volume | PIER Journals

Abstract

The problem of axially-symmetric TM-wave diffraction from a perfectly conducting bi-cone is analyzed. Bi-cone is formed by finite and semi-infinite conical shoulders and illuminated by ring magnetic source. The problem is formulated in a spherical coordinate system as a mixed boundary problem for Helmholtz equation. The unknown H_φ-diffracted field is sought as expansion in series of eigenfunctions for each region, formed by the bi-cone. The solution of the problem then is reduced to the infinite set of linear algebraic equations (ISLAE) of the first kind by means of mode matching technique and orthogonality properties of the eigen functions. The main parts of the asymptotic expressions of ISLAE matrix elements, determined for large indexes, identify the convolution type operator. The corresponding inversed operator is represented in an explicit form. Two of these operators are applied to reduce the problem to the ISLAE of the second kind and to determine the new analytical regularization method for the solution of wave diffraction problems for bi-conical scatterers. The unknown expansion coefficients can be determined from the ISLAE with the given accuracy by the reduction method. The particular cases such as low frequency approximation and transition from bi-cone to conical monopole and disc-cone scatterer are analyzed. The numerically obtained results are applied to the analysis of scattering properties of hollow conical monopoles and disc-conical scatterers.

1. Rostomyan, N., A. T. Ott, M. D. Blech, R. Brem, C. J. Eisner, and T. F. Eibert, "Balanced impulse radiating omnidirectional ultrawideband stacked biconical antenna," IEEE Trans. on Antennas and Propagation, Vol. 63, No. 1, 59-68, 2015.
doi:10.1109/TAP.2014.2368574

2. Khorshidi, M. and E. Tahanian, "A new conical band-reject UWB antenna with uniform rejection and stable omnidirectional behavior," Progress In Electromagnetics Research C, Vol. 59, 31-40, 2015.
doi:10.2528/PIERC15071102

3. Gilbert, A. M. and L. Ryan, Ultra-wideband biconical antenna with excellent gain and impedance matching, US Pattent 20150280317 A1, Oct. 1, 2015.

4. Palud, S., F. Colombel, M. Himdi, and C. L. Meins, "A novel broadband eighth-wave conical antenna," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 7, 2112-2116, Jul. 2008.
doi:10.1109/TAP.2008.924775

5. Amert, A. K. and K. W. Whites, "Miniaturization of the biconical antenna for ultrawideband applications," IEEE Transactions on Antennas and Propagation, Vol. 57, No. 12, 3728-3735, Dec. 2009.
doi:10.1109/TAP.2009.2026667

6. Kudpik, R., N. Siripon, K. Meksamoot, and S. Kosulvit, "Design of a compact biconical antenna for UWB applications," Proc. International Symposium on Intelligent Signal Processing and Communications Systems (ISPACS), 1-6, Chiang Mai, Thailand, Dec. 7-9, 2011.

7. Yeoh, W. S. and W. S. T. Rowe, "An UWB conical monopole for multi-service wireless application," Antennas and Wireless Propagation Letters, Vol. 14, 1085-1088, 2015.
doi:10.1109/LAWP.2015.2394295

8. Lodge, O. J., Electric telegraphy, US Pattent 609,154, Aug. 16, 1898.

9. Carter, P. S., Wide band, short wave antenna and transmission line system, US Pattent 2,181,870, Oct. 10, 1939.

10. Barrow, W. L., Biconical electromagnetic horn, US Pattent 2,602,894. Jul. 8, 1952.

11. Schelkunoff, S. A., "Theory of antennas of arbitrary size and shape," Proc. IRE, Vol. 29, No. 9, 493-521, 1941.
doi:10.1109/JRPROC.1941.231669

12. Schelkunoff, S. A., "Principal and complementary waves in antennas," Proc. IRE, Vol. 34, 23-32, 1946.
doi:10.1109/JRPROC.1946.231574

13. Schelkunoff, S. A., "General theory of symmetric biconical antennas," J. Appl. Phys., Vol. 22, No. 11, 1330-1332, 1951.
doi:10.1063/1.1699861

14. Smith, P. D. P., "The conical dipole of wide angle," J. App. Phys., Vol. 19, No. 1, 11-13, 1948.
doi:10.1063/1.1697866

15. Tai, C. T., "On the theory of biconical antennas," J. App. Phys., Vol. 19, No. 12, 1155-1160, 1948.
doi:10.1063/1.1715036

16. Hahn, R. and J. G. Fikioris, "Impedance and radiation pattern of antennas above flat discs," IEEE Trans. on Antennas and Propagation, Vol. 21, No. 1, 97-100, 1973.
doi:10.1109/TAP.1973.1140402

17. Papas, C. H. and R. W. King, "Input impedance of wide-angle conical antennas fed by a coaxial line," Poc. IRE, Vol. 37, No. 11, 1269-1271, 1949.
doi:10.1109/JRPROC.1949.234607

18. Papas, C. H. and R. W. King, "Radiation from wide-angle conical antennas fed by a coaxial Line," Proc. IRE, Vol. 39, No. 1, 49-51, 1951.
doi:10.1109/JRPROC.1951.230420

19. Kadakia, D. R. and J. G. Fikioris, "Monopole antenna above a hemisphere," IEEE Trans. Antennas Propagation, Vol. 19, No. 5, 687-690, 1971.
doi:10.1109/TAP.1971.1140018

20. Bolle, D. M. and M. D. Morganstern, "Monopole and conic antennas on spherical vehicles," IEEE Trans. on Antennas and Propagation, Vol. 17, No. 4, 477-484, 1969.
doi:10.1109/TAP.1969.1139479

21. Bevensee, R. M., A Handbook of Conical Antennas and Scatterers, Gordon and Breach, New York, 1973.

22. Kuryliak, D. B., "Biconical line with slots in an axially symmetric electromagnetic field," Proc. International Conference on Direct and Inverse Problems of Electromagenetic and Acoustic Wave Theory, 46-47, 1995.

23. Kuryliak, D. B. and Z. T. Nazarchuk, "One conical waveguide bifurcation problem," Technical Report of Electromagnetic Theory, Institute of Electrical Engineers of Japan, No. EMT9750, 5156, 1997.

24. Kuryliak, D. B., "Wave diffaction from bifurcation of the conical region," Izvestiya Vuzov. Radioelectronika, Vol. 41, No. 9, 13-22, 1998 (in Russian).

25. Goshin, G. G., Electrodynamics Value Boundary Problems for Conical Regions, Izdatelstvo Tomsk Univ., Tomsk, 1987 (in Russian).

26. Doroshenko, V. A. and V. F. Kravchenko, Electromagnetic Waves Diffraction on Unclosed Conical Structures, Fizmatlit, Moscow, 2009 (in Russian).

27. Mohammadi, A., F. Kaminski, V. Sandoghdar, and M. Agio, "Fluorescence enhancement with the optical (bi-)conical antenna," J. Phys. Chem. C, Vol. 114, No. 16, 7372-7377, 2010.
doi:10.1021/jp9094084

28. Helfenstein, P., A. Mustonen, T. Feurer, and S. Tsujino, "Collimated field emission beams from metal double-gate nanotip arrays optically excited via surface plasmon resonance," Applied Physics Express, Vol. 6, 114301, 2013.
doi:10.7567/APEX.6.114301

29. Legenkiy, M. N. and A. Y. Butrym, "Method of mode matching in time domain," Progress In Electromagnetics Research B, Vol. 22, 257-283, 2010.
doi:10.2528/PIERB10043003

30. Tretyakov, O. A., "Mode basis method," Radiotekhnika and Elektronika, Vol. 31, No. 6, 1071-1082, 1986 (in Russian).

31. Shestopalov, V. P., A. A. Kirilenko, and S. A. Masalov, Convolution-type Matrix Equations in the Theory of Diffraction, Naukova Dumka, Kyiv, 1984 (in Russian).

32. Kuryliak, D. B. and Z. T. Nazarchuk, Analytical-numerical Methods in the Theory of Wave Di®raction on Conical and Wedge-shaped Surfaces, Naukova Dumka, Kyiv, 2006 (in Ukrainian).

33. Kuryliak, D. B. and Z. T. Nazarchuk, "Convolution type operators for wave diffraction by conical structures," Radio Science, Vol. 43, RS4S03, 2008.

34. Kuryliak, D. B., Z. T. Nazarchuk, and V. O. Lysechko, "Diffraction of a plane acoustic wave from a finite soft (rigid) cone in axial irradiation," Open Journal of Acoustics, Vol. 5, 193-206, 2015.
doi:10.4236/oja.2015.54015

35. Kuryliak, D. B. and O. M. Sharabura, "Axisymmetric electromagnetic excitation of a metallic discone scatterer," Telecommunications and Radio Engineering, Vol. 74, No. 4, 563-576, 2015.
doi:10.1615/TelecomRadEng.v74.i7.10

36. Gradshteyn, I. S. and I. M. Ryzhik, Tables of Integrals, Series and Products, Dover, New York, 1972.

Professor Dozyslav B. Kuryliak

Dr. Oleksiy M. Sharabura