Abstract

A new type of integral equations called guided-mode extracted integral equations, which has been developed by the authors, is applied to the simulations of a two-dimensional near-field optical circuit. An optical manipulator is taken as an example of near-field optical circuits. New integral equations that were obtained can be solved numerically by the conventional boundary-element method or by the moment method. Examples of computer simulations for the optical manipulator are presented. Simulation results show the validity and the correctness of the proposed method and reveal physical properties of the manipulation of a small particle by laser light emitted from a fiber probe.

© 1998 Optical Society of America

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  1. D. W. Pohl, D. Courjon, eds., Near Field Optics (Kluwer Academic, Dordrecht, The Netherlands, 1993).
  2. E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
    [CrossRef] [PubMed]
  3. E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
    [CrossRef] [PubMed]
  4. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
    [CrossRef]
  5. A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
    [CrossRef] [PubMed]
  6. W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
    [CrossRef]
  7. K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. I. Rayleigh scatterers,” Optik 89, 174–180 (1992).
  8. K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. II. Mie scatterers,” Optik 90, 57–60 (1992).
  9. E. R. Lyons, G. J. Sonek, “Confinement and bistability in a tapered hemispherically lensed optical fiber trap,” Appl. Phys. Lett. 66, 1584–1586 (1995).
    [CrossRef]
  10. J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
    [CrossRef]
  11. E. Betzig, J. K. Trautman, R. Wolf, E. M. Gyorgy, P. L. Finn, M. H. Kryder, C.-H. Chang, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
    [CrossRef]
  12. C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
    [CrossRef]
  13. D. Van Labeke, D. Barchiesi, “Scanning-tunneling optical microscopy: a theoretical macroscopic approach,” J. Opt. Soc. Am. A 9, 732–739 (1992).
    [CrossRef]
  14. 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]
  15. O. Marti, V. I. Balykin, “Light force on dielectric particles and atoms,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1993).
  16. F. Depasse, D. Courjon, “Inductive forces generated by evanescent light fields: application to local probe microscopy,” Opt. Commun. 87, 79–83 (1992).
    [CrossRef]
  17. S. Kawata, T. Sugiura, “Movement of micrometer-sized particles in the evanescent field of a laser beam,” Opt. Lett. 17, 772–774 (1992).
    [CrossRef] [PubMed]
  18. C. Girard, A. Dereux, O. J. F. Martin, “Theoretical analysis of light-inductive forces in scanning probe microscopy,” Phys. Rev. B 49, 13872–13881 (1994).
    [CrossRef]
  19. P. Kaczmarski, P. E. Lagasse, “Bidirectional beam propagation method,” Electron. Lett. 24, 675–676 (1988).
    [CrossRef]
  20. D. Yevick, B. Hermansson, “New formulation of the matrix beam propagation method: application to rib waveguides,” IEEE J. Quantum Electron. 25, 221–229 (1989).
    [CrossRef]
  21. K. B. Koch, J. B. Davies, D. Wickramasinghe, “Finite element finite difference propagation algorithm for beam propagation,” Electron. Lett. 25, 515–516 (1990).
  22. 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]
  23. 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]
  24. K. Tanaka, M. Tanaka, “Computer-aided design of dielectric optical waveguide bends by the boundary-element method based on guided-mode extracted integral equations,” J. Opt. Soc. Am. A 13, 1362–1368 (1996).
    [CrossRef]
  25. M. Tanaka, K. Tanaka, “Computer simulations of a near-field optical circuit by integral equation method,” in 1994 Asia-Pacific Microwave Conference Proceedings, Tokyo, Japan, 1994, pp. 1245–1248.
  26. M. Tanaka, K. Tanaka, “Boundary integral equations for computer aided design of near-field optics,” Trans. IEICE Japan J79-C-I, 101–108 (1996).
  27. J. Van Bladel, Relativity and Engineering (Springer-Verlag, Berlin, 1994), Chap. 6.
  28. E. Almaas, I. Brevik, “Radiation forces on a micrometer-sized sphere in an evanescent field,” J. Opt. Soc. Am. B 12, 2429–2438 (1995).
    [CrossRef]
  29. J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
    [CrossRef]

1996 (2)

K. Tanaka, M. Tanaka, “Computer-aided design of dielectric optical waveguide bends by the boundary-element method 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 Japan J79-C-I, 101–108 (1996).

1995 (2)

E. Almaas, I. Brevik, “Radiation forces on a micrometer-sized sphere in an evanescent field,” J. Opt. Soc. Am. B 12, 2429–2438 (1995).
[CrossRef]

E. R. Lyons, G. J. Sonek, “Confinement and bistability in a tapered hemispherically lensed optical fiber trap,” Appl. Phys. Lett. 66, 1584–1586 (1995).
[CrossRef]

1994 (2)

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]

C. Girard, A. Dereux, O. J. F. Martin, “Theoretical analysis of light-inductive forces in scanning probe microscopy,” Phys. Rev. B 49, 13872–13881 (1994).
[CrossRef]

1993 (1)

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 (7)

F. Depasse, D. Courjon, “Inductive forces generated by evanescent light fields: application to local probe microscopy,” Opt. Commun. 87, 79–83 (1992).
[CrossRef]

S. Kawata, T. Sugiura, “Movement of micrometer-sized particles in the evanescent field of a laser beam,” Opt. Lett. 17, 772–774 (1992).
[CrossRef] [PubMed]

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

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

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. I. Rayleigh scatterers,” Optik 89, 174–180 (1992).

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. II. Mie scatterers,” Optik 90, 57–60 (1992).

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

1991 (1)

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef] [PubMed]

1990 (3)

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (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]

K. B. Koch, J. B. Davies, D. Wickramasinghe, “Finite element finite difference propagation algorithm for beam propagation,” Electron. Lett. 25, 515–516 (1990).

1989 (3)

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]

D. Yevick, B. Hermansson, “New formulation of the matrix beam propagation method: application to rib waveguides,” IEEE J. Quantum Electron. 25, 221–229 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

1988 (1)

P. Kaczmarski, P. E. Lagasse, “Bidirectional beam propagation method,” Electron. Lett. 24, 675–676 (1988).
[CrossRef]

1980 (1)

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
[CrossRef] [PubMed]

1973 (1)

J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
[CrossRef]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

Almaas, E.

Ashkin, A.

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Balykin, V. I.

O. Marti, V. I. Balykin, “Light force on dielectric particles and atoms,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1993).

Barchiesi, D.

Barton, J. P.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

Berns, M. W.

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

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. Wolf, E. M. Gyorgy, P. L. Finn, M. H. Kryder, C.-H. Chang, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef] [PubMed]

Brakenhoff, G. J.

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. I. Rayleigh scatterers,” Optik 89, 174–180 (1992).

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. II. Mie scatterers,” Optik 90, 57–60 (1992).

Brevik, I.

Chang, C.-H.

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

Courjon, D.

F. Depasse, D. Courjon, “Inductive forces generated by evanescent light fields: application to local probe microscopy,” Opt. Commun. 87, 79–83 (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]

Davies, J. B.

K. B. Koch, J. B. Davies, D. Wickramasinghe, “Finite element finite difference propagation algorithm for beam propagation,” Electron. Lett. 25, 515–516 (1990).

Depasse, F.

F. Depasse, D. Courjon, “Inductive forces generated by evanescent light fields: application to local probe microscopy,” Opt. Commun. 87, 79–83 (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]

C. Girard, A. Dereux, O. J. F. Martin, “Theoretical analysis of light-inductive forces in scanning probe microscopy,” Phys. Rev. B 49, 13872–13881 (1994).
[CrossRef]

Finn, P. L.

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

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]

C. Girard, A. Dereux, O. J. F. Martin, “Theoretical analysis of light-inductive forces in scanning probe microscopy,” Phys. Rev. B 49, 13872–13881 (1994).
[CrossRef]

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

Gordon, J. P.

J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
[CrossRef]

Gyorgy, E. M.

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

Harris, T. D.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef] [PubMed]

Hermansson, B.

D. Yevick, B. Hermansson, “New formulation of the matrix beam propagation method: application to rib waveguides,” IEEE J. Quantum Electron. 25, 221–229 (1989).
[CrossRef]

Kaczmarski, P.

P. Kaczmarski, P. E. Lagasse, “Bidirectional beam propagation method,” Electron. Lett. 24, 675–676 (1988).
[CrossRef]

Kawata, S.

Koch, K. B.

K. B. Koch, J. B. Davies, D. Wickramasinghe, “Finite element finite difference propagation algorithm for beam propagation,” Electron. Lett. 25, 515–516 (1990).

Kojima, M.

Kostelak, R. L.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef] [PubMed]

Kryder, M. H.

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

Lagasse, P. E.

P. Kaczmarski, P. E. Lagasse, “Bidirectional beam propagation method,” Electron. Lett. 24, 675–676 (1988).
[CrossRef]

Lyons, E. R.

E. R. Lyons, G. J. Sonek, “Confinement and bistability in a tapered hemispherically lensed optical fiber trap,” Appl. Phys. Lett. 66, 1584–1586 (1995).
[CrossRef]

Marti, O.

O. Marti, V. I. Balykin, “Light force on dielectric particles and atoms,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1993).

Martin, O. J. F.

C. Girard, A. Dereux, O. J. F. Martin, “Theoretical analysis of light-inductive forces in scanning probe microscopy,” Phys. Rev. B 49, 13872–13881 (1994).
[CrossRef]

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]

Schaub, S. A.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

Sonek, G. J.

E. R. Lyons, G. J. Sonek, “Confinement and bistability in a tapered hemispherically lensed optical fiber trap,” Appl. Phys. Lett. 66, 1584–1586 (1995).
[CrossRef]

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Sugiura, T.

Tadir, Y.

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Tanaka, K.

K. Tanaka, M. Tanaka, “Computer-aided design of dielectric optical waveguide bends by the boundary-element method 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 Japan J79-C-I, 101–108 (1996).

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]

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]

M. Tanaka, K. Tanaka, “Computer simulations of a near-field optical circuit by integral equation method,” in 1994 Asia-Pacific Microwave Conference Proceedings, Tokyo, Japan, 1994, pp. 1245–1248.

Tanaka, M.

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

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

M. Tanaka, K. Tanaka, “Computer simulations of a near-field optical circuit by integral equation method,” in 1994 Asia-Pacific Microwave Conference Proceedings, Tokyo, Japan, 1994, pp. 1245–1248.

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]

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. Wolf, E. M. Gyorgy, P. L. Finn, M. H. Kryder, C.-H. Chang, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef] [PubMed]

Van Bladel, J.

J. Van Bladel, Relativity and Engineering (Springer-Verlag, Berlin, 1994), Chap. 6.

Van Labeke, D.

Visscher, K.

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. II. Mie scatterers,” Optik 90, 57–60 (1992).

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. I. Rayleigh scatterers,” Optik 89, 174–180 (1992).

Weiner, J. S.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef] [PubMed]

Wickramasinghe, D.

K. B. Koch, J. B. Davies, D. Wickramasinghe, “Finite element finite difference propagation algorithm for beam propagation,” Electron. Lett. 25, 515–516 (1990).

Wolf, R.

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

Wright, W. H.

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Yevick, D.

D. Yevick, B. Hermansson, “New formulation of the matrix beam propagation method: application to rib waveguides,” IEEE J. Quantum Electron. 25, 221–229 (1989).
[CrossRef]

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]

Appl. Phys. Lett. (2)

E. R. Lyons, G. J. Sonek, “Confinement and bistability in a tapered hemispherically lensed optical fiber trap,” Appl. Phys. Lett. 66, 1584–1586 (1995).
[CrossRef]

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

Electron. Lett. (2)

P. Kaczmarski, P. E. Lagasse, “Bidirectional beam propagation method,” Electron. Lett. 24, 675–676 (1988).
[CrossRef]

K. B. Koch, J. B. Davies, D. Wickramasinghe, “Finite element finite difference propagation algorithm for beam propagation,” Electron. Lett. 25, 515–516 (1990).

IEEE J. Quantum Electron. (2)

D. Yevick, B. Hermansson, “New formulation of the matrix beam propagation method: application to rib waveguides,” IEEE J. Quantum Electron. 25, 221–229 (1989).
[CrossRef]

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

J. Appl. Phys. (1)

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

J. Opt. Soc. Am. A (3)

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

Opt. Commun. (1)

F. Depasse, D. Courjon, “Inductive forces generated by evanescent light fields: application to local probe microscopy,” Opt. Commun. 87, 79–83 (1992).
[CrossRef]

Opt. Lett. (1)

Optik (2)

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. I. Rayleigh scatterers,” Optik 89, 174–180 (1992).

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. II. Mie scatterers,” Optik 90, 57–60 (1992).

Phys. Rev. A (1)

J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
[CrossRef]

Phys. Rev. B (3)

C. Girard, A. Dereux, O. J. F. Martin, “Theoretical analysis of light-inductive forces in scanning probe microscopy,” Phys. Rev. B 49, 13872–13881 (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]

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

Phys. Rev. Lett. (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Radio Sci. (1)

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]

Science (3)

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
[CrossRef] [PubMed]

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Trans. IEICE Japan (1)

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

Other (4)

J. Van Bladel, Relativity and Engineering (Springer-Verlag, Berlin, 1994), Chap. 6.

M. Tanaka, K. Tanaka, “Computer simulations of a near-field optical circuit by integral equation method,” in 1994 Asia-Pacific Microwave Conference Proceedings, Tokyo, Japan, 1994, pp. 1245–1248.

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

O. Marti, V. I. Balykin, “Light force on dielectric particles and atoms,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1993).

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Figures (5)

Fig. 1
Fig. 1

NFO circuit considered in this paper. A particle is located in the vicinity of the optical fiber probe. The TE and the TM guided modes are incident from x=-.

Fig. 2
Fig. 2

(a) X-direction forces on the particle located on the x axis at a distance k0Lx from the fiber-probe tip in the case of the incident TE mode. Filled circles represent that the force is attractive; open circles represent that the force is repulsive. Particle radii k0a are given by k0a=0.1 (circles), k0a=0.5 (square), and k0a=1.0 (triangles). (b) The x-direction forces on the particle located on the x axis at a distance k0Lx from fiber-probe tip in the case of the incident TM mode. Filled circles represent that the force is attractive; open circles represent that the force is repulsive. Particle radii k0a are given by k0a=0.1 (circles), k0a=0.5 (squares), and k0a=1.0 (triangles).

Fig. 3
Fig. 3

(a) Dependence of the x-direction force on particle position for the incident TE mode. The x-axis value of the particle is fixed to k0Lx=1.0, and the y-axis value k0Ly is increased; i.e., the particle is moved vertically away from the fiber probe. Particle radii are given by k0a=0.1 (circles), k0a=0.5 (squares), and k0a=1.0 (triangle). (b) Dependence of the y-direction force on particle position for the incident TE mode. The x-axis value of the particle is fixed to k0Lx=1.0, and the y-axis value k0Ly is increased; i.e., the particle is moved vertically away from the fiber probe. Particle radii k0a are given by k0a=0.1 (circles), k0a=0.5 (squares), and k0a=1.0 (triangles). (c) Dependence of the x-direction force on particle position for the incident TM mode. The x-axis value of the particle is fixed to k0Lx=1.0, and the y-axis value k0Ly is increased; i.e., the particle is moved vertically away from the fiber probe. Particle radii k0a are given by k0a=0.1 (circles), k0a=0.5 (squares), and k0a=1.0 (triangles). (d) Dependence of the y-direction force on particle position for the incident TM mode. The x-axis value of the particle is fixed to k0Lx=1.0, and the y-axis value k0Ly is increased; i.e., the particle is moved vertically away from the fiber probe. Particle radii k0a are given by k0a=0.1 (circles), k0a=0.5 (squares), and k0a=1.0 (triangles).

Fig. 4
Fig. 4

(a) Force distribution on the particle located at a point (k0x, k0y) in the coordinates as shown in Fig. 1 for the incident TE mode expressed by vectors. The particle radius k0a is 0.1. (b) Force distribution on the particle located at a point (k0x, k0y) in the coordinates as shown in Fig. 1 for the incident TM mode expressed by vectors. The particle radius k0a is 0.1.

Fig. 5
Fig. 5

(a) Electric-field distribution for the incident TE mode in the no-particle case. (b) Electric-field distribution for the incident TM mode in the no-particle case.

Tables (4)

Tables Icon

Table 1 Power Reflection Coefficient ΓR, Normalized Radiation Power ΓS, and Their Total ΓTOTAL for the Incident TE Modea

Tables Icon

Table 2 Power Reflection Coefficient ΓR, Normalized Radiation Power ΓS, and Their Total ΓTOTAL For the Incident TM Modea

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Table 3 Force on the Particle for the Incident TE Modea

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Table 4 Force on the Particle for the Incident TM Modea

Equations (34)

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2ϕ(x)+k02ni2ϕ(x)=0(i=1, 2, 3),
2G(x|x)+k02ni2G(x|x)=-δ(x-x)
(i=1, 2, 3),
G(x|x)=-j4H0(2)(k0ni|x-x|)
12ϕ(x)=-C+CPG1(x|x)ϕ(x)n-ϕ(x)G1(x|x)ndl,
12ϕ(x)=CG2(x|x)ϕ(x)n-ϕ(x)G2(x|x)ndl,
12ϕ(x)=CPG3(x|x)ϕ(x)n-ϕ(x)G3(x|x)ndl,
ϕ(x)=ϕC(x)+Rϕ+(1)(x)+ϕ-(1)(x),
ϕ(x)=ϕC(x).
12[ϕC(x)+Rϕ+(1)(x)+ϕ-(1)(x)]
=CG2(x|x)ϕC(x)n-ϕC(x)G2(x|x)ndl
+RC1+C2G2(x|x)ϕ+(1)(x)n-ϕ+(1)(x)G2(x|x)ndl+C1+C2G2(x|x)ϕ-(1)(x)n-ϕ-(1)(x)G2(x|x)ndl.
C1+C2G2(x|x)ϕ±(1)(x)n-ϕ±(1)(x)G2(x|x)ndl=12ϕ±(1)(x)-U±(1)(x),
U2±(1)(x)=C20G2(x|x)ϕ±(1)(x)n-ϕ±(1)(x)G2(x|x)ndl,
12ϕC(x)=CG2(x|x)ϕC(x)n-ϕC(x)G2(x|x)ndl-RU2+(1)(x)-U2-(1)(x).
G2(x|x)=A2(r)g2(θ/x),
A2(r)=-j42jπn2k0rexp(-jn2k0r),
g2(θ|x)=exp[jn2k0(x cos θ+y sin θ)]
ϕC(r, π)2A2(r)=Cg2(π|x)ϕC(x)n-ϕC(x)g2(π|x)ndl-Ru2+(1)(π)-u2-(1)(π),
u2±(1)(θ)=C20g2(θ|x)ϕ±(1)(x)n-ϕ±(1)(x)g2(θ|x)ndl.
ϕC(r, π)A2(r)=0(r).
R=Cg2(π|x)ϕC(x)n-ϕC(x)g2(π|x)ndl-u2-(1)(π)/u2+(1)(π).
12ϕC(x)=CP2(x|x)ϕC(x|x)n-ϕC(x|x)P2(x|x)ndl-S2(x),
P2(x|x)=G2(x|x)-g2(π|x)U2+(1)(x)u2+(1)(π),
S2(x)=U2-(1)(x)-U2+(1)(x)u2-(1)(π)u2+(1)(π).
12ϕC(x)=-CP1(x|x)ϕC(x|x)n-ϕC(x|x)P1(x|x)ndl-CPG1(x|x)ϕC(x|x)n-ϕC(x|x)G1(x|x)ndl-S1(x),
12ϕC(x)=CPG3(x|x)ϕC(x|x)n-ϕC(x|x)G3(x|x)ndl,
P1(x|x)=G1(x|x)-g2(π|x)U1+(1)(x)u2+(1)(π),
S1(x)=U1-(1)(x)-U1+(1)(x)u2-(1)(π)u2+(1)(π),
U1±(1)(x)=C10G1(x|x)ϕ±(1)(x)n-ϕ±(1)(x)G1(x|x)ndl,
F=S div(T(e)+T(m))ds=C02Re[(E·n)E*]-04(E·E*)n+μ02Re[(H·n)H*]-μ04(H·H*)ndl,
F=12ReS(ρE*+J×B*)ds.
Qx=Fxa0|E0|2, Qy=Fya0|E0|2fortheTEmode,
Qx=Fxaμ0|H0|2,Qy=Fyaμ0|H0|2fortheTMmode,

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