Abstract

Diffraction of an optical field by an aperture in a thick metallic screen is analyzed numerically by use of a three-dimensional volume integral equation together with a generalized conjugate residual method and fast Fourier transformation. Numerical results were validated by reciprocity and the independence of the results of the truncated discretized volume size used in numerical calculations. Near and far fields of square, circular, and triangular apertures in a thick screen are obtained numerically. Some of the numerical results obtained in the present study agree with previously reported experimental results. The surface plasmon polaritons excited on the sidewalls of the aperture can explain the basic characteristics of near-field distribution of apertures. The Bethe–Bouwkamp theory was found to be insufficient to explain the basic characteristics of the near field around the subwavelength aperture in a practical metallic screen.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1993).
    [CrossRef] [PubMed]
  2. E. H. Synge, “A suggested method for extending microscopic resolution into the ultra-microscopic region,” Philos. Mag. 6, 356–362 (1928).
  3. D. W. Pohl, D. Courjon, eds., Near-Field Optics (Kluwer Academic, Dordrecht, The Netherlands, 1993).
    [CrossRef]
  4. M. Ohtsu, H. Hori, Near-Field Nano-Optics (Kluwer Academic, Dordrecht, The Netherlands, 1999).
    [CrossRef]
  5. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
    [CrossRef]
  6. C. J. Bouwkamp, “On the diffraction of electromagnetic waves by small circular disks and holes,” Philips Res. Rep. 5, 401–422 (1950).
  7. H. Levine, J. Schwinger, “On the theory of diffraction by an aperture in an infinite plane screen. I,” Phys. Rev. 74, 958–974 (1948).
    [CrossRef]
  8. Y. Leviatan, R. F. Harrington, J. R. Mautz, “Electromagnetic transmission through apertures in a cavity in a thick conductor,” IEEE Trans. Antennas Propag. AP-30, 1153–1165 (1982).
    [CrossRef]
  9. Y. Leviatan, “Study of near-zone fields of a small aperture,” J. Appl. Phys. 60, 1577–1583 (1986).
    [CrossRef]
  10. C. M. Butler, Y. Rahmat-Samii, R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,” IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
    [CrossRef]
  11. R. E. English, N. George, “Diffraction from a small square aperture: approximate aperture fields,” J. Opt. Soc. Am. A 5, 192–199 (1988).
    [CrossRef]
  12. A. Roberts, “Near-zone fields behind circular apertures in thick, perfectly conducting screens,” J. Appl. Phys. 65, 2896–2899 (1989).
    [CrossRef]
  13. A. Roberts, “Small-hole coupling of radiation into a near-field probe,” J. Appl. Phys. 70, 4045–4049 (1991).
    [CrossRef]
  14. H. Furukawa, S. Kawata, “Analysis of image formation in a near-field scanning optical microscope: effects of multiple scattering,” Opt. Commun. 132, 170–178 (1996).
    [CrossRef]
  15. R. Chang, P-K. Wei, W. S. Fann, M. Hayashi, S. H. Lin, “Theoretical investigation of near-field optical properties of tapered fiber tips and single molecule fluorescence,” J. Appl. Phys. 81, 3369–3376 (1997).
    [CrossRef]
  16. A. Chavez-Pirson, S. K. Chu, “A full vector analysis of near-field luminescence probing of a single quantum dot,” Appl. Phys. Lett. 74, 1507–1509 (1999).
    [CrossRef]
  17. O. J. F. Martin, “3D simulations of the experimental signal measured in near-field optical microscopy,” J. Microsc. (Oxford) 194, 235–239 (1999).
    [CrossRef]
  18. D. J. Shin, A. Chavez-Pirson, S. H. Kim, S. T. Jung, Y. H. Lee, “Diffraction by a subwavelength-sized aperture in a metal plane,” J. Opt. Soc. Am. A 18, 1477–1486 (2001).
    [CrossRef]
  19. C. Obermüller, K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
    [CrossRef]
  20. D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. (Oxford) 194, 353–359 (1999).
    [CrossRef]
  21. A. Liu, A. Rahmani, G. W. Bryant, L. J. Richter, S. Stranick, “Modeling illumination-mode near-field optical microscopy of Au nanoparticles,” J. Opt. Soc. Am. A 18, 704–716 (2001).
    [CrossRef]
  22. O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
    [CrossRef] [PubMed]
  23. D. Barchiesi, C. Girard, O. J. F. Martin, D. Van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
    [CrossRef]
  24. O. J. F. Martin, C. Girard, A. Dereux, “Dielectric versus topographic contrast in near-field microscopy,” J. Opt. Soc. Am. A 13, 1801–1808 (1996).
    [CrossRef]
  25. O. J. F. Martin, C. Girard, “Controlling and tuning strong optical field gradients at a local probe microscope tip apex,” Appl. Phys. Lett. 70, 705–707 (1997).
    [CrossRef]
  26. C. Girard, J.-C. Weeber, A. Dereux, O. J. F. Martin, J.-P. Goudonnet, “Optical magnetic near-field intensities around nanometer-scale surface structures,” Phys. Rev. B 55, 16487–16497 (1997).
    [CrossRef]
  27. K. Kobayashi, O. Watanuki, “Characteristics of photon scanning tunneling microscope read-out,” J. Vac. Sci. Technol. B 14, 804–808 (1996).
    [CrossRef]
  28. K. Kobayashi, O. Watanuki, “Polarization-dependent contrast in near-field optical microscopy,” J. Vac. Sci. Technol. B 15, 1966–1970 (1997).
    [CrossRef]
  29. K. Tanaka, M. Yan, M. Tanaka, “A simulation of near-field optics by three-dimensional volume integral equation of classical electromagnetic theory,” Opt. Rev. 8, 43–53 (2001).
    [CrossRef]
  30. K. Tanaka, M. Yan, M. Tanaka, “Simulated output images of near-field optics by volume integral equation: object placed on the dielectric substrate,” Opt. Rev. 9, 213–221 (2002).
    [CrossRef]
  31. E. K. Miller, L. Medgyesi-Mitschang, E. H. Newman, Computational Electromagnetics: Frequency-Domain Method of Moments (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1992).
  32. J. H. Wang, Generalized Moment Method in Electromagnetics: Formulation and Computer Solution of Integral Equations (Wiley, New York, 1991).
  33. J. Van Bladel, “Some remarks on Green’s dyadic for infinite space,” IEEE Trans. Antennas Propag. AP-9, 563–566 (1961).
  34. A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263 (1980).
    [CrossRef]
  35. J. J. H. Wang, J. R. Dubberley, “Computation of fields in an arbitrary shaped heterogeneous dielectric or biological body by an iterative conjugate gradient method,” IEEE Trans. Microwave Theory Tech. 37, 1119–1125 (1989).
    [CrossRef]
  36. C.-C. Su, “Electromagnetic scattering by a dielectric body with arbitrary inhomogeneity and anisotropy,” IEEE Trans. Antennas Propag. AP-37, 384–389 (1989).
    [CrossRef]
  37. C.-C. Su, “The three-dimensional algorithm of solving the electric field integral equation using face-centered node points, conjugate gradient method, and FFT,” IEEE Trans. Microwave Theory Tech. 41, 510–515 (1993).
    [CrossRef]
  38. R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
    [CrossRef]
  39. A. B. Samokhin, “Integral equations of the electrodynamics for three-dimensional structure and iterative method of solving them,” J. Commun. Technol. Electron. 38, 15–34 (1993).
  40. D. Molenda, C. Höppener, H. Fuchs, A. Naber, Physics Institute, University of Münster, Wilhelm-Klemen Strasse 10, D-48149 Münster, Germany (personal communication, 2002).
  41. C. Höppener, D. Molenda, H. Fuchs, A. Naber, “Simultaneous topographical and optical characterization of near-field optical aperture probes by way of imaging fluorescent nanospheres,” Appl. Phys. Lett. 80, 1331–1333 (2002).
    [CrossRef]
  42. A. Naber, D. Molenda, U. C. Fischer, H.-J. Maas, C. Höppener, N. Lu, H. Fuchs, “Enhanced light confinement in a near-field optical probe with a triangular aperture,” Phys. Rev. Lett. 89, 210801 (2002).
    [CrossRef] [PubMed]
  43. A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, New York, 1982).
  44. K. Tanaka, M. Tanaka, “Simulation of an aperture in the thick metallic screen that gives high intensity and small spot size using surface plasmon polariton,” J. Microsc. (Oxford) 210, 294–300 (2003).
    [CrossRef]

2003 (1)

K. Tanaka, M. Tanaka, “Simulation of an aperture in the thick metallic screen that gives high intensity and small spot size using surface plasmon polariton,” J. Microsc. (Oxford) 210, 294–300 (2003).
[CrossRef]

2002 (3)

C. Höppener, D. Molenda, H. Fuchs, A. Naber, “Simultaneous topographical and optical characterization of near-field optical aperture probes by way of imaging fluorescent nanospheres,” Appl. Phys. Lett. 80, 1331–1333 (2002).
[CrossRef]

A. Naber, D. Molenda, U. C. Fischer, H.-J. Maas, C. Höppener, N. Lu, H. Fuchs, “Enhanced light confinement in a near-field optical probe with a triangular aperture,” Phys. Rev. Lett. 89, 210801 (2002).
[CrossRef] [PubMed]

K. Tanaka, M. Yan, M. Tanaka, “Simulated output images of near-field optics by volume integral equation: object placed on the dielectric substrate,” Opt. Rev. 9, 213–221 (2002).
[CrossRef]

2001 (3)

1999 (3)

A. Chavez-Pirson, S. K. Chu, “A full vector analysis of near-field luminescence probing of a single quantum dot,” Appl. Phys. Lett. 74, 1507–1509 (1999).
[CrossRef]

O. J. F. Martin, “3D simulations of the experimental signal measured in near-field optical microscopy,” J. Microsc. (Oxford) 194, 235–239 (1999).
[CrossRef]

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. (Oxford) 194, 353–359 (1999).
[CrossRef]

1997 (4)

R. Chang, P-K. Wei, W. S. Fann, M. Hayashi, S. H. Lin, “Theoretical investigation of near-field optical properties of tapered fiber tips and single molecule fluorescence,” J. Appl. Phys. 81, 3369–3376 (1997).
[CrossRef]

O. J. F. Martin, C. Girard, “Controlling and tuning strong optical field gradients at a local probe microscope tip apex,” Appl. Phys. Lett. 70, 705–707 (1997).
[CrossRef]

C. Girard, J.-C. Weeber, A. Dereux, O. J. F. Martin, J.-P. Goudonnet, “Optical magnetic near-field intensities around nanometer-scale surface structures,” Phys. Rev. B 55, 16487–16497 (1997).
[CrossRef]

K. Kobayashi, O. Watanuki, “Polarization-dependent contrast in near-field optical microscopy,” J. Vac. Sci. Technol. B 15, 1966–1970 (1997).
[CrossRef]

1996 (4)

K. Kobayashi, O. Watanuki, “Characteristics of photon scanning tunneling microscope read-out,” J. Vac. Sci. Technol. B 14, 804–808 (1996).
[CrossRef]

D. Barchiesi, C. Girard, O. J. F. Martin, D. Van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

O. J. F. Martin, C. Girard, A. Dereux, “Dielectric versus topographic contrast in near-field microscopy,” J. Opt. Soc. Am. A 13, 1801–1808 (1996).
[CrossRef]

H. Furukawa, S. Kawata, “Analysis of image formation in a near-field scanning optical microscope: effects of multiple scattering,” Opt. Commun. 132, 170–178 (1996).
[CrossRef]

1995 (2)

C. Obermüller, K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[CrossRef]

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

1993 (3)

C.-C. Su, “The three-dimensional algorithm of solving the electric field integral equation using face-centered node points, conjugate gradient method, and FFT,” IEEE Trans. Microwave Theory Tech. 41, 510–515 (1993).
[CrossRef]

A. B. Samokhin, “Integral equations of the electrodynamics for three-dimensional structure and iterative method of solving them,” J. Commun. Technol. Electron. 38, 15–34 (1993).

E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1993).
[CrossRef] [PubMed]

1991 (1)

A. Roberts, “Small-hole coupling of radiation into a near-field probe,” J. Appl. Phys. 70, 4045–4049 (1991).
[CrossRef]

1989 (3)

A. Roberts, “Near-zone fields behind circular apertures in thick, perfectly conducting screens,” J. Appl. Phys. 65, 2896–2899 (1989).
[CrossRef]

J. J. H. Wang, J. R. Dubberley, “Computation of fields in an arbitrary shaped heterogeneous dielectric or biological body by an iterative conjugate gradient method,” IEEE Trans. Microwave Theory Tech. 37, 1119–1125 (1989).
[CrossRef]

C.-C. Su, “Electromagnetic scattering by a dielectric body with arbitrary inhomogeneity and anisotropy,” IEEE Trans. Antennas Propag. AP-37, 384–389 (1989).
[CrossRef]

1988 (1)

1986 (1)

Y. Leviatan, “Study of near-zone fields of a small aperture,” J. Appl. Phys. 60, 1577–1583 (1986).
[CrossRef]

1982 (1)

Y. Leviatan, R. F. Harrington, J. R. Mautz, “Electromagnetic transmission through apertures in a cavity in a thick conductor,” IEEE Trans. Antennas Propag. AP-30, 1153–1165 (1982).
[CrossRef]

1980 (1)

A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263 (1980).
[CrossRef]

1978 (1)

C. M. Butler, Y. Rahmat-Samii, R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,” IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
[CrossRef]

1961 (1)

J. Van Bladel, “Some remarks on Green’s dyadic for infinite space,” IEEE Trans. Antennas Propag. AP-9, 563–566 (1961).

1950 (1)

C. J. Bouwkamp, “On the diffraction of electromagnetic waves by small circular disks and holes,” Philips Res. Rep. 5, 401–422 (1950).

1948 (1)

H. Levine, J. Schwinger, “On the theory of diffraction by an aperture in an infinite plane screen. I,” Phys. Rev. 74, 958–974 (1948).
[CrossRef]

1944 (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

1928 (1)

E. H. Synge, “A suggested method for extending microscopic resolution into the ultra-microscopic region,” Philos. Mag. 6, 356–362 (1928).

Barchiesi, D.

D. Barchiesi, C. Girard, O. J. F. Martin, D. Van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

Barrett, R.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
[CrossRef]

Berry, M.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
[CrossRef]

Bethe, H. A.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Betzig, E.

E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1993).
[CrossRef] [PubMed]

Bouwkamp, C. J.

C. J. Bouwkamp, “On the diffraction of electromagnetic waves by small circular disks and holes,” Philips Res. Rep. 5, 401–422 (1950).

Bryant, G. W.

Butler, C. M.

C. M. Butler, Y. Rahmat-Samii, R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,” IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
[CrossRef]

Chan, T. F.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
[CrossRef]

Chang, R.

R. Chang, P-K. Wei, W. S. Fann, M. Hayashi, S. H. Lin, “Theoretical investigation of near-field optical properties of tapered fiber tips and single molecule fluorescence,” J. Appl. Phys. 81, 3369–3376 (1997).
[CrossRef]

Chavez-Pirson, A.

D. J. Shin, A. Chavez-Pirson, S. H. Kim, S. T. Jung, Y. H. Lee, “Diffraction by a subwavelength-sized aperture in a metal plane,” J. Opt. Soc. Am. A 18, 1477–1486 (2001).
[CrossRef]

A. Chavez-Pirson, S. K. Chu, “A full vector analysis of near-field luminescence probing of a single quantum dot,” Appl. Phys. Lett. 74, 1507–1509 (1999).
[CrossRef]

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. (Oxford) 194, 353–359 (1999).
[CrossRef]

Chichester, R. J.

E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1993).
[CrossRef] [PubMed]

Chu, S. K.

A. Chavez-Pirson, S. K. Chu, “A full vector analysis of near-field luminescence probing of a single quantum dot,” Appl. Phys. Lett. 74, 1507–1509 (1999).
[CrossRef]

Courjon, D.

D. Barchiesi, C. Girard, O. J. F. Martin, D. Van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

Demmel, J.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
[CrossRef]

Dereux, A.

C. Girard, J.-C. Weeber, A. Dereux, O. J. F. Martin, J.-P. Goudonnet, “Optical magnetic near-field intensities around nanometer-scale surface structures,” Phys. Rev. B 55, 16487–16497 (1997).
[CrossRef]

O. J. F. Martin, C. Girard, A. Dereux, “Dielectric versus topographic contrast in near-field microscopy,” J. Opt. Soc. Am. A 13, 1801–1808 (1996).
[CrossRef]

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

Donato, J.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
[CrossRef]

Dongarra, J.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
[CrossRef]

Dubberley, J. R.

J. J. H. Wang, J. R. Dubberley, “Computation of fields in an arbitrary shaped heterogeneous dielectric or biological body by an iterative conjugate gradient method,” IEEE Trans. Microwave Theory Tech. 37, 1119–1125 (1989).
[CrossRef]

Eijkhout, V.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
[CrossRef]

English, R. E.

Fann, W. S.

R. Chang, P-K. Wei, W. S. Fann, M. Hayashi, S. H. Lin, “Theoretical investigation of near-field optical properties of tapered fiber tips and single molecule fluorescence,” J. Appl. Phys. 81, 3369–3376 (1997).
[CrossRef]

Fischer, U. C.

A. Naber, D. Molenda, U. C. Fischer, H.-J. Maas, C. Höppener, N. Lu, H. Fuchs, “Enhanced light confinement in a near-field optical probe with a triangular aperture,” Phys. Rev. Lett. 89, 210801 (2002).
[CrossRef] [PubMed]

Fuchs, H.

C. Höppener, D. Molenda, H. Fuchs, A. Naber, “Simultaneous topographical and optical characterization of near-field optical aperture probes by way of imaging fluorescent nanospheres,” Appl. Phys. Lett. 80, 1331–1333 (2002).
[CrossRef]

A. Naber, D. Molenda, U. C. Fischer, H.-J. Maas, C. Höppener, N. Lu, H. Fuchs, “Enhanced light confinement in a near-field optical probe with a triangular aperture,” Phys. Rev. Lett. 89, 210801 (2002).
[CrossRef] [PubMed]

D. Molenda, C. Höppener, H. Fuchs, A. Naber, Physics Institute, University of Münster, Wilhelm-Klemen Strasse 10, D-48149 Münster, Germany (personal communication, 2002).

Furukawa, H.

H. Furukawa, S. Kawata, “Analysis of image formation in a near-field scanning optical microscope: effects of multiple scattering,” Opt. Commun. 132, 170–178 (1996).
[CrossRef]

George, N.

Girard, C.

O. J. F. Martin, C. Girard, “Controlling and tuning strong optical field gradients at a local probe microscope tip apex,” Appl. Phys. Lett. 70, 705–707 (1997).
[CrossRef]

C. Girard, J.-C. Weeber, A. Dereux, O. J. F. Martin, J.-P. Goudonnet, “Optical magnetic near-field intensities around nanometer-scale surface structures,” Phys. Rev. B 55, 16487–16497 (1997).
[CrossRef]

O. J. F. Martin, C. Girard, A. Dereux, “Dielectric versus topographic contrast in near-field microscopy,” J. Opt. Soc. Am. A 13, 1801–1808 (1996).
[CrossRef]

D. Barchiesi, C. Girard, O. J. F. Martin, D. Van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

Goudonnet, J.-P.

C. Girard, J.-C. Weeber, A. Dereux, O. J. F. Martin, J.-P. Goudonnet, “Optical magnetic near-field intensities around nanometer-scale surface structures,” Phys. Rev. B 55, 16487–16497 (1997).
[CrossRef]

Harrington, R. F.

Y. Leviatan, R. F. Harrington, J. R. Mautz, “Electromagnetic transmission through apertures in a cavity in a thick conductor,” IEEE Trans. Antennas Propag. AP-30, 1153–1165 (1982).
[CrossRef]

Hayashi, M.

R. Chang, P-K. Wei, W. S. Fann, M. Hayashi, S. H. Lin, “Theoretical investigation of near-field optical properties of tapered fiber tips and single molecule fluorescence,” J. Appl. Phys. 81, 3369–3376 (1997).
[CrossRef]

Höppener, C.

C. Höppener, D. Molenda, H. Fuchs, A. Naber, “Simultaneous topographical and optical characterization of near-field optical aperture probes by way of imaging fluorescent nanospheres,” Appl. Phys. Lett. 80, 1331–1333 (2002).
[CrossRef]

A. Naber, D. Molenda, U. C. Fischer, H.-J. Maas, C. Höppener, N. Lu, H. Fuchs, “Enhanced light confinement in a near-field optical probe with a triangular aperture,” Phys. Rev. Lett. 89, 210801 (2002).
[CrossRef] [PubMed]

D. Molenda, C. Höppener, H. Fuchs, A. Naber, Physics Institute, University of Münster, Wilhelm-Klemen Strasse 10, D-48149 Münster, Germany (personal communication, 2002).

Hori, H.

M. Ohtsu, H. Hori, Near-Field Nano-Optics (Kluwer Academic, Dordrecht, The Netherlands, 1999).
[CrossRef]

Jung, S. T.

Karrai, K.

C. Obermüller, K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[CrossRef]

Kawata, S.

H. Furukawa, S. Kawata, “Analysis of image formation in a near-field scanning optical microscope: effects of multiple scattering,” Opt. Commun. 132, 170–178 (1996).
[CrossRef]

Kim, S. H.

Kobayashi, K.

K. Kobayashi, O. Watanuki, “Polarization-dependent contrast in near-field optical microscopy,” J. Vac. Sci. Technol. B 15, 1966–1970 (1997).
[CrossRef]

K. Kobayashi, O. Watanuki, “Characteristics of photon scanning tunneling microscope read-out,” J. Vac. Sci. Technol. B 14, 804–808 (1996).
[CrossRef]

Lee, Y. H.

D. J. Shin, A. Chavez-Pirson, S. H. Kim, S. T. Jung, Y. H. Lee, “Diffraction by a subwavelength-sized aperture in a metal plane,” J. Opt. Soc. Am. A 18, 1477–1486 (2001).
[CrossRef]

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. (Oxford) 194, 353–359 (1999).
[CrossRef]

Leviatan, Y.

Y. Leviatan, “Study of near-zone fields of a small aperture,” J. Appl. Phys. 60, 1577–1583 (1986).
[CrossRef]

Y. Leviatan, R. F. Harrington, J. R. Mautz, “Electromagnetic transmission through apertures in a cavity in a thick conductor,” IEEE Trans. Antennas Propag. AP-30, 1153–1165 (1982).
[CrossRef]

Levine, H.

H. Levine, J. Schwinger, “On the theory of diffraction by an aperture in an infinite plane screen. I,” Phys. Rev. 74, 958–974 (1948).
[CrossRef]

Lin, S. H.

R. Chang, P-K. Wei, W. S. Fann, M. Hayashi, S. H. Lin, “Theoretical investigation of near-field optical properties of tapered fiber tips and single molecule fluorescence,” J. Appl. Phys. 81, 3369–3376 (1997).
[CrossRef]

Liu, A.

Lu, N.

A. Naber, D. Molenda, U. C. Fischer, H.-J. Maas, C. Höppener, N. Lu, H. Fuchs, “Enhanced light confinement in a near-field optical probe with a triangular aperture,” Phys. Rev. Lett. 89, 210801 (2002).
[CrossRef] [PubMed]

Maas, H.-J.

A. Naber, D. Molenda, U. C. Fischer, H.-J. Maas, C. Höppener, N. Lu, H. Fuchs, “Enhanced light confinement in a near-field optical probe with a triangular aperture,” Phys. Rev. Lett. 89, 210801 (2002).
[CrossRef] [PubMed]

Martin, O. J. F.

O. J. F. Martin, “3D simulations of the experimental signal measured in near-field optical microscopy,” J. Microsc. (Oxford) 194, 235–239 (1999).
[CrossRef]

O. J. F. Martin, C. Girard, “Controlling and tuning strong optical field gradients at a local probe microscope tip apex,” Appl. Phys. Lett. 70, 705–707 (1997).
[CrossRef]

C. Girard, J.-C. Weeber, A. Dereux, O. J. F. Martin, J.-P. Goudonnet, “Optical magnetic near-field intensities around nanometer-scale surface structures,” Phys. Rev. B 55, 16487–16497 (1997).
[CrossRef]

O. J. F. Martin, C. Girard, A. Dereux, “Dielectric versus topographic contrast in near-field microscopy,” J. Opt. Soc. Am. A 13, 1801–1808 (1996).
[CrossRef]

D. Barchiesi, C. Girard, O. J. F. Martin, D. Van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

Mautz, J. R.

Y. Leviatan, R. F. Harrington, J. R. Mautz, “Electromagnetic transmission through apertures in a cavity in a thick conductor,” IEEE Trans. Antennas Propag. AP-30, 1153–1165 (1982).
[CrossRef]

Medgyesi-Mitschang, L.

E. K. Miller, L. Medgyesi-Mitschang, E. H. Newman, Computational Electromagnetics: Frequency-Domain Method of Moments (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1992).

Miller, E. K.

E. K. Miller, L. Medgyesi-Mitschang, E. H. Newman, Computational Electromagnetics: Frequency-Domain Method of Moments (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1992).

Mittra, R.

C. M. Butler, Y. Rahmat-Samii, R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,” IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
[CrossRef]

Molenda, D.

C. Höppener, D. Molenda, H. Fuchs, A. Naber, “Simultaneous topographical and optical characterization of near-field optical aperture probes by way of imaging fluorescent nanospheres,” Appl. Phys. Lett. 80, 1331–1333 (2002).
[CrossRef]

A. Naber, D. Molenda, U. C. Fischer, H.-J. Maas, C. Höppener, N. Lu, H. Fuchs, “Enhanced light confinement in a near-field optical probe with a triangular aperture,” Phys. Rev. Lett. 89, 210801 (2002).
[CrossRef] [PubMed]

D. Molenda, C. Höppener, H. Fuchs, A. Naber, Physics Institute, University of Münster, Wilhelm-Klemen Strasse 10, D-48149 Münster, Germany (personal communication, 2002).

Naber, A.

C. Höppener, D. Molenda, H. Fuchs, A. Naber, “Simultaneous topographical and optical characterization of near-field optical aperture probes by way of imaging fluorescent nanospheres,” Appl. Phys. Lett. 80, 1331–1333 (2002).
[CrossRef]

A. Naber, D. Molenda, U. C. Fischer, H.-J. Maas, C. Höppener, N. Lu, H. Fuchs, “Enhanced light confinement in a near-field optical probe with a triangular aperture,” Phys. Rev. Lett. 89, 210801 (2002).
[CrossRef] [PubMed]

D. Molenda, C. Höppener, H. Fuchs, A. Naber, Physics Institute, University of Münster, Wilhelm-Klemen Strasse 10, D-48149 Münster, Germany (personal communication, 2002).

Newman, E. H.

E. K. Miller, L. Medgyesi-Mitschang, E. H. Newman, Computational Electromagnetics: Frequency-Domain Method of Moments (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1992).

Obermüller, C.

C. Obermüller, K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[CrossRef]

Ohtsu, M.

M. Ohtsu, H. Hori, Near-Field Nano-Optics (Kluwer Academic, Dordrecht, The Netherlands, 1999).
[CrossRef]

Pozo, R.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
[CrossRef]

Rahmani, A.

Rahmat-Samii, Y.

C. M. Butler, Y. Rahmat-Samii, R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,” IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
[CrossRef]

Richter, L. J.

Roberts, A.

A. Roberts, “Small-hole coupling of radiation into a near-field probe,” J. Appl. Phys. 70, 4045–4049 (1991).
[CrossRef]

A. Roberts, “Near-zone fields behind circular apertures in thick, perfectly conducting screens,” J. Appl. Phys. 65, 2896–2899 (1989).
[CrossRef]

Romine, C.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
[CrossRef]

Samokhin, A. B.

A. B. Samokhin, “Integral equations of the electrodynamics for three-dimensional structure and iterative method of solving them,” J. Commun. Technol. Electron. 38, 15–34 (1993).

Schwinger, J.

H. Levine, J. Schwinger, “On the theory of diffraction by an aperture in an infinite plane screen. I,” Phys. Rev. 74, 958–974 (1948).
[CrossRef]

Shin, D. J.

D. J. Shin, A. Chavez-Pirson, S. H. Kim, S. T. Jung, Y. H. Lee, “Diffraction by a subwavelength-sized aperture in a metal plane,” J. Opt. Soc. Am. A 18, 1477–1486 (2001).
[CrossRef]

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. (Oxford) 194, 353–359 (1999).
[CrossRef]

Stranick, S.

Su, C.-C.

C.-C. Su, “The three-dimensional algorithm of solving the electric field integral equation using face-centered node points, conjugate gradient method, and FFT,” IEEE Trans. Microwave Theory Tech. 41, 510–515 (1993).
[CrossRef]

C.-C. Su, “Electromagnetic scattering by a dielectric body with arbitrary inhomogeneity and anisotropy,” IEEE Trans. Antennas Propag. AP-37, 384–389 (1989).
[CrossRef]

Synge, E. H.

E. H. Synge, “A suggested method for extending microscopic resolution into the ultra-microscopic region,” Philos. Mag. 6, 356–362 (1928).

Tanaka, K.

K. Tanaka, M. Tanaka, “Simulation of an aperture in the thick metallic screen that gives high intensity and small spot size using surface plasmon polariton,” J. Microsc. (Oxford) 210, 294–300 (2003).
[CrossRef]

K. Tanaka, M. Yan, M. Tanaka, “Simulated output images of near-field optics by volume integral equation: object placed on the dielectric substrate,” Opt. Rev. 9, 213–221 (2002).
[CrossRef]

K. Tanaka, M. Yan, M. Tanaka, “A simulation of near-field optics by three-dimensional volume integral equation of classical electromagnetic theory,” Opt. Rev. 8, 43–53 (2001).
[CrossRef]

Tanaka, M.

K. Tanaka, M. Tanaka, “Simulation of an aperture in the thick metallic screen that gives high intensity and small spot size using surface plasmon polariton,” J. Microsc. (Oxford) 210, 294–300 (2003).
[CrossRef]

K. Tanaka, M. Yan, M. Tanaka, “Simulated output images of near-field optics by volume integral equation: object placed on the dielectric substrate,” Opt. Rev. 9, 213–221 (2002).
[CrossRef]

K. Tanaka, M. Yan, M. Tanaka, “A simulation of near-field optics by three-dimensional volume integral equation of classical electromagnetic theory,” Opt. Rev. 8, 43–53 (2001).
[CrossRef]

Van Bladel, J.

J. Van Bladel, “Some remarks on Green’s dyadic for infinite space,” IEEE Trans. Antennas Propag. AP-9, 563–566 (1961).

van der Vorst, H.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
[CrossRef]

Van Labeke, D.

D. Barchiesi, C. Girard, O. J. F. Martin, D. Van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

Wang, J. H.

J. H. Wang, Generalized Moment Method in Electromagnetics: Formulation and Computer Solution of Integral Equations (Wiley, New York, 1991).

Wang, J. J. H.

J. J. H. Wang, J. R. Dubberley, “Computation of fields in an arbitrary shaped heterogeneous dielectric or biological body by an iterative conjugate gradient method,” IEEE Trans. Microwave Theory Tech. 37, 1119–1125 (1989).
[CrossRef]

Watanuki, O.

K. Kobayashi, O. Watanuki, “Polarization-dependent contrast in near-field optical microscopy,” J. Vac. Sci. Technol. B 15, 1966–1970 (1997).
[CrossRef]

K. Kobayashi, O. Watanuki, “Characteristics of photon scanning tunneling microscope read-out,” J. Vac. Sci. Technol. B 14, 804–808 (1996).
[CrossRef]

Weeber, J.-C.

C. Girard, J.-C. Weeber, A. Dereux, O. J. F. Martin, J.-P. Goudonnet, “Optical magnetic near-field intensities around nanometer-scale surface structures,” Phys. Rev. B 55, 16487–16497 (1997).
[CrossRef]

Wei, P-K.

R. Chang, P-K. Wei, W. S. Fann, M. Hayashi, S. H. Lin, “Theoretical investigation of near-field optical properties of tapered fiber tips and single molecule fluorescence,” J. Appl. Phys. 81, 3369–3376 (1997).
[CrossRef]

Yaghjian, A. D.

A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263 (1980).
[CrossRef]

Yan, M.

K. Tanaka, M. Yan, M. Tanaka, “Simulated output images of near-field optics by volume integral equation: object placed on the dielectric substrate,” Opt. Rev. 9, 213–221 (2002).
[CrossRef]

K. Tanaka, M. Yan, M. Tanaka, “A simulation of near-field optics by three-dimensional volume integral equation of classical electromagnetic theory,” Opt. Rev. 8, 43–53 (2001).
[CrossRef]

Appl. Phys. Lett. (4)

C. Obermüller, K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[CrossRef]

A. Chavez-Pirson, S. K. Chu, “A full vector analysis of near-field luminescence probing of a single quantum dot,” Appl. Phys. Lett. 74, 1507–1509 (1999).
[CrossRef]

O. J. F. Martin, C. Girard, “Controlling and tuning strong optical field gradients at a local probe microscope tip apex,” Appl. Phys. Lett. 70, 705–707 (1997).
[CrossRef]

C. Höppener, D. Molenda, H. Fuchs, A. Naber, “Simultaneous topographical and optical characterization of near-field optical aperture probes by way of imaging fluorescent nanospheres,” Appl. Phys. Lett. 80, 1331–1333 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. (4)

J. Van Bladel, “Some remarks on Green’s dyadic for infinite space,” IEEE Trans. Antennas Propag. AP-9, 563–566 (1961).

C.-C. Su, “Electromagnetic scattering by a dielectric body with arbitrary inhomogeneity and anisotropy,” IEEE Trans. Antennas Propag. AP-37, 384–389 (1989).
[CrossRef]

C. M. Butler, Y. Rahmat-Samii, R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,” IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
[CrossRef]

Y. Leviatan, R. F. Harrington, J. R. Mautz, “Electromagnetic transmission through apertures in a cavity in a thick conductor,” IEEE Trans. Antennas Propag. AP-30, 1153–1165 (1982).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

C.-C. Su, “The three-dimensional algorithm of solving the electric field integral equation using face-centered node points, conjugate gradient method, and FFT,” IEEE Trans. Microwave Theory Tech. 41, 510–515 (1993).
[CrossRef]

J. J. H. Wang, J. R. Dubberley, “Computation of fields in an arbitrary shaped heterogeneous dielectric or biological body by an iterative conjugate gradient method,” IEEE Trans. Microwave Theory Tech. 37, 1119–1125 (1989).
[CrossRef]

J. Appl. Phys. (4)

R. Chang, P-K. Wei, W. S. Fann, M. Hayashi, S. H. Lin, “Theoretical investigation of near-field optical properties of tapered fiber tips and single molecule fluorescence,” J. Appl. Phys. 81, 3369–3376 (1997).
[CrossRef]

Y. Leviatan, “Study of near-zone fields of a small aperture,” J. Appl. Phys. 60, 1577–1583 (1986).
[CrossRef]

A. Roberts, “Near-zone fields behind circular apertures in thick, perfectly conducting screens,” J. Appl. Phys. 65, 2896–2899 (1989).
[CrossRef]

A. Roberts, “Small-hole coupling of radiation into a near-field probe,” J. Appl. Phys. 70, 4045–4049 (1991).
[CrossRef]

J. Commun. Technol. Electron. (1)

A. B. Samokhin, “Integral equations of the electrodynamics for three-dimensional structure and iterative method of solving them,” J. Commun. Technol. Electron. 38, 15–34 (1993).

J. Microsc. (Oxford) (3)

K. Tanaka, M. Tanaka, “Simulation of an aperture in the thick metallic screen that gives high intensity and small spot size using surface plasmon polariton,” J. Microsc. (Oxford) 210, 294–300 (2003).
[CrossRef]

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. (Oxford) 194, 353–359 (1999).
[CrossRef]

O. J. F. Martin, “3D simulations of the experimental signal measured in near-field optical microscopy,” J. Microsc. (Oxford) 194, 235–239 (1999).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Vac. Sci. Technol. B (2)

K. Kobayashi, O. Watanuki, “Characteristics of photon scanning tunneling microscope read-out,” J. Vac. Sci. Technol. B 14, 804–808 (1996).
[CrossRef]

K. Kobayashi, O. Watanuki, “Polarization-dependent contrast in near-field optical microscopy,” J. Vac. Sci. Technol. B 15, 1966–1970 (1997).
[CrossRef]

Opt. Commun. (1)

H. Furukawa, S. Kawata, “Analysis of image formation in a near-field scanning optical microscope: effects of multiple scattering,” Opt. Commun. 132, 170–178 (1996).
[CrossRef]

Opt. Rev. (2)

K. Tanaka, M. Yan, M. Tanaka, “A simulation of near-field optics by three-dimensional volume integral equation of classical electromagnetic theory,” Opt. Rev. 8, 43–53 (2001).
[CrossRef]

K. Tanaka, M. Yan, M. Tanaka, “Simulated output images of near-field optics by volume integral equation: object placed on the dielectric substrate,” Opt. Rev. 9, 213–221 (2002).
[CrossRef]

Philips Res. Rep. (1)

C. J. Bouwkamp, “On the diffraction of electromagnetic waves by small circular disks and holes,” Philips Res. Rep. 5, 401–422 (1950).

Philos. Mag. (1)

E. H. Synge, “A suggested method for extending microscopic resolution into the ultra-microscopic region,” Philos. Mag. 6, 356–362 (1928).

Phys. Rev. (2)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

H. Levine, J. Schwinger, “On the theory of diffraction by an aperture in an infinite plane screen. I,” Phys. Rev. 74, 958–974 (1948).
[CrossRef]

Phys. Rev. B (1)

C. Girard, J.-C. Weeber, A. Dereux, O. J. F. Martin, J.-P. Goudonnet, “Optical magnetic near-field intensities around nanometer-scale surface structures,” Phys. Rev. B 55, 16487–16497 (1997).
[CrossRef]

Phys. Rev. E (1)

D. Barchiesi, C. Girard, O. J. F. Martin, D. Van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

A. Naber, D. Molenda, U. C. Fischer, H.-J. Maas, C. Höppener, N. Lu, H. Fuchs, “Enhanced light confinement in a near-field optical probe with a triangular aperture,” Phys. Rev. Lett. 89, 210801 (2002).
[CrossRef] [PubMed]

Proc. IEEE (1)

A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263 (1980).
[CrossRef]

Science (1)

E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1993).
[CrossRef] [PubMed]

Other (7)

D. W. Pohl, D. Courjon, eds., Near-Field Optics (Kluwer Academic, Dordrecht, The Netherlands, 1993).
[CrossRef]

M. Ohtsu, H. Hori, Near-Field Nano-Optics (Kluwer Academic, Dordrecht, The Netherlands, 1999).
[CrossRef]

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
[CrossRef]

E. K. Miller, L. Medgyesi-Mitschang, E. H. Newman, Computational Electromagnetics: Frequency-Domain Method of Moments (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1992).

J. H. Wang, Generalized Moment Method in Electromagnetics: Formulation and Computer Solution of Integral Equations (Wiley, New York, 1991).

A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, New York, 1982).

D. Molenda, C. Höppener, H. Fuchs, A. Naber, Physics Institute, University of Münster, Wilhelm-Klemen Strasse 10, D-48149 Münster, Germany (personal communication, 2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Geometry of the problem. The optical plane wave is scattered by an aperture in the infinite metallic screen placed in the coordinate systems (x, y, z) and (r, ϕ, θ). Screens are of metal 1 (ε1= -1.68 - j4.46) and metal 2 (ε1 = -7.38 - j7.18).

Fig. 2
Fig. 2

Dependence of near-field distributions |E x (k 0 x, 0.0, 0.1)|2 above the aperture on the discretized volume size of the screen used for the numerical calculation: (a) k 0 b x × k 0 b y × k 0 w = 3.2 × 3.2 × 0.3, (b) k 0 b x × k 0 b y × k 0 w = 7.2 × 7.2 × 0.3, (c) k 0 b x × k 0 b y × k 0 w = 11.2 × 11.2 × 0.3. The screen is metal 1 (ε1 = -1.68 - j4.46). The surrounding region is a vacuum (ε0 = 1), and the size of the SA is k 0 a x = k 0 a y = 1.2.

Fig. 3
Fig. 3

Dependence of near-field distributions |E z (k 0 x, 0.0, 0.1)|2 above the aperture on the discretized volume size of the screen used for the numerical calculation: (a) k 0 b x × k 0 b y × k 0 w = 3.2 × 3.2 × 0.3, (b) k 0 b x × k 0 b y × k 0 w = 7.2 × 7.2 × 0.3, (c) k 0 b x × k 0 b y × k 0 w = 11.2 × 11.2 × 0.3. The screen is metal 1 (ε1 = -1.68 - j4.46). The surrounding region is a vacuum (ε0 = 1), and the size of the SA is k 0 a x = k 0 a y = 1.2.

Fig. 4
Fig. 4

Dependence of scattering cross section W of the SA on the discretized volume size used for the numerical calculation. The screen thickness is fixed at k 0 w = 0.3. The size of the SA is k 0 a x = k 0 a y = 1.2.

Fig. 5
Fig. 5

Electric near-field distributions normalized by the intensity of the incident wave on the plane parallel to the xy plane placed at k 0 z = 0.1 for a SA in a metal 1 screen (ε1 = -1.68 - j4.46): (a) |E(k 0 x, k 0 y, 0.1)|2, (b) |E x (k 0 x, k 0 y, 0.1)|2, (c) |E y (k 0 x, k 0 y, 0.1)|2, (d) |E z (k 0 x, k 0 y, 0.1)|2. The thickness of the screen is k 0 w = 1.9. The square indicates the k 0 a x = k 0 a y = 1.2 aperture. The arrow in (a) indicates incident polarization. The intensity ranges are (a) (0–0.1), (b) (0–0.04), (c) (0–0.01), (d) (0–0.08).

Fig. 6
Fig. 6

Electric near-field distributions normalized by the intensity of the incident wave on the plane parallel to the xy plane placed at k 0 z = 0.1 for a SA in a metal 2 screen (ε1 = -7.38 - j7.18): (a) |E(k 0 x, k 0 y, 0.1)|2, (b) |E x (k 0 x, k 0 y, 0.1)|2, (c) |E y (k 0 x, k 0 y, 0.1)|2, (d) |E z (k 0 x, k 0 y, 0.1)|2. The thickness of the screen is k 0 w = 1.9. The square indicates the k 0 a x = k 0 a y = 1.2 aperture. The arrow in (a) indicates incident polarization. The intensity ranges are (a) (0–0.1), (b) (0–0.04), (c) (0–0.01), (d) (0–0.08).

Fig. 7
Fig. 7

Total electric near-field distributions normalized by the intensity of an incident wave on the plane parallel to the xy plane placed at k 0 z = 0.1 for a CA in a metal 2 screen (ε1 = -7.38 - j7.18). The thickness of the screen is k 0 w = 1.9. The circle indicates the aperture whose area is the same as that of a SA of k 0 a x = k 0 a y = 1.2. The arrow indicates incident polarization. The intensity ranges from 0 to 0.1.

Fig. 8
Fig. 8

Total electric near-field distributions |E(k 0 x, k 0 y, 0.1)|2 normalized by the intensity of the incident wave on the plane parallel to the xy plane placed at k 0 z = 0.1 for TAs in a metal 2 screen (ε1 = -7.38 - j7.18). The thickness of the screen is k 0 w = 1.9. The triangle indicates the aperture whose area is the same as that of a SA of k 0 a x = k 0 a y = 1.2. The arrows indicate incident polarization. The intensity ranges from 0 to 0.2.

Fig. 9
Fig. 9

Explanation of the numerical results obtained with SPPs on the sidewalls of the aperture.

Fig. 10
Fig. 10

Dependence of scattering cross section W of a SA on screen thickness k 0 w. The size of the SA is k 0 a x = k 0 a y = 1.2. The solid and dotted curves represent the power transmission coefficients |T| 2 of the metal 2 and metal 1 slabs without an aperture, respectively, of thickness k 0 w. The solid line represents Bethe’s results for the scattering cross section of a CA having an area equal to that of the SA.

Fig. 11
Fig. 11

Dependence of scattering cross section W of a SA in a thick metallic screen having an aperture area of k 0 a x × k 0 a y . The screen thickness is k 0 w = 1.9. The solid line represents the scattering cross section as calculated by use of Bethe’s theory.

Fig. 12
Fig. 12

Geometry of the problem used for derivation of reciprocity of the problem.

Tables (1)

Tables Icon

Table 1 Verification of Reciprocity of the Problem (θ1 = ϕ1 = ϕ2 = 0)

Equations (47)

Equations on this page are rendered with MathJax. Learn more.

Ex=k02Vεrx-1G¯x|x·Exdv+Eix,
Ex=Ecx+Eslabx, xV.
Ecx+Eslabx=k02Vεrx-1G¯x|x·Ecxdv+k02Vεrx-1G¯x|x·Eslabxdv+Eix, xV.
Eix+Erx:xIEslabx:xVEtx:xII =k02Vεslabx-1G¯x|x·Eslabxdv+Eix,
Ecx=k02Vεrx-1G¯x|x·Ecxdv+k02Vεrx-εslabxG¯x|x·Eslabxdv.
-k02Vεrx-1G¯x|x·Ecxdv+εrx+2/3Ecx=k02Vεrx-εslabxG¯x|x·Eslabxdv, xV.
-k02εrx-1VG¯x|x·χcxdv+εrx+2/3χcx=k02εrx-1Vεrx-εslabxG¯x|x·Eslabxdv, xV.
χcx=εrx-1Ecx.
Ex=k02Vεrx-1G¯x|x·Ecx+Eslabxdv+Eix=k02Vεrx-1G¯x|x·Ecxdv+k02Vεrx-εslabxG¯x|x·Eslabxdv+Etx, xII.
Esr, θ, ϕexp-jk0r/k0rFθ, ϕ, k0r  1,
Fθ, ϕ=-ir×ir×14πk03Vεrx-1Ecxexpjk0x·irdv+k03Vεrx-εslabxEslabxexpjk0x·irdv.
W=0π/202π |Fθ, ϕ|2 sin θdθdϕ.
R1·F2π-θ1, ϕ1+T1·F2θ1, ϕ1=R2·F1π-θ2, ϕ2+T2·F1θ2, ϕ2,
Esx=k02Vεrx-1G¯x|x·Ecxdv.
G¯x|x=I¯+1/k02gx, x,
2gx, x+k02gx, x=-δx, x,
gx, x=exp-k0|x-x|/4π|x-x|,
Esx=k02Vεrx-1- 1/k022gx, xI¯+1/k02gx, x·Ecxdv=vεrx-1-2gx, xI¯+gx, x·Ecxdv=vεrx-1××gx, xI¯·Ecxdv=××vεrx-1gx, xEcxdv.
gx, xexp-jk0r/4πr×expjk0x·ir, k0r  1,
×gx, xEx-jk0ir exp-jk0r/4πr×Exexpjk0x·ir, k0r1.
Esx=exp-jk0r/4πk0r-ir×ir×k03vεrx-1Ecxexpjk0x·irdv.
SE1×H2-E2×H1·inds=0,
Ek=Ekp+Eks, Hk=Hkp+Hks, k=1, 2,
Ekp=Eki+Ekr, x exists in region I,=Ekt, k=1, 2 x exists in region II,
Hkp=Hki+Hkr, x exists in region I,=Hkt, k=1, 2 x exists in region II,
Eki=k exp-jk0x·ik, Hki=1ζik×kexp-jk0x·ik, k=1, 2,
Ekr=Rk exp-jk0x·iRk, Hkr=1ζiRk×Rkexp-jk0x·iRk, k=1, 2,
Ekt=Tk exp-jk0x·ik, Hkt=1ζik×Tkexp-jk0x·ik, k=1, 2,
Eksr, θ, ϕexp-jk0rk0rFkθ, ϕ, k=1, 2,
Hksr, θ, ϕ1ζir×EkSr, θ, ϕ, k=1, 2.
SE1p+E1s×H2p+H2s-E2p+E2s×H1p+H1s]·inds=0.
SE1p×H2p-E2p×H1p·inds+SE1s×H2s-E2s×H1s·inds+SE1p×H2s-E2p×H1s·inds+SE1s×H2p-E2s×H1p·inds=0.
SE1p×H2p-E2p×H1p·inds=0,
SE1s×H2s-E2s×H1s·inds=0,
SE1p×H2s-E2p×H1s·inds+SE1s×H2p-E2s×H1p·inds=0.
S-E1i×H2s-E2i×H1s·inds+S-E1s×H2i-E2s×H1i·inds+S-E1r×H2S-E2r×H1s·inds+S-E1s×H2r-E2s×H1r·inds+S+E1t×H2s-E2t×H1s·inds+S+E1s×H2t-E2s×H1t·inds=0,
S-E1i×H2s-E2i×H1s·inds-=0, S-E1s×H2i-E2s×H1i·inds-=0.
SE1r×H2s-E2r×H1s·inds=SR1 exp-jk0x·iR1×exp-jk0rk0r1ζir×F2θ, ϕ-R2 exp-jk0x·iR2×exp-jk0rk0r1ζir×F1θ, ϕ·inds=1ζSexp-jk0rk0rexp-jk0r·iR1R1×ir×F2θ, ϕ-exp-jk0rk0rexp-jk0x·iR2R2×ir×F1θ, ϕ·inds.
in·R1×ir×F2θ, ϕ=in·R1·F2θ, ϕir-in·R1·irF2θ, ϕ=in·R1·F2θ, ϕir=R1·F2θ, ϕ.
1ζS-exp-jk0rk0rexp-jk0x·iR1R1·F2θ, ϕ-exp-jk0rk0rexp-jk0x·iR2R2·F1θ, ϕds =1ζ  exp-jk0rk0rexp-jk0x·iR1R1·F2θ, ϕr2 sin θdθdϕ -exp-jk0rk0rexp-jk0x·iR2R2·F1θ, ϕr2 sin θdθdϕ -2jπζk02exp-j2k0rR1·F2θR1, ϕR1+2jπζk02exp-j2k0rR2·F1θR2, ϕR2.
I=S gθ, ϕexpjkfθ, ϕdθdϕ j2πσαβ-γ2-1/2gθ0, ϕ0×expjkfθ0, ϕ0k for k,
fθθ, ϕ|θ=θ0,ϕ=ϕ0=0, fϕθ, ϕ|θ=θ0,y=ϕ0=0, α=fθθθ0, ϕ0, β=fϕϕθ0, ϕ0, γ=fθϕθ0, ϕ0, σ=+1αβ>γ2, α>0, -1αβ>γ2, α<0, -jαβ<γ2.
S-E1s×H2r-E2s×H1r·inds=S-exp-jk0rk0rF1θ, ϕ×1ζiR2×R2exp-jk0x·iR2-exp-jk0rk0rF2θ, ϕ×1ζiR1×R1exp-jk0x·iR1·inds =1ζS-exp-jk0rk0rexp-jk0x·iR2F1θ, ϕ×iR2×R2-exp-jk0rk0rexp-jk0x·iR1F2θ, ϕ×iR1×R1·inds.
in·F1θ, ϕ×iR2×R2=in·F1θ, ϕ·R2iR2-in·F1θ, ϕ·iR2R2=F1θ, ϕ·R2in·iR2-F1θ, ϕ·iR2in·iR2,
1ζS-exp-jk0rk0rexp-jk0x·iR2F1θ, ϕ·R2in·iR2-F1θ, ϕ·iR2in·R2-exp-jk0rk0rexp-jk0x·iR1F2θ, ϕ·R1in·iR1-F2θ, ϕ·iR1in·R1ds-2jπζk02exp-2jk0rR2·F1θR2, ϕR2+2jπζk02exp-2jk0rR1·F2θR1, ϕR1.
θR1=π-θ1, θR2=π-θ2, ϕR1=ϕ1, ϕR2=ϕ2.
R1·F2θR1, ϕR1+T1·F2θ1, ϕ1=R2·F1θR2, ϕR2+T2·F1θ2, ϕ2,

Metrics