Abstract

A hybrid finite-difference time-domain and angular-spectrum propagation modeling technique is used to study the imaging properties of a near-field optical scanning system with dielectric samples. The model is used to calculate system transfer functions based on scanning sinusoidal gratings of various spatial periods or on scanning a straight edge and then taking a derivative and a Fourier transform. Results from these two methods are in good agreement. A square-wave grating is simulated by linear addition of component sine-wave grating images that are weighted by the transfer function. The image generated by this method agrees well with an image generated by direct use of the hybrid model. In the region of parameter space investigated with the model, the near-field optical scanning system exhibits nearly linear behavior. The region of linear operation depends on the index of the sample and on the probe-to-sample spacing.

© 1995 Optical Society of America

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  1. E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
    [CrossRef] [PubMed]
  2. F. Froehlich, T. D. Milster, R. Uber, “High-resolution lithography with a near-field scanning sub-wavelength aperture,” in Miniature and Micro-optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 312–317 (1992).
    [CrossRef]
  3. E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
    [CrossRef]
  4. A. Dereux, D. W. Pohl, Near Field Optics, Vol. 242 of NATO Advanced Science Institutes Series E (Kluwer Academic, Dordrecht, The Netherlands, 1993).
  5. C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
    [CrossRef]
  6. C. Girard, X. Bouju, “Self-consistent study of dynamical and polarization effects in near-field optical microscopy,” J. Opt. Soc. Am. B 9, 298–305 (1992).
    [CrossRef]
  7. D. Van Labeke, D. Barchiesi, “Scanning-tunneling optical microscopy: a theoretical macroscopic approach,” J. Opt. Soc. Am. A 9, 732–739 (1992).
    [CrossRef]
  8. C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11344–11351 (1994).
    [CrossRef]
  9. S. Bozhevolnyi, S. Berntsen, E. Bozhevolnaya, “Extension of the macroscopic model for reflection near-field microscopy: regularization and image formation,” J. Opt. Soc. Am. A 11, 609–617 (1994).
    [CrossRef]
  10. L. Novotny, D. W. Pohl, P. Regli, “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]
  11. J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two dimensional probe,” Ultramicroscopy 57, 251–256 (1995).
    [CrossRef]
  12. J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1992).
    [CrossRef]
  13. K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, Boca Raton, Fla., 1993), p. 32.
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 48–51.
  15. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), pp. 40–80.
  16. J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978), pp. 343–345.
  17. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962), p. 108–116.
  18. This process is the subject of ongoing research at the Optical Sciences Center, University of Arizona, Tucson, Arizona 85721.
  19. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1990), pp. 345–351.
  20. J. M. Vigoureux, F. Depasse, C. Girard, “Superresolution of near-field optical microscopy defined from properties of confined electromagnetic waves,” App. Opt. 31, 3036–3045 (1992).
    [CrossRef]
  21. C. Pieralli, “Statistical estimation of point spread function applied to scanning near-field optical microscopy,” Opt. Commun. 108, 203–208 (1994).
    [CrossRef]

1995 (1)

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two dimensional probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

1994 (4)

C. Pieralli, “Statistical estimation of point spread function applied to scanning near-field optical microscopy,” Opt. Commun. 108, 203–208 (1994).
[CrossRef]

S. Bozhevolnyi, S. Berntsen, E. Bozhevolnaya, “Extension of the macroscopic model for reflection near-field microscopy: regularization and image formation,” J. Opt. Soc. Am. A 11, 609–617 (1994).
[CrossRef]

L. Novotny, D. W. Pohl, P. Regli, “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]

C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11344–11351 (1994).
[CrossRef]

1992 (6)

D. Van Labeke, D. Barchiesi, “Scanning-tunneling optical microscopy: a theoretical macroscopic approach,” J. Opt. Soc. Am. A 9, 732–739 (1992).
[CrossRef]

C. Girard, X. Bouju, “Self-consistent study of dynamical and polarization effects in near-field optical microscopy,” J. Opt. Soc. Am. B 9, 298–305 (1992).
[CrossRef]

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1992).
[CrossRef]

J. M. Vigoureux, F. Depasse, C. Girard, “Superresolution of near-field optical microscopy defined from properties of confined electromagnetic waves,” App. Opt. 31, 3036–3045 (1992).
[CrossRef]

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

1990 (1)

C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
[CrossRef]

Barchiesi, D.

Berntsen, S.

Betzig, E.

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

Bouju, X.

Bozhevolnaya, E.

Bozhevolnyi, S.

Courjon, D.

C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
[CrossRef]

Depasse, F.

J. M. Vigoureux, F. Depasse, C. Girard, “Superresolution of near-field optical microscopy defined from properties of confined electromagnetic waves,” App. Opt. 31, 3036–3045 (1992).
[CrossRef]

Dereux, A.

C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11344–11351 (1994).
[CrossRef]

A. Dereux, D. W. Pohl, Near Field Optics, Vol. 242 of NATO Advanced Science Institutes Series E (Kluwer Academic, Dordrecht, The Netherlands, 1993).

Finn, P. L.

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

Froehlich, F.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two dimensional probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1992).
[CrossRef]

F. Froehlich, T. D. Milster, R. Uber, “High-resolution lithography with a near-field scanning sub-wavelength aperture,” in Miniature and Micro-optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 312–317 (1992).
[CrossRef]

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978), pp. 343–345.

Girard, C.

C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11344–11351 (1994).
[CrossRef]

J. M. Vigoureux, F. Depasse, C. Girard, “Superresolution of near-field optical microscopy defined from properties of confined electromagnetic waves,” App. Opt. 31, 3036–3045 (1992).
[CrossRef]

C. Girard, X. Bouju, “Self-consistent study of dynamical and polarization effects in near-field optical microscopy,” J. Opt. Soc. Am. B 9, 298–305 (1992).
[CrossRef]

C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 48–51.

Gyorgy, E. M.

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

Judkins, J.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two dimensional probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1992).
[CrossRef]

Kann, J. L.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two dimensional probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1992).
[CrossRef]

Kunz, K. S.

K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, Boca Raton, Fla., 1993), p. 32.

Luebbers, R. J.

K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, Boca Raton, Fla., 1993), p. 32.

Milster, T. D.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two dimensional probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1992).
[CrossRef]

F. Froehlich, T. D. Milster, R. Uber, “High-resolution lithography with a near-field scanning sub-wavelength aperture,” in Miniature and Micro-optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 312–317 (1992).
[CrossRef]

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), pp. 40–80.

Novotny, L.

Papoulis, A.

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962), p. 108–116.

Pieralli, C.

C. Pieralli, “Statistical estimation of point spread function applied to scanning near-field optical microscopy,” Opt. Commun. 108, 203–208 (1994).
[CrossRef]

Pohl, D. W.

L. Novotny, D. W. Pohl, P. Regli, “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]

A. Dereux, D. W. Pohl, Near Field Optics, Vol. 242 of NATO Advanced Science Institutes Series E (Kluwer Academic, Dordrecht, The Netherlands, 1993).

Regli, P.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1990), pp. 345–351.

Trautman, J. K.

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

Uber, R.

F. Froehlich, T. D. Milster, R. Uber, “High-resolution lithography with a near-field scanning sub-wavelength aperture,” in Miniature and Micro-optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 312–317 (1992).
[CrossRef]

Van Labeke, D.

Vigoureux, J. M.

J. M. Vigoureux, F. Depasse, C. Girard, “Superresolution of near-field optical microscopy defined from properties of confined electromagnetic waves,” App. Opt. 31, 3036–3045 (1992).
[CrossRef]

Wolfe, R.

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

Ziolkowski, R. W.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two dimensional probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1992).
[CrossRef]

App. Opt. (1)

J. M. Vigoureux, F. Depasse, C. Girard, “Superresolution of near-field optical microscopy defined from properties of confined electromagnetic waves,” App. Opt. 31, 3036–3045 (1992).
[CrossRef]

Appl. Phys. Lett. (1)

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

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

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

C. Pieralli, “Statistical estimation of point spread function applied to scanning near-field optical microscopy,” Opt. Commun. 108, 203–208 (1994).
[CrossRef]

Phys. Rev. B (2)

C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
[CrossRef]

C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11344–11351 (1994).
[CrossRef]

Science (1)

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

Ultramicroscopy (1)

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two dimensional probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

Other (9)

F. Froehlich, T. D. Milster, R. Uber, “High-resolution lithography with a near-field scanning sub-wavelength aperture,” in Miniature and Micro-optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 312–317 (1992).
[CrossRef]

A. Dereux, D. W. Pohl, Near Field Optics, Vol. 242 of NATO Advanced Science Institutes Series E (Kluwer Academic, Dordrecht, The Netherlands, 1993).

K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, Boca Raton, Fla., 1993), p. 32.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 48–51.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), pp. 40–80.

J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978), pp. 343–345.

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962), p. 108–116.

This process is the subject of ongoing research at the Optical Sciences Center, University of Arizona, Tucson, Arizona 85721.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1990), pp. 345–351.

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Figures (4)

Fig. 1
Fig. 1

Setup used to calculate the system’s transfer function. A normally incident, TE-polarized plane wave illuminates the aperture. The aperture scans across a dielectric sample, and the total electric-field energy is calculated on a detection plane at a distance z0 past the aperture.

Fig. 2
Fig. 2

(a) System PSF’s normalized to their peak values. The abscissa in the x coordinate normalized to the wavelength. (b) Phase ϕ of the transfer function normalized to π. In (c) the MTF’s calculated by the scanning edge method are shown as the solid and the dotted curves, and the grating method results are denoted by the asterisks (h = 5 nm) and the circles (h = 35 nm). The abscissa is the direction cosine α. A logarithmic scale is used for the ordinate. A threshold modulation of 0.2, which is indicated by the horizontal dashed line, is chosen to determine the spatial resolution of the NFO systems. The inset is an expanded plot for MTF’s > 0.5 and is plotted on a linear scale. The PSF and ϕ are found only with the scanning edge method. For (a)–(c) the solid curve corresponds to h = 5 nm, whereas the dotted curve is for h = 35 nm.

Fig. 3
Fig. 3

Total amount of propagating energy in Eg(x), denoted by Tg and normalized to its peak value. The upper abscissa is the direction cosine α, and the lower abscissa represents the grating period Xg. The data points are indicated by filled circles. Tg is measured when the top of the grating is centered on the aperture, and h = 35 nm.

Fig. 4
Fig. 4

Comparison of two images that are computed when a square-wave grating of 500-nm period is scanned with the 100-nm aperture. The superposition image is found by linear addition of images from component sine-wave gratings that are weighted by the complex-valued transfer function and is shown as the dotted curve. The direct image is found by direct use of the FDTD–angular-spectrum code and is shown as the dashed curve. The grating (ideal image) is shown, for reference, as the solid curve. An expanded view is shown in (b). All the images are normalized to their peak values.

Equations (4)

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h i = h + a 2 cos [ 2 π X g ( x - x s ) ] ,
ω ec = exp ( - h i / h i c ) = j = 0 ( - h i / h i c ) j j ! 1 - h i h i c + h i 2 2 h i c 2 ,
V = i max - i min i max + i min
E d ( x , z = z 0 ) - n n ξ g ( α ) exp [ - i ( z 0 n 2 - α 2 + α x ) ] d α ,

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