Abstract

A new method for the analysis of the diffraction of a plane wave impinging on a perfectly conducting circular cylinder in front of a generally reflecting surface is presented. The surface is characterized by its complex reflection coefficient, enabling us to treat a wide class of reflecting surfaces. The presence of the surface is taken into account by means of a suitable expansion of the reflected field in terms of cylindrical functions. The method gives the solution of the scattering problem in both the near and the far field regardless of the polarization state of the incident field. Numerical examples for dielectric interfaces are presented, and comparisons are made with results presented in the literature.

© 1996 Optical Society of America

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References

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  1. J. J. Bowman, T. B. Senior, P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (Hemisphere, New York, 1987); J. T. Ruck, D. E. Barrick, W. D. Stuart, C. K. Krichbaum, Radar Cross Section Handbook (Plenum, New York, 1970).
  2. A. Ishimaru, Electromagnetic Wave Propagation, Radiation and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), Chap. 11.
  3. J. H. Richmond, “Scattering by an arbitrary array of parallel wires,” IEEE Trans. Microwave Theory Tech. MTT-13, 408–412 (1965).
    [CrossRef]
  4. C. R. Mullin, R. Sandburg, C. O. Velline, “A numerical technique for the determination of scattering cross sections of infinite cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. AP-13, 141–149 (1965).
    [CrossRef]
  5. W. A. Imbriale, R. Mittra, “The two-dimensional inverse scattering problem,” IEEE Trans. Antennas Propag. AP-18, 633–642 (1970).
    [CrossRef]
  6. D. R. Wilton, R. Mittra, “A new numerical approach to the calculation of electromagnetic scattering properties of two-dimensional bodies of arbitrary cross section,” IEEE Trans. Antennas Propag. AP-20, 310–317 (1972).
    [CrossRef]
  7. F. Zolla, R. Petit, M. Cadilhac, “Electromagnetic theory of diffraction by a system of parallel rods: the method of fictitious sources,” J. Opt. Soc. Am. A 11, 1087–1096 (1994).
    [CrossRef]
  8. J. R. Wait, “Reflection from a wire grid parallel to a conducting plane,” Can. J. Phys. 32, 571–579 (1954).
    [CrossRef]
  9. T. C. Rao, R. Barakat, “Plane-wave scattering by a conducting cylinder partially buried in a ground plane. 1. TM case,” J. Opt. Soc. Am. A 6, 1270–1280 (1989).
    [CrossRef]
  10. T. C. Rao, R. Barakat, “Plane-wave scattering by a conducting cylinder partially buried in a ground plane. 2. TE case,” J. Opt. Soc. Am. A 8, 1986–1990 (1991).
    [CrossRef]
  11. T. C. Rao, R. Barakat, “Near field scattering by a conducting cylinder partially buried in a conducting plane,” Opt. Commun. 111, 18–25 (1994).
    [CrossRef]
  12. H. A. Ragheb, M. Hamid, “Scattering by Nparallel conducting circular cylinders,” Int. J. Electron. 59, 407–421 (1985).
    [CrossRef]
  13. A. Z. Elsherbeni, “A comparative study of two-dimensional multiple scattering techniques,” Radio Sci. 29, 1023–1033 (1994).
    [CrossRef]
  14. D. Felbacq, G. Tayreb, D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526–2538 (1994).
    [CrossRef]
  15. P. J. Valle, F. González, F. Moreno, “Electromagnetic wave scattering from conducting cylindrical structures on flat substrates: study by means of the extinction theorem,” Appl. Opt. 33, 512–523 (1994).
    [CrossRef] [PubMed]
  16. P. J. Valle, F. Moreno, J. M. Saiz, F. González, “Near-field scattering from subwavelength metallic protuberances on conducting flat substrates,” Phys. Rev. B 51, 13681–13690 (1995).
    [CrossRef]
  17. A. Madrazo, M. Nieto-Vesperinas, “Scattering of electromagnetic waves from a cylinder in front of a conducting plane,” J. Opt. Soc. Am. A 12, 1298–1309 (1995).
    [CrossRef]
  18. P. G. Cottis, J. D. Kanellopoulos, “Scattering from a conducting cylinder above a lossy medium,” Int. J. Electron. 65, 1031–1038 (1988).
    [CrossRef]
  19. M. A. Taubenblatt, “Light scattering from cylindrical structures on surfaces,” Opt. Lett. 15, 255–257 (1990).
    [CrossRef] [PubMed]
  20. P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica 137A, 209–242 (1986).
  21. K. B. Nahm, W. L. Wolfe, “Light scattering for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
    [CrossRef] [PubMed]
  22. G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991).
    [CrossRef]
  23. G. Videen, M. G. Turner, V. J. Iafelice, W. S. Bickel, W. L. Wolfe, “Scattering from a small sphere near a surface,” J. Opt. Soc. Am. A 10, 118–126 (1993).
    [CrossRef]
  24. B. R. Johnson, “Light scattering from a spherical particle on a conducting plane: I. Normal incidence,” J. Opt. Soc. Am. A 9, 1341–1351 (1992).
    [CrossRef]
  25. I. V. Lindell, A. H. Sihlova, K. O. Muinonen, P. W. Barber, “Scattering by a small object close to an interface. I. Exact-image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991).
    [CrossRef]
  26. M. A. Taubenblatt, T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993).
    [CrossRef]
  27. F. Moreno, F. González, J. M. Saiz, P. J. Valle, D. L. Jordan, “Experimental study of copolarized light scattering by spherical metallic particles on conducting flat substrates,” J. Opt. Soc. Am. A 10, 141–157 (1993).
    [CrossRef]
  28. J. R. Wait, “The impedance of a wire grid parallel to a dielectric interface,” IRE Trans. Microwave Theory Tech. 5, 99–102 (1957).
    [CrossRef]
  29. J. R. Wait, “Note on solution for scattering from parallel wires in an interface,” J. Electromagn. Waves Appl. 4, 1151–1155 (1990).
    [CrossRef]
  30. F. Frezza, F. Gori, M. Santarsiero, F. Santini, G. Schettini, “Quasi-optical launchers for lower hybrid waves: a full-wave approach,” Nucl. Fusion 34, 1239–1246 (1994).
    [CrossRef]
  31. J. R. Wait, Electromagnetic Radiation from Cylindrical Structures (Peter Peregrinus, London, 1988).
  32. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  33. A. J. Pidduck, D. J. Robbins, I. M. Young, A. G. Cullis, A. R. S. Martin, “The formation of dislocations and their in-situdetection during silicon vapor phase epitaxy at reduced temperature,” Mater. Sci. Eng. B 4, 417–422 (1989).
    [CrossRef]
  34. G. Cincotti, F. Gori, M. Santarsiero, F. Frezza, F. Furnò, G. Schettini, “Plane wave expansion of cylindrical functions,” Opt. Commun. 95, 192–198 (1993).
    [CrossRef]
  35. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
  36. J. R. Wait, Electromagnetic Wave Theory (Harper & Row, New York, 1985).
  37. W. Wang, R. Simon, E. Wolf, “Changes in the coherence and spectral properties of partially coherent light reflected from a dielectric slab,” J. Opt. Soc. Am. A 9, 287–297 (1992).
    [CrossRef]
  38. Ref. 36, Sec. 4.15.
  39. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).
  40. E. Wolf, “A generalized extinction theorem and its rule in scattering theory,” in Coherence and Quantum Optics, L. Mandel, E. Wolf, eds. (Plenum, New York, 1973), pp. 339–357.
    [CrossRef]
  41. A. I. Markushevich, The Theory of Analytic Functions: a Brief Course (Mir, Moscow, 1983).

1995 (2)

P. J. Valle, F. Moreno, J. M. Saiz, F. González, “Near-field scattering from subwavelength metallic protuberances on conducting flat substrates,” Phys. Rev. B 51, 13681–13690 (1995).
[CrossRef]

A. Madrazo, M. Nieto-Vesperinas, “Scattering of electromagnetic waves from a cylinder in front of a conducting plane,” J. Opt. Soc. Am. A 12, 1298–1309 (1995).
[CrossRef]

1994 (6)

T. C. Rao, R. Barakat, “Near field scattering by a conducting cylinder partially buried in a conducting plane,” Opt. Commun. 111, 18–25 (1994).
[CrossRef]

A. Z. Elsherbeni, “A comparative study of two-dimensional multiple scattering techniques,” Radio Sci. 29, 1023–1033 (1994).
[CrossRef]

D. Felbacq, G. Tayreb, D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526–2538 (1994).
[CrossRef]

P. J. Valle, F. González, F. Moreno, “Electromagnetic wave scattering from conducting cylindrical structures on flat substrates: study by means of the extinction theorem,” Appl. Opt. 33, 512–523 (1994).
[CrossRef] [PubMed]

F. Zolla, R. Petit, M. Cadilhac, “Electromagnetic theory of diffraction by a system of parallel rods: the method of fictitious sources,” J. Opt. Soc. Am. A 11, 1087–1096 (1994).
[CrossRef]

F. Frezza, F. Gori, M. Santarsiero, F. Santini, G. Schettini, “Quasi-optical launchers for lower hybrid waves: a full-wave approach,” Nucl. Fusion 34, 1239–1246 (1994).
[CrossRef]

1993 (4)

1992 (2)

1991 (3)

1990 (2)

M. A. Taubenblatt, “Light scattering from cylindrical structures on surfaces,” Opt. Lett. 15, 255–257 (1990).
[CrossRef] [PubMed]

J. R. Wait, “Note on solution for scattering from parallel wires in an interface,” J. Electromagn. Waves Appl. 4, 1151–1155 (1990).
[CrossRef]

1989 (2)

A. J. Pidduck, D. J. Robbins, I. M. Young, A. G. Cullis, A. R. S. Martin, “The formation of dislocations and their in-situdetection during silicon vapor phase epitaxy at reduced temperature,” Mater. Sci. Eng. B 4, 417–422 (1989).
[CrossRef]

T. C. Rao, R. Barakat, “Plane-wave scattering by a conducting cylinder partially buried in a ground plane. 1. TM case,” J. Opt. Soc. Am. A 6, 1270–1280 (1989).
[CrossRef]

1988 (1)

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

1987 (1)

1986 (1)

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica 137A, 209–242 (1986).

1985 (1)

H. A. Ragheb, M. Hamid, “Scattering by Nparallel conducting circular cylinders,” Int. J. Electron. 59, 407–421 (1985).
[CrossRef]

1972 (1)

D. R. Wilton, R. Mittra, “A new numerical approach to the calculation of electromagnetic scattering properties of two-dimensional bodies of arbitrary cross section,” IEEE Trans. Antennas Propag. AP-20, 310–317 (1972).
[CrossRef]

1970 (1)

W. A. Imbriale, R. Mittra, “The two-dimensional inverse scattering problem,” IEEE Trans. Antennas Propag. AP-18, 633–642 (1970).
[CrossRef]

1965 (2)

J. H. Richmond, “Scattering by an arbitrary array of parallel wires,” IEEE Trans. Microwave Theory Tech. MTT-13, 408–412 (1965).
[CrossRef]

C. R. Mullin, R. Sandburg, C. O. Velline, “A numerical technique for the determination of scattering cross sections of infinite cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. AP-13, 141–149 (1965).
[CrossRef]

1957 (1)

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

1954 (1)

J. R. Wait, “Reflection from a wire grid parallel to a conducting plane,” Can. J. Phys. 32, 571–579 (1954).
[CrossRef]

Abramowitz, M.

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

Barakat, R.

Barber, P. W.

Bickel, W. S.

Bobbert, P. A.

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica 137A, 209–242 (1986).

Bowman, J. J.

J. J. Bowman, T. B. Senior, P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (Hemisphere, New York, 1987); J. T. Ruck, D. E. Barrick, W. D. Stuart, C. K. Krichbaum, Radar Cross Section Handbook (Plenum, New York, 1970).

Cadilhac, M.

Cincotti, G.

G. Cincotti, F. Gori, M. Santarsiero, F. Frezza, F. Furnò, G. Schettini, “Plane wave expansion of cylindrical functions,” Opt. Commun. 95, 192–198 (1993).
[CrossRef]

Cottis, P. G.

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

Cullis, A. G.

A. J. Pidduck, D. J. Robbins, I. M. Young, A. G. Cullis, A. R. S. Martin, “The formation of dislocations and their in-situdetection during silicon vapor phase epitaxy at reduced temperature,” Mater. Sci. Eng. B 4, 417–422 (1989).
[CrossRef]

Elsherbeni, A. Z.

A. Z. Elsherbeni, “A comparative study of two-dimensional multiple scattering techniques,” Radio Sci. 29, 1023–1033 (1994).
[CrossRef]

Felbacq, D.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Frezza, F.

F. Frezza, F. Gori, M. Santarsiero, F. Santini, G. Schettini, “Quasi-optical launchers for lower hybrid waves: a full-wave approach,” Nucl. Fusion 34, 1239–1246 (1994).
[CrossRef]

G. Cincotti, F. Gori, M. Santarsiero, F. Frezza, F. Furnò, G. Schettini, “Plane wave expansion of cylindrical functions,” Opt. Commun. 95, 192–198 (1993).
[CrossRef]

Furnò, F.

G. Cincotti, F. Gori, M. Santarsiero, F. Frezza, F. Furnò, G. Schettini, “Plane wave expansion of cylindrical functions,” Opt. Commun. 95, 192–198 (1993).
[CrossRef]

González, F.

Gori, F.

F. Frezza, F. Gori, M. Santarsiero, F. Santini, G. Schettini, “Quasi-optical launchers for lower hybrid waves: a full-wave approach,” Nucl. Fusion 34, 1239–1246 (1994).
[CrossRef]

G. Cincotti, F. Gori, M. Santarsiero, F. Frezza, F. Furnò, G. Schettini, “Plane wave expansion of cylindrical functions,” Opt. Commun. 95, 192–198 (1993).
[CrossRef]

Hamid, M.

H. A. Ragheb, M. Hamid, “Scattering by Nparallel conducting circular cylinders,” Int. J. Electron. 59, 407–421 (1985).
[CrossRef]

Iafelice, V. J.

Imbriale, W. A.

W. A. Imbriale, R. Mittra, “The two-dimensional inverse scattering problem,” IEEE Trans. Antennas Propag. AP-18, 633–642 (1970).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), Chap. 11.

Johnson, B. R.

Jordan, D. L.

Kanellopoulos, J. D.

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

Lindell, I. V.

Madrazo, A.

Markushevich, A. I.

A. I. Markushevich, The Theory of Analytic Functions: a Brief Course (Mir, Moscow, 1983).

Martin, A. R. S.

A. J. Pidduck, D. J. Robbins, I. M. Young, A. G. Cullis, A. R. S. Martin, “The formation of dislocations and their in-situdetection during silicon vapor phase epitaxy at reduced temperature,” Mater. Sci. Eng. B 4, 417–422 (1989).
[CrossRef]

Maystre, D.

Mittra, R.

D. R. Wilton, R. Mittra, “A new numerical approach to the calculation of electromagnetic scattering properties of two-dimensional bodies of arbitrary cross section,” IEEE Trans. Antennas Propag. AP-20, 310–317 (1972).
[CrossRef]

W. A. Imbriale, R. Mittra, “The two-dimensional inverse scattering problem,” IEEE Trans. Antennas Propag. AP-18, 633–642 (1970).
[CrossRef]

Moreno, F.

Muinonen, K. O.

Mullin, C. R.

C. R. Mullin, R. Sandburg, C. O. Velline, “A numerical technique for the determination of scattering cross sections of infinite cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. AP-13, 141–149 (1965).
[CrossRef]

Nahm, K. B.

Nieto-Vesperinas, M.

Petit, R.

Pidduck, A. J.

A. J. Pidduck, D. J. Robbins, I. M. Young, A. G. Cullis, A. R. S. Martin, “The formation of dislocations and their in-situdetection during silicon vapor phase epitaxy at reduced temperature,” Mater. Sci. Eng. B 4, 417–422 (1989).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Ragheb, H. A.

H. A. Ragheb, M. Hamid, “Scattering by Nparallel conducting circular cylinders,” Int. J. Electron. 59, 407–421 (1985).
[CrossRef]

Rao, T. C.

Richmond, J. H.

J. H. Richmond, “Scattering by an arbitrary array of parallel wires,” IEEE Trans. Microwave Theory Tech. MTT-13, 408–412 (1965).
[CrossRef]

Robbins, D. J.

A. J. Pidduck, D. J. Robbins, I. M. Young, A. G. Cullis, A. R. S. Martin, “The formation of dislocations and their in-situdetection during silicon vapor phase epitaxy at reduced temperature,” Mater. Sci. Eng. B 4, 417–422 (1989).
[CrossRef]

Saiz, J. M.

P. J. Valle, F. Moreno, J. M. Saiz, F. González, “Near-field scattering from subwavelength metallic protuberances on conducting flat substrates,” Phys. Rev. B 51, 13681–13690 (1995).
[CrossRef]

F. Moreno, F. González, J. M. Saiz, P. J. Valle, D. L. Jordan, “Experimental study of copolarized light scattering by spherical metallic particles on conducting flat substrates,” J. Opt. Soc. Am. A 10, 141–157 (1993).
[CrossRef]

Sandburg, R.

C. R. Mullin, R. Sandburg, C. O. Velline, “A numerical technique for the determination of scattering cross sections of infinite cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. AP-13, 141–149 (1965).
[CrossRef]

Santarsiero, M.

F. Frezza, F. Gori, M. Santarsiero, F. Santini, G. Schettini, “Quasi-optical launchers for lower hybrid waves: a full-wave approach,” Nucl. Fusion 34, 1239–1246 (1994).
[CrossRef]

G. Cincotti, F. Gori, M. Santarsiero, F. Frezza, F. Furnò, G. Schettini, “Plane wave expansion of cylindrical functions,” Opt. Commun. 95, 192–198 (1993).
[CrossRef]

Santini, F.

F. Frezza, F. Gori, M. Santarsiero, F. Santini, G. Schettini, “Quasi-optical launchers for lower hybrid waves: a full-wave approach,” Nucl. Fusion 34, 1239–1246 (1994).
[CrossRef]

Schettini, G.

F. Frezza, F. Gori, M. Santarsiero, F. Santini, G. Schettini, “Quasi-optical launchers for lower hybrid waves: a full-wave approach,” Nucl. Fusion 34, 1239–1246 (1994).
[CrossRef]

G. Cincotti, F. Gori, M. Santarsiero, F. Frezza, F. Furnò, G. Schettini, “Plane wave expansion of cylindrical functions,” Opt. Commun. 95, 192–198 (1993).
[CrossRef]

Senior, T. B.

J. J. Bowman, T. B. Senior, P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (Hemisphere, New York, 1987); J. T. Ruck, D. E. Barrick, W. D. Stuart, C. K. Krichbaum, Radar Cross Section Handbook (Plenum, New York, 1970).

Sihlova, A. H.

Simon, R.

Stegun, I.

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

Taubenblatt, M. A.

Tayreb, G.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Tran, T. K.

Turner, M. G.

Uslenghi, P. L. E.

J. J. Bowman, T. B. Senior, P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (Hemisphere, New York, 1987); J. T. Ruck, D. E. Barrick, W. D. Stuart, C. K. Krichbaum, Radar Cross Section Handbook (Plenum, New York, 1970).

Valle, P. J.

Velline, C. O.

C. R. Mullin, R. Sandburg, C. O. Velline, “A numerical technique for the determination of scattering cross sections of infinite cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. AP-13, 141–149 (1965).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Videen, G.

Vlieger, J.

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica 137A, 209–242 (1986).

Wait, J. R.

J. R. Wait, “Note on solution for scattering from parallel wires in an interface,” J. Electromagn. Waves Appl. 4, 1151–1155 (1990).
[CrossRef]

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

J. R. Wait, “Reflection from a wire grid parallel to a conducting plane,” Can. J. Phys. 32, 571–579 (1954).
[CrossRef]

J. R. Wait, Electromagnetic Radiation from Cylindrical Structures (Peter Peregrinus, London, 1988).

J. R. Wait, Electromagnetic Wave Theory (Harper & Row, New York, 1985).

Wang, W.

Wilton, D. R.

D. R. Wilton, R. Mittra, “A new numerical approach to the calculation of electromagnetic scattering properties of two-dimensional bodies of arbitrary cross section,” IEEE Trans. Antennas Propag. AP-20, 310–317 (1972).
[CrossRef]

Wolf, E.

W. Wang, R. Simon, E. Wolf, “Changes in the coherence and spectral properties of partially coherent light reflected from a dielectric slab,” J. Opt. Soc. Am. A 9, 287–297 (1992).
[CrossRef]

E. Wolf, “A generalized extinction theorem and its rule in scattering theory,” in Coherence and Quantum Optics, L. Mandel, E. Wolf, eds. (Plenum, New York, 1973), pp. 339–357.
[CrossRef]

Wolfe, W. L.

Young, I. M.

A. J. Pidduck, D. J. Robbins, I. M. Young, A. G. Cullis, A. R. S. Martin, “The formation of dislocations and their in-situdetection during silicon vapor phase epitaxy at reduced temperature,” Mater. Sci. Eng. B 4, 417–422 (1989).
[CrossRef]

Zolla, F.

Appl. Opt. (2)

Can. J. Phys. (1)

J. R. Wait, “Reflection from a wire grid parallel to a conducting plane,” Can. J. Phys. 32, 571–579 (1954).
[CrossRef]

IEEE Trans. Antennas Propag. (3)

C. R. Mullin, R. Sandburg, C. O. Velline, “A numerical technique for the determination of scattering cross sections of infinite cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. AP-13, 141–149 (1965).
[CrossRef]

W. A. Imbriale, R. Mittra, “The two-dimensional inverse scattering problem,” IEEE Trans. Antennas Propag. AP-18, 633–642 (1970).
[CrossRef]

D. R. Wilton, R. Mittra, “A new numerical approach to the calculation of electromagnetic scattering properties of two-dimensional bodies of arbitrary cross section,” IEEE Trans. Antennas Propag. AP-20, 310–317 (1972).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. H. Richmond, “Scattering by an arbitrary array of parallel wires,” IEEE Trans. Microwave Theory Tech. MTT-13, 408–412 (1965).
[CrossRef]

Int. J. Electron. (2)

H. A. Ragheb, M. Hamid, “Scattering by Nparallel conducting circular cylinders,” Int. J. Electron. 59, 407–421 (1985).
[CrossRef]

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

IRE Trans. Microwave Theory Tech. (1)

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

J. Electromagn. Waves Appl. (1)

J. R. Wait, “Note on solution for scattering from parallel wires in an interface,” J. Electromagn. Waves Appl. 4, 1151–1155 (1990).
[CrossRef]

J. Opt. Soc. Am. A (12)

G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991).
[CrossRef]

G. Videen, M. G. Turner, V. J. Iafelice, W. S. Bickel, W. L. Wolfe, “Scattering from a small sphere near a surface,” J. Opt. Soc. Am. A 10, 118–126 (1993).
[CrossRef]

B. R. Johnson, “Light scattering from a spherical particle on a conducting plane: I. Normal incidence,” J. Opt. Soc. Am. A 9, 1341–1351 (1992).
[CrossRef]

I. V. Lindell, A. H. Sihlova, K. O. Muinonen, P. W. Barber, “Scattering by a small object close to an interface. I. Exact-image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991).
[CrossRef]

M. A. Taubenblatt, T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Geometry of the problem and notation used throughout the paper.

Fig. 2
Fig. 2

Notation used in Section 2.

Fig. 3
Fig. 3

Behavior of the modulus of expansion coefficients cl for a dielectric interface (n = 50), for (a) TM and (b) TE polarization and different values of the truncation index (N = 1, 3, 9, 15). The other parameters are ka = 3, kh = 4, φ = 0°.

Fig. 4
Fig. 4

2-D plots of the modulus of the E field, for TM polarization: (a) ka = π, kh = 3π; n = 1.1, 2, 50; (b) ka = π, kh = 3.5π; n = 1.1, 2, 50; (c) ka = π/10, kh = 3π; n = 1.1, 2, 50; (d) ka = π/10, kh = 3.5π; n = 1.1, 2, 50. On the right-hand side, schematic drawings of the geometrical arrangement are sketched. The arrows indicate the direction of the incident plane wave.

Fig. 5
Fig. 5

2-D plot of the modulus of the (a) H and (b) E fields for TE polarization: ka = π/2, kh = 3π, n = 2. On the right-hand side, a schematic drawing of the geometrical arrangement is sketched. The arrow indicates the direction of the incident plane wave.

Fig. 6
Fig. 6

Semilogarithmic plots (a.u.) of the scattering cross section σS as a function of the scattering angle ϑ ¯ for the case of a dielectric interface: ka = π, kh = 2π, φ = 0°, 30°, and n = 1.1, 2, 50, for TE (solid curves) and TM (dashed curves) polarization.

Fig. 7
Fig. 7

Semilogarithmic plot (a.u.) of the scattering cross section σS as a function of the scattering angle ϑ ¯ for an ideal mirror: ka = kh = 4, φ = 0°, for TE (solid curve) and TM (dashed curve) polarization.

Fig. 8
Fig. 8

Semilogarithmic plot (a.u.) of the scattering cross section σS as a function of the scattering angle ϑ ¯ for a dielectric lossy medium and TM polarization: n = 4.0 + i 0.18, kh = 20.94, φ = 20°, ka = 4.19 (solid curve), ka = 10.47 (dashed curve).

Equations (67)

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k i = k sin φ , k i = k cos φ ,
V i ( ξ , ζ ) = V 0 exp ( i n i ξ + i n i ζ ) = V 0 l = - + i l exp ( - i l φ ) J l ( ρ ) exp ( i l ϑ ) .
C W l ( ξ , ζ ) = H l ( 1 ) ( ρ ) exp ( i l ϑ ) ,
V d ( ξ , ζ ) = V 0 l = - + i l exp ( - i l φ ) c l C W l ( ξ , ζ ) ,
V r ( ξ , ζ ) = V 0 Γ ( n i ) exp ( i n i 2 χ - i n i ξ + i n i ζ ) = V 0 Γ ( n i ) exp ( i n i 2 χ ) l = - + i l J l ( ρ ) exp [ i l ( ϑ - φ ) ] ,
V d r ( ξ , ζ ) = V d ( 2 χ - ξ , ζ ) * Γ ^ ( ζ ) ,
Γ ^ ( ζ ) = 1 2 π - + Γ ( n ) exp ( i n ζ ) d n .
V d r ( ξ , ζ ) = V 0 l = - + i l exp ( - i l φ ) c l C W l ( 2 χ - ξ , ζ ) * Γ ^ ( ζ ) = V 0 l = - + i l exp ( - i l φ ) c l R W l ( 2 χ - ξ , ζ ) ,
C W l ( ξ , ζ ) = 1 2 π - + F l ( ξ , n ) exp ( i n ζ ) d n .
R W l ( ξ , ζ ) = 1 2 π - + Γ ( n ) F l ( ξ , n ) exp ( i n ζ ) d n .
F l ( ξ , n ) = 2 exp ( i n ξ ) n exp ( - i l arccos n ) ,
V d r ( ξ , ζ ) = V 0 l = - + i l exp ( - i l φ ) c l 1 2 π - + Γ ( n ) F l ( 2 χ , n ) × exp ( - i n ξ + i n ζ ) d n .
V d r ( ξ , ζ ) = V 0 l = - + i l exp ( - i l φ ) c l m = - + i m J m ( ρ ) × exp [ i m ( ϑ - ψ ) ] × 1 2 π - + Γ ( n ) F l ( 2 χ , n ) d n ,
V d r ( ξ , ζ ) = V 0 l = - + i l exp ( - i l φ ) c l m = - + i m J m ( ρ ) ( - 1 ) m exp ( i m ϑ ) × 1 2 π - + Γ ( n ) 2 exp ( i n 2 χ ) n exp ( - i l arccos n ) × exp ( i m arcsin n ) d n = V 0 l = - + i l exp ( - i l φ ) c l m = - + J m ( ρ ) exp ( i m ϑ ) × 1 2 π - + Γ ( n ) 2 exp ( i n 2 χ ) n × exp [ - i ( l + m ) arccos n ] d n ,
exp ( i m arcsin n ) = i m exp ( - i m arccos n )
V d r ( ξ , ζ ) = V 0 l = - + i l exp ( - i l φ ) c l m = - + J m ( ρ ) exp ( i m ϑ ) × 1 2 π - + Γ ( n ) F l + m ( 2 χ , n ) d n = V 0 l = - + i l exp ( - i l φ ) c l m = - + J m ( ρ ) × exp ( i m ϑ ) R W l + m ( 2 χ , 0 ) .
[ V i + V r + V d + V d r ] ρ = k a = 0 for TM polarization , [ V i + V r + V d + V d r ] ρ = k a = 0 for TE polarization ,
l = - + A m l c l = b m ,
A m l = exp ( - i l φ ) [ δ m l + i l - m G m ( k a ) R W l + m ( 2 χ , 0 ) ] ,
b m = - G m ( k a ) { exp ( - i m φ ) + Γ ( n i ) exp ( i 2 n i χ ) × exp [ - i m ( π - φ ) ] } ,
G m ( x ) = { J m ( x ) H m ( 1 ) ( x ) for TM polarization J m ( x ) H m ( 1 ) ( x ) for TE polarization .
E = i ω × H , H = - i ω μ × E .
= k ˜ ,
E ( ρ ) = i k ω ˜ × H ( ρ ) = i Z ˜ × H ( ρ ) , H ( ρ ) = - i k ω μ ˜ × E ( ρ ) = 1 i Z ˜ × E ( ρ ) ,
˜ × V ( ξ , ζ ) y ^ = - ζ V ( ξ , ζ ) x ^ + ξ V ( ξ , ζ ) z ^ .
E ( ξ , ζ ) = V ( ξ , ζ ) y ^ , H ( ξ , ζ ) = - 1 i Z ζ V ( ξ , ζ ) x ^ + 1 i Z ξ V ( ξ , ζ ) z ^ ,
E ( ξ , ζ ) = - i Z ζ V ( ξ , ζ ) x ^ + i Z ξ V ( ξ , ζ ) z ^ , H ( ξ , ζ ) = V ( ξ , ζ ) y ^ .
ξ C W l ( ξ , ζ ) = ½ [ C W l - 1 ( ξ , ζ ) - C W l + 1 ( ξ , ζ ) ] ,
ζ C W l ( ξ , ζ ) = / 2 i [ C W l - 1 ( ξ , ζ ) + C W l + 1 ( ξ , ζ ) ] ,
ξ R W l ( ξ , ζ ) = ½ [ R W l - 1 ( ξ , ζ ) - R W l + 1 ( ξ , ζ ) ] ,
ζ R W l ( ξ , ζ ) = / 2 i [ R W l - 1 ( ξ , ζ ) + R W l + 1 ( ξ , ζ ) ] .
V d tot ( ξ , ζ ) = V 0 [ l = - + c ^ l C W l ( ξ , ζ ) + l = - + c ^ l R W l ( 2 χ - ξ , ζ ) ] = V 0 l = - + c ^ l [ C W l ( ξ , ζ ) + R W l ( 2 χ - ξ , ζ ) ] ,
H l ( 1 ) ( ρ ) - 2 i / π ρ i - l exp ( i ρ ) .
C W l ( ξ , ζ ) - 2 i / π ρ i - l exp ( i ρ + i l ϑ ) ,
R W l ( ξ , ζ ) - 2 i / π ρ Γ ( sin ϑ ) i - l exp ( i ρ + i l ϑ ) ,
R W l ( 2 χ - ξ , ζ ) - 2 i / π ρ ¯ Γ ( sin ϑ ¯ ) i - l exp ( i ρ ¯ + i l ϑ ¯ ) ,
1 ρ ¯ 1 ρ , ϑ ¯ π - ϑ , exp ( i ρ ¯ ) exp ( - 2 i χ cos ϑ ) exp ( i ρ ) .
V d tot ( ξ , ζ ) V 0 - 2 i / π ρ exp ( i ρ ) l = - + i - l c ^ l × [ exp ( i l ϑ ) + ( - 1 ) l Γ ( sin ϑ ) × exp ( - 2 i χ cos ϑ ) exp ( - i l ϑ ) ] .
g ( ϑ ) l = - + i - l c ^ l [ exp ( i l ϑ ) + ( - 1 ) l Γ ( sin ϑ ) × exp ( - 2 i χ cos ϑ ) exp ( - i l ϑ ) ] .
l = - N + N A m l c l = b m             ( m = - N , , N ) .
V i ( 0 , ζ ) = 1 2 π - + A i ( 0 , n ) exp ( i n ζ ) d n ,
V i ( χ , ζ ) = 1 2 π - + A i ( χ , n ) exp ( i n ζ ) d n = 1 2 π - + A i ( 0 , n ) exp ( i n χ + i n ζ ) d n .
A r ( χ , n ) = A i ( χ , n ) Γ ( n ) = A i ( 0 , n ) exp ( i n χ ) Γ ( n ) .
V r ( χ , ζ ) = 1 2 π - + A r ( χ , n ) exp ( i n ζ ) d n = 1 2 π - + A i ( 0 , n ) Γ ( n ) exp ( i n χ + i n ζ ) d n .
V r ( ξ , ζ ) = 1 2 π - + A i ( 0 , n ) Γ ( n ) exp ( i n χ ) × exp [ i n ( χ - ξ ) + i n ζ ] d n
= 1 2 π - + A i ( 0 , n ) Γ ( n ) × exp [ i n ( 2 χ - ξ ) + i n ζ ] d n ,
V r ( ξ , ζ ) = V i ( 2 χ - ξ , ζ ) * Γ ^ ( ζ ) ,
Γ ^ ( ζ ) = 1 2 π - + Γ ( n ) exp ( i n ζ ) d n .
H l ( ρ ) exp ( i l α ) = - + F l ( η , β ) exp ( i β ξ ) d β ,
H l ( ρ ) exp ( i l ϑ ) = 1 2 π - + F l ( ξ , n ) exp ( i n ζ ) d n .
α π / 2 - ϑ ,             ξ ζ ,             η ξ ,             β n .
i l H l ( ρ ) exp ( - i l ϑ ) = - + F l ( ξ , n ) exp ( i n ζ ) d n .
i - l ( - 1 ) l H l ( ρ ) exp ( i l ϑ ) = - + F l ( ξ , n ) exp ( i n ζ ) d n ,
H l ( ρ ) exp ( i l ϑ ) = - + ( - i ) l F - l ( ξ , n ) exp ( i n ζ ) d n .
F l ( ξ , n ) = 2 π ( - i ) l F - l ( ξ , n ) .
F l ( ξ , n ) = { ( - 1 ) l 2 exp ( - ξ n 2 - 1 ) i n 2 - 1 ( n 2 - 1 - n ) - l for n ( - , - 1 ) 2 exp ( i ξ 1 - n 2 - i l arccos n ) 1 - n 2 for n ( - 1 , 1 ) 2 exp ( - ξ n 2 - 1 ) i n 2 - 1 ( n 2 - 1 + n ) l for n ( 1 , + ) .
( - 1 ) l ( n 2 - 1 - n ) - l = ( n 2 - 1 + n ) l ,
F l ( ξ , n ) = 2 exp ( i ξ 1 - n 2 ) 1 - n 2 g l ( n ) ,
g l ( n ) = { ( n 2 - 1 + n ) l for n 1 exp ( - i l arccos n ) for n 1 .
F l ( ξ , n ) = 2 exp ( i ξ 1 - n 2 - i l arccos n ) 1 - n 2             for n ( - , + ) ,
R W m ( ξ , ζ ) = 1 2 π - + Γ ( n ) F m ( ξ , n ) exp ( i n ζ ) d n .
R W m + 1 ( ξ , ζ ) = 1 2 π - + Γ ( n ) 2 exp ( i ξ n ) n × exp [ - i ( m + 1 ) arccos n ] exp ( i ζ n ) d n = 1 2 π - + Γ ( n ) F m ( ξ , n ) exp ( - i arccos n ) × exp ( i n ζ ) d n .
exp ( - i arccos n ) = cos ( arccos n ) - i sin ( arccos n ) = n - i n ,
R W m + 1 ( ξ , ζ ) = 1 2 π - + Γ ( n ) F m ( ξ , n ) ( n - i n ) exp ( i n ζ ) d n = 1 2 π - + n Γ ( n ) F m ( ξ , n ) exp ( i n ζ ) d n - 1 2 π - + i n Γ ( n ) F m ( ξ , n ) exp ( i n ζ ) d n = - i ζ R W m ( ξ , ζ ) - ξ R W m ( ξ , ζ ) .
R W m + 1 ( ξ , ζ ) = - i ζ R W m ( ξ , ζ ) - ξ R W m ( ξ , ζ ) , R W m - 1 ( ξ , ζ ) = - i ζ R W m ( ξ , ζ ) + ξ R W m ( ξ , ζ ) ,
ξ R W m ( ξ , ζ ) = ½ [ R W m - 1 ( ξ , ζ ) - R W m + 1 ( ξ , ζ ) ] ,
ζ R W m ( ξ , ζ ) = / 2 i [ R W m - 1 ( ξ , ζ ) + R W m + 1 ( ξ , ζ ) ] .

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