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Applied Optics

Applied Optics


  • Vol. 43, Iss. 8 — Mar. 10, 2004
  • pp: 1734–1746

Analysis and Numerical Computation of Diffraction of an Optical Field by a Subwavelength-Size Aperture in a Thick Metallic Screen by Use of a Volume Integral Equation

Kazuo Tanaka and Masahiro Tanaka  »View Author Affiliations

Applied Optics, Vol. 43, Issue 8, pp. 1734-1746 (2004)

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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

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1960) Diffraction and gratings : Diffraction theory
(180.5810) Microscopy : Scanning microscopy
(230.7370) Optical devices : Waveguides
(350.5400) Other areas of optics : Plasmas

Kazuo Tanaka and Masahiro Tanaka, "Analysis and Numerical Computation of Diffraction of an Optical Field by a Subwavelength-Size Aperture in a Thick Metallic Screen by Use of a Volume Integral Equation," Appl. Opt. 43, 1734-1746 (2004)

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  1. E. Betzig and R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1993).
  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 and D. Courjon, eds., Near-Field Optics (Kluwer Academic, Dordrecht, The Netherlands, 1993).
  4. M. Ohtsu and H. Hori, Near-Field Nano-Optics (Kluwer Academic, Dordrecht, The Netherlands, 1999).
  5. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
  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 and J. Schwinger, “On the theory of diffraction by an aperture in an infinite plane screen. I,” Phys. Rev. 74, 958–974 (1948).
  8. Y. Leviatan, R. F. Harrington, and J. R. Mautz, “Electromagnetic transmission through apertures in a cavity in a thick conductor,” IEEE Trans. Antennas Propag. AP-30, 1153–1165 (1982).
  9. Y. Leviatan, “Study of near-zone fields of a small aperture,” J. Appl. Phys. 60, 1577–1583 (1986).
  10. C. M. Butler, Y. Rahmat-Samii, and R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,” IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
  11. R. E. English, Jr. and N. George, “Diffraction from a small square aperture: approximate aperture fields,” J. Opt. Soc. Am. A 5, 192–199 (1988).
  12. A. Roberts, “Near-zone fields behind circular apertures in thick, perfectly conducting screens,” J. Appl. Phys. 65, 2896–2899 (1989).
  13. A. Roberts, “Small-hole coupling of radiation into a near-field probe,” J. Appl. Phys. 70, 4045–4049 (1991).
  14. H. Furukawa and S. Kawata, “Analysis of image formation in a near-field scanning optical microscope: effects of multiple scattering,” Opt. Commun. 132, 170–178 (1996).
  15. R. Chang, P-K. Wei, W. S. Fann, M. Hayashi, and 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).
  16. A. Chavez-Pirson and S. K. Chu, “A full vector analysis of near-field luminescence probing of a single quantum dot,” Appl. Phys. Lett. 74, 1507–1509 (1999).
  17. O. J. F. Martin, “3D simulations of the experimental signal measured in near-field optical microscopy,” J. Microsc. (Oxford) 194, 235–239 (1999).
  18. D. J. Shin, A. Chavez-Pirson, S. H. Kim, S. T. Jung, and Y. H. Lee, “Diffraction by a subwavelength-sized aperture in a metal plane,” J. Opt. Soc. Am. A 18, 1477–1486 (2001).
  19. C. Obermüller and K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
  20. D. J. Shin, A. Chavez-Pirson, and Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. (Oxford) 194, 353–359 (1999).
  21. A. Liu, A. Rahmani, G. W. Bryant, L. J. Richter, and S. Stranick, “Modeling illumination-mode near-field optical microscopy of Au nanoparticles,” J. Opt. Soc. Am. A 18, 704–716 (2001).
  22. O. J. F. Martin, C. Girard, and A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
  23. D. Barchiesi, C. Girard, O. J. F. Martin, D. Van Labeke, and 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).
  24. O. J. F. Martin, C. Girard, and A. Dereux, “Dielectric versus topographic contrast in near-field microscopy,” J. Opt. Soc. Am. A 13, 1801–1808 (1996).
  25. O. J. F. Martin and C. Girard, “Controlling and tuning strong optical field gradients at a local probe microscope tip apex,” Appl. Phys. Lett. 70, 705–707 (1997).
  26. C. Girard, J.-C. Weeber, A. Dereux, O. J. F. Martin, and J.-P. Goudonnet, “Optical magnetic near-field intensities around nanometer-scale surface structures,” Phys. Rev. B 55, 16487–16497 (1997).
  27. K. Kobayashi and O. Watanuki, “Characteristics of photon scanning tunneling microscope read-out,” J. Vac. Sci. Technol. B 14, 804–808 (1996).
  28. K. Kobayashi and O. Watanuki, “Polarization-dependent contrast in near-field optical microscopy,” J. Vac. Sci. Technol. B 15, 1966–1970 (1997).
  29. K. Tanaka, M. Yan, and M. Tanaka, “A simulation of near-field optics by three-dimensional volume integral equation of classical electromagnetic theory,” Opt. Rev. 8, 43–53 (2001).
  30. K. Tanaka, M. Yan, and 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).
  31. E. K. Miller, L. Medgyesi-Mitschang, and 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).
  35. J. J. H. Wang and 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).
  36. C.-C. Su, “Electromagnetic scattering by a dielectric body with arbitrary inhomogeneity and anisotropy,” IEEE Trans. Antennas Propag. AP-37, 384–389 (1989).
  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).
  38. R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and 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).
  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, and 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, and 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).
  42. A. Naber, D. Molenda, U. C. Fischer, H.-J. Maas, C. Höppener, N. Lu, and H. Fuchs, “Enhanced light confinement in a near-field optical probe with a triangular aperture,” Phys. Rev. Lett. 89, 210801 (2002).
  43. A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, New York, 1982).
  44. K. Tanaka and 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).

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