Diffraction Of Plane Wave Research Articles

A Solution for the Plane Wave Diffraction by the Discontinuity Between Two Co-Planar Metamaterial Sheets

A high-frequency approach is described to investigate the scattering by a junction between double negative metamaterial (DNG MTM) sheets. These last are lit by an incident plane wave and have same thickness, but different electric and magnetic parameters, thus assuring discontinuities of reflected and transmitted fields across the junction. The proposed methodology permits to evaluate the diffraction contribution as the sum of two independent terms arising from the scattering process including electric and magnetic equivalent sources under the physical optics (PO) approximation. The formulation of this wave contribution permits its use in the enclosure of the uniform geometrical theory of diffraction (UTD). Useful approximations and integral representations are adopted together with asymptotic evaluations to obtain the diffraction matrix elements. Accordingly, these last account for convenient reference systems, the approximated equivalent currents, and the typical function of the UTD. A full-wave numerical tool is exploited to assess the correctness of the proposed formulation.

A new approach in electromagnetic plane wave diffraction by two concentric slotted cylinders with variably placed slits: E and H polarized cases

The study investigates the electromagnetic plane wave diffraction by two concentric slotted cylinders with variably placed slits. Unlike the previous studies, the effect of rotation on the resonance characteristics and near-field distributions is analyzed in the present work, which is not studied yet. The study focuses on diffraction by both E- and H-polarized plane waves. A semi-analytical method is preferred to obtain the physical properties such as resonances and near and far-field radiation patterns. The advantage of the method is to employ the analytical and numerical tools together. Due to having both E- and H-polarized plane waves, Dirichlet and Neumann Boundary conditions are considered and analyzed, respectively. After obtaining the mathematical expressions for the current density, near and far-field, and total radar cross-section, the different results are compared with the Method of Moment and the Method of Auxiliary Sources. The comparison demonstrates that the proposed method coincides with other well-known methods. The outcomes reveal that the aperture size and the rotation angle have a significant role in the radiation characteristics.

Optical response of dielectric&metal-core/metal-shell nanoparticles: Near electromagnetic field and resonance frequencies

We study the diffraction of a monochromatic electromagnetic plane wave by a dielectric&metal-core/metal-shell nanoparticle surrounded by a dielectric medium. This problem was solved by using generalized Mie’s theory and both the scattering cross section and the square module of the electric field were calculated as a function of shell thickness. Numerically, the first particles studied were gold-core/silver-shell nanoparticles and their inverse configuration. The gold-core/silver-shell particle presented more variation of their optical properties. The second particles were vacuum-core/metal-shell surrounded by vacuum, symmetric configurations. In this case, the dispersive Drude dielectric function for the metal was used, and a comparative study between the positions of the resonance frequencies obtained from quasi-static limit and electrodynamic theory was performed. Thus, consequently the formula obtained from the quasi-static limit can be used to calculate the positions of the resonance frequencies instead of the electrodynamic theory, when the external radius is smaller than 20 nm.

Theoretical investigation of electromagnetic diffraction focusing in the near zone of a sub-wavelength aperture

The recently predicted phenomenon of diffraction lensless electromagnetic focusing in small volume of the near zone of a sub-wavelength nanoaperture (Semiconductors, 2020, Vol. 54, p. 1814) is analyzed theoretically. For this, we use the rigorous solution of the problem of plane wave diffraction by a slot in a perfectly conducting screen of arbitrary thickness with a thin dielectric film on a substrate, which plays a part of a radiation receiver (detector) behind the slot. The scalar focusing parameter is introduced for estimation of quality of a diffraction image of a slot in a film from the standpoint of local spectroscopy and optical lithography. It is convenient to use for search of domains of variability of the problem parameters, where the phenomenon of sub-wavelength focusing exists.

Electromagnetic plane wave diffraction by a cylindrical arc with edges: H-polarized case

An accurate hybrid method (numerical-analytical method) for the diffraction of H-polarized electromagnetic plane wave by perfectly electric conducting cylindrical bodies containing edges and a longitudinal slit aperture is proposed. This method is the combination of the Method of Moment and semi-inversion method. The current density function is expressed as the Chebyshev polynomials forming a complete orthogonal set of basis functions. Then, the initial problem is reduced to a system of linear algebraic equations. After inversion, the unknown coefficients are obtained. Then, near and far-field distributions, radar cross-sections are obtained. The resonances are observed for different values of the aperture size, radius of the arc, and the results are compared with previous outcomes.

Rigorous accounting diffraction on non-plane gratings irradiated by non-planar waves

The modified boundary integral equation method (MIM) is considered a rigorous theoretical application for the diffraction of cylindrical waves by arbitrary profiled plane gratings, as well as for the diffraction of plane/non-planar waves by concave/convex gratings. This study investigates 2D diffraction problems of the filiform source electromagnetic field scattered by a plane lamellar grating and of plane waves scattered by a similar cylindrical-shaped grating. Unlike the problem of plane wave diffraction by a plane grating, the field of a localised source does not satisfy the quasi-periodicity requirement. Fourier transform is used to reduce the solution of the problem of localised source diffraction by the grating in the whole region to the solution of the problem of diffraction inside one Floquet channel. By considering the periodicity of the geometry structure, the problem of Floquet terms for the image can be formulated so that it enables the application of the MIM developed for plane wave diffraction problems. Accounting of the local structure of an incident field enables both the prediction of the corresponding efficiencies and the specification of the bounds within which the approximation of the incident field with plane waves is correct. For 2D diffraction problems of the high-conductive plane grating irradiated by cylindrical waves and the cylindrical high-conductive grating irradiated by plane waves, decompositions in sets of plane waves/sections are investigated. The application of such decomposition, including the dependence on the number of plane waves/sections and radii of the grating and wave front shape, was demonstrated for lamellar, sinusoidal and saw-tooth grating examples in the 0th and −1st orders as well as in the transverse electric and transverse magnetic polarisations. The primary effects of plane wave/section partitions of non-planar wave fronts and curved grating shapes on the exact solutions for 2D and 3D (conical) diffraction problems are discussed.

ОПЕРАТОРНИЙ МЕТОД В ЗАДАЧІ ПРО ДИФРАКЦІЮ ПЛОСКОЇ ХВИЛІ НА НЕСКІНЧЕННО ТОНКИХ ІДЕАЛЬНО ПРОВІДНИХ НАПІВПЛОЩИНІ ТА ДВОХ ДИСКАХ

Subject and Purpose. Considered in the paper is diffraction of a plane wave by a structure involving a half-plane and two disks. The disks and the half-plane, lying within parallel planes, are assumed to be infinitely thin and perfectly conducting. The problem is to be analyzed for two cases, namely for that of both disks located on the same side with respect to the half-plane, and for the other where they are placed on opposite sides against the half-plane. The purpose of the paper is to develop a suitable operator method for performing the analysis of the structure described. Methods and Methodology. The solution to the problem has been sought for within the operator method suggested. The electric field components tangential to the half-plane and the disks are expressed, with the aid of Fourier integrals, via some unknown functions having the sense of amplitudes. The unknown amplitudes shall obey the operator equations formulated in terms of wave scattering operators for individual disks and the sole half-plane. Results. When subjected to certain transformations, the operator equations allow obtaining integral equations relative amplitudes of the spherical waves involved. The integral equations permit investigating scattered wave fields for the cases where the disks stay in the shadow region behind the half-plane or in the penumbra, or else in the region which is illuminated by the incident wave. As has been shown, in the case of plane wave scattering at the edge of the half-plane the resulting cylindrical waves possess non-zero amplitudes even with the disks placed totally in the shadow region, hence not illuminated by the incident plane wave. Conclusions. Making use of an operator method, an original solution has been obtained for the problem of plane wave diffraction by a structure consisting of a perfectly conducting, infinitely thin half-plane and two disks. The operator equations of the problem have been shown to be reducible to integral equations, further solvable numerically with the use of discretization based on quadrature rules. The behavior of far and near fields relative to the disks has been studied for a variety of values of the disk radii and their positions relative to the half-plane.

ОПЕРАТОРНИЙ МЕТОД В ЗАДАЧІ ПРО ДИФРАКЦІЮ Н-ПОЛЯРИЗОВАНОЇ ХВИЛІ НА ДВОХ ОДНАКОВИХ НАПІВНЕСКІНЧЕННИХ РЕШІТКАХ, РОЗТАШОВАНИХ В ОДНІЙ ПЛОЩИНІ

Purpose: Problem of the H-polarized plane wave diffraction by the structure, which consists of two semi-infinite strip gratings, is considered. The gratings are placed in the same plane. The gap between the gratings is arbitrary. The purpose of the paper is to develop the operator method to the structures, which scattered fields have both discrete and continuous spatial spectra. Design/methodology/approach: In the spectral domain, in the domain of the Fourier transform, the scattered field is expressed in terms of the unknown Fourier amplitude. The field reflected by the considered structure is represented as a sum of two fields of currents on the strips of semi-infinite gratings. The operator equations are obtained for the Fourier amplitudes. These equations use the operators of reflection of semi-infinite gratings, which are supposed to be known. The field scattered by a semi-infinite grating can be represented as a sum of plane and cylindrical waves. The reflection operator of a semi-infinite grating has singularities at the points, which correspond to the propagation constants of plane waves. Consequently, the unknown Fourier amplitudes of the fi eld scattered by the considered structure also have singularities. To eliminate these latter, the regularization procedure has been carried out. As a result of this procedure, the operator equations are reduced to the system of integral equations containing the integrals, which should be understood as the Cauchy principal value and Hadamar finite part integrals. The discretization has been carried out. As a result, the system of linear equations is obtained, which is solved with the use of the iterative procedure. Findings: The operator equations with respect to the Fourier amplitudes of the field scattered by the structure, which consists of two semi-infinite gratings, are obtained. The computational investigation of convergence has been made. The near and far scattered fields are investigated for different values of the grating parameters. Conclusions: The effective algorithm to study the fields scattered by the strip grating, which has both discrete and continuous spatial spectra, is proposed. The developed approach can be an effective instrument in solving a series of problems of antennas and microwave electronics. Key words: semi-infinite grating, operator method, singular integral, hypersingular integral, regularization procedure

An adaptive edge finite element DtN method for Maxwell’s equations in biperiodic structures

Abstract We consider the diffraction of an electromagnetic plane wave by a biperiodic structure. This paper is concerned with a numerical solution of the diffraction grating problem for three-dimensional Maxwell’s equations. Based on the Dirichlet-to-Neumann (DtN) operator, an equivalent boundary value problem is formulated in a bounded domain by using a transparent boundary condition. An a posteriori error estimate-based adaptive edge finite element method is developed for the variational problem with the truncated DtN operator. The estimate takes account of both the finite element approximation error and the truncation error of the DtN operator, where the former is used for local mesh refinements and the latter is shown to decay exponentially with respect to the truncation parameter. Numerical experiments are presented to demonstrate the competitive behaviour of the proposed method.

Plane Wave Diffraction by a Strongly Elongated Three-Axis Ellipsoid

Plane Wave Diffraction by a Strongly Elongated Three-Axis Ellipsoid

Higher-Order Airy Patterns and Their Application in Tailoring Orbital Angular Momentum Beams with Fiber Laser Arrays

Airy patterns, formed by the Fraunhofer diffraction of plane waves via circular apertures, have been widely utilized as criterions in areas such as imaging optics and energy transmission. With deeper insights into the spatial structure of light, the use of Airy patterns as criterions today becomes inadequate in many scenarios. Here, a new concept of higher-order Airy patterns is proposed by introducing the orbital angular momentum (OAM) of light, namely the Fraunhofer diffraction pattern of a plane wave via the defined annular aperture with helical wavefront tailoring. For the m-order Airy pattern, the tailored helicity is m, and the scaling factor of the annular aperture and is determined by the m-related equation set, which is derived based on the paraxial diffraction theory. As a potential application of the proposed concept, a coherent fiber laser array system capable of customizing OAM beams is presented and analyzed. Using the higher-order Airy pattern to define the performance metric of combined beam, the fiber laser array system is optimally designed and the properties in energy concentration and high mode purity of the generated OAM beams could be realized. This work could be beneficial to the theoretical study and applications of OAM beams, especially the generation and manipulation of high-power, fast switchable OAM beams with fiber laser arrays.

Complex eigenvalues of natural TM ‐oscillations in an open resonator formed by two sinusoidally corrugated metallic strips

The diffraction of an E-polarized plane wave from two finite sinusoidal gratings is investigated by a rigorous approach, based on the Method of Analytical Regularization. This allows us to analyse the problem in a wide frequency band without limitations on the depth of the sinusoidal corrugation, the wave size of the gratings, or their relative location. The homogeneous version of the equations obtained is used for accurate computation of the complex eigenvalues in an open resonator of Fabry–Perot type with sinusoidally corrugated strips. In the calculations, two types of structures were used: one is formed by parallel translation of the sinusoidally corrugated strips and the other is obtained by rotation of one of the strips in the first structure. For each relative location of the corrugated strips, the resonance excitation of the structure by an obliquely incident E-polarized plane wave is considered. Based on the calculation of the surface current density for different incidence angles, their specific values for optimal excitation of the complex modes are established.

Experimental observation of asymmetrical microwave jets and far-field distribution generated by a dual-material system

In this paper, we report the experimental and numerical investigation of plane wave diffraction by an all-dielectric dual-material cuboid. Edge diffraction by a cuboid leads to the generation of a narrow, high intensity beam in the near-field region called a photonic jet. We examine the dependence of the jet behavior and orientation on the materials and dimensions of constitutive parts in the microwave frequency domain. The possibility to shift and deviate the resultant microwave jet in the near-field region of such a structure depending on the size of constitutive parts is demonstrated numerically. Experimentally, we observe a shift in the spatial position of the jet. The experimental asymmetric electric field profile observed in the far-field region is attributed to the input of multiple edge waves generated by the dual-material cuboid. The presented results may be scaled at different frequency bands such as optical frequencies for designing nanostructures enabling the focusing and deviation functionality and creation of new optical devices which would satisfy the needs of emerging nanophotonic applications.

Vertex Green’s Functions of a Quarter-Plane: Links Between the Functional Equation, Additive Crossing and Lamé Functions

Summary In our previous work (R. C. Assier and A. V. Shanin, Q. J. Mech. Appl. Math., 72, 2019), we gave a new spectral formulation in two complex variables associated with the problem of plane-wave diffraction by a quarter-plane. In particular, we showed that the unknown spectral function satisfies a condition of additive crossing about its branch set. In this article, we study a very similar class of spectral problem and show how the additive crossing can be exploited in order to express its solution in terms of Lamé functions. The solutions obtained can be thought of as tailored vertex Green’s functions whose behaviours in the near-field are directly related to the eigenvalues of the Laplace–Beltrami operator. This is important since the correct near-field behaviour at the tip of the quarter-plane had so far never been obtained via a multivariable complex analysis approach.

The Diffraction by the Half-plane with the Fractional Boundary Condition

In this article, there is considered the electromagnetic plane wave diffraction by the half-plane with fractional boundary conditions. As a mathematical tool, the fractional calculus is used. The theoretical part is given based on which the near field, Poynting vector and energy density distribution are calculated. Interesting results are obtained for the fractional order between marginal values, which describes a new type of material with new properties. The results are analyzed.

Plane Wave Diffraction by a Semi-Infinite Plate With Fractional Boundary Conditions

Plane Wave Diffraction by a Semi-Infinite Plate With Fractional Boundary Conditions

Plane-Wave Diffraction by a Slit in a Thin Material Screen

Plane-Wave Diffraction by a Slit in a Thin Material Screen

The UAPO Solution for the Plane Wave Diffraction by a Resistive Half Plane: Validation Tests

The UAPO Solution for the Plane Wave Diffraction by a Resistive Half Plane: Validation Tests

DIFFRACTION BY CASCADED THICK HALF PLANES COMPOSED OF PEMC METAMATERIAL

An analytic solution of plane wave diffraction by three parallel thick half planes composed of PEMC metamaterial is developed. Duality transformation introduced by Lindell and Sihvola is applied to transform the field produced by three semi-infinite, parallel, thick, PEC half planes to the case of three semi-infinite, parallel, thick half planes in PEMC medium. It is observed that PEC medium is the limiting case of PEMC medium. Numerical results are also produced and discussed for the effects of thickness and admittance parameters on the amplitude of the diffracted field. Numerical results are found to be in good agreement with the available numerical results on PEMC metamaterial.

3D elastic plane-wave diffraction by a stress-free wedge for incident skew angles below the critical angle in diffraction

Elastic plane wave diffraction by a stress-free wedge is a canonical problem of interest to researchers in many different fields. To our knowledge, no fully analytical resolution has been found and semi-analytical evaluations of asymptotic approximations have therefore become a common approach. In this paper, a method called the spectral functions method is developed in a 3D configuration, meaning that the incident ray is not necessarily in the plane normal to the wedge edge. The diffracted displacement field is expressed as an integral in terms of two unknown functions called the spectral functions. These functions are decomposed into two parts: one which can be computed analytically and the other which is approached numerically using a collocation method. The details of the corresponding numerical scheme are given and first numerical validations are presented. The presented method is valid for incident skew angles which are below the critical angle in diffraction.