Abstract

Boundary integral equations called guided-mode extracted integral equations are applied to simulations of a two-dimensional photon scanning tunneling microscope (2D-PSTM) for an incident TE mode (s polarization). The method presented is global. Complete and rigorous integral equations for a given configuration of the 2D-PSTM are derived. They can be solved numerically by the conventional boundary-element method with high accuracy. To confirm numerical results, three universal laws, i.e., the optical theorem, the energy conservation law, and the reciprocity relation, are derived. Physical characteristics of the interaction between the probe tip and the near field are investigated in detail by using numerical simulations. Many important and interesting physical properties of the 2D-PSTM can be simulated in detail by using the proposed method.

© 1998 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  41. R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, T. L. Ferrell, “Photon scanning tunneling microscopy,” Rev. Sci. Instrum. 61, 3669–3677 (1990).
    [CrossRef]
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    [CrossRef]

1998

1996

S. I. Bozhevolnyi, B. Vohnsen, E. A. Bozhevolnaya, S. Bernstein, “Self-consistent model for photon tunneling microscopy: implications for image formation and light scattering near a phase-conjugating mirror,” J. Opt. Soc. Am. A 13, 2381–2392 (1996).
[CrossRef]

A. Castiaux, A. Dereux, J. Virneron, C. Girard, “Electrodynamics in complex systems: application to near-field probing of optical microresonators,” Phys. Rev. E 54, 5752–5760 (1996).
[CrossRef]

K. Tanaka, M. Tanaka, “Computer-aided design of dielectric waveguide bends by the boundary-element methods based on guided-mode extracted integral equations,” J. Opt. Soc. Am. A 13, 1362–1368 (1996).
[CrossRef]

M. Tanaka, K. Tanaka, “Boundary integral equations for computer aided design of near field optics,” Trans. IEICE Jpn. J79-C-I, 101–108 (1996) (in Japanese).

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]

F. de Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J.-J. Greffet, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 35–45 (1996).
[CrossRef]

J. C. Weeber, F. de Fornel, J. P. Goudonnet, “Computation of the field diffracted by a local surface defect: application to tip–sample interaction in the photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 944–951 (1996).
[CrossRef]

M. Ohtsu, “Photon scanning tunneling microscope and related technologies,” Oyo Buturi 65, 2–12 (1996) (in Japanese).

K. Jang, W. Jhe, “Nonglobal model for a near-field optical microscope using diffraction of the optical near-field,” Opt. Lett. 21, 236–238 (1996).
[CrossRef] [PubMed]

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

J. L. Kann, T. D. Milster, F. F. Froehlich, R. W. Ziolkowski, J. J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1995).
[CrossRef]

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

D. Van Labeke, D. Barchiesi, F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695–703 (1995).
[CrossRef]

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope,” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

S. I. Bozhevolnyi, E. A. Bozhevolnaya, S. Bernstein, “Theoretical model for phase conjunction of optical near fields,” J. Opt. Soc. Am. A 12, 2645–2654 (1995).
[CrossRef]

R. Carminati, J.-J. Greffet, “Two dimensional simulation of photon scanning tunneling microscope. Concept of transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

R. Carminati, J.-J. Greffet, “Influence of dielectric contrast and topography on the near field scattered by an inhomogeneous surface,” J. Opt. Soc. Am. A 12, 2716–2725 (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]

A. Castiaux, A. Dereux, J. Virneron, C. Girard, O. J. F. Martin, “Electric fields in two-dimensional models of near-field optical microscope tip,” Ultramicroscopy 60, 1–9 (1995).
[CrossRef]

1994

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 on real space,” Phys. Rev. B 49, 11344–11351 (1994).
[CrossRef]

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Importance of confined fields in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14467–14473 (1994).
[CrossRef]

1993

D. Van Labeke, D. Barchiesi, “Probes for scanning tunneling optical microscopy: a theoretical comparison,” J. Opt. Soc. Am. A 10, 2193–2201 (1993).
[CrossRef]

K. Tanaka, M. Tanaka, H. Tashima, H. Ootera, Y. Yoshino, “New integral equation method for CAD of open waveguide bends,” Radio Sci. 28, 1219–1227 (1993).
[CrossRef]

1992

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

J. Cites, M. F. Sanhadasa, C. C. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

1991

L. Salomon, F. De Fornel, J. P. Goudonnet, “Simple-tip coupling efficiencies of the photon-scanning tunneling microscope,” J. Opt. Soc. Am. A 8, 2009–2015 (1991).
[CrossRef]

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

W. Denk, D. W. Pohl, “Near-field optics: microscopy with nanometer-size fields,” J. Vac. Sci. Technol. B 9, 510–513 (1991).
[CrossRef]

P. G. Petropoulos, G. A. Kriegsmann, “Optical theorems for electromagnetic scattering by inhomogeneities in layered dielectric media,” IEEE Trans. Antennas Propag. 39, 1119–1124 (1991).
[CrossRef]

1990

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, T. L. Ferrell, “Photon scanning tunneling microscopy,” Rev. Sci. Instrum. 61, 3669–3677 (1990).
[CrossRef]

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

B. Labani, C. Girard, D. Courjon, D. Van Labeke, “Optical interaction between a dielectric tip and a nanometric lattice: implications for near-field microscopy,” J. Opt. Soc. Am. B 7, 936–943 (1990).
[CrossRef]

C. Girard, M. Spajer, “Model for reflection near field optical microscopy,” Appl. Opt. 29, 3726–3733 (1990).
[CrossRef] [PubMed]

1989

J. M. Vigoureux, C. Girard, D. Courjon, “General principle of scanning tunneling microscope,” Opt. Lett. 14, 1039–1041 (1989).
[CrossRef] [PubMed]

K. Tanaka, M. Kojima, “New boundary integral equations for computer-aided design of dielectric waveguide circuits,” J. Opt. Soc. Am. A 6, 667–674 (1989).
[CrossRef]

J.-J. Greffet, “Scattering of s-polarized electromagnetic waves by a 2D obstacle near an interface,” Opt. Commun. 72, 20–24 (1989).
[CrossRef]

R. C. Reddick, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

Adam, P. M.

Baida, F.

D. Van Labeke, D. Barchiesi, F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695–703 (1995).
[CrossRef]

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope,” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

Barchiesi, D.

Bernstein, S.

Bozhevolnaya, E. A.

Bozhevolnyi, S. I.

Carminati, R.

Castiaux, A.

A. Castiaux, A. Dereux, J. Virneron, C. Girard, “Electrodynamics in complex systems: application to near-field probing of optical microresonators,” Phys. Rev. E 54, 5752–5760 (1996).
[CrossRef]

A. Castiaux, A. Dereux, J. Virneron, C. Girard, O. J. F. Martin, “Electric fields in two-dimensional models of near-field optical microscope tip,” Ultramicroscopy 60, 1–9 (1995).
[CrossRef]

Chilcott, D. W.

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, T. L. Ferrell, “Photon scanning tunneling microscopy,” Rev. Sci. Instrum. 61, 3669–3677 (1990).
[CrossRef]

Cites, J.

J. Cites, M. F. Sanhadasa, C. C. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

Courjon, D.

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope,” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

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

B. Labani, C. Girard, D. Courjon, D. Van Labeke, “Optical interaction between a dielectric tip and a nanometric lattice: implications for near-field microscopy,” J. Opt. Soc. Am. B 7, 936–943 (1990).
[CrossRef]

J. M. Vigoureux, C. Girard, D. Courjon, “General principle of scanning tunneling microscope,” Opt. Lett. 14, 1039–1041 (1989).
[CrossRef] [PubMed]

de Fornel, F.

Denk, W.

W. Denk, D. W. Pohl, “Near-field optics: microscopy with nanometer-size fields,” J. Vac. Sci. Technol. B 9, 510–513 (1991).
[CrossRef]

Dereux, A.

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]

A. Castiaux, A. Dereux, J. Virneron, C. Girard, “Electrodynamics in complex systems: application to near-field probing of optical microresonators,” Phys. Rev. E 54, 5752–5760 (1996).
[CrossRef]

A. Castiaux, A. Dereux, J. Virneron, C. Girard, O. J. F. Martin, “Electric fields in two-dimensional models of near-field optical microscope tip,” Ultramicroscopy 60, 1–9 (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]

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

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Importance of confined fields in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14467–14473 (1994).
[CrossRef]

Devel, M.

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Importance of confined fields in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14467–14473 (1994).
[CrossRef]

Ferrell, T. L.

J. Cites, M. F. Sanhadasa, C. C. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, T. L. Ferrell, “Photon scanning tunneling microscopy,” Rev. Sci. Instrum. 61, 3669–3677 (1990).
[CrossRef]

R. C. Reddick, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

Froehlich, F. F.

J. L. Kann, T. D. Milster, F. F. Froehlich, R. W. Ziolkowski, J. J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1995).
[CrossRef]

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

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]

Girard, C.

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]

A. Castiaux, A. Dereux, J. Virneron, C. Girard, “Electrodynamics in complex systems: application to near-field probing of optical microresonators,” Phys. Rev. E 54, 5752–5760 (1996).
[CrossRef]

A. Castiaux, A. Dereux, J. Virneron, C. Girard, O. J. F. Martin, “Electric fields in two-dimensional models of near-field optical microscope tip,” Ultramicroscopy 60, 1–9 (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]

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Importance of confined fields in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14467–14473 (1994).
[CrossRef]

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

B. Labani, C. Girard, D. Courjon, D. Van Labeke, “Optical interaction between a dielectric tip and a nanometric lattice: implications for near-field microscopy,” J. Opt. Soc. Am. B 7, 936–943 (1990).
[CrossRef]

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, M. Spajer, “Model for reflection near field optical microscopy,” Appl. Opt. 29, 3726–3733 (1990).
[CrossRef] [PubMed]

J. M. Vigoureux, C. Girard, D. Courjon, “General principle of scanning tunneling microscope,” Opt. Lett. 14, 1039–1041 (1989).
[CrossRef] [PubMed]

Goudonnet, J. P.

Greffet, J.-J.

Jang, K.

Jhe, W.

Judkins, J. J.

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

J. L. Kann, T. D. Milster, F. F. Froehlich, R. W. Ziolkowski, J. J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1995).
[CrossRef]

Kann, J. L.

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

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

Kojima, M.

Kriegsmann, G. A.

P. G. Petropoulos, G. A. Kriegsmann, “Optical theorems for electromagnetic scattering by inhomogeneities in layered dielectric media,” IEEE Trans. Antennas Propag. 39, 1119–1124 (1991).
[CrossRef]

Labani, B.

Madrazo, A.

Martin, O. J. F.

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]

A. Castiaux, A. Dereux, J. Virneron, C. Girard, O. J. F. Martin, “Electric fields in two-dimensional models of near-field optical microscope tip,” Ultramicroscopy 60, 1–9 (1995).
[CrossRef]

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Importance of confined fields in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14467–14473 (1994).
[CrossRef]

Milster, T. D.

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

J. L. Kann, T. D. Milster, F. F. Froehlich, R. W. Ziolkowski, J. J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1995).
[CrossRef]

Moyer, P. J.

M. A. Paesler, P. J. Moyer, Near-Field Optics: Theory, Instrumentation and Applications (Wiley, New York, 1996).

Nieto-Vesperinas, M.

Novotny, L.

Ohtsu, M.

M. Ohtsu, “Photon scanning tunneling microscope and related technologies,” Oyo Buturi 65, 2–12 (1996) (in Japanese).

Ootera, H.

K. Tanaka, M. Tanaka, H. Tashima, H. Ootera, Y. Yoshino, “New integral equation method for CAD of open waveguide bends,” Radio Sci. 28, 1219–1227 (1993).
[CrossRef]

Paesler, M. A.

M. A. Paesler, P. J. Moyer, Near-Field Optics: Theory, Instrumentation and Applications (Wiley, New York, 1996).

Petropoulos, P. G.

P. G. Petropoulos, G. A. Kriegsmann, “Optical theorems for electromagnetic scattering by inhomogeneities in layered dielectric media,” IEEE Trans. Antennas Propag. 39, 1119–1124 (1991).
[CrossRef]

Pohl, D. W.

Reddick, R. C.

J. Cites, M. F. Sanhadasa, C. C. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, T. L. Ferrell, “Photon scanning tunneling microscopy,” Rev. Sci. Instrum. 61, 3669–3677 (1990).
[CrossRef]

R. C. Reddick, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

Regli, P.

Roberts, A.

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

Salomon, L.

Sanhadasa, M. F.

J. Cites, M. F. Sanhadasa, C. C. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

Sentenac, A.

Sharp, S. L.

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, T. L. Ferrell, “Photon scanning tunneling microscopy,” Rev. Sci. Instrum. 61, 3669–3677 (1990).
[CrossRef]

Spajer, M.

Sung, C. C.

J. Cites, M. F. Sanhadasa, C. C. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

Tanaka, K.

Tanaka, M.

M. Tanaka, K. Tanaka, “Boundary integral equations for computer-aided design and simulations of near-field optics: two-dimensional optical manipulator,” J. Opt. Soc. Am. A 15, 101–108 (1998).
[CrossRef]

K. Tanaka, M. Tanaka, “Computer-aided design of dielectric waveguide bends by the boundary-element methods based on guided-mode extracted integral equations,” J. Opt. Soc. Am. A 13, 1362–1368 (1996).
[CrossRef]

M. Tanaka, K. Tanaka, “Boundary integral equations for computer aided design of near field optics,” Trans. IEICE Jpn. J79-C-I, 101–108 (1996) (in Japanese).

K. Tanaka, M. Tanaka, H. Tashima, H. Ootera, Y. Yoshino, “New integral equation method for CAD of open waveguide bends,” Radio Sci. 28, 1219–1227 (1993).
[CrossRef]

Tashima, H.

K. Tanaka, M. Tanaka, H. Tashima, H. Ootera, Y. Yoshino, “New integral equation method for CAD of open waveguide bends,” Radio Sci. 28, 1219–1227 (1993).
[CrossRef]

Van Labeke, D.

Vigoureux, J. M.

Virneron, J.

A. Castiaux, A. Dereux, J. Virneron, C. Girard, “Electrodynamics in complex systems: application to near-field probing of optical microresonators,” Phys. Rev. E 54, 5752–5760 (1996).
[CrossRef]

A. Castiaux, A. Dereux, J. Virneron, C. Girard, O. J. F. Martin, “Electric fields in two-dimensional models of near-field optical microscope tip,” Ultramicroscopy 60, 1–9 (1995).
[CrossRef]

Vohnsen, B.

Warmack, R. J.

J. Cites, M. F. Sanhadasa, C. C. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, T. L. Ferrell, “Photon scanning tunneling microscopy,” Rev. Sci. Instrum. 61, 3669–3677 (1990).
[CrossRef]

R. C. Reddick, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

Weeber, J. C.

Yoshino, Y.

K. Tanaka, M. Tanaka, H. Tashima, H. Ootera, Y. Yoshino, “New integral equation method for CAD of open waveguide bends,” Radio Sci. 28, 1219–1227 (1993).
[CrossRef]

Ziolkowski, R. W.

J. L. Kann, T. D. Milster, F. F. Froehlich, R. W. Ziolkowski, J. J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1995).
[CrossRef]

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

Appl. Opt.

IEEE Trans. Antennas Propag.

P. G. Petropoulos, G. A. Kriegsmann, “Optical theorems for electromagnetic scattering by inhomogeneities in layered dielectric media,” IEEE Trans. Antennas Propag. 39, 1119–1124 (1991).
[CrossRef]

J. Appl. Phys.

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

J. Cites, M. F. Sanhadasa, C. C. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

J. Opt. Soc. Am. A

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]

J. L. Kann, T. D. Milster, F. F. Froehlich, R. W. Ziolkowski, J. J. Judkins, “Near-field optical detection of asperities in dielectric surfaces,” J. Opt. Soc. Am. A 12, 501–512 (1995).
[CrossRef]

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

D. Van Labeke, D. Barchiesi, “Probes for scanning tunneling optical microscopy: a theoretical comparison,” J. Opt. Soc. Am. A 10, 2193–2201 (1993).
[CrossRef]

D. Van Labeke, D. Barchiesi, F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695–703 (1995).
[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]

R. Carminati, J.-J. Greffet, “Influence of dielectric contrast and topography on the near field scattered by an inhomogeneous surface,” J. Opt. Soc. Am. A 12, 2716–2725 (1995).
[CrossRef]

F. de Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J.-J. Greffet, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 35–45 (1996).
[CrossRef]

J. C. Weeber, F. de Fornel, J. P. Goudonnet, “Computation of the field diffracted by a local surface defect: application to tip–sample interaction in the photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 944–951 (1996).
[CrossRef]

S. I. Bozhevolnyi, E. A. Bozhevolnaya, S. Bernstein, “Theoretical model for phase conjunction of optical near fields,” J. Opt. Soc. Am. A 12, 2645–2654 (1995).
[CrossRef]

S. I. Bozhevolnyi, B. Vohnsen, E. A. Bozhevolnaya, S. Bernstein, “Self-consistent model for photon tunneling microscopy: implications for image formation and light scattering near a phase-conjugating mirror,” J. Opt. Soc. Am. A 13, 2381–2392 (1996).
[CrossRef]

L. Salomon, F. De Fornel, J. P. Goudonnet, “Simple-tip coupling efficiencies of the photon-scanning tunneling microscope,” J. Opt. Soc. Am. A 8, 2009–2015 (1991).
[CrossRef]

A. Madrazo, R. Carminati, M. Nieto-Vesperinas, J.-J. Greffet, “Polarization effects in the optical interaction between a nanoparticle and a corrugated surface: implications for apertureless near-field microscopy,” J. Opt. Soc. Am. A 15, 109–119 (1998).
[CrossRef]

K. Tanaka, M. Kojima, “New boundary integral equations for computer-aided design of dielectric waveguide circuits,” J. Opt. Soc. Am. A 6, 667–674 (1989).
[CrossRef]

K. Tanaka, M. Tanaka, “Computer-aided design of dielectric waveguide bends by the boundary-element methods based on guided-mode extracted integral equations,” J. Opt. Soc. Am. A 13, 1362–1368 (1996).
[CrossRef]

M. Tanaka, K. Tanaka, “Boundary integral equations for computer-aided design and simulations of near-field optics: two-dimensional optical manipulator,” J. Opt. Soc. Am. A 15, 101–108 (1998).
[CrossRef]

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J. Vac. Sci. Technol. B

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[CrossRef]

Opt. Commun.

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope,” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

J.-J. Greffet, “Scattering of s-polarized electromagnetic waves by a 2D obstacle near an interface,” Opt. Commun. 72, 20–24 (1989).
[CrossRef]

R. Carminati, J.-J. Greffet, “Two dimensional simulation of photon scanning tunneling microscope. Concept of transfer function,” Opt. Commun. 116, 316–321 (1995).
[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]

Opt. Lett.

Oyo Buturi

M. Ohtsu, “Photon scanning tunneling microscope and related technologies,” Oyo Buturi 65, 2–12 (1996) (in Japanese).

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

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Importance of confined fields in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14467–14473 (1994).
[CrossRef]

R. C. Reddick, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

Phys. Rev. E

A. Castiaux, A. Dereux, J. Virneron, C. Girard, “Electrodynamics in complex systems: application to near-field probing of optical microresonators,” Phys. Rev. E 54, 5752–5760 (1996).
[CrossRef]

Phys. Rev. Lett.

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]

Radio Sci.

K. Tanaka, M. Tanaka, H. Tashima, H. Ootera, Y. Yoshino, “New integral equation method for CAD of open waveguide bends,” Radio Sci. 28, 1219–1227 (1993).
[CrossRef]

Rev. Sci. Instrum.

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, T. L. Ferrell, “Photon scanning tunneling microscopy,” Rev. Sci. Instrum. 61, 3669–3677 (1990).
[CrossRef]

Trans. IEICE Jpn.

M. Tanaka, K. Tanaka, “Boundary integral equations for computer aided design of near field optics,” Trans. IEICE Jpn. J79-C-I, 101–108 (1996) (in Japanese).

Ultramicroscopy

A. Castiaux, A. Dereux, J. Virneron, C. Girard, O. J. F. Martin, “Electric fields in two-dimensional models of near-field optical microscope tip,” Ultramicroscopy 60, 1–9 (1995).
[CrossRef]

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

Other

M. A. Paesler, P. J. Moyer, Near-Field Optics: Theory, Instrumentation and Applications (Wiley, New York, 1996).

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

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Figures (9)

Fig. 1
Fig. 1

Geometry of the photon scanning tunneling microscope (PSTM) considered in this paper: (a) collection mode (C mode or scanning near-field optical microscope), (b) illumination mode (I mode or reflection scanning near-field microscope), (c) boundaries and indices of refraction of various regions.

Fig. 2
Fig. 2

Practical shapes of the probe tip and a square object placed on the substrate. Parameters used in the numerical simulations are shown.

Fig. 3
Fig. 3

Total field intensity distribution |E|2 above the substrate for the C mode of an incident TE mode (s polarization) without a dielectric probe. A square dielectric object is placed so that its center lies at k0x=0.

Fig. 4
Fig. 4

Dependence of the power transmission coefficient ΓT of the C mode on the positions of the probe tip, k0lx and k0ly, for (a) k0R=1.0, (b) k0R=0.5, (c) k0R=0.1. The tip angle is fixed at φ=10°.

Fig. 5
Fig. 5

Field intensity distribution |E|2 of the C mode with k0lx=-1.2 and k0ly=0.1 for (a) k0R=1.0, (b) k0R=0.5, (c) k0R=0.1. The field intensity is normalized by the amplitude of the incident plane wave.

Fig. 6
Fig. 6

Dependence of the power transmission coefficient ΓT of the C mode on the incident angle θi of the plane wave in the substrate of k0ly=0.1 and k0R=0.5.

Fig. 7
Fig. 7

Dependence of the power reflection coefficient ΓR of the I mode on the positions of probe tip, k0lx and k0ly, for (a) k0R=1.0, (b) k0R=0.5, (c) k0R=0.1. The tip angle is fixed at φ=10°.

Fig. 8
Fig. 8

Field intensity distribution |E|2 of the I mode with k0lx=-0.6 and k0ly=0.1 for (a) k0R=1.0, (b) k0R=0.5, (c) k0R=0.1. The field intensity is normalized by the amplitude of the incident guided mode.

Fig. 9
Fig. 9

Region S and boundaries C0, C+, and C- used in the derivation of three universal laws.

Tables (3)

Tables Icon

Table 1 Verification of the Optical Theorem for the C Mode (k0R=0.5)

Tables Icon

Table 2 Verification of the Energy Conservation Law for the I Mode (k0R=0.5)

Tables Icon

Table 3 Verification of Reciprocity between the C Mode and the I Mode (k0R=0.5)

Equations (75)

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

E(x)/2=C1+C2[G2(x|x)E(x)/n-E(x)G2(x|x)/n]dl
forxonC1+C2,
Gi(x|x)=-j/4H0(2)(k0ni|x-x|)(i=1, 2, 3, 4),
E(x)=Ec(x)+TE+(1)(x)forxonC1,
E(x)=Ec(x)forxonC2.
Ec(x)/2=C1+C2[G2(x|x)Ec(x)/n-Ec(x)G2(x|x)/n]dl-TU2+(1)(x)forxonC1+C2.
U2+(1)(x)=C12[G2(x|x)E+(1)(x)/n-E+(1)(x)G2(x|x)/n]dl,
Ec(r, π/2)/2A(r)C1+C2[g2(π/2|x)Ec(x)/n
-Ec(x)g2(π/2|x)/n]dl-A(r)Tu2+(1)(π/2)
A(r)=(-j/4)[2/(πn2k0r)]1/2 exp(-jn2k0r+jπ/4),
gi(θ|x)=exp(jnik0x cos θ+jnik0y sin θ)
(i=1, 2).
U2+(1)(x)A(r)u2+(1)(θ)(r),
ui±(1)(θ)=C1i[gi(θ|x)E±(1)(x)/n-E±(1)(x)gi(θ|x)/n]dl
(i=1, 2).
T=C1+C2[g2(π/2|x)Ec(x)/n-Ec(x)g2(π/2|x)/n]dl/u2+(1)(π/2)
E(x)=Ec(x)+RE+(1)(x)+E-(1)(x)forxonC1,
R=C1+C2[g2(π/2|x)Ec(x)/n-Ec(x)×g2(π/2|x)/n]dl-u2-(1)(π/2)u2+(1)(π/2).
E(x)=Ec(x)+Et(x)forxontheuppersideofC4Ec(x)+Er(x)+Ei(x)forxonthelowersideofC4,
Ei(x)=exp(jn4k0x sin θi-jn4k0y cos θi),
Er(x)=pr exp(jn4k0x sin θi+jn4k0y cos θi),
Et(x)=pt exp[jn4k0x sin θi-k0y(n42 sin2 θi-n12)1/2],
pr=[jn4 cos θi-(n42 sin2 θi-n12)1/2]/[jn4 cos θi+(n42 sin2 θi-n12)1/2],
pt=(j2n4 cos θi)/[jn4 cos θi+(n42 sin2 θi-n12)1/2].
E(x)=Ec(x)forxonC4
E(x)=Ec(x)forxonC3
E(x)/2=-C1+C2+C3+C4[G1(x|x)E(x)/n-E(x)×G1(x|x)/n]dl
forxonC1+C2+C3+C4,
E(x)/2=C1+C2[G2(x|x)E(x)/n-E(x)×G2(x|x)/n]dlforxonC1+C2,
E(x)/2=C3[G3(x|x)E(x)/n-E(x)×G3(x|x)/n]dlforxonC3,
E(x)/2=C4[G4(x|x)E(x)/n-E(x)×G4(x|x)/n]dlforxonC4.
Ec(x)/2=-C1+C2[P1(x|x)Ec(x)/n-Ec(x)×P1(x|x)/n]dl-C3+C4[G1(x|x)Ec(x)/n-Ec(x)×G1(x|x)/n]dl-S1(x)
forxonC1+C2+C3+C4,
Ec(x)/2=C1+C2[P2(x|x)Ec(x)/n-Ec(x)×P2(x|x)/n]dl-S2(x)
forxonC1+C2,
Ec(x)/2=C3[G3(x|x)Ec(x)/n-Ec(x)×G3(x|x)/n]dlforxonC3,
Ec(x)2=C4[G4(x|x)Ec(x)/n-Ec(x)×G4(x|x)/n]dlforxonC4,
S1(x)=Et(x)0for x on C1+C2+C3,for x on C4S2(x)=0for the C mode,
Si(x)=Ui-(1)(x)-Ui+(1)(x)u2-(1)(π/2)/u2+(1)(π/2)
(i=1, 2)forthe I mode.
U1±(1)(x)=C11[G1(x|x)E±(1)(x)/n-E±(1)(x)G1(x|x)/n]dl.
Pi(x|x)=Gi(x|x)-g2(π/2|x)×Ui+(1)(x)/u2+(1)(π/2)(i=1, 2).
Et(x)=-C4[G1(x|x)Et(x)/n-Et(x)×G1(x|x)/n]dl
ECs(r, θ)=(-j/4)[2/(πn1k0r)]1/2 exp(-jn1k0r+jπ/4)BC+(θ),0<θπ(-j/4)[2/(πn4k0r)]1/2 exp(-jn4k0r+jπ/4)BC-(θ),π<θ2π,
BC+(θ)=-C1+C2+C3+C4[g1(θ|x)Ec(x)/n-Ec(x)×g1(θ|x)/n]dl-Tu1(θ)+(1),
BC-(θ)=C4[g4(θ|x)Ec(x)/n-Ec(x)×g4(θ|x)/n]dl
U1±(1)(x)A(r)u1±(1)(θ)
EIs(r, θ)=(-j/4)[2/(πn1k0r)]1/2 exp(-jn1k0r+jπ/4)BI+(θ),0<θπ(-j/4)[2/(πn4k0r)]1/2 exp(-jn4k0r+jπ/4)BI-(θ),π<θ2π,
BI+(θ)=-C1+C2+C3+C4[g1(θ|x)Ec(x)/n-Ec(x)×g1(θ|x)/n]dl-Ru1(θ)+(1)-u1(θ)-(1),
BI-(θ)=C4[g4(θ|x)Ec(x)/n-Ec(x)×g4(θ|x)/n]dl.
18π0π|BC+(θ)|2 dθ+π2π|BC-(θ)|2 dθ+β|T|2-|E+(1)(x, const.)|2dx
=Im[p r*BC-(3π/2-θi)],
β-|E-(1)(x, const.)|2 dx
=β|R|2-|E+(1)(x, const.)|2 dx+18π0π|BI+(θ)|2 dθ+π2π|BI-(θ)|2 dθ.
2βT-|E+(1)(x, const)|2 dx=BI-(3π/2+θi).
2E+k02n2(x)E=0,
S[·(E*E-EE*)]ds=-2jk02S Im[n(x)|E|2]ds,
C0+C++C-Im(E*E/n)dC=0,
E=Et+ECs+TE+(1)onC0+C+Ei+Er+ECsonC-
ImC-[(Ei+Er)*ECs/n+ECs*(Ei+Er)/n]dl+C0+C++C-(ECs*ECs/n)dl+|T|2C0(E+(1)*E+(1)/n)dl=0.
C0+C++C-(ECs*ECs/n)dl=-j8π0π|BC+(θ)|2 dθ-j/(8π)π2π|BC-(θ)|2 dθ.
|T|2C0[E+(1)*E+(1)/n]dl=-jβ|T|2-|E+(1)(x, const)|2 dx.
C-[(Ei+Er)*ECs/n+ECs*(Ei+Er)/n]dl=(-1/4)(2n4k0r/π)1/2 exp(jπ/4)×π2π{exp[jn4k0r(ηi-1)]+pr* exp[jn4k0r(ηr-1)]}BC-(θ)dθ+(1/4)(2n4k0r/π)1/2 exp(-jπ/4)×π2π{ηi exp[-jn4k0r(ηi-1)]+ηrpr exp[-jn4k0r(ηr-1)]}BC-*(θ)dθ,
ηi=-cos(3π/2+θi)cos-sin(3π/2+θi)sin θ,
ηr=cos(3π/2+θi)cos θ-sin(3π/2+θi)sin θ.
π2π exp[jn4k0r(ηi-1)]BC-(θ)dθ[2π/(n4k0r)]1/2 exp(-j2n4k0r+jπ/4)×BC-(3π/2+θi),
π2πpr* exp[jn4k0r(ηr-1)]BC-(θ)dθ[2π/(n4k0r)]1/2×exp(j3π/4)pr*BC-(3π/2-θi),
π2πηi exp[jn4k0r(ηi-1)]BC-*(θ)dθ-[2π/(n4k0r)]1/2×exp(-j2n4k0r+jπ/4)BC-*(3π/2+θi),
π2πηrpr exp[jn4k0r(ηr-1)]BC-(θ)*dθ[2π/(n4k0r)]1/2×exp(-j3π/4)prBC-*(3π/2-θi).
C0+C++C-(EIEC/n-ECEI/n)dl=0,
EI=EIs+E-(1)+RE+(1)ontheboundaryC0+C+EIsontheboundaryC-,
EC=ECs+Et+TE+(1)ontheboundaryC0+C+ECs+Ei+ErontheboundaryC-,
C0+C+{E-(1)[ECs+TE+(1)]/n-[ECs+TE+(1)]E-(1)/n}dl=C-[(Ei+Er)EIs/n-EIs(Ei+Er)/n]dl.
TC0[E-(1)E+(1)/n-E+(1)E-(1)/n]dl=-jβT-|E+(1)(x, const)|2 dx.
C-[(Ei+Er)EIs/n-EIs(Ei+Er)n]dl-jBI-(3π/2+θi).

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