Abstract
An analytical-numerical technique for the solution of the two-dimensional scattering of an electromagnetic wave by a set of circular cylinders in the presence of a plane discontinuity for the electromagnetic constants is discussed. Since the interface is only characterized by its reflection coefficient, a wide class of reflecting surfaces can be treated with the same formalism. The solution is obtainable for both the near and the far region, regardless the polarization state of the incident wave. The method exploits the possibility of representing any two-dimensional field in terms of a suitable superposition of cylindrical waves. The expansion coefficients represent the unknowns in a typical scattering problem and can be determined by imposing the boundary conditions. The presence of the interface leads to the necessity of evaluating the reflected cylindrical waves, and this is achieved starting from the Fourier spectrum of the cylindrical functions on a plane.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramowitz M., Stegun I. (1972) Handbook of Mathematical Functions. Dover Publications, New York
Bowman J. J., Senior T. B. et al. (1987) Electromagnetic and acoustic scattering by simple shapes. Hemisphere, New York
Balanis C. A. (1989), Advanced Engineering Electromagnetics. John Wiley & Sons, New York
Wilton D. R., Mittra R. (1972) A new numerical approach to the calculation of electromagnetic scattering properties of two-dimensional bodies of arbitrary cross section. IEEE Trans. Antennas Propagat. AP-20, 310–317
Alexopoulos N. G., Park P. K. (1972) Scattering of waves with normal amplitude distribution from cylinders. IEEE Trans. Antennas Propagat. AP-20, 216–217
Kozaki S. (1982) A new expression for the scattering of a Gaussian beam by a conducting cylinder. IEEE Trans. Antennas Propagat. AP-30, 881–887
Kozaki S. (1982), Scattering of a Gaussian beam by a homogeneous dielectric cylinder. J. Appl. Phys. 53, 7195–7200
Richmond J. H. (1965) Scattering by an arbitrary array of parallel wires. IEEE Trans. Microwave Theory and Techniques MTT-13, 408–412
Elsherbeni A. Z., Kishk A. A. (1992) Modeling of cylindrical objects by circular dielectric and conducting cylinders. IEEE Trans. Antennas Propagat. AP-40, 96–99
Mullin C. R., Sandburg R. et al. (1965) A numerical technique for the determination of scattering cross sections of infinite cylinders of arbitrary cross section. IEEE Trans. Antennas Propagat. AP-13, 141–149
Millar R. F. (1970) On the legitimacy of an assumption underlying the point-matching method. IEEE Trans. Microwave Theory and Techniques 18, 325–327
Elsherbeni A. Z. (1994) A comparative study of two-dimensional multiple scattering techniques. Radio Science 29, 1023–1033
Cottis P. G., Kanellopoulos J. D (1988) Scattering from a conducting cylinder above a lossy medium. Int. J. Electron. 65, 1031–1038
Petit R., ed.(1980) Electromagnetic Theory of Gratings Springer, Berlin
Frezza F., Gori F. et al. (1994) Quasi-optical launchers for lower hybrid waves: a full-wave approach. Nucl. Fusion 34, 1239–1246
Preinhaelter L. (1996) Quasi-optical grill mounted in Hyperguide. Nucl. Fusion 36, 593–611
Petelin M. I., Suvorov E. V. et al. (1996) Quasi-optical diffraction grill for excitation of lower-hybrid waves in tokamaks. Plasma Phys. Control. Fusion 38, 593–610
Avantaggiati V. A., Borghi R. et al. (1997) Gaussian-beam excitation of quasi-optical launchers for lower hybrid waves. Nucl. Fusion 37, 689–699
Borghi R., Frezza F. et al. (1998) Quasi-Optical Grill Launching of Lower-Hybrid Waves for a Linearly Increasing Plasma Density. IEEE Trans. Plasma Science 26, 1330–1338
Pidduck A. J., Robbins D. J. et al. (1989) The formation of dislocations and their in-situ detection during silicon vapor phase epitaxy at reduced temperature. Mater. Sci. Eng. B4, 417–422
Wait J. R. (1954) Reflection from a wire grid parallel to a conducting plane. Can. Journal of Physics 32, 571–579
Wait J. R (1957) The impedance of a wire grid parallel to a dielectric interface. IRE Trans. Microwave Theory Tech. 5, 99–102
Wait J. R. (1988) Electromagnetic radiation from cylindrical structures. Peter Peregrinus, London
Taubenblatt M. A. (1990) Light scattering from cylindrical structures on surfaces. Opt. Lett. 15, 255–257
Valle P. J., González F. et al. (1994) Electromagnetic wave scattering from conducting cylindrical structures on flat substrates: study by means of the extinction theorem Appl. Opt. 33, 512–523
Valle P. J., Moreno F. et al. (1995) Near-field scattering from subwavelenght metallic protuberances on conducting flat substrates. Phys. Rev. B 51, 13681–13690
Madrazo A., Nieto-Vesperinas M. (1995) Scattering of electromagnetic waves from a cylinder in front of a conducting plane. J. Opt. Soc. Am. A 12, 1298–1309
Valle P. J., Moreno F. et al. (1996) Electromagnetic interaction between two parallel circular cylinders on a planar interface. IEEE Trans. Antennas Propa-gat. AP-44, 321–325
Videen G., Ngo D. (1997) Light scattering from a cylinder near a plane interface: theory and comparison with experimental data. J. Opt. Soc. Am. A 14, 70–73
Nahm K. B., Wolfe W. L. (1987) Light scattering for spheres on a conducting plane: comparison with experiment. Appl. Opt. 26, 2995–2999
Lindell I. V., Sihlova A. H. et al. Scattering by a small object close to an interface. I. Exact-image theory formulation. J. Opt. Soc. Am. A 8, 472–476
Taubenblatt M. A., Tran T. K. (1993) Calculation of light scattering from particles and structures on a surface by the coupled-dipole method. J. Opt. Soc. Am. A 10, 912–919
Moreno F., González F. et al. (1993) Experimental study of copolarized light scattering by spherical metallic particles on conducting flat substrates. J. Opt. Soc. Am. A 10, 141–157
Wait J. R. (1990) Note on solution for scattering from parallel wires in an interface. J. Electr. Waves Appls 4, 1151–1155
Rao T. C., Barakat R. (1994) Plane wave scattering by a finite array of conducting cylinders partially buried in a ground plane: TM polarization. Pure and Appl. Opt. 3, 1023–1048
Clemmow P. C. (1996) The plane-wave spectrum representation of electromagnetic fields. IEEE Press and Oxford University Press, Oxford
Cincotti G., Gori F. et al. (1993) Plane wave expansion of cylindrical functions. Opt. Commun. 95, 192–198
Borghi R., Gori F. et al. (1996) Plane-wave scattering by a set of perfectly conducting circular cylinders in the presence of a plane surface. J. Opt. Soc. Am. A 13, 2441–2452
Borghi R., Gori F. et al. (1996) Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach. J. Opt. Soc. Am. A 13, 483–493
Borghi R., Frezza F. et al. (1999) “Numerical study of the reflection of cylindrical waves of arbitrary order by a generic planar interface,” J. Electromagn. Waves Appl., in press
Borghi R., Santarsiero M. et al. (1997) Plane-wave scattering by a dielectric circular cylinder parallel to a general reflecting flat surface. J. Opt. Soc. Am. A 14, 1500–1504
Nieto-Vesperinas M., Dainty J. C., eds., (1991) Scattering in Volumes and Surfaces. North-Holland, Amsterdam
Madrazo A., Nieto-Vesperinas M. (1996) Surface structure and polariton interactions in the scattering of electromagnetic waves from a cylinder in front of a conducting grating: theory for the reflection photon scanning tunneling microscope. J. Opt. Soc. Am. A 13, 785–795
Cairns R. A. (1991) Radiofrequency heating of plasmas. Adam Hilger, Bristol
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Borghi, R., Frezza, F., Santarsiero, M., Schettini, G. (2000). Electromagnetic Scattering by Cylindrical Objects on Generic Planar Substrates: Cylindrical-Wave Approach. In: Moreno, F., González, F. (eds) Light Scattering from Microstructures. Lecture Notes in Physics, vol 534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46614-2_6
Download citation
DOI: https://doi.org/10.1007/3-540-46614-2_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66937-1
Online ISBN: 978-3-540-46614-7
eBook Packages: Springer Book Archive