## Integral equation analysis of an arbitrary-profile and varying-resistivity cylindrical reflector illuminated by an E-polarized complex-source-point beam

JOSA A, Vol. 26, Issue 7, pp. 1525-1532 (2009)

http://dx.doi.org/10.1364/JOSAA.26.001525

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### Abstract

A two-dimensional reflector with resistive-type boundary conditions and varying resistivity is considered. The incident wave is a beam emitted by a complex-source-point feed simulating an aperture source. The problem is formulated as an electromagnetic time-harmonic boundary value problem and cast into the electric field integral equation form. This is a Fredholm second kind equation that can be solved numerically in several ways. We develop a Galerkin projection scheme with entire-domain expansion functions defined on an auxiliary circle and demonstrate its advantage over a conventional moment-method solution in terms of faster convergence. Hence, larger reflectors can be computed with a higher accuracy. The results presented relate to the elliptic, parabolic, and hyperbolic profile reflectors fed by in-focus feeds. They demonstrate that a partially or fully resistive parabolic reflector is able to form a sharp main beam of the far-field pattern in the forward half-space; however, partial transparency leads to a drop in the overall directivity of emission due to the leakage of the field to the shadow half-space. This can be avoided if only small parts of the reflector near the edges are made resistive, with resisitivity increasing to the edge.

© 2009 Optical Society of America

**OCIS Codes**

(050.1940) Diffraction and gratings : Diffraction

(050.1755) Diffraction and gratings : Computational electromagnetic methods

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: January 9, 2009

Revised Manuscript: April 14, 2009

Manuscript Accepted: April 17, 2009

Published: June 9, 2009

**Citation**

Taner Oğuzer, Ayhan Altintas, and Alexander I. Nosich, "Integral equation analysis of an arbitrary-profile and varying-resistivity cylindrical reflector illuminated by an E-polarized complex-source-point beam," J. Opt. Soc. Am. A **26**, 1525-1532 (2009)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-7-1525

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### References

- J. M. Bendickson, E. M. Glytsis, and T. K. Gaylord, “Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors,” J. Opt. Soc. Am. A 16, 113-130 (1999). [CrossRef]
- H. Yokoi and H. Fukumuru, “Low sidelobes of paraboloidal antennas with microwave absorbers,” Electron. Commun. Jpn. 54-B, 34-49 (1971).
- O. Bucci and G. Franceschetti, “Rim loaded reflector antennas,” IEEE Trans. Antennas Propag. 28, 297-304 (1980). [CrossRef]
- O. Bucci, G. Di Massa, and C. Savarese, “Control of reflector antennas performance by rim loading,” IEEE Trans. Antennas Propag. 29, 773-779 (1981). [CrossRef]
- E. G. Njoku, Y. Rahmat-Samii, J. Sercel, W. J. Wilson, and M. Moghaddam, “Evaluation of an inflatable antenna concept for microwave sensing of soil moisture and ocean salinity,” IEEE Trans. Geosci. Remote Sens. 37, 63-78 (1999). [CrossRef]
- D. C. Jenn, M. A. Morgan, and R. J. Pogorzelski, “Characteristics of approximate numerical modeling techniques applied to resonance-sized reflectors,” Electromagnetics 15, 41-53 (1995). [CrossRef]
- M. R. Barclay and W. V. T. Rusch, “Moment-method analysis of large, axially symmetric reflector antennas using entire-domain functions,” IEEE Trans. Antennas Propag. 39, 491-496 (1991). [CrossRef]
- B. Philips, M. Philippakis, G. Y. Philippou, and D. J. Brain, “Study of modeling methods for large reflector antennas,” ERA Report 96-0902, U.K., ERA Rep. 96-0902 (1996).
- A. Heldring, J. M. Rius, L. P. Ligthart, and A. Cardama, “Accurate numerical modeling of the TARA reflector system,” IEEE Trans. Antennas Propag. 52, 1758-1766 (2004). [CrossRef]
- T. Oguzer, A. I. Nosich, A. and Altintas, “Analysis of arbitrary conic section profile cylindrical reflector antenna, H-polarization case,” IEEE Trans. Antennas Propag. 52, 3156-3162 (2004). [CrossRef]
- F. J. V. Hasselmann and L. B. Felsen, “Asymptotic analysis of parabolic reflector antennas,” IEEE Trans. Antennas Propag. 30, 677-685 (1982). [CrossRef]
- G. A. Suedan and E. V. Jull, “Beam diffraction by planar and parabolic reflectors,” IEEE Trans. Antennas Propag. 39, 521-527 (1991). [CrossRef]
- M. Martinez-Burdalo, A. Martin, and R. Villar, “Uniform PO and PTD solution for calculating plane wave backscattering from a finite cylindrical shell of arbitrary cross section,” IEEE Trans. Antennas Propag. 41, 1336-1339 (1993). [CrossRef]
- H. Anastassiu and P. Pathak, “High-frequency analysis of Gaussian beam scattering by a two-dimensional parabolic contour of finite width,” Radio Sci. 30, 493-503 (1995). [CrossRef]
- U. Yalcin, “Scattering from a cylindrical reflector: modified theory of physical optics solution,” J. Opt. Soc. Am. A 24, 502-506 (2007). [CrossRef]
- Y. Z. Umul, “Scattering of a line source by a cylindrical parabolic impedance surface,” J. Opt. Soc. Am. A 25, 1652-1659 (2008). [CrossRef]
- H.-T. Chou, P. H. Pathak, and R. J. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” Proc. Inst. Electr. Eng. 150, 177-183 (2003).
- C. Rieckmann, “Novel modular approach based on Gaussian beam diffraction for analysing quasi-optical multireflector antennas,” Proc. Inst. Elect. Eng. Microwaves 149, 160-167 (2002). [CrossRef]
- A. Tzoulis and T. F. Eibert, “A hybrid FEBI-MLFMM-UTD method for numerical solutions of electromagnetic problems including arbitrarily shaped and electrically large objects,” IEEE Trans. Antennas Propag. 53, 3358-3366 (2005). [CrossRef]
- M. Idemen and A. Büyükaksoy, “High frequency surface currents induced on a perfectly conducting cylindrical reflector,” IEEE Trans. Antennas Propag. 32, 501-507 (1984). [CrossRef]
- A. I. Nosich, “MAR in the wave-scattering and eigenvalue problems: foundations and review of solutions,” IEEE Antennas Propag. Mag. 42, 34-49 (1999). [CrossRef]
- A. I. Nosich, “Green's function--dual series approach in wave scattering from combined resonant scatterers,” in M.Hashimoto, M.Idemen and O.A.Tretyakov, eds., Analytical and Numerical Methods in Electromagnetic Wave Theory (Tokyo: Science House, 1993), pp. 419-469.
- T. Oğuzer, A. Altintas, and A. I. Nosich,“Accurate simulation of reflector antennas by the complex source--dual series approach,” IEEE Trans. Antennas Propag. 43, 793-802 (1995). [CrossRef]
- V. B. Yurchenko, A. Altintas, and A. I. Nosich, “Numerical optimization of a cylindrical reflector-in-radome antenna system,” IEEE Trans. Antennas Propag. 47, 668-673 (1999). [CrossRef]
- S. V. Boriskina, A. I. Nosich, A. and Altintas, “Effect of the imperfect flat earth on the vertically-polarized radiation of a cylindrical reflector antenna,” IEEE Trans. Antennas Propag. 48, 285-292 (2000). [CrossRef]
- T. Oğuzer, A. I. Nosich, and A. Altintas, “E-polarized beam scattering by an open cylindrical PEC strip having arbitrary conical-section profile,” Microwave Opt. Technol. Lett. 31, 480-484 (2001). [CrossRef]
- A. A. Nosich and Y. V. Gandel, “Numerical analysis of quasioptical multi-reflector antennas in 2-D with the method of discrete singularities: E-wave case,” IEEE Trans. Antennas Propag. 57, 399-406 (2007). [CrossRef]
- A. A. Nosich, Y. V. Gandel, T. Magath, and A. Altintas, “Numerical analysis and synthesis of 2-D quasioptical reflectors and beam waveguides based on an integral-equation approach with Nystrom's discretization,” J. Opt. Soc. Am. A 24, 2831-2836 (2007). [CrossRef]
- T. B. A. Senior, “Some problems involving imperfect half-planes,” in P.L. E.Uslenghi, ed., Electromagnetic Scattering (Academic, 1978), pp. 185-219.
- Y. Z. Umul, “Scattering of a Gaussian beam by an impedance half-plane,” J. Opt. Soc. Am. A 24, 3159-3167 (2007). [CrossRef]
- A. I. Nosich, Y. Okuno, and T. Shiraishi, “Scattering and absorption of E and H-polarized plane waves by a circularly curved resistive strip,” Radio Sci. 31, 1733-1742 (1996). [CrossRef]
- A. I. Nosich, V. B. Yurchenko, and A. Altintas, “Numerically exact analysis of a two-dimensional variable-resistivity reflector fed by a complex point source,” IEEE Trans. Antennas Propag. 45, 1592-1601 (1997). [CrossRef]
- D. Colton and R. Kress, Integral Equation Method in Scattering Theory (Wiley, 1983).
- E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “Surface-integral equations for electromagnetic scattering from impenetrable and penetrable sheets,” IEEE Trans. Antennas Propag. 35, 14-25 (1993).
- G. Bouchitte and R. Petit, “On the concepts of a perfectly conducting material and of a perfectly conducting and infinitely thin screen,” Radio Sci. 24, 13-26 (1989). [CrossRef]
- M. M. Lavrentyev, V. G. Romanov, and S. P. Shishatskii, Ill-Posed Problems in Analysis and Mathematical Physics (Moscow, Nauka Publ., 1980) (in Russian).
- A. B. Bakushinsky, “About one numerical method of solving the Fredholm first-kind integral equations,” Comput. Math. Math. Phys. 5, 744-749 (1965).

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