Method Of Analytical Regularization Research Articles

Resonance scattering of plane waves by a soft elliptic cavity with a variably placed longitudinal slit.

Using previous results [Vinogradova, J. Acoust. Soc. Am. 144(3), 1146-1153 (2018)] on the spectrum of complex eigenvalues for an open elliptic cavity with variably placed longitudinal slits, the author investigates the resonance excitation of such a cavity by obliquely incident plane waves. The complete investigation of the resonance response is based on accurate calculation of the monostatic and bi-static sonar cross-sections, as well as calculation of the jump in normal velocity at the cavity surface. High-accuracy calculations are obtained by employing the rigorous Method of Analytical Regularization. Furthermore, studies of semi-elliptic cavities with high eccentricities, modelling the extremely deep acoustical cavities, are also performed.

Method of analytical regularization in the analysis of axially symmetric excitation of imperfect circular disk antennas

This work presents accurate numerical method and computational results in the modeling of the axisymmetric radiation of resistive and thin-dielectric circular disk-on-substrate antennas. To simulate resistive and thin-dielectric disk features, we use two-side Generalized Boundary Conditions (GBC). The analysis is based on the singular integral equations (IEs) and the Method of Analytical Regularization (MAR) exploiting a Galerkin Method (GM) with judicious basis functions, which convert IEs into the Fredholm second-kind infinite matrix equations. Unlike previously known numerical techniques, this guarantees convergence and enables us to compute the solution with controlled accuracy even in sharp resonances. Numerical results demonstrate the effect of disk losses and transparency on the fundamental radiation phenomena and help improve antenna characteristics such as radiation efficiency.

Acoustic Plane Wave Diffraction from a Circular Soft Ring

The paper presents the implementation of the rigorous method of analytical regularization to the canonical problem of axially-symmetric diff raction from a soft ring. The series equations of the problem are reduced to an infinite series of linear algebraic equations (ISLAE) and the technique of analytical regularization is applied. Finally, the resulting matrix equation is the ISLAE of the second kind and can be solved numerically by the truncation method with any desired accuracy. The near field in the vicinity of the aperture of the ring is presented in the form of maps of the normalised total field. The far field features of the ring are obtained and discussed. The validation of our calculation is confirmed by testing of the mode matching conditions and through the comparison of the results with those for a disc.

Diffraction by semi-infinite cone formed with electric and magnetic surfaces: analytical regularization and Wiener–Hopf techniques

The problem of axially symmetric E-polarized electromagnetic waves diffraction from the circular cone formed by the junction of the perfectly electro-conducting (PEC) semi-infinite truncated cone and the perfectly magneto-conducting (PMC) finite cone is studied rigorously by applying the Kontorovich–Lebedev integral transformation technique, the mode-matching method, and the analytical regularization procedure. The convolution-type operator and its inverse operator are used to conduct the regularization procedure and to reduce the problem to the infinite systems of linear algebraic equations of the second kind. The left side and the right side of the regularization procedures are considered. Transition from the cone to the PEC plane with the circular magnetic window is analysed. The exact solution of the problem is obtained for the static limit, and the low-frequency approximate is derived. The Wiener–Hopf technique is also applied to obtain the solution. Both solutions obtained using the analytical regularization method and by the Wiener–Hopf technique are compared, and the relation between them is derived. Within the framework of the Macdonald’s model, the solution is applied to analyse the far field scattered from the two partially absorbing conical scatterers; (1) the PEC semi-infinite cone with the “black” vertex; and (2) the semi-infinite PMC cone with the “black” truncated conical surface.

Full wave analysis of plane wave diffraction by a finite sinusoidal grating: E-polarization case

Plane wave diffraction studies of a finite sinusoidal grating have previously assumed that the grating length is large in wavelengths and the depth of its corrugations is small compared to a wavelength. This paper introduces a rigorous technique, the Method of Analytical Regularization (MAR), which removes these restrictions. The solution obtained by this method is free from limitations on the parameters of sinusoidal grating and possesses the capability to achieve predetermined accuracy of computations uniformly in a wide frequency band. The results of previous studies, which employed the Wiener–Hopf technique combined with a perturbation method, are compared with those obtained by the MAR; excellent concordance of results in the common parameter regimes of applicability of both methods is found. The different regimes of applicability of each approach are identified; within these, the MAR provides effective and efficient solutions to benchmark problems for testing other approximate techniques.

Axially Symmetric Compact Range Reflectors: Application of the Analytic Regularization Method

An axially symmetric compact range reflector with a blended rolled edge was analyzed and optimized in a rigorous formulation of the diffraction problem. The corresponding boundary-value diffraction problem is solved with the analytic regularization method, which reduces the problem to an operator equation of the second kind, thus guaranteeing a numerically stable and effective solution. The distribution of the surface density and the fields at the aperture and in the near-field zone were obtained and analyzed for different types of the reflector-edge curvature. In addition, a “blending function” was used that esures an infinitely smooth contour across the junction between the paraboloid part of the reflector and its rolled edge. The procedure for determining the optimal edge is carried out in the rigorous formulation of the diffraction problem by minimizing the deviation from a plane wave.

Reflectivity of two-dimensional airfoils illuminated by H-polarized plane wave: Rigorous approach

ABSTRACTThis article presents the implementation of the rigorous method of analytical regularization for the scattering of an H-polarized plane wave by the classical airfoil described by the Zhukovski transform. The reflectivity of airfoils is studied over a wide frequency band. The results obtained complement the previous studies concerning E-polarized waves. A comparative analysis for cases of the E- and H-polarization is carried out. Accurate calculations of the induced surface current, far-field scattering patterns, and frequency dependence of the monostatic radar cross section are presented.

Acoustic plane wave diffraction from a truncated semi-infinite cone in axial irradiation

The diffraction problem of the plane acoustic wave on the semi-infinite truncated soft and rigid cones in the case of axial incidence is solved. The problem is formulated as a boundary-value problem in terms of Helmholtz equation, with Dirichlet and Neumann boundary conditions, for scattered velocity potential. The incident field is taken to be the total field of semi-infinite cone, the expression of which is obtained by solving the auxiliary diffraction problem by the use of Kontorovich-Lebedev integral transformation. The diffracted field is sought via the expansion in series of the eigenfunctions for subdomains of the Helmholtz equation taking into account the edge condition. The corresponding diffraction problem is reduced to infinite system of linear algebraic equations (ISLAE) making use of mode matching technique and orthogonality properties of the Legendre functions. The method of analytical regularization is applied in order to extract the singular part in ISLAE, invert it exactly and reduce the problem to ISLAE of the second kind, which is readily amenable to calculation. The numerical solution of this system relies on the reduction method; and its accuracy depends on the truncation order. The case of degeneration of the truncated semi-infinite cone into an aperture in infinite plane is considered. Characteristic features of diffracted field in near and far fields as functions of cone's parameters are examined.

Development of 2.5D Analytical Regularization Method for reflector antenna analysis

A novel and efficient approach, which is called two-and-a-half dimensional Analytical Regularization Method (2.5D ARM), is proposed to analyse reflector antennas for microwave, millimeter wave or ultra-wide band applications. To present computational performance of the proposed method, its results are compared with well known Physical Optics (PO) and Method of Moments (MoM) solutions for a PEC hollow cylinder and an open-ended corner reflector. Moreover, radiation pattern of a ridged horn fed parabolic reflector antenna is measured to validate the method experimentally. It is observed that either the simulated or the measured data and the 2.5D ARM results are in close agreement with each other.

Method of analytical regularization in computational photonics

AbstractWe discuss the advantages of the conversion of electromagnetic field problems to the Fredholm second‐kind integral equations (analytical regularization) and Fredholm second‐kind infinite‐matrix equations (analytical preconditioning). Special attention is paid to specific features of the characterization of metals and dielectrics in the optical range and their effect on the problem formulation and on the methods applicable to the mentioned conversion.

Diffraction of a Plane Acoustic Wave from a Finite Soft (Rigid) Cone in Axial Irradiation

The problem of diffraction of a plane acoustic wave by a finite soft (rigid) cone is investigated. This one is formulated as a mixed boundary value problem for the three-dimensional Helmholtz equation with Dirichlet (Neumann) boundary condition on the cone surface. The diffracted field is sought as expansion of unknown velocity potential in series of eigenfunctions for each region of the existence of sound pressure. The solution of the problem then is reduced to the infinite set of linear algebraic equations (ISLAE) of the first kind by means of mode matching technique and orthogonality properties of the Legendre functions. The main part of asymptotic of ISLAE matrix element determined for large indexes identifies the convolution type operator amenable to explicit inversion. This analytical treatment allows one to transform the initial diffraction problem into the ISLAE of the second kind that can be readily solved by the reduction method with desired accuracy depending on a number of truncation. All these determine the analytical regularization method for solution of wave diffraction problems for conical scatterers. The boundary transition to soft (rigid) disc is considered. The directivity factors, scattering cross sections, and far-field diffraction patterns are investigated in both soft and rigid cases whereas the main attention in the near-field is focused on the rigid case. The numerically obtained results are compared with those known for the disc.

Design of horn fed offset parabolic reflector antennas with analytical regularization method

This paper presents two-dimensional (2D) parametric design of offset parabolic reflectors with horn feeders to achieve pencil beam and cosecant-squared (csc2) patterns for communication systems and surveillance radars. Analytical regularization method (ARM) is used as a fast and accurate pre-design tool to compute radiation characteristics of the feeders and the reflectors. The numerical procedure is initially verified by the analytical methods and the calculated results are presented for the proposed novel designs.

DIFFRACTION FROM A GRATING ON A CHIRAL MEDIUM: APPLICATION OF ANALYTICAL REGULARIZATION METHOD

Theoretical results on the electromagnetic wave difiraction from a periodic strip grating placed on a chiral medium are obtained. Analytical Regularization Method based on the solution to the vector Riemann-Hilbert boundary value problem was used to get robust numerical results in the resonant domain, where direct solution methods typically fail. It was shown that in the case of normal incidence of linearly polarized wave the cross-polarized fleld appears in the re∞ected fleld. For elliptically polarized incident wave the difiraction character essentially depends on the polarization direction of the incident wave. These difiraction peculiarities are more pronounced in the resonant domain. In∞uence of the dichroism caused by chiral medium losses is thoroughly studied. The combination of a chiral medium and a grating can be efiectively used for a frequency and polarization selection and for a mode conversion.

Analysis of an arbitrary-profile, cylindrical, impedance reflector surface illuminated by an E-polarized complex line source beam

Electromagnetic scattering from a cylindrical reflector surface having an arbitrary conic section profile is studied. We assumed an electrically thin layer antenna illuminated by a complex line source in E-polarization mode. Our boundary value formulation, without loss of generality, involves an integral equation approach having impedance-type thin-layer boundary conditions. For simplicity, we also considered both faces of the reflector of the same uniform impedance value. Our computation employs the Method of Analytical Regularization (MAR) technique: the integral equations are converted into the discrete Fourier transform domain yielding two coupled dual series equations, which are then solved by the Fourier inversion and Riemann Hilbert Problem techniques. We demonstrate the accuracy and the convergence behaviors of our numerically solved MAR results that can serve as an accurate benchmark for comparison with widely used results obtained by approximate boundary conditions.

Wave Diffraction on a Stripe Grating at a Boundary of a Layered Inhomogeneous Medium: Method of Analytic Regularization

In this work, we develop a novel numerical-analytic method for solving the problem of wave diffraction on a stripe array situated at a boundary of a layered inhomogeneous medium. A high-efficiency algorithm for calculation of the diffraction characteristics of such a structure in the case where a plane electromagnetic wave is incident on it obliquely has been developed. The operation of the algorithm is demonstrated by the example of the problem about diffraction of a plane E-polarized wave on certain layered inhomogeneous media, including plasma-like ones, with a stripe grating at one of its boundaries.

Accurate Analysis of Light Scattering and Absorption by an Infinite Flat Grating of Thin Silver Nanostrips in Free Space Using the Method of Analytical Regularization

We study the plane wave scattering and absorption by a flat grating of thin silver nanostrips located in free space, in the visible-light range. The formulation involves generalized boundary conditions imposed on the strip median lines. We use an accurate numerical solution to this problem based on the dual-series equations and the method of analytical regularization. This guarantees fast convergence and controlled accuracy of computations. Reflectance, transmittance, and absorbance as a function of the wavelength and the grating parameters are analyzed. In addition to well-known surface-plasmon resonances, sharp resonances are revealed in the H-polarized scattering near but not equal to the Rayleigh wavelengths of nonzero diffraction orders; in the E-polarized scattering these resonances are not visible. Asymptotic formulas for the frequencies and natural fields of the grating resonances are presented.

Radiation and absorption of waves emitted by a radial dipole in the presence of a layered dielectric sphere with a spherical screen

Considered is the problem of electromagnetic wave radiation and absorption in the presence of a two-layer lossy dielectric sphere partially covered with a metal screen and illuminated by an elementary electric dipole. To find the field, the authors expand it in terms of spherical functions and use the method of analytical regularisation to reduce the problem to a matrix equation with favourable features. This enables us to obtain the radiation and absorption characteristics in a wide range of parameter variations and compare the efficiencies of shielding by different screens of varying angular size. As the studied structure can be viewed as a model of a head phantom with a helmet, the presented analysis can be useful for a control of specific microwave absorption rate levels.

Analytical Regularization Method for Rigorous Diffraction Analysis of Knife Edges for TM Waves

A direct full-wave solution via the Analytical Regularization Method (ARM) is proposed for the diffraction problem concerning knife edges under TM wave excitation. This problem is reduced to solving an infinite linear algebraic equation system of the second kind which, in principle, can be solved with arbitrary predetermined accuracy via a truncation procedure.

Parametric analysis of flare edge rolling throat bending and asymmetric flare effects for H-plane horn radiator

In this paper, radiation characteristics of H-plane sectoral horn antenna are treated systematically by investigation of main structural design parameters and, flare edge rolling, throat bending and asymmetric flare effects. The analytical regularization method (ARM) is used to solve the problem of E-polarized wave diffraction in a fast and accurate way. The numerical procedure is initially verified by the analytical solutions, and then the calculated directivity gain patterns are demonstrated for the modeled horn antenna configurations. Proper choices of the antenna parameters, such as horn depth, aperture length, feeder waveguide width, flare angle, wall thickness, flare edge rolling and throat bending are proposed for the designers to reach high directivity gain, narrow beam width, suppressed side lobe levels, increased front-to back ratio and improved aperture efficiency.

Accurate quantification of the Purcell effect in the presence of a dielectric microdisk of nanoscale thickness

The spontaneous emission of a molecular dipole in the presence of a thin dielectric microdisk is studied as a 3D solution of Maxwell's equations with two-sided generalised boundary conditions on the disk median plane, local energy finiteness and a radiation condition at infinity. Results presented show that the radiative and non-radiative decay rates display resonance maxima associated with the disk natural frequencies which can be explained through the effective-refractive-index approximation. The numerical solution is based on a set of coupled integral equations of the Fredholm second kind, with smooth kernel functions, obtained with the aid of the method of analytical regularisation.