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Using the recently developed method based on the rigorous theory of singular and hypersingular integral equations (IEs) and Nystrom-type discretization, a paraboloidal reflector assisted with a conical shield is investigated. To decrease the computation time we propose a new method of calculation of the Modal Green's Functions in the quasi-optical range. The far and near fields of the studied reflector are analyzed in the transmission and reception cases, and reveal fine features that escape asymptotic analysis. Elementary numerical optimization of the shield-assisted paraboloidal antenna is performed.

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.

We consider boundary-value problems of mathematical diffraction theory and discuss the possibility of reducing them to boundary hypersingular integral equations and solving them numerically. The analytic technique of parametric representations of pseudodifferential and integral operators and the numerical method of discrete singularities are essentially used. We discuss the reasoning in applying this approach to constructing mathematical models of wave diffraction problems and solving them numerically.

For the first time rigorous theory is developed for eigen traveling TM modes in the resonator of the coaxial cavity gyrotron with a corrugated insert. This mathematical model can be applied for any corrugation parameters and wavelengths. Gyrotron simulation software is developed and allows to calculate mode eigenvalues, electromagnetic field components and Ohmic losses for eigen TE and TM modes. Results of the numerical investigations are presented for the ITER relevant 170 GHz coaxial cavity gyrotron developed in Forschungszentrum Karlsruhe, Germany.

Numerical method for modeling the E-polarized wave scattering by electrically large quasioptical two-dimensional (2-D) reflectors is presented. Reflectors are assumed zero-thickness and perfectly electrically conducting. Efficient numerical solution is obtained from the coupled singular integral equations discretized using new quadrature formulas of interpolation type. It has controlled accuracy and deals with small-size matrices. To simulate a small-horn feeding, the incident field is taken as a beam generated by a complex-source-point (CSP) current. Presented numerical results validate empirical rule of -10 dB edge illumination needed to provide the best electromagnetic performance of reflector

The full-wave analysis based on the singular integral equation method is developed to correctly investigate dispersion properties and field distributions inside a rectangular waveguide grating used in low-voltage traveling wave amplifiers. Simplified treatments of periodic structures with rectangular grating are widely used in the analysis of microwave electron beam devices, providing an actually good accuracy for the calculation of dispersion curves of natural modes in a wide range of grating parameters. However, they do not guarantee the correct field distributions in a close proximity to the grating just where an electron beam is usually passed to get more effective beam-wave coupling. The amplitude of the minus-first spatial harmonic, which is mostly responsible for the resonant beam-wave interaction, can be substantially larger than that predicted by the simplified analysis. In addition, the contribution of the higher spatial harmonics to the total field is shown to be significantly larger than that evaluated from the simplified treatment. Consequences of the enhanced influence of higher harmonics on beam-wave interaction are discussed.

Mathematical models of 2D electrodynamic wave diffraction and 3D scalar diffraction problems are the external boundary-value problems for the Helmholtz equation with boundary conditions of the first, second or third kind on the boundary surfaces. One of the effective ways of solving these boundary-value problems consists in their reduction to a singular and hypersingular boundary integral equations by the method of parametric representations of integral and pseudo-differential operators. The numerical solution of integral equations is obtained by using the modifications of discrete singularities method. The reasoning in applying this approach to constructing mathematical models of wave diffraction problems had been discussed.

A problem of time-harmonic electromagnetic wave diffraction by a perfectly electrically conducting (PEC) finite surface of rotation located in a free space is investigated. The problem is split to independent azimuthal orders and reduced to sets of hypersingular and singular integral equations. These equations are solved numerically by the method of discrete singularities (Nystrom method), using interpolation type quadrature formulas. From the solutions of these sets the surface-current components, near field and the far — zone scattering patterns are obtained. The presented method has a guaranteed convergence for an arbitrary non-axially symmetric primary field. This method is applied to the analysis of a paraboloidal reflector antenna with a conical shield designed to reduce the side radiation.

A full-wave numerical study of 2-D models of dual-reflector omnidirectional ADE (axially-displaced ellipse subreflector and parabolic main reflector, Fig. 1a) and PACO (parabolic subreflector and conical/corner reflector, Fig. 1b) antennas is performed in the E-polarization case. The analysis is based on the recently developed Method of Discrete Singularities (MDS) [1]–[3] which uses coupled singular electric-field integral equations (SIE) applied to accurate modelling of the considered axially-symmetric dual-reflector (actually, three-reflector in the considered 2-D case) antenna systems.

In this paper we perform full-wave two-dimensional (2-D) simulation of the e-polarized beam wave guidance and scattering by a chain of four finite-size reflectors and mirrors modelling a typical fragment of quasioptical feeding circuit of a deep-space communication antenna. Elementary geometry tuning aimed at the maximum circuit transmission is also demonstrated. The feed beam generated by the aperture of a corrugated horn is simulated with the incident complex-source-point (CSP) field. Numerical solution is obtained from the coupled singular integral equations (IEs) discretized using new quadrature formulas of interpolation type that take full account of the IE kernel singularity and the edge behaviour.

In this paper we perform full-wave two-dimensional (2-D) simulation and performance comparison of the E-polarized beam wave guidance and scattering by two variations of a typical fragment of quasioptical feeding circuit of a deep-space communication antenna. The fragments are similar and consist of a chain of four finite-size reflectors and mirrors with varied position of the second pair. The feed beam generated by the aperture of a corrugated horn is simulated with the incident complex-source-point (CSP) field. Numerical solution is obtained from the coupled singular integral equations (IEs) discretized using new quadrature formulas of interpolation type that take full account of the IE kernel singularity and the edge behaviour.

We present a full-wave numerical study and design of the 2-D model of a perfectly electric conducting (PEC) parallel-plate lens structure. The underlining idea is that the power of electromagnetic waves can be focused or collimated by arranging flat metal strips in parallel to one another (for instance, see Fig. 1-a) and adjusting the transverse and longitudinal dimensions of the waveguide regions to provide a necessary phase correction. Simple engineering principles for designing such metal-plate lenses are known from [1-3]. As for the full-wave analysis, they seem to have been accurately considered only in [4] with the coupled Singular Integral Equations (SIEs) regularized by using a projection on the weighted Chebyshev polynomials, which are the orthogonal eigenfunctions of the static parts of the SIE operators.

Considered is the beam wave guidance and scattering by 2D quasi-optical reflectors modeling the components of beam waveguides. The incident field is taken as the complex-source-point field to simulate a finite-width beam generated by a small-aperture source. A numerical solution is obtained from the coupled singular integral equations (SIEs) for the surface currents on reflectors, discretized by using the recently introduced Nystrom-type quadrature formulas. This analysis is applied to study what effect the edge illumination has on the performance of a chain of confocal elliptic reflectors. We also develop a semianalytical approach for shaped reflector synthesis after a prescribed near-field pattern. Here a new point is the use of auxiliary SIEs of the same type as in the scattering analysis problem, however, for the gradient of the objective function. Sample results are presented for the synthesis of a reflector-type beam splitter. © 2007 Optical Society of America.

Date of Conference: 9-15 June 2007 Conference name: 2007 IEEE Antennas and Propagation Society International Symposium A new diffraction synthesis method is proposed for computing quasioptical 2-D reflector beam splitters in the E-polarization case. It is a combination of a numerical gradient (NG) optimization and an efficient analysis method based on singular integral equations (SIEs) which are discretized using a fast and accurate numerical Nystrom-type method of discrete singularities (MDS). The results of design are shown for a 40-quasioptical power splitter obtained from an offset parabolic reflector fed by in-focus beam source.

We study the e-polarized beam wave guidance and scattering by a chain of finite-size reflectors modeling quasioptical beam waveguide. The incident complex-source-point (CSP) field simulates a beam generated by a small-horn aperture. Numerical solution is obtained from the coupled singular integral equations (IEs) discretized by using new quadrature formulas of interpolation type. The analysis shows that the edge illumination of the nearest to the feed reflector plays a crucial role and should not exceed -12 dB.

This paper presents the investigative study to derive a computational model based on hypersingular integral equations for the pre-Cantor plane-parallel diffraction structure. Such structure consists of finite numbers of the thin impedance strips located in the XY plane. A plane transverse magnetic wave is incident from infinity on considered diffraction structure at an angle and need to find the total field resulting from the scattering. The model which is considered in this work is an approximation of real fractal antennas in two-dimensional case. Pre-fractal properties of grating allow producing the newest antennas for modern mobile devices due to their compact size and broadband properties. The purpose of this work is to develop computer model their structure using parametric representation of hypersingular integral operator, Nystrom method with specific quadrature formulas. The numerical results have been obtained and investigated for pre-Cantor structures for calculating physics characteristics. These results have been compared and analyzed in different mathematical models and softwares.

For the first time rigorous mathematical model is developed for standing TE and TM waves in the longitudinal direction in coaxial cavity gyrotron with a corrugated insert. Based on this theory simulations are performed and novel numerical results are presented in particular for the ITER relevant gyrotron developed in FZK Karlsruhe, Germany. Connection between eigenvalues of the traveling waves and eigenfrequencies of the longitudinal standing ones is discussed. Rigorous method to study standing waves in the azimuthal direction is proposed. This technique can be used to design and develop more efficient gyrotrons resonators.

A full-wave numerical study of a 2-D model of dual-reflector PACO (parabolic subreflector and conical reflector) antenna is performed. Analysis tool is two coupled singular electric field integral equations (SEFIE) discretized with the Method of Discrete Singularities (MDS), for both polarizations. MDS is numerical method similar to the Nystrom method however adapted to zero-thickness perfectly-electric-conducting (PEC) scatterers. Numerical results are shown.

Rigorous mathematical model is developed for eigen traveling TM modes in a coaxial cavity gyrotron with a corrugated insert. This theory has no simplifying assumptions and can be applied for any corrugation parameters and wavelengths. Eigenvalues of the corresponding modes, electromagnetic field components and Ohmic losses can be calculated by a gyrotron simulation software developed for eigen TE and TM modes. This software also gives an ability to determine optimal corrugation parameters for which energy losses are minimal. Novel numerical results are presented for the ITER relevant 170GHz coaxial cavity gyrotron developed by Forschungszentrum Karlsruhe, Germany.

In this paper, the wave scattering by finite-size cylindrical reflectors and multielement strip gratings are studied. The use of parametric representations of integral and pseudo-differential equations for deriving singular and hypersingular integral equations is demonstrated in simplest cases. These equations are solved numerically by the method of discrete singularities, which has been completely grounded.

Parametric representations of integral and pseudodifferential operators are used in the derivation of singular and hypersingular integral equations for a number of diffraction prnhlems. These equations can be solved numerically by the Method of Discrete Singularities, which has been completely grounded.

We study the E and H-polarized beam wave guidance and scattering by finite-size reflectors modeling quasioptical beam waveguides. The incident complex-source-point (CSP) field simulates a beam generated by a small-horn aperture. Numerical solution is obtained from the coupled singular integral equations (SIEs) discretized by using new quadrature formulas of interpolation type.

Two mathematical models are proposed for analyzing a linearly polarized plane wave scattering by a strip grating placed on isotropic-gyrotropic media interface in the case of oblique incidence. The first mathematical model is based on reducing the original boundary value problem to the Riemann-Hilbert problem. The second model is based on reducing the same problem to a singular integral equation of the first kind with a Cauchy kernel and its numerical solution by the discrete singularities method.

A new theory based on the full wave analysis and valid for arbitrary size corrugations has bee developed and applied for an ITER relevant coaxial gyrotron cavity.

A mathematical model of diffraction of plane linear polarized monochromatic waves on the band grating located on one side of the planar gyrotropic layer is suggested. It is based on reducing the problem under consideration in its exact formulation to a singular integral equation and its numerical solution by the method of discrete singularities. This approach is interesting both for the possibility of discretization of the considered problem by the direct numerical method and the possibility of extending it to the corresponding problem with a multielement grating.

Summary form only given, as follows. Numerical analysis problems of REB interaction with a finite length diffraction grating in resonant region (/spl lambda//spl sim/l, where /spl lambda/ is wavelength of the radiation, l is grating period) is important for the theory and simulation of physical processes in grating based electronic devices. The proposed new approach is based on two main steps: (a) reduction of the initial two-dimensional boundary problem for Maxwell equations to the system of one-dimensional singular integral equations (SSIE); (b) rigorous numerical solving of the SSIE by direct numerical method. It allow us to correctly describe multimode regimes of the interaction to be usually realized in high power electronic devices. As a result the effective algorithm for finite length grating with rectangular form of elements has been built up. Particular attention is paid to the study of grating length influence on the interaction regimes near Wood's anomalies and n/spl pi/-point frequencies. A number of numerical results for far field angular distribution and transverse and longitudinal field structures near the grating was obtained.