Abstract

Exact calculations of the scattering of light and other electromagnetic waves by a tip, metallic or dielectric, in front of surface-relief grating are made by means of the extinction theorem generalized to multiply connected bodies. The configuration addressed is two dimensional; specifically, it pertains to the plane of incidence, and the tip is simulated by a cylinder. The scattered near fields between the surface and the cylinder are calculated, as well as the scattered intensity detected inside the tip as it scans along a line parallel to the interface. Two different regimes of grating parameters are studied, depending on whether the grating period is equal to, or smaller than, the wavelength. The results show that, as a result of multiple scattering, this intensity distribution does not generally follow the surface topography. Tips of diameter not larger than 0.1λ and dielectric permittivity similar to that of glass do not appreciably perturb the field reflected by the grating. The detection of surface polaritons as the tip approaches the interface is also addressed.

© 1996 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. 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]
  15. D. N. Pattanayak, E. Wolf, “General form and a new interpretation of the Ewald–Oseen extinction theorem,” Opt. Commun. 6, 217–220 (1972).
    [CrossRef]
  16. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chaps. 1 and 7.
  17. J. D. Kanellopoulos, N. E. Buris, “Scattering from conducting cylinders embedded in a lossy medium,” Int. J. Electron. 57, 391–401 (1984); P. G. Cottis, J. D. Kanellopoulos, “Scattering from a conducting cylinder above a lossy medium,” Int. J. Electron. 65, 1031–1038 (1988); C. N. Vazouras, P. G. Cottis, J. D. Kanellopoulos, “Scattering from a conducting cylinder above a lossy medium of sinusoidal interface,” Radio Sci. 27, 883–892 (1992).
    [CrossRef]
  18. X. A. Xu, Ch. M. Butler, “Current induced by TE excitation on a conducting cylinder located near the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. AP-34, 880–890 (1986); Ch. M. Butler, X. B. Xu, “TE scattering by partially buried and coupled cylinders at the interface between two media,” IEEE Trans. Antennas Propag. 38, 1829–1834 (1990).
    [CrossRef]
  19. M. Nieto-Vesperinas, J. M. Soto-Crespo, “Monte Carlo simulations for the scattering of electromagnetic waves from perfectly conductive random rough surfaces,” Opt. Lett. 12, 979–981 (1987); “Electromagnetic scattering from very rough random surfaces and deep reflection gratings,” J. Opt. Soc. Am. A 6, 367–384 (1989); J. A. Sanchez-Gil, M. Nieto-Vesperinas, “Light scattering from random rough dielectric surfaces,” J. Opt. Soc. Am. 8, 1270–1286 (1991).
    [CrossRef] [PubMed]
  20. A. A. Maradudin, E. R. Mendez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large amplitude random metallic grating,” Opt. Lett. 14, 151–153 (1989); A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
    [CrossRef] [PubMed]
  21. M. Nieto-Vesperinas, “Enhanced backscattering,” in “The decade in optics. Perspectives on the ’80s,” B. D. Guenther, ed., Opt. Photon. News1(12), 50–52 (1990); M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North-Holland, Amsterdam, 1991).
  22. L. Tsang, Ch. H. Chan, K. Pak, “Backscattering enhancement of a two-dimensional random rough surface (three-dimensional scattering) based on Monte Carlo simulations,” J. Opt. Soc. Am. A 11, 711–715 (1994).
    [CrossRef]
  23. P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional, randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
    [CrossRef]
  24. N. Garcia, M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 24, 2090–2092 (1993).
    [CrossRef]
  25. R. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a perfectly conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
    [CrossRef]
  26. N. Garcia, M. Nieto-Vesperinas, “A direct solution to the inverse scattering problem for surfaces from near field intensities without phase retrieval,” Opt. Lett. 20, 949–951 (1995); N. Garcia, M. Nieto-Vesperinas, “Theory for the apertureless near field optical microscope: image resolution,” Appl. Phys. Lett. 66, 3399 (1995).
    [CrossRef] [PubMed]
  27. M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
    [CrossRef]
  28. N. Garcia, “Exact calculations of p-polarized electromagnetic fields incident on gratings surfaces: surface polariton resonances,” Opt. Commun. 45, 307–310 (1983).
    [CrossRef]
  29. U. Ch. Fischer, D. W. Pohl, “Observation of single-particle plasmons by near-field optical microscopy,” Phys. Rev. Lett. 62, 458–461 (1989).
    [CrossRef] [PubMed]
  30. P. M. Adam, L. Salomon, F. de Fornel, J. P. Goudonnet, “Determination of the spatial extension of the surface-plasmon evanescent field of a silver film with a photon scanning tunneling microscope,” Phys. Rev. B 48, 2680–2683 (1993).
    [CrossRef]
  31. D. Maystre, M. Nevière, “Sur une méthode d’ étude théorique quantitative des anomalies de Wood des réseaux de diffraction: application aux anomalies de plasmons,” J. Opt. (Paris) 8, 165–174 (1977).
    [CrossRef]
  32. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and Gratings, Vol. III of Springer Tracts on Modern Physics (Springer-Verlag, Berlin, 1988), Chap. 1.
  33. P. Dawson, F. de Fornel, J. P. Goudonnet, “Imaging of surface plasmon propagation and edge interaction using a photon scanning tunneling microscope,” Phys. Rev. Lett. 72, 2927–2930 (1994).
    [CrossRef] [PubMed]

1995 (2)

1994 (6)

1993 (2)

P. M. Adam, L. Salomon, F. de Fornel, J. P. Goudonnet, “Determination of the spatial extension of the surface-plasmon evanescent field of a silver film with a photon scanning tunneling microscope,” Phys. Rev. B 48, 2680–2683 (1993).
[CrossRef]

N. Garcia, M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 24, 2090–2092 (1993).
[CrossRef]

1991 (2)

1990 (2)

1989 (3)

1987 (1)

1986 (2)

X. A. Xu, Ch. M. Butler, “Current induced by TE excitation on a conducting cylinder located near the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. AP-34, 880–890 (1986); Ch. M. Butler, X. B. Xu, “TE scattering by partially buried and coupled cylinders at the interface between two media,” IEEE Trans. Antennas Propag. 38, 1829–1834 (1990).
[CrossRef]

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica (Utrecht) 137A, 209–242 (1986); K. Nahm, W. L. Wolfe, “Light scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
[CrossRef] [PubMed]

1984 (1)

J. D. Kanellopoulos, N. E. Buris, “Scattering from conducting cylinders embedded in a lossy medium,” Int. J. Electron. 57, 391–401 (1984); P. G. Cottis, J. D. Kanellopoulos, “Scattering from a conducting cylinder above a lossy medium,” Int. J. Electron. 65, 1031–1038 (1988); C. N. Vazouras, P. G. Cottis, J. D. Kanellopoulos, “Scattering from a conducting cylinder above a lossy medium of sinusoidal interface,” Radio Sci. 27, 883–892 (1992).
[CrossRef]

1983 (1)

N. Garcia, “Exact calculations of p-polarized electromagnetic fields incident on gratings surfaces: surface polariton resonances,” Opt. Commun. 45, 307–310 (1983).
[CrossRef]

1977 (1)

D. Maystre, M. Nevière, “Sur une méthode d’ étude théorique quantitative des anomalies de Wood des réseaux de diffraction: application aux anomalies de plasmons,” J. Opt. (Paris) 8, 165–174 (1977).
[CrossRef]

1976 (1)

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[CrossRef]

1972 (1)

D. N. Pattanayak, E. Wolf, “General form and a new interpretation of the Ewald–Oseen extinction theorem,” Opt. Commun. 6, 217–220 (1972).
[CrossRef]

Adam, P. M.

P. M. Adam, L. Salomon, F. de Fornel, J. P. Goudonnet, “Determination of the spatial extension of the surface-plasmon evanescent field of a silver film with a photon scanning tunneling microscope,” Phys. Rev. B 48, 2680–2683 (1993).
[CrossRef]

Ban^os, A.

A. Ban̂os, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, Oxford, 1966).

Barakat, R.

Barber, P.

Bobbert, P. A.

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica (Utrecht) 137A, 209–242 (1986); K. Nahm, W. L. Wolfe, “Light scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
[CrossRef] [PubMed]

Buris, N. E.

J. D. Kanellopoulos, N. E. Buris, “Scattering from conducting cylinders embedded in a lossy medium,” Int. J. Electron. 57, 391–401 (1984); P. G. Cottis, J. D. Kanellopoulos, “Scattering from a conducting cylinder above a lossy medium,” Int. J. Electron. 65, 1031–1038 (1988); C. N. Vazouras, P. G. Cottis, J. D. Kanellopoulos, “Scattering from a conducting cylinder above a lossy medium of sinusoidal interface,” Radio Sci. 27, 883–892 (1992).
[CrossRef]

Butler, Ch. M.

X. A. Xu, Ch. M. Butler, “Current induced by TE excitation on a conducting cylinder located near the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. AP-34, 880–890 (1986); Ch. M. Butler, X. B. Xu, “TE scattering by partially buried and coupled cylinders at the interface between two media,” IEEE Trans. Antennas Propag. 38, 1829–1834 (1990).
[CrossRef]

Carminati, R.

R. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a perfectly conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
[CrossRef]

Celli, V.

Chan, Ch. H.

Courjon, D.

Dawson, P.

P. Dawson, F. de Fornel, J. P. Goudonnet, “Imaging of surface plasmon propagation and edge interaction using a photon scanning tunneling microscope,” Phys. Rev. Lett. 72, 2927–2930 (1994).
[CrossRef] [PubMed]

de Fornel, F.

P. Dawson, F. de Fornel, J. P. Goudonnet, “Imaging of surface plasmon propagation and edge interaction using a photon scanning tunneling microscope,” Phys. Rev. Lett. 72, 2927–2930 (1994).
[CrossRef] [PubMed]

P. M. Adam, L. Salomon, F. de Fornel, J. P. Goudonnet, “Determination of the spatial extension of the surface-plasmon evanescent field of a silver film with a photon scanning tunneling microscope,” Phys. Rev. B 48, 2680–2683 (1993).
[CrossRef]

Fischer, U. Ch.

U. Ch. Fischer, D. W. Pohl, “Observation of single-particle plasmons by near-field optical microscopy,” Phys. Rev. Lett. 62, 458–461 (1989).
[CrossRef] [PubMed]

Garcia, N.

N. Garcia, M. Nieto-Vesperinas, “A direct solution to the inverse scattering problem for surfaces from near field intensities without phase retrieval,” Opt. Lett. 20, 949–951 (1995); N. Garcia, M. Nieto-Vesperinas, “Theory for the apertureless near field optical microscope: image resolution,” Appl. Phys. Lett. 66, 3399 (1995).
[CrossRef] [PubMed]

N. Garcia, M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 24, 2090–2092 (1993).
[CrossRef]

N. Garcia, “Exact calculations of p-polarized electromagnetic fields incident on gratings surfaces: surface polariton resonances,” Opt. Commun. 45, 307–310 (1983).
[CrossRef]

Girard, C.

Goudonnet, J. P.

P. Dawson, F. de Fornel, J. P. Goudonnet, “Imaging of surface plasmon propagation and edge interaction using a photon scanning tunneling microscope,” Phys. Rev. Lett. 72, 2927–2930 (1994).
[CrossRef] [PubMed]

P. M. Adam, L. Salomon, F. de Fornel, J. P. Goudonnet, “Determination of the spatial extension of the surface-plasmon evanescent field of a silver film with a photon scanning tunneling microscope,” Phys. Rev. B 48, 2680–2683 (1993).
[CrossRef]

Greffet, J. J.

Hutley, M. C.

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[CrossRef]

Kanellopoulos, J. D.

J. D. Kanellopoulos, N. E. Buris, “Scattering from conducting cylinders embedded in a lossy medium,” Int. J. Electron. 57, 391–401 (1984); P. G. Cottis, J. D. Kanellopoulos, “Scattering from a conducting cylinder above a lossy medium,” Int. J. Electron. 65, 1031–1038 (1988); C. N. Vazouras, P. G. Cottis, J. D. Kanellopoulos, “Scattering from a conducting cylinder above a lossy medium of sinusoidal interface,” Radio Sci. 27, 883–892 (1992).
[CrossRef]

Labani, B.

Lindell, I. V.

Madrazo, A.

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. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a perfectly conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
[CrossRef]

Maradudin, A. A.

Maystre, D.

D. Maystre, M. Nevière, “Sur une méthode d’ étude théorique quantitative des anomalies de Wood des réseaux de diffraction: application aux anomalies de plasmons,” J. Opt. (Paris) 8, 165–174 (1977).
[CrossRef]

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[CrossRef]

Mendez, E. R.

Michel, T.

Muinonen, K. O.

Nevière, M.

D. Maystre, M. Nevière, “Sur une méthode d’ étude théorique quantitative des anomalies de Wood des réseaux de diffraction: application aux anomalies de plasmons,” J. Opt. (Paris) 8, 165–174 (1977).
[CrossRef]

Nieto-Vesperinas, M.

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]

N. Garcia, M. Nieto-Vesperinas, “A direct solution to the inverse scattering problem for surfaces from near field intensities without phase retrieval,” Opt. Lett. 20, 949–951 (1995); N. Garcia, M. Nieto-Vesperinas, “Theory for the apertureless near field optical microscope: image resolution,” Appl. Phys. Lett. 66, 3399 (1995).
[CrossRef] [PubMed]

R. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a perfectly conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
[CrossRef]

N. Garcia, M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 24, 2090–2092 (1993).
[CrossRef]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Monte Carlo simulations for the scattering of electromagnetic waves from perfectly conductive random rough surfaces,” Opt. Lett. 12, 979–981 (1987); “Electromagnetic scattering from very rough random surfaces and deep reflection gratings,” J. Opt. Soc. Am. A 6, 367–384 (1989); J. A. Sanchez-Gil, M. Nieto-Vesperinas, “Light scattering from random rough dielectric surfaces,” J. Opt. Soc. Am. 8, 1270–1286 (1991).
[CrossRef] [PubMed]

M. Nieto-Vesperinas, “Enhanced backscattering,” in “The decade in optics. Perspectives on the ’80s,” B. D. Guenther, ed., Opt. Photon. News1(12), 50–52 (1990); M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North-Holland, Amsterdam, 1991).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chaps. 1 and 7.

Novotny, L.

Pak, K.

Pattanayak, D. N.

D. N. Pattanayak, E. Wolf, “General form and a new interpretation of the Ewald–Oseen extinction theorem,” Opt. Commun. 6, 217–220 (1972).
[CrossRef]

Pincemin, F.

Pohl, D. W.

L. Novotny, D. W. Pohl, P. Regali, “Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope,” J. Opt. Soc. Am. A 11, 1768–1779 (1994).
[CrossRef]

U. Ch. Fischer, D. W. Pohl, “Observation of single-particle plasmons by near-field optical microscopy,” Phys. Rev. Lett. 62, 458–461 (1989).
[CrossRef] [PubMed]

D. W. Pohl, “Scanning near field optical microscopy (SNOM),” in Advances in Optical and Electron Microscopy, J. R. Sheppard, T. Mulvey, eds. (Academic, New York, 1990), p. 243.

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and Gratings, Vol. III of Springer Tracts on Modern Physics (Springer-Verlag, Berlin, 1988), Chap. 1.

Rao, T. C.

Regali, P.

Salomon, L.

P. M. Adam, L. Salomon, F. de Fornel, J. P. Goudonnet, “Determination of the spatial extension of the surface-plasmon evanescent field of a silver film with a photon scanning tunneling microscope,” Phys. Rev. B 48, 2680–2683 (1993).
[CrossRef]

Sentenac, A.

Sihvola, A. H.

Sommerfeld, A.

A. Sommerfeld, Lectures on Theoretical Physics (Academic, New York, 1964), Vol. 6, Chap. 6; “Ueber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. (Leipzig) 28, 665–695 (1909); “Ueber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. (Leipzig) 81, 1135–1153 (1926).

Soto-Crespo, J. M.

Tran, P.

Tsang, L.

Van Labeke, D.

Videen, G.

Vlieger, J.

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica (Utrecht) 137A, 209–242 (1986); K. Nahm, W. L. Wolfe, “Light scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
[CrossRef] [PubMed]

Wolf, E.

D. N. Pattanayak, E. Wolf, “General form and a new interpretation of the Ewald–Oseen extinction theorem,” Opt. Commun. 6, 217–220 (1972).
[CrossRef]

Xu, X. A.

X. A. Xu, Ch. M. Butler, “Current induced by TE excitation on a conducting cylinder located near the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. AP-34, 880–890 (1986); Ch. M. Butler, X. B. Xu, “TE scattering by partially buried and coupled cylinders at the interface between two media,” IEEE Trans. Antennas Propag. 38, 1829–1834 (1990).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

X. A. Xu, Ch. M. Butler, “Current induced by TE excitation on a conducting cylinder located near the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. AP-34, 880–890 (1986); Ch. M. Butler, X. B. Xu, “TE scattering by partially buried and coupled cylinders at the interface between two media,” IEEE Trans. Antennas Propag. 38, 1829–1834 (1990).
[CrossRef]

Int. J. Electron. (1)

J. D. Kanellopoulos, N. E. Buris, “Scattering from conducting cylinders embedded in a lossy medium,” Int. J. Electron. 57, 391–401 (1984); P. G. Cottis, J. D. Kanellopoulos, “Scattering from a conducting cylinder above a lossy medium,” Int. J. Electron. 65, 1031–1038 (1988); C. N. Vazouras, P. G. Cottis, J. D. Kanellopoulos, “Scattering from a conducting cylinder above a lossy medium of sinusoidal interface,” Radio Sci. 27, 883–892 (1992).
[CrossRef]

J. Opt. (Paris) (1)

D. Maystre, M. Nevière, “Sur une méthode d’ étude théorique quantitative des anomalies de Wood des réseaux de diffraction: application aux anomalies de plasmons,” J. Opt. (Paris) 8, 165–174 (1977).
[CrossRef]

J. Opt. Soc. Am. A (8)

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]

L. Tsang, Ch. H. Chan, K. Pak, “Backscattering enhancement of a two-dimensional random rough surface (three-dimensional scattering) based on Monte Carlo simulations,” J. Opt. Soc. Am. A 11, 711–715 (1994).
[CrossRef]

P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional, randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
[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); “Plane wave scattering by a conducting cylinder partially buried in a ground plane. 2. TE case,” J. Opt. Soc. Am. 8, 1986–1990 (1991); P. J. Valle, F. Gonzalez, F. Moreno, “Electromagnetic wave scattering from conducting cylindrical structures on flat substrates,” Appl. Opt. 33, 512–523 (1994).
[CrossRef] [PubMed]

G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991); “Light scattering from a sphere behind a surface,” J. Opt. Soc. Am. A 10, 110–117 (1993); G. Videen, W. S. Bickel, V. J. Iafelice, D. Abromson, “Experimental light scattering Mueller matrix for a fiber on a reflecting optical surface as a function of incidence angle,” J. Opt. Soc. Am. A 9, 312–315 (1992); 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]

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Figures (12)

Fig. 1
Fig. 1

Scattering geometry.

Fig. 2
Fig. 2

Normalized near-field scattered intensity in arbitrary units (a.u.) at z = 0.25λ for the grating with parameters b = 1.25λ, h = 0.1λ, and 2 = (−17.2, 0.498) for s polarization. Thin curve: a = 0.05λ, 1 = 2.12, d = 10λ; thick curve: a = 0.25λ, 1 = 2.12, d = 0.6λ. The grating profile is shown at the top.

Fig. 3
Fig. 3

Variation of the integrated intensity with the cylinder position moved along z = d for several radii a of the cylinder and cylinder–plane distances d. The cylinder has a dielectric permittivity of 1 = 2.12. The parameters of the grating are b = 1.25λ, h = 0.1λ, and 2 = (−17.2, 0.498). The results are for p polarization at θ0 = 0°. (a) a = 0.5λ, d = 0.8λ, z0 = 0.2λ; (b) a = 0.2λ, d = 0.5λ, z0 = 0.2λ; (c) a = 0.2λ, d = 1λ, z0 = 0.7λ. Solid curves with circles: intensity inside the cylinder and integrated over its diameter; solid curves: scattered intensity outside the cylinder and integrated on a segment of length 2a on a line below it at distance z = z0. (d) Intensity distribution on the plane z = 0.5λ that is due to the grating alone: (1) total, i.e., incident plus scattered, intensity; (2) total intensity integrated on the interval 2a; (3) scattered intensity; (4) scattered intensity integrated on the interval 2a. The grating profile is shown at the top.

Fig. 4
Fig. 4

Total reflected intensity near resonance for the grating alone and the grating in the presence of a cylinder of radius a at distance d = 0.8λ for p polarization. The parameters are b = 0.6λ, h = 0.02λ, and 2 = (−17.2, 0.498). Solid curve: without cylinder; solid curve with circles: a = 0.2λ, 1 = 2.12; dashed curve: a = 0.5λ, 1 = 3.55; dotted curve: a = 0.5λ, 1 = 2.12.

Fig. 5
Fig. 5

Variation of the minimum of the total reflected intensity with the distance d from the cylinder to the grating for several radii of the cylinder and dielectric permittivities for p polarization. The parameters are b = 0.6λ, h = 0.02λ, and 2 = (−17.2, 0.498). (a) 1 = 2.12, (b) 1 = 5, (c) 1 = (−17.2, 0.498).

Fig. 6
Fig. 6

Normalized scattered intensity in a.u. at z = 0.08λ for a plane wave at two angles of incidence for p polarization. The parameters are b = 0.6λ, h = 0.02λ, and 2 = (−17.2, 0.498). (a) Without cylinder, (b) d = 0.8λ, a = 0.5λ, 1 = 2.12, (c) d = 0.8λ, a = 0.1λ, 1 = 2.12. Thick curves: θi = 0°; thin curves: resonant angle of incidence.

Fig. 7
Fig. 7

(a) Scattered near-field intensity (arbitrary units) at z = 0.12λ for a grating with b = 0.6λ, h = 0.02λ, and 2 = (−17.2, 0.498). The incident field is a Gaussian beam with w = 8λ. Solid curve: θi = −39.1°; dotted curve: θi = 0°. (b) Integrated intensity over the interval 2a inside a cylinder with a = 0.1λ and 1 = 2.12 as this cylinder moves with its center on z = d = 0.17λ. The incident wave and the grating are the same as that for the solid curve of (a). The scan has been limited to the interval (−15λ, 45λ). Details of this distribution for x in the interval (10λ, 25λ) are shown at the top.

Fig. 8
Fig. 8

Same as Fig. (4) but for b = 1.25λ and h = 0.1λ.

Fig. 9
Fig. 9

Same as Fig. (5), but for b = 1.25λ and h = 0.1λ: (a) 1 = 2.12, (b) 1 = 5, (c) 1 = (−9.89, 1.05), (d) 1 = (−17.2, 0.498).

Fig. 10
Fig. 10

Same as Fig. (5), but for a = 0.1λ. (a) 1 = 2.12, (b) 1 = (−17.2, 0.498). Solid curves: The center of the cylinder is located along the line x = 0, at which there is a maximum of the grating profile. Dashed curves: The center of the cylinder is located along the line x = (a/2)λ, at which there is a minimum of the grating profile.

Fig. 11
Fig. 11

Near-field scattered intensity in a.u. at z = 0.2λ for a grating with b = 1.25λ, h = 0.1λ, and 2 = (−17.2, 0.498). The incident field is a Gaussian beam with w = 8λ. The results are for d = 0.8λ, 1 = 2.12, and p polarization. (a) a = 0.2λ, (b) a = 0.5λ. Solid curves: θi = 0°, dotted curves: θi = 14.8°.

Fig. 12
Fig. 12

Variation of the near-field intensity inside the cylinder and integrated over its diameter versus the distance d from the cylinder to the grating. The parameters are b = 1.25λ, h = 0.1λ, 2 = (−17.2, 0.498), and 1 = 2.12. Solid curve: a = 0.5λ; solid line with asterisks: a = 0.2λ; solid curve with circles: a = 0.1λ; solid curve with triangles: a = 0.05λ.

Equations (25)

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E ( i ) ( r ) = E ( i ) exp [ i ( K 0 x - q 0 z ) ] j ^             for s polarization ,
H ( i ) ( r ) = H ( i ) exp [ i ( K 0 x - q 0 z ) ] j ^             for p polarization ,
E ( 0 ) ( r ) = E ( i ) ( r ) + 1 4 π C d s [ G 0 ( r , r ) n E ( 1 ) ( r ) - G 0 ( r , r ) E ( 1 ) ( r ) n ] + 1 4 π D d s [ G 0 ( r , r ) n E ( 2 ) ( r ) - G 0 ( r , r ) E ( 2 ) ( r ) n ] ,
E ( 1 ) ( r ) = - 1 4 π C d s [ G 1 ( r , r ) n E ( 1 ) ( r ) - G 1 ( r , r ) E ( 1 ) ( r ) n ] ,
E ( 2 ) ( r ) = - 1 4 π D d s [ G 2 ( r , r ) n E ( 2 ) ( r ) - G 2 ( r , r ) E ( 2 ) ( r ) n ] .
G 0 ( r , r ) = π i H 0 ( 1 ) ( k 0 r - r ) , G 1 ( r , r ) = π i H 0 ( 1 ) ( 1 k 0 r - r ) , G 2 ( r , r ) = π i H 0 ( 1 ) ( 2 k 0 r - r ) ,
E ( 1 ) ( r ) = E ( i ) ( r ) + i 4 C d s [ H 0 ( 1 ) ( k 0 r - r ) n E ( 1 ) ( r ) - H 0 ( 1 ) ( k 0 r - r ) E ( 1 ) ( r ) n ] + i 4 D d s [ H 0 ( 1 ) ( k 0 r - r ) n E ( 2 ) ( r ) - H 0 ( 1 ) ( k 0 r - r ) E ( 2 ) ( r ) n ] ,
0 = - i 4 C d s [ H 0 ( 1 ) ( 1 k 0 r - r ) n E ( 1 ) ( r ) - H 0 ( 1 ) ( 1 k 0 r - r ) E ( 1 ) ( r ) n ] ,
r = ( a sin α , d - a cos α ) ,
r = [ x , D ( x ) ] .
E ( 2 ) ( r ) = E ( i ) ( r ) + i 4 C d s [ H 0 ( 1 ) ( k 0 r - r ) n E ( 1 ) ( r ) - H 0 ( 1 ) ( k 0 r - r ) E ( 1 ) ( r ) n ] + i 4 D d s [ H 0 ( 1 ) ( k 0 r - r ) n E ( 2 ) ( r ) - H 0 ( 1 ) ( k 0 r - r ) E ( 2 ) ( r ) n ] ,
0 = - i 4 D d s [ H 0 ( 1 ) ( 2 k 0 r - r ) n E ( 2 ) ( r ) - H 0 ( 1 ) ( 2 k 0 r - r ) E ( 2 ) ( r ) n ] .
E ( r ) ( r > , θ r ) = exp [ i ( k 0 r > - π / 4 ) ] ( 8 π k 0 r > ) 1 / 2 C d s × [ ( n · k r ) E ( 1 ) ( r ) - i E ( 1 ) ( r ) n ] × exp ( - i k r · r ) + D d s [ ( n · k r ) E ( 2 ) ( r ) - i E ( 2 ) ( r ) n ] × exp ( - i k r · r )
E ( t ) ( r < , θ t ) = exp [ i ( 2 k 0 r < - π / 4 ) ] ( 8 π 2 k 0 r < ) 1 / 2 D d s × [ ( n · k t ) E ( 2 ) ( r ) - i E ( 2 ) ( r ) n ] × exp ( - i k t · r )
k r = k 0 ( sin θ r , cos θ r ) , k t = 2 k 0 ( sin θ t , - cos θ t ) ,
n = { ( sin α , - cos α ) if r belongs to C [ - D ( x ) , 1 ] 1 + [ D ( x ) ] 2 if r belongs to D .
H ( 0 ) ( r ) = H ( i ) ( r ) + 1 4 π C d s [ G 0 ( r , r ) n H ( 1 ) ( r ) - G 0 ( r , r ) H ( 1 ) ( r ) n ] + 1 4 π D d s [ G 0 ( r , r ) n H ( 2 ) ( r ) - G 0 ( r , r ) H ( 2 ) ( r ) n ] ,
H ( 1 ) ( r ) = - 1 4 π C d s [ G 1 ( r , r ) n H ( 1 ) ( r ) - G 1 ( r , r ) H ( 1 ) ( r ) n ] ,
H ( 2 ) ( r ) = - 1 4 π D d s [ G 2 ( r , r ) n H ( 2 ) ( r ) - G 2 ( r , r ) h ( 2 ) ( r ) n ] ,
H ( 1 ) ( r ) = H ( i ) ( r ) + i 4 C d s [ H 0 ( 1 ) ( k 0 r - r ) n H ( 1 ) ( r ) - H 0 ( 1 ) ( k 0 r - r ) H ( 1 ) ( r ) n ] + i 4 D d s [ H 0 ( 1 ) ( k 0 r - r ) n H ( 2 ) ( r ) - H 0 ( 1 ) ( k 0 r - r ) H ( 2 ) ( r ) n ] ,
0 = - i 4 C d s [ H 0 ( 1 ) ( 1 k 0 r - r ) n H ( 1 ) ( r ) - 1 H 0 ( 1 ) ( 1 k 0 r - r H ( 1 ) ( r ) n ] .
H ( 2 ) ( r ) = H ( i ) ( r ) + i 4 C d s [ H 0 ( 1 ) ( k 0 r - r ) n H ( 1 ) ( r ) - H 0 ( 1 ) ( k 0 r - r ) H ( 1 ) ( r ) n ] + i 4 D d s [ H 0 ( 1 ) ( k 0 r - r ) n H ( 2 ) ( r ) - H 0 ( 1 ) ( k 0 r - r ) H ( 2 ) ( r ) n ] ,
0 = - i 4 C d s [ H 0 ( 1 ) ( 2 k 0 r - r ) n H ( 2 ) ( r ) - 2 H 0 ( 1 ) ( 2 k 0 r - r ) H ( 2 ) ( r ) n ] .
H ( r ) ( r > , θ r ) = exp [ i ( k 0 r > - π / 4 ) ] ( 8 π k 0 r > ) 1 / 2 C d s × [ ( n · k r ) H ( 1 ) ( r ) - i H ( 1 ) ( r ) n ] × exp ( - i k r · r ) + D d s [ ( n · k r ) H ( 2 ) ( r ) - i H ( 2 ) ( r ) n ] × exp ( - i k r · r ) ,
H ( t ) ( r < , θ t ) = exp [ i ( 2 k 0 r < - π / 4 ) ] ( 8 π 2 k 0 r < ) 1 / 2 D d s × [ ( n · k t ) H ( 2 ) ( r ) - i 2 H ( 2 ) ( r ) n ] × exp ( - i k t · r ) .

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