Kobayashi Potential Method Research Articles

Scattered Acoustic Field Above a Rigid Rectangular Cuboid Shape in a Rigid Plane

A model is presented for the scattered acoustic field above a bulky rigid cuboid shape in a rigid plane insonified by an acoustic field. The Kobayashi Potential method and the image sources method were used in order to derive the scattered acoustic field in a modal form. The incident source was then decomposed into plane waves. The total scattered field was determined by summing all the elementary scattered fields. This model was compared to finite element modeling and experimental results for three bulky cuboid shapes in an infinite rigid screen and a rectangular corner insonified by a spherical source. A good agreement between numerical and experimental results was obtained supporting the validity of the model.

Rigorous EM Scattering Solution From a Slit in an IBC Plate With Different Surface Impedances Placed Between Two Different Chiral Media

A Kobayashi potential (KP) method is an accurate and fast technique for analyzing electromagnetic (EM) scattering. In this article, the EM scattering from a slit in an impedance boundary condition (IBC) plate with different surface impedances on its both sides placed on interface of two different chiral media is analyzed by the KP method for both right circularly polarized (RCP) and left circularly polarized (LCP) excitations. A chirality parameter is a more degree of freedom—than dielectrics—presented by a chiral medium to affect the EM scattering. Initially, Fresnel coefficients are calculated as closed-form formulas; then, the slit’s contribution is expressed in terms of unknown weighting functions. Next, the method automatically and analytically satisfies boundary and radiation conditions applying Weber–Schafheitlin (WS) integrals, which leads to infinite summations. The infinite summations are effectively truncated with high accuracy. Finally, the weighting functions and, subsequently, the EM scattering are calculated. A finite-element method (FEM) and a convergence analysis are carried out to validate the formulations. The effects of different parameters of the problem on the EM scattering are also analyzed. It is shown that the maximum scattered fields are occurred at non-specular angles. Also, this solution can be a facilitator to analyze the inverse scattering of the problem to determine the properties of the structure.

Study of scattering from a PEC strip placed at the planar interface of NID dielectric and dielectric-magnetic medium using the KP method

Mathematical expressions for electromagnetic scattering from a Perfect electric conductor strip positioned at the planar non-integer dimension (NID) dielectric- magnetic interface are determined by using the Kobayashi potential (KP) method. The Lorentz-Drude model is used to include dispersion and losses in both permeability and permittivity of the dielectric- magnetic medium. Based on the KP method, the unknown scattered fields are presumed in terms of the spectrum with an undetermined weighting function. By imposing the appropriate boundary conditions, the dual integral equations for undetermined weighting functions obtained, the integrals are further solved by utilizing the property of Weber-Schafheitilin integrals. Then, using the orthogonal properties of Jacobi polynomials, the set of matrix equations satisfying the WSIs along with edge boundary conditions are obtained. This set of equations is solved numerically to find the undetermined expansion coefficients. Far-field expressions are studied to note the impact of the NID parameter on the scattered field. Based on the operating frequency, dielectric-magnetic medium behaves as double positive/mu negative/double negative/epsilon negative. It is studied that how the type of medium for lower half-space along with the presence of NID medium in upper half-space affects scattering characteristics of the strip.

Electromagnetic scattering of the PEMC strip located at the interface of topological insulator-dielectric by utilizing Kobayashi potential method

The scattering of electromagnetic wave by a perfect electromagnetic conductor (PEMC) strip is investigated in this article. The strip is located at the interface of semi-finite topological insulator (TI) and a dielectric. Kobayashi potential (KP) method is a fast semi-analytical approach that is applied to proposed structure. In KP, unknown weighting functions are employed to customize the scattered fields’ expressions in order to transform some of the boundary conditions to the Weber–Schafheitlin integrals, which can satisfy boundary and some of the edge conditions simultaneously. Moreover, Jacobi polynomials are used to simplify formulations and model the edge condition. The rapid rate of convergence and acceptable level of error in the proposed approach is analyzed profoundly. Furthermore, validation of the solution is investigated by comparing results with physical optics (PO) and method of moment (MoM) results. Radar cross-section (RCS) and its variation versus some crucial parameters are investigated and represented as final results.

Scattering from a PEMC strip deeply buried beneath a dielectric slab using Kobayashi potential method

Kobayashi potential method is applied to get the scattering behavior by a perfect electromagnetic conducting strip deeply buried underneath a flat dielectric slab. Using the two-dimensional solution of homogeneous Helmholtz’s equation, Fourier transformed representation of scattered field is written in terms of the unknown characteristic functions. Application of the boundary conditions on tangential components of electromagnetic fields gives dual integral equations (DIEs) which through Weber–Schafheitlin’s discontinuous integrals and Jacobi polynomials are used to satisfy the edge condition. The resulting DIEs are written in matrix equations, and those that involve infinite integrals are computed numerically. The saddle point method of integration is used to obtain an expression for the far-zone scattered field. To validate the results, obtained results are firstly compared with corresponding obtained through the physical optics method. The width of the strip, the thickness of the slab, and the angle of incidence of plane wave are taken as parameters to study their influence on the scattered field.

Semi-analytical solution of electromagnetic scattering of a slit in PEC plane located in TI medium

The electromagnetic scattering of a slit in the perfect electric conductor (PEC) plane embedded in the topological insulator (TI) medium is analyzed in this paper. The problem is solved by utilizing Kobayashi Potential method, which is a rapid semi-analytical approach with decent accuracy. In solving process, scattered fields are consist of some variables known as weighting functions. By applying boundary conditions, unknowns will be found. Also, discontinuous properties of Weber-Schafheitlin integrals and Rodriguez representation of Jacobi polynomials are employed to satisfy some of the boundary conditions and edge conditions of the problem simultaneously. By performing convergence analysis and error analysis, validation of the proposed approach is confirmed. Finally, by sweeping some parameters, the scattering behavior of the structure is investigated.

Analytical solution of electromagnetic scattering from PEMC strip located at TI medium

Topological insulator (TI) and perfect electromagnetic conductor (PEMC) are new type of matter with remarkable electromagnetic behavior. Despite of conventional scattered fields terms, cross-component terms are generated when the electromagnetic wave interacts with these matters. In this paper, TI is utilized as host medium for PEMC strip and diffraction of electromagnetic wave from proposed strip is assessed by Kobayashi potential (KP) method which yields exact answer. Pivotal elements in KP are Weber-Schafheitlin integrals which are specific integrals with exact solution. Whereby, boundary and some edge conditions of configurations satisfy automatically and simultaneously. Initially, formulation and theoretical calculations of KP method is provided and far-zone scattered field is calculated. To demonstrate the efficiency of method, convergence analysis is provided and for the validation, comparison with other methods is made. Variations of scattered field pattern due to configuration's parameters are illustrated and discussed meticulously.

Plane-wave electromagnetic scattering from a PEC strip placed at the interface of non-integer dimensional spaces

In this paper, scattering from a perfectly conducting strip placed at planar interface of non-integer dimensional (NID) dielectric media is formulated and investigated using the Kobayashi Potential (KP) method. The KP method is a semi analytical technique to address scattering problems. According to this method, longitudinal component of the unknown scattered field is assumed in terms of unknown weighting functions. Use of the related boundary conditions leads to the formation of algebraic equations and dual integral equations (DIEs). Integrands of the DIEs are expanded in terms of the characteristic functions with unknown expansion coefficients which must satisfy, simultaneously, the required edge and boundary conditions. The expressions derived from expansion of the integrands are combined with algebraic equations in order to express the unknown weighting function in terms of unknown expansion coefficients. Moreover, the projection treatment is applied using properties of the Jacobi polynomials, yielding matrix equation for unknown expansion coefficients. Matrix equation has been solved numerically. The far zone scattering width is investigated with respect to different parameters of the geometry, e.g., size of the strip and dimension of the NID space. Significant effects of different parameters on the scattering width are noted.

Use of Kobayashi potential method and Lorentz–Drude model to study scattering from a PEC strip buried below a lossy dispersive NID dielectric-magnetic slab

Kobayashi potential method is applied to investigate the scattering behavior of a perfect electric conducting (PEC) strip buried below a lossy dispersive non-integer dimensional (NID) dielectric-magnetic slab. Dispersion characteristics are introduced through the Lorentz–Drude model. Due to dispersive nature of the medium occupying the slab, it operates as epsilon negative (ENG), double negative (DNG), mu negative (MNG), or double positive (DPS) material depending upon the operating frequency. Scattered fields have been obtained when the slab behaves as ENG/MNG/DNG or DPS. Efforts have also been made to highlight the impact of NID parameter and dispersion characteristics of the material of the slab. It has been observed that increase/decrease in the thickness of the slab decreases/increases the scattered field from the strip below the slab. Moreover, it also decreases as size of the obstacle increases. It has been noted that the effect of real part of constitutive parameters on scattering pattern is opposite to that of imaginary part of constitutive parameters for ENG, MNG and DPS slab while for DNG slab the trend remains same.

Scattering from a PEC strip buried in non-integer dimensional planar grounded dielectric slab by using Kobayashi potential method

Solution for electromagnetic scattering from a perfect electric conducting strip buried in a planar grounded dielectric slab is determined by using the Kobayashi Potential Method. It is assumed that the dimension of mediums, above and within the slab, is non-integer in the direction normal to interface of the slab. The scattering problem is divided into two parts. In the first part, fields in the absence of strip are determined for plane wave excitation. In the second part, presence of the strip is taken into account. It has been assumed that spacings between the strip and interfaces of the slab are comparatively very larger than the wavelength of monochromatic operating frequency. Due to this assumption, scattered field after reflection from the interfaces has no interaction with the strip. In order to gains more insight, several special cases of the geometry are treated. Using saddle point method, far-zone scattered field for region above the grounded slab is also determined.

Scattering from a cylindrical obstacle deeply buried beneath a planar non-integer dimensional dielectric slab using Kobayashi potential method

Mathematical formulation for the far-zone field scattered by a cylindrical obstacle deeply buried beneath a planar dielectric slab has been presented. Method known as Kobayashi potential method has been employed for this purpose and transverse electric uniform plane wave has been used as a source of excitation. It has been assumed that dimension of space within slab is non-integer in the direction normal to planar interfaces of the slab. Moreover, it has also been assumed that distance of each interface of the slab from obstacle is very large as compared to size of the obstacle. Due to this assumption scattered field after reflection from the slab has no interaction with the obstacle and the situation has been called deeply buried. Field pattern has also been obtained and compared with the published work.

Scattering from a perfect electromagnetic conducting (PEMC) strip buried in non-integer dimensional dielectric half-space using Kobayashi potential method

Using Kobayashi potential method, mathematical formulation and solution have been provided for scattering from a perfect electromagnetic conducting (PEMC) strip buried under a planar dielectric interface. Mediums occupying half spaces on both sides of the dielectric interface are non-integer dimensional in direction normal to the dielectric interface. Far zone scattered field, which takes into account asymptotic contributions of all multiple interaction between the strip and the dielectric interface, has been derived for a special case when half space hosting the strip is of integer dimension. Results for limiting cases of the strip have also been obtained for verification.

Scattering from a PEC strip located at planar interface of free-space and lossy dispersive dielectric-magnetic medium using Kobayashi potential method

Kobayashi potential method has been used to study the scattering of electromagnetic plane wave from a perfect electric conducting (PEC) strip placed at planar interface of the free space and dielectric-magnetic medium. The strip has been assumed to be thicker than the skin depth and also, it is thinner than a tenth of the free-space wavelength. Furthermore, it has been assumed that dielectric-magnetic medium is homogeneous, lossy and dispersive. Lorentz-Drude model has been used to incorporate losses and dispersion both in permittivity and permeability of the dielectric-magnetic medium. Depending upon the frequency, the lossy dispersive dielectric-magnetic medium may behave as ENG Re (ϵ)<0, MNG Re(μ)<0, DNG Re(ϵ,μ)<0, and DPS Re(ϵ,μ)>0. Scattered field pattern was observed at different operating frequencies by varying different parameters of the considered geometry. The monostatic and bistatic scattering widths were studied by varying angle of incidence, size of the strip and number of iterations. It was observed that losses become more effective in case of free space–DPS interface as compared to other cases for the interface. Minimum value of the main lobe of scattering widths was produced when the strip was placed on free space–DPS interface.

Scattering from a cylindrical obstacle buried in non-integer dimensional dielectric half-space using Kobayashi potential method

Kobayashi potential method has been used to derive mathematical expression for the far-zone scattered field from a cylindrical obstacle buried in dielectric half space. Linearly polarized electromagnetic plane wave has been used as source of excitation. Geometry of the problem has been taken non-integer dimensional (NID) in direction normal to the interface separating two half spaces. Asymptotic contribution of multiple interactions between the buried obstacle and NID-dielectric interface has been taken into account for the far-zone scattered field.

A fast solution of TM wave scattering by a coated 2D partially filled rectangular crack

An analytical technique of kobayashi potential (KP) method is applied to study the TM plane wave scattering by a coated 2D partially filled rectangular crack in a ground plane. Initially, by expanding a summation of waveguide modal eigenfunctions, the electric field inside the coating layer is found. Then, the crack contribution is taken into account by addition of the Bessel eigenfunctions in both the coating layer and the semi-infinite half space. By applying the KP method and utilizing the Weber–Schafheitlin discontinuous integrals, the governing equations of an infinite summations with unknown coefficients are derived. Then, by imposing the boundary conditions, the unknown coefficients are determined. The proposed method is validated by comparisons made with the finite element method results. Finally, the effect of a progressively filling crack and the dielectric layer height increase on the far-field scattered field is investigated. The permittivities and permeabilities of the coating and the filling dielectric could be lossy or lossless. The proposed method is applicable to both narrow and wide cracks and is accurate and computationally efficient.

Scattering of electromagnetic plane wave from a perfect electric conducting strip placed at interface of topological insulator–chiral medium

In this manuscript, scattering from a perfect electric conducting strip located at planar interface of topological insulator (TI)–chiral medium is investigated using the Kobayashi Potential method. Longitudinal components of electric and magnetic vector potential in terms of unknown weighting function are considered. Use of related set of boundary conditions yields two algebraic equations and four dual integral equations (DIEs). Integrand of two DIEs are expanded in terms of the characteristic functions with expansion coefficients which must satisfy, simultaneously, the discontinuous property of the Weber–Schafheitlin integrals, required edge and boundary conditions. The resulting expressions are then combined with algebraic equations to express the weighting function in terms of expansion coefficients, these expansion coefficients are then substituted in remaining DIEs. The projection is applied using the Jacobi polynomials. This treatment yields matrix equation for expansion coefficients which is solved numerically. These unknown expansion coefficients are used to find the scattered field. The far zone scattering width is investigated with respect to different parameters of the geometry, i.e, chirality of chiral medium, angle of incidence, size of the strip. Significant effects of different parameters including TI parameter on the scattering width are noted.

Scattering of electromagnetic plane wave from a perfect electric conducting strip located in topological insulator medium

In this article, scattering from a perfectly electric conducting strip located in an infinitely extended topological insulator (IT) medium is investigated using the Kobayashi potential method. For solving mixed boundary value problem, KP method is a fast and semi-analytical technique. In this method, edge conditions and boundary conditions are incorporated simultaneously. The scattered field is calculated from the strip geometry embedded in IT medium. The far zone scattered field is investigated with respect to different parameters of the geometry, i.e. topological parameter of the IT medium, size of the strip etc. It has been observed that the scattered field can be enhanced by increasing topological parameter of the IT medium. On the other hand, size of strip, permittivity of IT medium may also be used to enhance the main lobe of the scattering width/scattered field.

A fast solution of TE wave scattering by a 2D partially dielectric filled and coated rectangular crack

A two-dimensional transverse-electric Electromagnetic (EM) plane-wave scattering by a partially filled rectangular crack in a ground plane that is coated by a dielectric layer is presented here by Kobayashi Potential (KP) method. First, the EM field inside the coating layer is expanded by a summation of waveguide modal eigenfunctions. Consequently, the crack contribution in terms of the Bessel eigenfunctions is added as a perturbation to the coating layer and the semi-infinite half-space fields. Then, using the Weber–Schafheitlin discontinuous integrals and applying the KP method, the governing equations of infinite summations with unknown coefficients are derived. Next, by imposing the boundary conditions, the unknown coefficients are determined. Besides validating the method with the finite element method, an extensive comparative analysis with other methods is also provided. Finally, the effect of a progressively filling of the coated crack on the far-field scattering is investigated. Both lossy and lossless permittivities and permeabilities are considered for the coating and the filling. The method is extremely accurate and computationally efficient, and could be applied to both narrow and wide cracks.

Scattering of electromagnetic plane wave from a perfect electric conducting strip placed at free space–chiral interface

The scattering of electromagnetic plane wave from a perfect electric conducting strip of finite width is investigated in this study. The strip is placed at the planar interface of free space and chiral medium. The Kobayashi potential method is used to determine the scattering from the strip. The dual integral equations are acquired through the boundary conditions. These equations as well as the edge conditions are satisfied through the properties of Weber–Schafheitlin integrals and the Jacobi polynomials. The projection of the Jacobi polynomials is used to get the matrix equations which are solved numerically to determine the unknown coefficients. Monostatic and bistatic scattering widths are examined in the free space region of the geometry. The far-zone scattered fields are analyzed by changing the values of different parameters, i.e. chirality and incident angle.

Scattering of electromagnetic plane wave by an impedance strip embedded in homogeneous isotropic chiral medium

In this article, Kobayashi potential method has been used to investigate scattering from an impedance strip embedded in a homogeneous isotropic chiral medium. The discontinuous properties of the Weber-Schafheitlin's integral have been applied to incorporate the edge conditions. A set of matrix equations are obtained, using the projection properties of Jacobi's polynomials, and solved for unknown expansion coefficients of the fields. Monostatic and bistatic scattering widths have been determined for left and right handed Beltrami field excitations. Effects of variation in values of chirality, incident angle, impedance and width of strip on scattered fields have been investigated. The numerical results of the scattered fields for various parameters have been produced for comparison.