volume | PIER Journals

Abstract

An effective numerical technique is demonstrated for the plane wave scattering from an infinite periodic array of hollow circular cylinders of finite length. The cylinders are made of infinitely thin perfect conductor and allocated in the axial direction. We formulate the boundary value problem into a set of integral equations for the unknown electric current densities flowing in the circumferential and longitudinal directions. Employment of the Galerkin method allows us to solve simultaneous linear equations for the expansion coefficients of the unknown current, from which we can find the field distributions in both far and near regions. The procedure of analytical regularization makes the linear system into the Fredholm second kind that is contributory to stable and rapidly convergent results. Resonance is detected as abrupt changes in the total scattering cross sections for each grating mode, and it is accompanied by the formation of circular cavity mode pattern in the cylinder.

1. Williams, W. E., "Diffraction by a cylinder of finite length," Proc. Camb. Phil. Soc., Vol. 52, No. 2, 322-335, 1956.
doi:10.1017/S0305004100031303 Google Scholar

2. Aoki, K., "Diffraction of plane electromagnetic waves from a conductive circular cylinder of finite length," J. IECE, Vol. 44, No. 9, 51-56, 1961 (in Japanese). Google Scholar

3. Kinoshita, T. and T. Sekiguchi, "Scattering of a plane electromagnetic wave by a conducting circular cylinder of finite length," Electron. Commun. Jpn. (Part I), Vol. 64, No. 5, 80-88, 1981.
doi:10.1002/ecja.4410640510 Google Scholar

4. Kao, C. C., "Three-dimensional electromagnetic scattering from a circular tube of finite length," J. Appl. Phys., Vol. 40, No. 12, 4732-4740, 1969.
doi:10.1063/1.1657281 Google Scholar

5. Medgyesi-Mitschang, L. N. and C. Eftimiu, "Scattering from wires and open circular cylinders of finite length using entire domain Galerkin expansions," IEEE Trans. Antennas Propag., Vol. 30, No. 4, 628-636, 1982.
doi:10.1109/TAP.1982.1142873 Google Scholar

6. Davis, A. M. J. and R. W. Scharstein, "Electromagnetic plane wave excitation of an open-ended, finite-length conducting cylinder," Journal of Electromagnetic Waves and Applications, Vol. 7, No. 2, 301-319, 1993.
doi:10.1163/156939393X00354 Google Scholar

7. Lucido, M., M. D. Migliore, and D. Pinchera, "A new analytically regularizing method for the analysis of the scattering by a hollow finite-length PEC circular cylinder," Progress In Electromagnetics Research B, Vol. 70, 55-71, 2016.
doi:10.2528/PIERB16081404 Google Scholar

8. Harrington, R. F., Field Computation by Moment Methods, Macmillan, New York, 1968.

9. Nosich, A. I., "Method of analytical regularization in computational photonics," Radio Sci., Vol. 51, No. 8, 1421-1430, 2016.
doi:10.1002/2016RS006044 Google Scholar

10. Freni, A., C. Mias, and R. L. Ferrari, "Hybrid finite-element analysis of electromagnetic plane wave scattering from axially periodic cylindrical structures," IEEE Trans. Antennas Propagat., Vol. 46, No. 12, 1859-1866, 1998.
doi:10.1109/8.743824 Google Scholar

11. Kishk, A. A., P.-S. Kildal, A. Monorchio, and G. Manara, "Asymptotic boundary condition for corrugated surfaces, and its application to scattering from circular cylinders with dielectric filled corrugations," IEE Proc. Microw. Antennas Propagat., Vol. 145, No. 1, 116-122, 1998.
doi:10.1049/ip-map:19981569 Google Scholar

12. Kishk, A. A., "Electromagnetic scattering from transversely corrugated cylindrical structures using the asymptotic corrugated boundary conditions," IEEE Trans. Antennas Propagat., Vol. 52, No. 11, 3104-3108, 2004.
doi:10.1109/TAP.2004.835234 Google Scholar

13. Dincer, F., M. Karaaslan, S. Colak, E. Tetik, O. Akgol, O. Altıntas, and C. Sabah, "Multiband polarization independent cylindrical metamaterial absorber and sensor application," Modern Physics Letters B, Vol. 30, No. 8, 1650095, 2016.
doi:10.1142/S0217984916500950 Google Scholar

14. Bakir, M., M. Karaaslan, O. Akgol, O. Altıntas, E. Unal, and C. Sabah, "Sensory applications of resonator based metamaterial absorber," Optik, Vol. 168, 741-746, 2018.
doi:10.1016/j.ijleo.2018.05.002 Google Scholar

15. Alkurt, F. O., O. Altıntas, A. Atci, M. Bakir, E. Unal, O. Akgol, K. Delihacioglu, M. Karaaslan, and C. Sabah, "Antenna-based microwave absorber for imaging in the frequencies of 1.8, 2.45, and 5.8GHz," Optical Engineering, Vol. 57, No. 11, 113102, 2018.
doi:10.1117/1.OE.57.11.113102 Google Scholar

16. Agranovich, Z. S. and V. P. Shestopalov, "Distribution of electromagnetic waves in a circular waveguide," Soviet Phys. — Tech. Phys., Vol. 9, No. 11, 1504-1511, 1965. Google Scholar

17. Zinenko, T. L., A. Matsushima, and A. I. Nosich, "Surface-plasmon, grating-mode, and slab-mode Resonances in the H- and E-polarized THz wave scattering by a graphene strip grating embedded into a dielectric slab," IEEE J. Selected Topics in Quantum Electronics, Vol. 23, No. 4, 4601809, 2017.
doi:10.1109/JSTQE.2017.2684082 Google Scholar

18. Matsushima, A. and T. Itakura, "Singular integral equation approach to electromagnetic scattering from a finite periodic array of conducting strips," Journal of Electromagnetic Waves and Applications, Vol. 5, No. 6, 545-562, 1991.
doi:10.1163/156939391X00680 Google Scholar

19. Matsushima, A. and T. Itakura, "Accurate numerical analysis of inductive windows in a rectangular waveguide by singular integral equations," Electron. Commun. Jpn. (Part I), Vol. 70, No. 6, 111-121, 1987.
doi:10.1002/ecja.4410700611 Google Scholar

20. Mittra, R., T. Itoh, T. S. Li, and , "Analytical and numerical studies of the relative convergence phenomenon arising in the solution of an integral equation by the moment method," IEEE Trans. Microwave Theory Tech., Vol. 20, No. 2, 96-104, 1972.
doi:10.1109/TMTT.1972.1127691 Google Scholar

21. Geng, N. and L. Carin, "Wide-band electromagnetic scattering from a dielectric BOR buried in a layered lossy dispersive medium," IEEE Trans. Antennas Propagat., Vol. 47, No. 4, 610-619, 1999.
doi:10.1109/8.768799 Google Scholar

22. Amitay, N. and V. Galindo, "On energy conservation and the method of moments in scattering problems," IEEE Trans. Antennas Propagat., Vol. 17, No. 7, 747-751, 1969.
doi:10.1109/TAP.1969.1139549 Google Scholar

23. Hessel, A. and A. A. Oliner, "A new theory of Wood’s anomalies on optical gratings," Applied Optics, Vol. 4, No. 10, 1275-1297, 1965.
doi:10.1364/AO.4.001275 Google Scholar

24. Pozar, D. M., Microwave Engineering, 4th Edition, John Wiley & Sons, 2012.

25. Kundracik, F., M. Kocifaj, G. Videen, and J. Klaˇcka, "Effect of charged-particle surface excitations on near-field optics," Applied Optics, Vol. 54, No. 22, 6674-6681, 2015.
doi:10.1364/AO.54.006674 Google Scholar

26. Klacka, J., M. Kocifaj, F. Kundracik, G. Videen, and I. Kohut, "Generalization of electromagnetic scattering by charged grains through incorporation of interband and intraband effects," Optics Letters, Vol. 40, No. 21, 5070-5073, 2015.
doi:10.1364/OL.40.005070 Google Scholar

27. Bleszynski, E., M. Bleszynski, and T. Jaroszewicz, "Surface-integral equations for electromagnetic scattering from impenetrable and penetrable sheets," IEEE Antennas Propag. Mag., Vol. 35, No. 6, 14-25, 1993.
doi:10.1109/74.248480 Google Scholar

28. Ji, X., D. Sakomura, A. Matsushima, and T. Suyama, "Light scattering from two-dimensional periodic arrays of noble-metal disks and complementary circular apertures," Progress In Electromagnetics Research M, Vol. 43, 119-133, 2015.
doi:10.2528/PIERM15040201 Google Scholar

Dr. Hongchang An

Prof. Akira Matsushima