model microwave rectangular and cylindrical dielectric resonators, namely magnetic wall method [1], variational method [2] and integral equation methods [3,4].Finite Difference Time Domain (FDTD) method, Finite Element (FE) method and Integral Equation (IE) methods have all been applied to optical resonators. Of special interest are the contour IE methods that use the Muller IEs and the Method of Analytical Regularisation (MAR) [5,6] to convert the original matrix set to the one with more favourable features, namely to the Fredholm type equations of the 2 nd kind. This approach has been applied to two-dimensional (2D) cases where the reduction from 3D to 2D is done using the Effective Refractive Index method. This has shown good agreement with experimental data for thin microdisks [6]. Recently MARbased analysis have been extended to modelling a thin circular dielectric disk characterized by generalized boundary conditions imposed on the disk median section [7].Our final objective is to extend the Muller IEs to the full 3D case without making any approximating assumptions. In this paper we present a valuable intermediate step, method based on the combination of Muller IE and the Body of Revolution (BOR) approach [4]. The BOR method is IE based method that is applicable to bodies that possess axial (rotational) symmetry and can thus be obtained by rotating a so-called generic arc around the axis of symmetry. The attraction of the BOR method lays in the explicit integration of the azimuthal dependence within the free space Green's function to yield the so-called Modal Green's functions (MGF) and thus reducing the 3D structure to the 2D one without any loss of accuracy [4]. In this paper the electric and magnetic surface current densities are approximated by Legendre polynomials that leads to accurate and fast mathematical model. The results for resonant frequencies and Q-factors of microwave pi...
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