OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING
Abstract
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
Manuscript submitted 01.09.2021
Radio phys. radio astron. 2021, 26(4): 350-357
REFERENCES
1. BLACK, D. N. and WILTSE, J. C., 1987. Millimeter-Wave Characteristics of Phase-Correcting Fresnel Zone Plates. IEEE Trans. Microw. Theory Techn. vol. 35, is. 12, pp. 1122–1129. DOI: https://doi.org/10.1109/TMTT.1987.1133826
2. JI, Y. and FUJITA, M., 1994. Design and Analysis of a Folded Fresnel Zone Plate Antenna. Int. J. Infrared Milli. Waves. vol. 15, is. 8, pp. 1385–1406. DOI: https://doi.org/10.1007/BF02096066
3. SAIDOGLU, N. Y. and NOSICH, A. I., 2020. Method ofanalytical regularization in the analysis of axially symmetricexcitation of imperfect circular disk antennas. Comput. Math. Appl. vol. 79, is. 10, pp. 2872–2884. DOI: https://doi.org/10.1016/j.camwa.2019.12.020
4. DIKMEN, F., KARACHUHA, E. and TUCHKIN, Y. A., 2001. Scalar Wave Diffraction by a Perfectly Soft Infi nitely Thin Circular Ring. Turk. J. Elec. Eng. Comp. Sci. vol. 9, no. 2, pp. 199–219.
5. AGAFONOVA, M. A., 2013. Methods of Integral Equations in Problems of Diffraction on Strip and Slots. T-comm.no. 11, pp. 21–24. (in Russian).
6. DIKMEN, F. and TUCHKIN, Y. A., 2009. Analytical Regularization Method for Electromagnetic Wave Diffraction by Axially Symmetrical Thin Annular Strips. Turk. J. Elec. Eng. Comp. Sci. vol. 17, no. 2, pp. 107–124. DOI: 10.3906/elk-0811-10
7. KAZ’MIN, I. A., LERER, A. M. and SHEVCHENKO, V. N., 2008. Electromagnetic-Wave Diffraction by a 2D Periodic Grating of Circular and Ring Slots. J. Commun. Technol. Electron. vol. 53, no. 2, pp. 177–183. DOI: https://doi.org/10.1134/S1064226908020071
8. LI, S. and SCHARSTEIN, R. W., 2005. High Frequency Scattering by a Conducting Ring. IEEE Trans. Antennas Propag. vol. 53, is. 6, pp. 1927–1938. DOI: https://doi.org/10.1109/TAP.2005.848506
9. LYTVYNENKO, L. M. and PROSVIRNIN, S. L., 2009. Wave reflection by a periodic layered metamaterial. Eur. Phys. J. Appl. Phys. vol. 46, no. 3, id. 32608. DOI: https://doi.org/10.1051/epjap:2008128
10. KALIBERDA, M. E., LYTVYNENKO, L. M. and POGARSKY, S. A., 2021. Operator Method in the Problem of the the H-Polarized Wave Diffraction by Two Semi-Infinite Gratings Placed in the Same Plane. Radio Phys. Radio Astron. vol. 26, no. 3, pp. 239–249. (in Ukrainian). DOI: https://doi.org/10.15407/rpra26.03.239
11. KALIBERDA, M. E., LYTVYNENKO, L. M. and POGARSKY, S. A., 2018. Operator Method in the Scalar Wave Diffraction by Axially-Symmetric Discontinuities in the Screen. Radio Phys. Radio Astron. vol. 23, no. 1, pp. 36–42. (in Russian). DOI: https://doi.org/10.15407/rpra23.01.036
12. KALIBERDA, M. E., POGARSKY, S. A. and LYTVYNENKO, L. M., 2020. Operator Method in Scalar Wave Scatteringby Circular Slot in Screen in Case of Dirichlet Conditions. In: 2020 IEEE Ukrainian Microwave Week (UkrMW) Proceedings. Kharkiv, Ukraine, 21-25 Sept., 2020. pp. 1–4.DOI: https://doi.org/10.1109/UkrMW49653.2020.9252632
13. NOMURA, Y. and KATSURA, S., 1955. Diffraction of Electromagnetic Waves by Circular Plate and Circular Hole. J. Phys. Soc. Jpn. vol. 10, no. 4, pp. 285–304. DOI: https://doi.org/10.1143/JPSJ.10.285
14. LYTVYNENKO, L. M., PROSVIRNIN, S. L. and KHIZHNYAK, A. N., 1988. Semiinversion of the Operator with the Using of Method of Moments in the Scattering Problems by the Structures Consisting of the Thin Disks. Preprint No. 19. Institute of Radio Astronomy, Academy of Sciences of Ukrainian SSR. 31 p. (in Russian).
Keywords
Full Text:
PDFCreative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0)