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Electromagnetic Scattering by Cylindrical Objects on Generic Planar Substrates: Cylindrical-Wave Approach

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Light Scattering from Microstructures

Part of the book series: Lecture Notes in Physics ((LNP,volume 534))

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.

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References

  1. Abramowitz M., Stegun I. (1972) Handbook of Mathematical Functions. Dover Publications, New York

    MATH  Google Scholar 

  2. Bowman J. J., Senior T. B. et al. (1987) Electromagnetic and acoustic scattering by simple shapes. Hemisphere, New York

    Google Scholar 

  3. Balanis C. A. (1989), Advanced Engineering Electromagnetics. John Wiley & Sons, New York

    Google Scholar 

  4. 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

    Article  ADS  Google Scholar 

  5. Alexopoulos N. G., Park P. K. (1972) Scattering of waves with normal amplitude distribution from cylinders. IEEE Trans. Antennas Propagat. AP-20, 216–217

    Article  ADS  Google Scholar 

  6. 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

    Article  ADS  Google Scholar 

  7. Kozaki S. (1982), Scattering of a Gaussian beam by a homogeneous dielectric cylinder. J. Appl. Phys. 53, 7195–7200

    Article  ADS  Google Scholar 

  8. Richmond J. H. (1965) Scattering by an arbitrary array of parallel wires. IEEE Trans. Microwave Theory and Techniques MTT-13, 408–412

    Article  ADS  Google Scholar 

  9. 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

    Article  ADS  Google Scholar 

  10. 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

    Article  ADS  Google Scholar 

  11. Millar R. F. (1970) On the legitimacy of an assumption underlying the point-matching method. IEEE Trans. Microwave Theory and Techniques 18, 325–327

    Article  ADS  Google Scholar 

  12. Elsherbeni A. Z. (1994) A comparative study of two-dimensional multiple scattering techniques. Radio Science 29, 1023–1033

    Article  ADS  Google Scholar 

  13. Cottis P. G., Kanellopoulos J. D (1988) Scattering from a conducting cylinder above a lossy medium. Int. J. Electron. 65, 1031–1038

    Article  Google Scholar 

  14. Petit R., ed.(1980) Electromagnetic Theory of Gratings Springer, Berlin

    Google Scholar 

  15. Frezza F., Gori F. et al. (1994) Quasi-optical launchers for lower hybrid waves: a full-wave approach. Nucl. Fusion 34, 1239–1246

    Article  ADS  CAS  Google Scholar 

  16. Preinhaelter L. (1996) Quasi-optical grill mounted in Hyperguide. Nucl. Fusion 36, 593–611

    Article  ADS  CAS  Google Scholar 

  17. 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

    Article  ADS  CAS  Google Scholar 

  18. Avantaggiati V. A., Borghi R. et al. (1997) Gaussian-beam excitation of quasi-optical launchers for lower hybrid waves. Nucl. Fusion 37, 689–699

    Article  CAS  ADS  Google Scholar 

  19. 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

    Article  ADS  CAS  Google Scholar 

  20. 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

    Article  CAS  Google Scholar 

  21. Wait J. R. (1954) Reflection from a wire grid parallel to a conducting plane. Can. Journal of Physics 32, 571–579

    MATH  Google Scholar 

  22. Wait J. R (1957) The impedance of a wire grid parallel to a dielectric interface. IRE Trans. Microwave Theory Tech. 5, 99–102

    Article  MathSciNet  ADS  Google Scholar 

  23. Wait J. R. (1988) Electromagnetic radiation from cylindrical structures. Peter Peregrinus, London

    Google Scholar 

  24. Taubenblatt M. A. (1990) Light scattering from cylindrical structures on surfaces. Opt. Lett. 15, 255–257

    Article  ADS  CAS  PubMed  Google Scholar 

  25. 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

    Article  ADS  CAS  PubMed  Google Scholar 

  26. 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

    Article  CAS  Google Scholar 

  27. 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

    Article  ADS  Google Scholar 

  28. 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

    Google Scholar 

  29. 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

    Article  ADS  MathSciNet  Google Scholar 

  30. Nahm K. B., Wolfe W. L. (1987) Light scattering for spheres on a conducting plane: comparison with experiment. Appl. Opt. 26, 2995–2999

    Article  ADS  CAS  PubMed  Google Scholar 

  31. 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

    Google Scholar 

  32. 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

    Article  ADS  Google Scholar 

  33. 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

    Article  ADS  CAS  Google Scholar 

  34. Wait J. R. (1990) Note on solution for scattering from parallel wires in an interface. J. Electr. Waves Appls 4, 1151–1155

    Article  Google Scholar 

  35. 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

    Article  ADS  Google Scholar 

  36. Clemmow P. C. (1996) The plane-wave spectrum representation of electromagnetic fields. IEEE Press and Oxford University Press, Oxford

    MATH  Google Scholar 

  37. Cincotti G., Gori F. et al. (1993) Plane wave expansion of cylindrical functions. Opt. Commun. 95, 192–198

    Article  ADS  Google Scholar 

  38. 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

    Article  ADS  MathSciNet  Google Scholar 

  39. 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

    Article  ADS  MathSciNet  Google Scholar 

  40. 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

    Google Scholar 

  41. 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

    Article  ADS  MathSciNet  Google Scholar 

  42. Nieto-Vesperinas M., Dainty J. C., eds., (1991) Scattering in Volumes and Surfaces. North-Holland, Amsterdam

    Google Scholar 

  43. 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

    Article  ADS  Google Scholar 

  44. Cairns R. A. (1991) Radiofrequency heating of plasmas. Adam Hilger, Bristol

    Google Scholar 

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© 2000 Springer-Verlag Berlin Heidelberg

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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

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  • DOI: https://doi.org/10.1007/3-540-46614-2_6

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  • Print ISBN: 978-3-540-66937-1

  • Online ISBN: 978-3-540-46614-7

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