Operator method in the problem of wave diffraction by flat semi-infinite strip grating

2005 ◽  
Author(s):  
S.N. Vorobyov
Keyword(s):  
Wave Diffraction ◽  
Operator Method ◽  
Infinite Strip

scholarly journals OPERATOR METHOD IN THE PROBLEM OF THE H-POLARIZED WAVE DIFFRACTION BY TWO SEMI-INFINITE GRATINGS PLACED IN THE SAME PLANE

2021 ◽  
Vol 26 (3) ◽  
pp. 239-249
Author(s):  
M. E. Kaliberda ◽  
◽  
L. M. Lytvynenko ◽  
S. A. Pogarsky ◽  
◽  
...  
Keyword(s):  
Wave Diffraction ◽  
Linear Equations ◽  
Plane Waves ◽  
Operator Method ◽  
Infinite Strip ◽  
Operator Equations ◽  
Regularization Procedure ◽  
Microwave Electronics ◽  
Spatial Spectra ◽  
Scattered Fields

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

scholarly journals OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING

2021 ◽  
Vol 26 (4) ◽  
pp. 350-357
Author(s):  
M. E. Kaliberda ◽  
◽  
L. M. Lytvynenko ◽  
S. A. Pogarsky ◽  
◽  
...  
Keyword(s):  
Electromagnetic Wave ◽  
Circular Hole ◽  
Wave Diffraction ◽  
Scattered Field ◽  
Plane Electromagnetic Wave ◽  
Operator Method ◽  
Fredholm Integral Equations ◽  
Fourier Amplitude ◽  
Annular Slot ◽  
Electromagnetic Wave Diffraction

Purpose: The problem of a plane electromagnetic wave diffraction by an annular slot in the perfectly conducting zero thickness plane is considered. As a dual problem, the problem of diffraction by a perfectly conducting zero thickness ring is also considered. The paper aims at developing the operator method for the axially symmetric structures placed in free space. Design/methodology/approach: The problem is considered in the spectral domain. The scattered field is expressed in terms of unknown Fourier amplitudes (spectral functions). The annular slot is given as a unity of two simple discontinuities, namely of a disk and a circular hole in the plane, which interact with each other. The Fourier amplitude of the scattered field is sought as a sum of two amplitudes, the Fourier amplitude of the field of currents on the disk and Fourier amplitude of the field of currents on the perfectly conducting plane with circular hole. The operator equations are written for these amplitudes, which take into account the electromagnetic coupling of the disk and the hole in the plane. The equations use the reflection operators of a single isolated disk and a single hole in the plane. They are supposed to be known and can be obtained for example by the method of moments.The reflection operators can have singularities. After transformations, the equations are obtained, which are equivalent to the Fredholm integral equations of second kind and they can be solved numerically. Findings: The operator equations relative to the Fourier amplitudes of the field scattered by the discussed structure are obtained. The far zone scattered field for an annular slot and a ring for different values of parameters are studied. Conclusions: The rigorous solution of the problem of the electromagnetic wave diffraction by an annular slot in the plane and by a circular ring is obtained. The problem is reduced to the Fredholm integral equations of second kind. The far field distribution for different parameters is studied. The developed approach is an effective instrument for a number of problems of antenna technique to be solved. Key words: circular hole; disk; annular slot; ring; operator method; diffraction

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