Abstract

A general approach is presented for treating the two-dimensional scattering of a plane wave by an arbitrary configuration of perfectly conducting circular cylinders in front of a plane surface with general reflection properties. The method exploits the angular spectrum representation of cylindrical waves and turns out to be fairly efficient, as demonstrated by a number of examples. Our approach seems promising for several applications both in optics and in microwaves.

© 1996 Optical Society of America

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    [CrossRef]
  2. V. Twersky, “On scattering of waves by an infinite grating of circular cylinders,” IRE Trans. Antennas Propag. AP-10, 737–765 (1962).
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  3. W. Wasylkiwskyj, “On the transmission coefficient of an infinite grating of parallel perfectly conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-19, 704–708 (1971).
    [CrossRef]
  4. J. R. Wait, “Reflection at arbitrary incidence from a parallel wire grid,” Appl. Sci. Res. B 4, 393–400 (1954).
    [CrossRef]
  5. J. H. Richmond, “Scattering by an arbitrary array of parallel wires,” IEEE Trans. Microwave Theory Tech. MTT-13, 408–412 (1965).
    [CrossRef]
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    [CrossRef]
  7. R. Vescovo, “Electromagnetic scattering from cylindrical arrays of infinitely long thin wires,” Electron. Lett. 31, 1646–1647 (1995).
    [CrossRef]
  8. A. C. Ludwig, “Wire grid modeling of surfaces,” IEEE Trans. Antennas Propag. AP-35, 1045–1048 (1987).
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    [CrossRef]
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  16. A. Z. Elsherbeni, “A comparative study of two-dimensional multiple scattering techniques,” Radio Sci. 29, 1023–1033 (1994).
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  29. 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]
  30. 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).
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  31. K. B. Nahm, W. L. Wolfe, “Light scattering for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
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  32. 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).
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  36. T. C. Rao, R. Barakat, “Plane wave scattering by a finite array of conducting cylinders partially buried in a ground plane: TM polarization,” Pure Appl. Opt. 3, 1023–1048 (1994).
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    [CrossRef] [PubMed]
  39. A. Dipace, A. Doria, G. P. Gallerano, M. F. Kimmit, P. Raimondi, A. Renieri, E. Sabia, “Compact free electron laser resonators utilizing electron transparent mirrors,” IEEE J. Quantum Electron. 27, 2629–2635 (1991).
    [CrossRef]
  40. H. A. Ragheb, M. Hamid, “Simulation of a cylindrical reflector by conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-35, 349–353 (1987).
    [CrossRef]
  41. A. Z. Elsherbeni, A. A. Kishk, “Modeling of cylindrical objects by circular dielectric and conducting cylinders,” IEEE Trans. Antennas Propag. 40, 96–99 (1992).
    [CrossRef]
  42. G. L. Wojcik, D. K. Vaughn, L. K. Galbraith, “Calculation of light scatter from structures on silicon surfaces,” in Lasers in Microlithography, J. S. Batchelder, O. J. Enrlich, J. Y. Tsao, eds., Proc. SPIE774, 21–31 (1987).
    [CrossRef]
  43. A. J. Pidduck, D. J. Robbins, I. M. Young, A. G. Cullis, A. R. S. Martin, “The formation of dislocations and their insitudetection during silicon vapor phase epitaxy at reduced temperature,” Mater. Sci. Eng. B 4, 417–422 (1989).
    [CrossRef]
  44. M. I. Petelin, E. V. Suvorov, “Quasi optical grill for excitation of lower hybrid wave in a toroidal plasma,” Sov. Tech. Phys. Lett. 15, 882–886 (1989).
  45. 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]
  46. F. Frezza, G. Gerosa, F. Gori, M. Santarsiero, F. Santini, G. Schettini, M. Sgroi, “Gaussian beam diffraction by a quasi-optical grating for coupling to lower-hybrid plasma waves,” Int. J. Infrared Mill. Waves 16, 1009–1024 (1995).
    [CrossRef]
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  50. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 364.
  51. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. 1, p. 36.
  52. 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]
  53. M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North-Holland, Amsterdam, 1991).
  54. 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]
  55. J. J. Bowman, T. B. Senior, P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (Hemisphere, New York, 1987), p. 7.
  56. P. F. Davis, P. Rabinowitz, Methods of Numerical Integration (Academic, New York, 1984), Chap. 3.
  57. P. J. Valle, F. Moreno, J. M. Saiz, F. Gonzàlez, “Electromagnetic interaction between two parallel circular cylinders on a planar interface,” IEEE Trans. Antennas Propag. 44, 321–325 (1996).
    [CrossRef]
  58. A. Madrazo, M. Nieto-Vesperinas, “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 (1996).
    [CrossRef]
  59. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [CrossRef]

1996 (3)

1995 (4)

F. Frezza, G. Gerosa, F. Gori, M. Santarsiero, F. Santini, G. Schettini, M. Sgroi, “Gaussian beam diffraction by a quasi-optical grating for coupling to lower-hybrid plasma waves,” Int. J. Infrared Mill. Waves 16, 1009–1024 (1995).
[CrossRef]

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]

R. Vescovo, “Electromagnetic scattering from cylindrical arrays of infinitely long thin wires,” Electron. Lett. 31, 1646–1647 (1995).
[CrossRef]

1994 (6)

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

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

T. C. Rao, R. Barakat, “Plane wave scattering by a finite array of conducting cylinders partially buried in a ground plane: TM polarization,” Pure Appl. Opt. 3, 1023–1048 (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 (3)

1992 (2)

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]

A. Z. Elsherbeni, A. A. Kishk, “Modeling of cylindrical objects by circular dielectric and conducting cylinders,” IEEE Trans. Antennas Propag. 40, 96–99 (1992).
[CrossRef]

1991 (3)

A. Dipace, A. Doria, G. P. Gallerano, M. F. Kimmit, P. Raimondi, A. Renieri, E. Sabia, “Compact free electron laser resonators utilizing electron transparent mirrors,” IEEE J. Quantum Electron. 27, 2629–2635 (1991).
[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]

R. J. Paknys, “The near field of a wire grid model,” IEEE Trans. Antennas Propag. 39, 994–999 (1991).
[CrossRef]

1990 (2)

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

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

1989 (2)

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

M. I. Petelin, E. V. Suvorov, “Quasi optical grill for excitation of lower hybrid wave in a toroidal plasma,” Sov. Tech. Phys. Lett. 15, 882–886 (1989).

1988 (2)

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

T. G. Tsuei, P. W. Barber, “Multiple scattering by two parallel dielectric cylinders,” Appl. Opt. 27, 3375–3381 (1988).
[CrossRef] [PubMed]

1987 (5)

B. Schlicht, K. F. Wall, R. K. Chang, P. W. Barber, “Light scattering by two parallel glass fibers,” J. Opt. Soc. Am. A 4, 800–809 (1987).
[CrossRef]

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]

A. Z. Elsherbeni, M. Hamid, “Scattering by parallel conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-35, 355–358 (1987).
[CrossRef]

A. C. Ludwig, “Wire grid modeling of surfaces,” IEEE Trans. Antennas Propag. AP-35, 1045–1048 (1987).
[CrossRef]

H. A. Ragheb, M. Hamid, “Simulation of a cylindrical reflector by conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-35, 349–353 (1987).
[CrossRef]

1985 (1)

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

1978 (2)

K. Hongo, “Multiple scattering by two conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-26, 748–751 (1978).
[CrossRef]

A. Sentz, M. Pyee, C. Gastaud, J. Auvray, J. P. Letur, “Construction of parallel grids acting as semitransparent flat mirrors in the far infrared,” Rev. Sci. Instrum. 49, 926–927 (1978).
[CrossRef] [PubMed]

1975 (1)

H. A. Kalhor, Armand, “Scattering of waves by gratings of conducting cylinders,” Proc. IEE 122, 245–248 (1975).

1974 (1)

L. O. Wilson, “The shielding of a plane wave by a cylindrical array of infinitely thin wires,” IEEE Trans. Antennas Propag. AP-22, 689–696 (1974).
[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]

1971 (1)

W. Wasylkiwskyj, “On the transmission coefficient of an infinite grating of parallel perfectly conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-19, 704–708 (1971).
[CrossRef]

1970 (2)

1965 (1)

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

1962 (1)

V. Twersky, “On scattering of waves by an infinite grating of circular cylinders,” IRE Trans. Antennas Propag. AP-10, 737–765 (1962).
[CrossRef]

1961 (1)

N. Zitron, S. N. Karp, “Higher-order approximations in multiple scattering. Two-dimensional scalar case,” J. Math. Phys. 2, 394–406 (1961).
[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 (2)

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

J. R. Wait, “Reflection at arbitrary incidence from a parallel wire grid,” Appl. Sci. Res. B 4, 393–400 (1954).
[CrossRef]

1952 (1)

V. Twersky, “Multiple scattering of radiation by an arbitrary configuration of parallel cylinders,” J. Acoust. Soc. Am. 24, 42–46 (1952).
[CrossRef]

1914 (1)

W. Von Ignatowsky, “Zur theorie der Gitter,” Ann. Physik 44, 369–436 (1914).
[CrossRef]

Abramowitz, M.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 358.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 363.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 364.

Armand,

H. A. Kalhor, Armand, “Scattering of waves by gratings of conducting cylinders,” Proc. IEE 122, 245–248 (1975).

Auvray, J.

A. Sentz, M. Pyee, C. Gastaud, J. Auvray, J. P. Letur, “Construction of parallel grids acting as semitransparent flat mirrors in the far infrared,” Rev. Sci. Instrum. 49, 926–927 (1978).
[CrossRef] [PubMed]

Barakat, R.

T. C. Rao, R. Barakat, “Plane wave scattering by a finite array of conducting cylinders partially buried in a ground plane: TM polarization,” Pure Appl. Opt. 3, 1023–1048 (1994).
[CrossRef]

Barber, P. W.

Borghi, R.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. 1, p. 36.

Bowman, J. J.

J. J. Bowman, T. B. Senior, P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (Hemisphere, New York, 1987), p. 7.

Bridges, T. J.

Cadilhac, M.

Chang, R. K.

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 insitudetection during silicon vapor phase epitaxy at reduced temperature,” Mater. Sci. Eng. B 4, 417–422 (1989).
[CrossRef]

Davis, P. F.

P. F. Davis, P. Rabinowitz, Methods of Numerical Integration (Academic, New York, 1984), Chap. 3.

Dipace, A.

A. Dipace, A. Doria, G. P. Gallerano, M. F. Kimmit, P. Raimondi, A. Renieri, E. Sabia, “Compact free electron laser resonators utilizing electron transparent mirrors,” IEEE J. Quantum Electron. 27, 2629–2635 (1991).
[CrossRef]

Doria, A.

A. Dipace, A. Doria, G. P. Gallerano, M. F. Kimmit, P. Raimondi, A. Renieri, E. Sabia, “Compact free electron laser resonators utilizing electron transparent mirrors,” IEEE J. Quantum Electron. 27, 2629–2635 (1991).
[CrossRef]

Elsherbeni, A. Z.

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

A. Z. Elsherbeni, A. A. Kishk, “Modeling of cylindrical objects by circular dielectric and conducting cylinders,” IEEE Trans. Antennas Propag. 40, 96–99 (1992).
[CrossRef]

A. Z. Elsherbeni, M. Hamid, “Scattering by parallel conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-35, 355–358 (1987).
[CrossRef]

Felbacq, D.

Frezza, F.

R. Borghi, F. Frezza, F. Gori, M. Santarsiero, G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A 13, 483–493 (1996).
[CrossRef]

F. Frezza, G. Gerosa, F. Gori, M. Santarsiero, F. Santini, G. Schettini, M. Sgroi, “Gaussian beam diffraction by a quasi-optical grating for coupling to lower-hybrid plasma waves,” Int. J. Infrared Mill. Waves 16, 1009–1024 (1995).
[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]

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]

Galbraith, L. K.

G. L. Wojcik, D. K. Vaughn, L. K. Galbraith, “Calculation of light scatter from structures on silicon surfaces,” in Lasers in Microlithography, J. S. Batchelder, O. J. Enrlich, J. Y. Tsao, eds., Proc. SPIE774, 21–31 (1987).
[CrossRef]

Gallerano, G. P.

A. Dipace, A. Doria, G. P. Gallerano, M. F. Kimmit, P. Raimondi, A. Renieri, E. Sabia, “Compact free electron laser resonators utilizing electron transparent mirrors,” IEEE J. Quantum Electron. 27, 2629–2635 (1991).
[CrossRef]

Gastaud, C.

A. Sentz, M. Pyee, C. Gastaud, J. Auvray, J. P. Letur, “Construction of parallel grids acting as semitransparent flat mirrors in the far infrared,” Rev. Sci. Instrum. 49, 926–927 (1978).
[CrossRef] [PubMed]

Gerosa, G.

F. Frezza, G. Gerosa, F. Gori, M. Santarsiero, F. Santini, G. Schettini, M. Sgroi, “Gaussian beam diffraction by a quasi-optical grating for coupling to lower-hybrid plasma waves,” Int. J. Infrared Mill. Waves 16, 1009–1024 (1995).
[CrossRef]

González, F.

Gonzàlez, F.

P. J. Valle, F. Moreno, J. M. Saiz, F. Gonzàlez, “Electromagnetic interaction between two parallel circular cylinders on a planar interface,” IEEE Trans. Antennas Propag. 44, 321–325 (1996).
[CrossRef]

Gori, F.

R. Borghi, F. Frezza, F. Gori, M. Santarsiero, G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A 13, 483–493 (1996).
[CrossRef]

F. Frezza, G. Gerosa, F. Gori, M. Santarsiero, F. Santini, G. Schettini, M. Sgroi, “Gaussian beam diffraction by a quasi-optical grating for coupling to lower-hybrid plasma waves,” Int. J. Infrared Mill. Waves 16, 1009–1024 (1995).
[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]

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, “Simulation of a cylindrical reflector by conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-35, 349–353 (1987).
[CrossRef]

A. Z. Elsherbeni, M. Hamid, “Scattering by parallel conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-35, 355–358 (1987).
[CrossRef]

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

Hongo, K.

K. Hongo, “Multiple scattering by two conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-26, 748–751 (1978).
[CrossRef]

Jordan, D. L.

Kalhor, H. A.

H. A. Kalhor, Armand, “Scattering of waves by gratings of conducting cylinders,” Proc. IEE 122, 245–248 (1975).

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]

Karp, S. N.

N. Zitron, S. N. Karp, “Higher-order approximations in multiple scattering. Two-dimensional scalar case,” J. Math. Phys. 2, 394–406 (1961).
[CrossRef]

Kimmit, M. F.

A. Dipace, A. Doria, G. P. Gallerano, M. F. Kimmit, P. Raimondi, A. Renieri, E. Sabia, “Compact free electron laser resonators utilizing electron transparent mirrors,” IEEE J. Quantum Electron. 27, 2629–2635 (1991).
[CrossRef]

Kishk, A. A.

A. Z. Elsherbeni, A. A. Kishk, “Modeling of cylindrical objects by circular dielectric and conducting cylinders,” IEEE Trans. Antennas Propag. 40, 96–99 (1992).
[CrossRef]

Letur, J. P.

A. Sentz, M. Pyee, C. Gastaud, J. Auvray, J. P. Letur, “Construction of parallel grids acting as semitransparent flat mirrors in the far infrared,” Rev. Sci. Instrum. 49, 926–927 (1978).
[CrossRef] [PubMed]

Lindell, I. V.

Ludwig, A. C.

A. C. Ludwig, “Wire grid modeling of surfaces,” IEEE Trans. Antennas Propag. AP-35, 1045–1048 (1987).
[CrossRef]

Madrazo, A.

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 insitudetection 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]

Moreno, F.

P. J. Valle, F. Moreno, J. M. Saiz, F. Gonzàlez, “Electromagnetic interaction between two parallel circular cylinders on a planar interface,” IEEE Trans. Antennas Propag. 44, 321–325 (1996).
[CrossRef]

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]

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. 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]

Muinonen, K. O.

Nahm, K. B.

Nieto-Vesperinas, M.

Olaofe, G. O.

G. O. Olaofe, “Scattering by two cylinders,” Radio Sci. 5, 1351–1360 (1970).
[CrossRef]

Paknys, R. J.

R. J. Paknys, “The near field of a wire grid model,” IEEE Trans. Antennas Propag. 39, 994–999 (1991).
[CrossRef]

Petelin, M. I.

M. I. Petelin, E. V. Suvorov, “Quasi optical grill for excitation of lower hybrid wave in a toroidal plasma,” Sov. Tech. Phys. Lett. 15, 882–886 (1989).

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 insitudetection during silicon vapor phase epitaxy at reduced temperature,” Mater. Sci. Eng. B 4, 417–422 (1989).
[CrossRef]

Pollack, M. A.

Pyee, M.

A. Sentz, M. Pyee, C. Gastaud, J. Auvray, J. P. Letur, “Construction of parallel grids acting as semitransparent flat mirrors in the far infrared,” Rev. Sci. Instrum. 49, 926–927 (1978).
[CrossRef] [PubMed]

Rabinowitz, P.

P. F. Davis, P. Rabinowitz, Methods of Numerical Integration (Academic, New York, 1984), Chap. 3.

Ragheb, H. A.

H. A. Ragheb, M. Hamid, “Simulation of a cylindrical reflector by conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-35, 349–353 (1987).
[CrossRef]

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

Raimondi, P.

A. Dipace, A. Doria, G. P. Gallerano, M. F. Kimmit, P. Raimondi, A. Renieri, E. Sabia, “Compact free electron laser resonators utilizing electron transparent mirrors,” IEEE J. Quantum Electron. 27, 2629–2635 (1991).
[CrossRef]

Rao, T. C.

T. C. Rao, R. Barakat, “Plane wave scattering by a finite array of conducting cylinders partially buried in a ground plane: TM polarization,” Pure Appl. Opt. 3, 1023–1048 (1994).
[CrossRef]

Renieri, A.

A. Dipace, A. Doria, G. P. Gallerano, M. F. Kimmit, P. Raimondi, A. Renieri, E. Sabia, “Compact free electron laser resonators utilizing electron transparent mirrors,” IEEE J. Quantum Electron. 27, 2629–2635 (1991).
[CrossRef]

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 insitudetection during silicon vapor phase epitaxy at reduced temperature,” Mater. Sci. Eng. B 4, 417–422 (1989).
[CrossRef]

Sabia, E.

A. Dipace, A. Doria, G. P. Gallerano, M. F. Kimmit, P. Raimondi, A. Renieri, E. Sabia, “Compact free electron laser resonators utilizing electron transparent mirrors,” IEEE J. Quantum Electron. 27, 2629–2635 (1991).
[CrossRef]

Saiz, J. M.

P. J. Valle, F. Moreno, J. M. Saiz, F. Gonzàlez, “Electromagnetic interaction between two parallel circular cylinders on a planar interface,” IEEE Trans. Antennas Propag. 44, 321–325 (1996).
[CrossRef]

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]

Santarsiero, M.

R. Borghi, F. Frezza, F. Gori, M. Santarsiero, G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A 13, 483–493 (1996).
[CrossRef]

F. Frezza, G. Gerosa, F. Gori, M. Santarsiero, F. Santini, G. Schettini, M. Sgroi, “Gaussian beam diffraction by a quasi-optical grating for coupling to lower-hybrid plasma waves,” Int. J. Infrared Mill. Waves 16, 1009–1024 (1995).
[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]

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, G. Gerosa, F. Gori, M. Santarsiero, F. Santini, G. Schettini, M. Sgroi, “Gaussian beam diffraction by a quasi-optical grating for coupling to lower-hybrid plasma waves,” Int. J. Infrared Mill. Waves 16, 1009–1024 (1995).
[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]

Schettini, G.

R. Borghi, F. Frezza, F. Gori, M. Santarsiero, G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A 13, 483–493 (1996).
[CrossRef]

F. Frezza, G. Gerosa, F. Gori, M. Santarsiero, F. Santini, G. Schettini, M. Sgroi, “Gaussian beam diffraction by a quasi-optical grating for coupling to lower-hybrid plasma waves,” Int. J. Infrared Mill. Waves 16, 1009–1024 (1995).
[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]

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]

Schlicht, B.

Senior, T. B.

J. J. Bowman, T. B. Senior, P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (Hemisphere, New York, 1987), p. 7.

T. B. Senior, P. L. E. Uslenghi, “The circular cylinder,” in Electromagnetic and Acoustic Scattering by Simple Shapes, J. J. Bowman, T. B. Senior, P. L. E. Uslenghi, eds. (Hemisphere, New York, 1987), Chap. 2, p. 93.

Sentz, A.

A. Sentz, M. Pyee, C. Gastaud, J. Auvray, J. P. Letur, “Construction of parallel grids acting as semitransparent flat mirrors in the far infrared,” Rev. Sci. Instrum. 49, 926–927 (1978).
[CrossRef] [PubMed]

Sgroi, M.

F. Frezza, G. Gerosa, F. Gori, M. Santarsiero, F. Santini, G. Schettini, M. Sgroi, “Gaussian beam diffraction by a quasi-optical grating for coupling to lower-hybrid plasma waves,” Int. J. Infrared Mill. Waves 16, 1009–1024 (1995).
[CrossRef]

Sihlova, A. H.

Simon, R.

Stegun, I.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 363.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 358.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 364.

Suvorov, E. V.

M. I. Petelin, E. V. Suvorov, “Quasi optical grill for excitation of lower hybrid wave in a toroidal plasma,” Sov. Tech. Phys. Lett. 15, 882–886 (1989).

Taubenblatt, M. A.

Tayreb, G.

Tran, T. K.

Tsuei, T. G.

Twersky, V.

V. Twersky, “On scattering of waves by an infinite grating of circular cylinders,” IRE Trans. Antennas Propag. AP-10, 737–765 (1962).
[CrossRef]

V. Twersky, “Multiple scattering of radiation by an arbitrary configuration of parallel cylinders,” J. Acoust. Soc. Am. 24, 42–46 (1952).
[CrossRef]

Ulrich, R.

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), p. 7.

T. B. Senior, P. L. E. Uslenghi, “The circular cylinder,” in Electromagnetic and Acoustic Scattering by Simple Shapes, J. J. Bowman, T. B. Senior, P. L. E. Uslenghi, eds. (Hemisphere, New York, 1987), Chap. 2, p. 93.

Valle, P. J.

P. J. Valle, F. Moreno, J. M. Saiz, F. Gonzàlez, “Electromagnetic interaction between two parallel circular cylinders on a planar interface,” IEEE Trans. Antennas Propag. 44, 321–325 (1996).
[CrossRef]

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]

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. 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]

Vaughn, D. K.

G. L. Wojcik, D. K. Vaughn, L. K. Galbraith, “Calculation of light scatter from structures on silicon surfaces,” in Lasers in Microlithography, J. S. Batchelder, O. J. Enrlich, J. Y. Tsao, eds., Proc. SPIE774, 21–31 (1987).
[CrossRef]

Vescovo, R.

R. Vescovo, “Electromagnetic scattering from cylindrical arrays of infinitely long thin wires,” Electron. Lett. 31, 1646–1647 (1995).
[CrossRef]

Von Ignatowsky, W.

W. Von Ignatowsky, “Zur theorie der Gitter,” Ann. Physik 44, 369–436 (1914).
[CrossRef]

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, “Reflection at arbitrary incidence from a parallel wire grid,” Appl. Sci. Res. B 4, 393–400 (1954).
[CrossRef]

Wall, K. F.

Wang, W.

Wasylkiwskyj, W.

W. Wasylkiwskyj, “On the transmission coefficient of an infinite grating of parallel perfectly conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-19, 704–708 (1971).
[CrossRef]

Wilson, L. O.

L. O. Wilson, “The shielding of a plane wave by a cylindrical array of infinitely thin wires,” IEEE Trans. Antennas Propag. AP-22, 689–696 (1974).
[CrossRef]

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]

Wojcik, G. L.

G. L. Wojcik, D. K. Vaughn, L. K. Galbraith, “Calculation of light scatter from structures on silicon surfaces,” in Lasers in Microlithography, J. S. Batchelder, O. J. Enrlich, J. Y. Tsao, eds., Proc. SPIE774, 21–31 (1987).
[CrossRef]

Wolf, E.

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 insitudetection during silicon vapor phase epitaxy at reduced temperature,” Mater. Sci. Eng. B 4, 417–422 (1989).
[CrossRef]

Zitron, N.

N. Zitron, S. N. Karp, “Higher-order approximations in multiple scattering. Two-dimensional scalar case,” J. Math. Phys. 2, 394–406 (1961).
[CrossRef]

Zolla, F.

Ann. Physik (1)

W. Von Ignatowsky, “Zur theorie der Gitter,” Ann. Physik 44, 369–436 (1914).
[CrossRef]

Appl. Opt. (4)

Appl. Sci. Res. B (1)

J. R. Wait, “Reflection at arbitrary incidence from a parallel wire grid,” Appl. Sci. Res. B 4, 393–400 (1954).
[CrossRef]

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]

Electron. Lett. (1)

R. Vescovo, “Electromagnetic scattering from cylindrical arrays of infinitely long thin wires,” Electron. Lett. 31, 1646–1647 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Dipace, A. Doria, G. P. Gallerano, M. F. Kimmit, P. Raimondi, A. Renieri, E. Sabia, “Compact free electron laser resonators utilizing electron transparent mirrors,” IEEE J. Quantum Electron. 27, 2629–2635 (1991).
[CrossRef]

IEEE Trans. Antennas Propag. (10)

H. A. Ragheb, M. Hamid, “Simulation of a cylindrical reflector by conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-35, 349–353 (1987).
[CrossRef]

A. Z. Elsherbeni, A. A. Kishk, “Modeling of cylindrical objects by circular dielectric and conducting cylinders,” IEEE Trans. Antennas Propag. 40, 96–99 (1992).
[CrossRef]

P. J. Valle, F. Moreno, J. M. Saiz, F. Gonzàlez, “Electromagnetic interaction between two parallel circular cylinders on a planar interface,” IEEE Trans. Antennas Propag. 44, 321–325 (1996).
[CrossRef]

A. C. Ludwig, “Wire grid modeling of surfaces,” IEEE Trans. Antennas Propag. AP-35, 1045–1048 (1987).
[CrossRef]

R. J. Paknys, “The near field of a wire grid model,” IEEE Trans. Antennas Propag. 39, 994–999 (1991).
[CrossRef]

K. Hongo, “Multiple scattering by two conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-26, 748–751 (1978).
[CrossRef]

A. Z. Elsherbeni, M. Hamid, “Scattering by parallel conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-35, 355–358 (1987).
[CrossRef]

W. Wasylkiwskyj, “On the transmission coefficient of an infinite grating of parallel perfectly conducting circular cylinders,” IEEE Trans. Antennas Propag. AP-19, 704–708 (1971).
[CrossRef]

L. O. Wilson, “The shielding of a plane wave by a cylindrical array of infinitely thin wires,” IEEE Trans. Antennas Propag. AP-22, 689–696 (1974).
[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]

Int. J. Infrared Mill. Waves (1)

F. Frezza, G. Gerosa, F. Gori, M. Santarsiero, F. Santini, G. Schettini, M. Sgroi, “Gaussian beam diffraction by a quasi-optical grating for coupling to lower-hybrid plasma waves,” Int. J. Infrared Mill. Waves 16, 1009–1024 (1995).
[CrossRef]

IRE Trans. Antennas Propag. (1)

V. Twersky, “On scattering of waves by an infinite grating of circular cylinders,” IRE Trans. Antennas Propag. AP-10, 737–765 (1962).
[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. Acoust. Soc. Am. (1)

V. Twersky, “Multiple scattering of radiation by an arbitrary configuration of parallel cylinders,” J. Acoust. Soc. Am. 24, 42–46 (1952).
[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. Math. Phys. (1)

N. Zitron, S. N. Karp, “Higher-order approximations in multiple scattering. Two-dimensional scalar case,” J. Math. Phys. 2, 394–406 (1961).
[CrossRef]

J. Opt. Soc. Am. A (10)

R. Borghi, F. Frezza, F. Gori, M. Santarsiero, G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A 13, 483–493 (1996).
[CrossRef]

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]

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

B. Schlicht, K. F. Wall, R. K. Chang, P. W. Barber, “Light scattering by two parallel glass fibers,” J. Opt. Soc. Am. A 4, 800–809 (1987).
[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]

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]

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]

A. Madrazo, M. Nieto-Vesperinas, “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 (1996).
[CrossRef]

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]

Mater. Sci. Eng. B (1)

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

Nucl. Fusion (1)

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]

Opt. Commun. (1)

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]

Opt. Lett. (1)

Phys. Rev. B (1)

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]

Proc. IEE (1)

H. A. Kalhor, Armand, “Scattering of waves by gratings of conducting cylinders,” Proc. IEE 122, 245–248 (1975).

Pure Appl. Opt. (1)

T. C. Rao, R. Barakat, “Plane wave scattering by a finite array of conducting cylinders partially buried in a ground plane: TM polarization,” Pure Appl. Opt. 3, 1023–1048 (1994).
[CrossRef]

Radio Sci. (2)

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

G. O. Olaofe, “Scattering by two cylinders,” Radio Sci. 5, 1351–1360 (1970).
[CrossRef]

Rev. Sci. Instrum. (1)

A. Sentz, M. Pyee, C. Gastaud, J. Auvray, J. P. Letur, “Construction of parallel grids acting as semitransparent flat mirrors in the far infrared,” Rev. Sci. Instrum. 49, 926–927 (1978).
[CrossRef] [PubMed]

Sov. Tech. Phys. Lett. (1)

M. I. Petelin, E. V. Suvorov, “Quasi optical grill for excitation of lower hybrid wave in a toroidal plasma,” Sov. Tech. Phys. Lett. 15, 882–886 (1989).

Other (10)

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 358.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 363.

T. B. Senior, P. L. E. Uslenghi, “The circular cylinder,” in Electromagnetic and Acoustic Scattering by Simple Shapes, J. J. Bowman, T. B. Senior, P. L. E. Uslenghi, eds. (Hemisphere, New York, 1987), Chap. 2, p. 93.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 364.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. 1, p. 36.

G. L. Wojcik, D. K. Vaughn, L. K. Galbraith, “Calculation of light scatter from structures on silicon surfaces,” in Lasers in Microlithography, J. S. Batchelder, O. J. Enrlich, J. Y. Tsao, eds., Proc. SPIE774, 21–31 (1987).
[CrossRef]

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

J. J. Bowman, T. B. Senior, P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (Hemisphere, New York, 1987), p. 7.

P. F. Davis, P. Rabinowitz, Methods of Numerical Integration (Academic, New York, 1984), Chap. 3.

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

Fig. 1
Fig. 1

Geometry of the problem and notation used throughout the paper.

Fig. 2
Fig. 2

Geometry for the far-field analysis.

Fig. 3
Fig. 3

Scattering configuration used for the convergence test: N = 3; ka1 = 1, χ1 = 10, ζ1 = 10; ka2 = 3, χ2 = 5, ζ2 = 0; ka3 = 5, χ3 = 15, ζ3 = −15. The refractive index of the dielectric medium is n = 1.5, and the incidence angle of the impinging plane wave is φ = 45°.

Fig. 4
Fig. 4

Behavior of the modulus of the expansion coefficients csm for the configuration illustrated in Fig. 3 for increasing values of the truncation order Ms = μkas for (a) TM and (b) TE polarization (s = 1, 2, 3; m = −Ms,…, Ms).

Fig. 5
Fig. 5

Semilogarithmic plot [arbitrary units (a.u.)] of the scattering cross section σs as a function of the scattering angle ϑ ¯ for the configuration illustrated in Fig. 3, for (a) TM and (b) TE polarization. φ = 45°, n = 1.5.

Fig. 6
Fig. 6

Geometrical layout for the study of two interacting cylinders on a perfect mirror.

Fig. 7
Fig. 7

Semilogarithmic plot (a.u.) of the scattering cross section σs as a function of the scattering angle ϑ ¯ for the configuration illustrated in Fig. 6, for (a) TM and (b) TE polarization. ka = π, kh = π, φ = 30°, kd = 30ka.

Fig. 8
Fig. 8

Same as in Fig. 7, except that kd = 12ka.

Fig. 9
Fig. 9

Same as in Fig. 7, except that kd = 4ka.

Fig. 10
Fig. 10

A finite grating parallel to the interface.

Fig. 11
Fig. 11

Semilogarithmic plot (a.u.) of the scattering cross section σs as a function of the scattering angle ϑ for an optical grill placed near a vacuumσdielectric interface (see Fig. 10). n = 2, φ = 0°, N = 10, ka = 1.0, kh = 3.0, kd = 7.0, for (a) TM and (b) TE polarization.

Fig. 12
Fig. 12

Same as in Fig. 11, except that φ = 30°.

Fig. 13
Fig. 13

Same as in Fig. 11, except that φ = 60°.

Fig. 14
Fig. 14

Semilogarithmic plot (a.u.) of the scattering cross section σs as a function of the scattering angle ϑ for the case shown in Fig. 13, except that N = 20, for (a) TM and (b) TE polarization.

Equations (41)

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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 i ( ξ , ζ ) = V 0 exp ( i n i ξ t 0 + i n i ζ t 0 ) exp ( i n i ξ t + i n i ζ t ) = V 0 exp ( i n i ξ t 0 + i n i ζ t 0 ) m = + i m × exp ( i m φ ) J m ( ρ t ) exp ( i m ϑ t ) ,
V r ( ξ , ζ ) = V 0 Γ ( n i ) exp ( i n i ξ + i n i ζ ) .
V r ( ξ , ζ ) = V 0 Γ ( n i ) exp ( i n i ξ t 0 + i n i ζ t 0 ) × exp ( i n i ξ t + i n i ζ t ) = V 0 Γ ( n i ) exp ( i n i ξ t 0 + i n i ζ t 0 ) × m = + i m exp ( i m φ ¯ ) × J m ( ρ t ) exp ( i m ϑ t ) ,
V d ( ξ , ζ ) = V 0 s = 1 N m = + i m exp ( i m φ ) c s m CW m ( ξ s , ζ s ) ,
CW m ( ξ s , ζ s ) = H m ( 1 ) ( ρ s ) exp ( i m ϑ s )
V d ( ξ , ζ ) = V 0 m = + i m exp ( i m φ ) c t m CW m ( ξ t , ζ t ) + V 0 s = 1 s t N m = + i m exp ( i m φ ) c s m × exp ( i m ϑ s t ) l = + ( 1 ) l H m + l ( 1 ) ( ρ s t ) × exp ( i l ϑ s t ) J l ( ρ t ) exp ( i l ϑ t ) ,
V d ( ξ , ζ ) = V 0 m = + i m exp ( i m φ ) c t m CW m ( ξ t , ζ t ) + V 0 s = 1 s t N l = + i l exp ( i l φ ) c s l × m = + H l + m ( 1 ) ( ρ s t ) exp [ i ( l + m ) ϑ s t ] × ( 1 ) m J m ( ρ t ) exp ( i m ϑ t ) ;
V d ( ξ , ζ ) = V 0 m = + i m exp ( i m φ ) c t m CW m ( ξ t , ζ t ) + V 0 s = 1 s t N l = + i l exp ( i l φ ) c s l × m = + CW l m ( ξ s t , ζ s t ) J m ( ρ t ) exp ( i m ϑ t ) ,
V d ( ξ , ζ ) = V 0 m = + J m ( ρ t ) exp ( i m ϑ t ) s = 1 N l = + i l × exp ( i l φ ) c s l [ CW l m ( ξ s t , ζ s t ) × ( 1 δ s t ) + δ s t δ l m H m ( 1 ) ( ρ t ) J m ( ρ t ) ] .
RW m ( ξ , ζ ) = 1 2 π + Γ ( n ) F m ( ξ , n ) exp ( i n ζ ) d n ,
F m ( ξ , n ) = + CW m ( ξ , ζ ) exp ( i n ζ ) d ζ .
V d r ( ξ , ζ ) = V 0 s = 1 N m = + i m exp ( i m φ ) × c s m RW m ( 2 χ s ξ s , ζ s ) .
F m ( ξ , n ) = 2 exp ( i n ξ ) n exp ( i m arccos n ) , n ( , + ) ,
RW m ( 2 χ s ξ s , ζ s ) = 1 2 π + Γ ( n ) F m ( 2 ξ s 0 ξ + ξ s 0 , n ) × exp ( i n ζ s 0 ) exp ( i n ζ ) d n = 1 2 π + Γ ( n ) F m ( χ s , n ) × exp [ i n ( ζ ζ s 0 ) ] exp ( i n ξ ) d n .
RW m ( 2 χ s ξ s , ζ s ) = 1 2 π + Γ ( n ) F m ( χ s , n ) exp [ i n ( ζ t 0 ζ s 0 ) ] × exp [ i n χ t ] exp ( i n ξ t + i n ζ t ) d n .
exp ( i n ξ t + i n ζ t ) = l = + i l exp ( i l ψ ¯ ) J l ( ρ t ) exp ( i l ϑ t ) ,
R W m ( 2 χ s ξ s , ζ s ) = l = + i l J l exp ( i l ϑ t ) ( 1 ) l 2 π × + Γ ( n ) F m ( χ s + χ t , n ) × exp [ i n ( ζ t 0 ζ s 0 ) ] exp ( i l arcsin n ) d n = l = + J l ( ρ t ) exp ( i l ϑ t ) 1 2 π × + Γ ( n ) F l + m ( χ s + χ t , n ) × exp [ i n ( ζ t 0 ζ s 0 ) ] d n = l = + J l ( ρ t ) exp ( i l ϑ t ) RW t + m ( χ s + χ t , ζ t 0 , ζ s 0 ) ,
exp ( i arcsin n ) = i exp ( i arccos n ) .
V d r ( ξ , ζ ) = V 0 m = + J m ( ρ t ) exp ( i m ϑ t ) × s = 1 N l = + i l exp ( i l φ ) c s l RW l + m × ( χ s + χ t , ζ t 0 , ζ s 0 ) .
V ( ξ , ζ ) = V i ( ξ , ζ ) + V r ( ξ , ζ ) + V d ( ξ , ζ ) + V d r ( ξ , ζ ) = V 0 m = + J m ( ρ t ) exp ( i m ϑ t ) × { i m exp ( i m φ ) exp ( i n t ξ t 0 + i n t ξ t 0 ) + i m exp ( i m φ ) Γ ( n i ) exp ( i n i ξ t 0 + i n i ξ t 0 ) + s = 1 N l = + i l exp ( i l φ ) c s l [ C W l m ( ξ s t , ζ s t ) × ( 1 δ s t ) + RW l + m ( χ s + χ t , ζ t 0 , ζ s 0 ) + δ s t δ l m H m ( 1 ) ( ρ t ) J m ( ρ t ) ] } .
{ V | ρ t = k a t = 0 ( t = 1 , , N ) for TE polarization ρ t V | ρ t = k a t = 0 ( t = 1 , , N ) for TE polarization .
s = 1 N l = + A m l s t c s l = B m t , ( m = 0 , ± 1 , ± 2 , t = 1 , , N ) ,
A l m s t = i l exp ( i l φ ) { [ CW l m ( ξ s t , ζ s t ) ( 1 δ s t ) + I l + m s t ] G m ( k a t ) + δ s t δ l m } ,
I p s t = RW p ( χ s + χ t , ζ t 0 ζ s 0 ) ,
B m t = i m exp ( i n i ζ t 0 ) G m ( k a t ) × [ exp ( i n i ξ t 0 ) exp ( i m φ ) + Γ ( n i ) exp ( i n i ξ t 0 ) exp ( i m φ ¯ ) ] ,
G m ( x ) = { J m ( x ) H m ( 1 ) ( x ) for TM polarization J m ( x ) H m ( 1 ) ( x ) for TE polarization ,
I p s t = ( 1 ) p I p s t .
I p s t = Γ C W p ( χ s + χ t , ζ t 0 ζ s 0 ) ;
V d tot ( ξ , ζ ) = V d ( ξ , ζ ) + V d r ( ξ , ζ ) = V 0 s = 1 N m = + c ̂ s m [ CW m ( ξ s , ζ s ) + RW m ( 2 χ s ξ s , ζ s ) ] ,
c ̂ s m = i m exp ( i m φ ) c s m
CW m ( ξ s , ζ s ) ( 2 i π ρ s ) 1 / 2 i m exp ( i ρ s ) exp ( i m ϑ s ) ,
RW m ( 2 χ s ξ s , ζ s ) ( 2 i π ρ s ) 1 / 2 Γ ( sin ϑ ¯ s ) i m × exp ( i ρ ¯ s ) exp ( i m ϑ ¯ s ) ,
1 ρ ¯ s 1 ρ s 1 ρ , ϑ s ϑ , ϑ ¯ s π ϑ , exp ( i ρ s ) exp ( i ρ ) exp ( i χ s cos ϑ i ζ s 0 sin ϑ ) , exp ( i ρ ¯ s ) exp ( i ρ ) exp ( i χ s cos ϑ i ζ s 0 sin ϑ ) ,
V d tot ( ξ , ζ ) V 0 ( 2 i π ρ ) 1 / 2 exp ( i ρ ) g ( ϑ ) ,
g ( ϑ ) = s = 1 N m = + i m c ̂ s m exp ( i χ s cos ϑ i ζ s o sin ϑ ) × [ exp ( i m ϑ ) + ( 1 ) m Γ ( sin ϑ ) × exp ( i 2 χ s cos ϑ ) exp ( i m ϑ ) ]
s = 1 N ( 2 M s + 1 ) = N + 2 s = 1 N M s .
sin ϑ ¯ m = sin φ + m 2 π k d ( m = 0 , ± 1 , ± 2 , ) ,
I p t s = RW p ( χ t + χ s , ζ s 0 ζ t 0 ) = 1 2 π + Γ ( n ) F p ( χ t + χ s , n ) × exp [ i n ( ζ s 0 ζ t 0 ) ] d n = 1 2 π + Γ ( n ) F p ( χ t + χ s , n ) × exp [ i n ( ζ t 0 ζ s 0 ) ] d n = 1 2 π + Γ ( n ) F p ( χ s + χ t , n ) × exp [ i n ( ζ t 0 ζ s 0 ) ] d n = 1 2 π + Γ ( n ) ( 1 ) p F p ( χ s + χ t , n ) × exp [ i n ( ζ t 0 ζ s 0 ) ] d n = ( 1 ) p I p s t ,
F p ( χ , n ) = ( 1 ) p F p ( χ , n ) .

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