Abstract

We present a theoretical investigation of a semiconductor quantum dot interacting with a strongly localized optical field as encountered in high-resolution near-field optical microscopy. The strong gradients of these localized fields suggest that higher-order multipolar interactions will affect the standard electric dipole transition rates and selection rules. For a semiconductor quantum dot in the strong confinement limit we calculated the interband electric quadrupole absorption rate and the associated selection rules. We found that the electric quadrupole absorption rate is comparable with the absorption rate calculated in the electric dipole approximation. This implies that near-field optical techniques can extend the range of spectroscopic measurements beyond the standard dipole approximation. However, we also show that spatial resolution cannot be improved by the selective excitation of electric quadrupole transitions.

© 2002 Optical Society of America

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  1. For a recent review, see, R. C. Dunn, “Near-field scanning optical microscopy,” Chem. Rev. 99, 2891–2927 (1999).
    [CrossRef]
  2. N. van Hulst, ed., Proceedings of the 6th International Near-field Optics Conference, J. Microsc. (Oxford) 202, 1–450 (2001).
    [CrossRef]
  3. R. D. Grober, T. D. Harris, J. K. Trautman, E. Betzig, W. Wegscheider, L. Pfeiffer, and K. W. West, “Optical spectros-copy of GaAs/AlGaAs quantum wire structure using near-field scanning optical microscopy,” Appl. Phys. Lett. 64, 1421–1423 (1994).
    [CrossRef]
  4. J. Levy, V. Nikitin, J. M. Kikkawa, A. Cohen, N. Samarth, R. Garcia, and D. D. Awschalom, “Spatiotemporal near-field spin microscopy in patterned magnetic heterostructures,” Phys. Rev. Lett. 76, 1948–1951 (1996).
    [CrossRef] [PubMed]
  5. A. Richter, M. Stüptitz, Ch. Lienau, T. Elsaesser, M. Ramsteiner, R. Nötzel, and K. H. Ploog, “Carrier trapping into single GaAs quantum wires studied by variable temperature near-field spectroscopy,” Ultramicroscopy 71, 205–212 (1998).
    [CrossRef]
  6. A. von der Heydt, A. Knorr, B. Hanewinkel, and S. W. Koch, “Optical near-field excitation at the semiconductor band edge: field distributions, anisotropic transitions and quadrupole enhancement,” J. Chem. Phys. 112, 7831–7838 (2000).
    [CrossRef]
  7. O. Mauritz, G. Goldoni, F. Rossi, and E. Molinari, “Local optical spectroscopy in quantum confined systems: a theoretical description,” Phys. Rev. Lett. 82, 847–850 (1999).
    [CrossRef]
  8. A. Knorr, S. W. Koch, and W. W. Chow, “Optics in the multipole approximation: from atomic systems to solids,” Opt. Commun. 179, 167–178 (2000).
    [CrossRef]
  9. B. Hanewinkel, A. Knorr, P. Thomas, and S. W. Koch, “Optical near-field response of semiconductor quantum dots,” Phys. Rev. B 55, 13,715–13,725 (1997).
    [CrossRef]
  10. G. W. Bryant, “Probing quantum nanostructures with near-field microscopy and vice versa,” Appl. Phys. Lett. 72, 768–770 (1998).
    [CrossRef]
  11. A. Chavez-Pirson and S. T. Chu, “A full vector analysis of near-field luminescence probing of a single quantum dot,” Appl. Phys. Lett. 74, 1507–1509 (1999).
    [CrossRef]
  12. H. F. Hamann, M. Kuno, A. Gallagher, and D. J. Nesbitt, “Molecular fluorescence in the vicinity of a nanoscopic probe,” J. Chem. Phys. 114, 8596–8609 (2001).
    [CrossRef]
  13. Y. C. Martin, H. F. Hamann, and H. K. Wickramasinghe, “Strength of the electric field in apertureless optical near-field microscopy,” J. Appl. Phys. 89, 5774–5778 (2001).
    [CrossRef]
  14. E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014–4017 (1999), and references therein.
    [CrossRef]
  15. L. Novotny, “Forces in optical near-fields,” in Near-Field Optics and Surface Plasmon Polaritons, S. Kawata, ed. (Springer-Verlag, Berlin, 2001), pp. 123–141.
  16. R. G. Woolley, “A comment on ‘The multiple Hamiltonian for time dependent fields,’” J. Phys. B 6, L97–L99 (1973).
    [CrossRef]
  17. L. D. Barron and C. G. Gray, “The multiple interaction Hamiltonian for time dependent fields,” J. Phys. A 6, 59–61 (1973).
    [CrossRef]
  18. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1993).
  19. L. Bányai and S. W. Koch, Semiconductor Quantum Dots (World Scientific, Singapore, 1993).
  20. Ch. Hafner, The Generalized Multiple Multipole Technique for Computational Electromagnetics (Artech House, Norwood, Mass., 1990).
  21. L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79, 645–648 (1997).
    [CrossRef]
  22. C. T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1993).
  23. P. Yu and M. Cardona, Fundamentals of Semiconductors (Springer-Verlag, Berlin, 1996).

2001 (3)

N. van Hulst, ed., Proceedings of the 6th International Near-field Optics Conference, J. Microsc. (Oxford) 202, 1–450 (2001).
[CrossRef]

H. F. Hamann, M. Kuno, A. Gallagher, and D. J. Nesbitt, “Molecular fluorescence in the vicinity of a nanoscopic probe,” J. Chem. Phys. 114, 8596–8609 (2001).
[CrossRef]

Y. C. Martin, H. F. Hamann, and H. K. Wickramasinghe, “Strength of the electric field in apertureless optical near-field microscopy,” J. Appl. Phys. 89, 5774–5778 (2001).
[CrossRef]

2000 (2)

A. von der Heydt, A. Knorr, B. Hanewinkel, and S. W. Koch, “Optical near-field excitation at the semiconductor band edge: field distributions, anisotropic transitions and quadrupole enhancement,” J. Chem. Phys. 112, 7831–7838 (2000).
[CrossRef]

A. Knorr, S. W. Koch, and W. W. Chow, “Optics in the multipole approximation: from atomic systems to solids,” Opt. Commun. 179, 167–178 (2000).
[CrossRef]

1999 (4)

O. Mauritz, G. Goldoni, F. Rossi, and E. Molinari, “Local optical spectroscopy in quantum confined systems: a theoretical description,” Phys. Rev. Lett. 82, 847–850 (1999).
[CrossRef]

For a recent review, see, R. C. Dunn, “Near-field scanning optical microscopy,” Chem. Rev. 99, 2891–2927 (1999).
[CrossRef]

E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014–4017 (1999), and references therein.
[CrossRef]

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

1998 (2)

A. Richter, M. Stüptitz, Ch. Lienau, T. Elsaesser, M. Ramsteiner, R. Nötzel, and K. H. Ploog, “Carrier trapping into single GaAs quantum wires studied by variable temperature near-field spectroscopy,” Ultramicroscopy 71, 205–212 (1998).
[CrossRef]

G. W. Bryant, “Probing quantum nanostructures with near-field microscopy and vice versa,” Appl. Phys. Lett. 72, 768–770 (1998).
[CrossRef]

1997 (2)

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79, 645–648 (1997).
[CrossRef]

B. Hanewinkel, A. Knorr, P. Thomas, and S. W. Koch, “Optical near-field response of semiconductor quantum dots,” Phys. Rev. B 55, 13,715–13,725 (1997).
[CrossRef]

1996 (1)

J. Levy, V. Nikitin, J. M. Kikkawa, A. Cohen, N. Samarth, R. Garcia, and D. D. Awschalom, “Spatiotemporal near-field spin microscopy in patterned magnetic heterostructures,” Phys. Rev. Lett. 76, 1948–1951 (1996).
[CrossRef] [PubMed]

1994 (1)

R. D. Grober, T. D. Harris, J. K. Trautman, E. Betzig, W. Wegscheider, L. Pfeiffer, and K. W. West, “Optical spectros-copy of GaAs/AlGaAs quantum wire structure using near-field scanning optical microscopy,” Appl. Phys. Lett. 64, 1421–1423 (1994).
[CrossRef]

1973 (2)

R. G. Woolley, “A comment on ‘The multiple Hamiltonian for time dependent fields,’” J. Phys. B 6, L97–L99 (1973).
[CrossRef]

L. D. Barron and C. G. Gray, “The multiple interaction Hamiltonian for time dependent fields,” J. Phys. A 6, 59–61 (1973).
[CrossRef]

Awschalom, D. D.

J. Levy, V. Nikitin, J. M. Kikkawa, A. Cohen, N. Samarth, R. Garcia, and D. D. Awschalom, “Spatiotemporal near-field spin microscopy in patterned magnetic heterostructures,” Phys. Rev. Lett. 76, 1948–1951 (1996).
[CrossRef] [PubMed]

Barron, L. D.

L. D. Barron and C. G. Gray, “The multiple interaction Hamiltonian for time dependent fields,” J. Phys. A 6, 59–61 (1973).
[CrossRef]

Betzig, E.

R. D. Grober, T. D. Harris, J. K. Trautman, E. Betzig, W. Wegscheider, L. Pfeiffer, and K. W. West, “Optical spectros-copy of GaAs/AlGaAs quantum wire structure using near-field scanning optical microscopy,” Appl. Phys. Lett. 64, 1421–1423 (1994).
[CrossRef]

Bian, R. X.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79, 645–648 (1997).
[CrossRef]

Bryant, G. W.

G. W. Bryant, “Probing quantum nanostructures with near-field microscopy and vice versa,” Appl. Phys. Lett. 72, 768–770 (1998).
[CrossRef]

Chavez-Pirson, A.

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

Chow, W. W.

A. Knorr, S. W. Koch, and W. W. Chow, “Optics in the multipole approximation: from atomic systems to solids,” Opt. Commun. 179, 167–178 (2000).
[CrossRef]

Chu, S. T.

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

Cohen, A.

J. Levy, V. Nikitin, J. M. Kikkawa, A. Cohen, N. Samarth, R. Garcia, and D. D. Awschalom, “Spatiotemporal near-field spin microscopy in patterned magnetic heterostructures,” Phys. Rev. Lett. 76, 1948–1951 (1996).
[CrossRef] [PubMed]

Dunn, R. C.

For a recent review, see, R. C. Dunn, “Near-field scanning optical microscopy,” Chem. Rev. 99, 2891–2927 (1999).
[CrossRef]

Elsaesser, T.

A. Richter, M. Stüptitz, Ch. Lienau, T. Elsaesser, M. Ramsteiner, R. Nötzel, and K. H. Ploog, “Carrier trapping into single GaAs quantum wires studied by variable temperature near-field spectroscopy,” Ultramicroscopy 71, 205–212 (1998).
[CrossRef]

Gallagher, A.

H. F. Hamann, M. Kuno, A. Gallagher, and D. J. Nesbitt, “Molecular fluorescence in the vicinity of a nanoscopic probe,” J. Chem. Phys. 114, 8596–8609 (2001).
[CrossRef]

Garcia, R.

J. Levy, V. Nikitin, J. M. Kikkawa, A. Cohen, N. Samarth, R. Garcia, and D. D. Awschalom, “Spatiotemporal near-field spin microscopy in patterned magnetic heterostructures,” Phys. Rev. Lett. 76, 1948–1951 (1996).
[CrossRef] [PubMed]

Goldoni, G.

O. Mauritz, G. Goldoni, F. Rossi, and E. Molinari, “Local optical spectroscopy in quantum confined systems: a theoretical description,” Phys. Rev. Lett. 82, 847–850 (1999).
[CrossRef]

Gray, C. G.

L. D. Barron and C. G. Gray, “The multiple interaction Hamiltonian for time dependent fields,” J. Phys. A 6, 59–61 (1973).
[CrossRef]

Grober, R. D.

R. D. Grober, T. D. Harris, J. K. Trautman, E. Betzig, W. Wegscheider, L. Pfeiffer, and K. W. West, “Optical spectros-copy of GaAs/AlGaAs quantum wire structure using near-field scanning optical microscopy,” Appl. Phys. Lett. 64, 1421–1423 (1994).
[CrossRef]

Hamann, H. F.

Y. C. Martin, H. F. Hamann, and H. K. Wickramasinghe, “Strength of the electric field in apertureless optical near-field microscopy,” J. Appl. Phys. 89, 5774–5778 (2001).
[CrossRef]

H. F. Hamann, M. Kuno, A. Gallagher, and D. J. Nesbitt, “Molecular fluorescence in the vicinity of a nanoscopic probe,” J. Chem. Phys. 114, 8596–8609 (2001).
[CrossRef]

Hanewinkel, B.

A. von der Heydt, A. Knorr, B. Hanewinkel, and S. W. Koch, “Optical near-field excitation at the semiconductor band edge: field distributions, anisotropic transitions and quadrupole enhancement,” J. Chem. Phys. 112, 7831–7838 (2000).
[CrossRef]

B. Hanewinkel, A. Knorr, P. Thomas, and S. W. Koch, “Optical near-field response of semiconductor quantum dots,” Phys. Rev. B 55, 13,715–13,725 (1997).
[CrossRef]

Harris, T. D.

R. D. Grober, T. D. Harris, J. K. Trautman, E. Betzig, W. Wegscheider, L. Pfeiffer, and K. W. West, “Optical spectros-copy of GaAs/AlGaAs quantum wire structure using near-field scanning optical microscopy,” Appl. Phys. Lett. 64, 1421–1423 (1994).
[CrossRef]

Kikkawa, J. M.

J. Levy, V. Nikitin, J. M. Kikkawa, A. Cohen, N. Samarth, R. Garcia, and D. D. Awschalom, “Spatiotemporal near-field spin microscopy in patterned magnetic heterostructures,” Phys. Rev. Lett. 76, 1948–1951 (1996).
[CrossRef] [PubMed]

Knorr, A.

A. Knorr, S. W. Koch, and W. W. Chow, “Optics in the multipole approximation: from atomic systems to solids,” Opt. Commun. 179, 167–178 (2000).
[CrossRef]

A. von der Heydt, A. Knorr, B. Hanewinkel, and S. W. Koch, “Optical near-field excitation at the semiconductor band edge: field distributions, anisotropic transitions and quadrupole enhancement,” J. Chem. Phys. 112, 7831–7838 (2000).
[CrossRef]

B. Hanewinkel, A. Knorr, P. Thomas, and S. W. Koch, “Optical near-field response of semiconductor quantum dots,” Phys. Rev. B 55, 13,715–13,725 (1997).
[CrossRef]

Koch, S. W.

A. Knorr, S. W. Koch, and W. W. Chow, “Optics in the multipole approximation: from atomic systems to solids,” Opt. Commun. 179, 167–178 (2000).
[CrossRef]

A. von der Heydt, A. Knorr, B. Hanewinkel, and S. W. Koch, “Optical near-field excitation at the semiconductor band edge: field distributions, anisotropic transitions and quadrupole enhancement,” J. Chem. Phys. 112, 7831–7838 (2000).
[CrossRef]

B. Hanewinkel, A. Knorr, P. Thomas, and S. W. Koch, “Optical near-field response of semiconductor quantum dots,” Phys. Rev. B 55, 13,715–13,725 (1997).
[CrossRef]

Kuno, M.

H. F. Hamann, M. Kuno, A. Gallagher, and D. J. Nesbitt, “Molecular fluorescence in the vicinity of a nanoscopic probe,” J. Chem. Phys. 114, 8596–8609 (2001).
[CrossRef]

Levy, J.

J. Levy, V. Nikitin, J. M. Kikkawa, A. Cohen, N. Samarth, R. Garcia, and D. D. Awschalom, “Spatiotemporal near-field spin microscopy in patterned magnetic heterostructures,” Phys. Rev. Lett. 76, 1948–1951 (1996).
[CrossRef] [PubMed]

Lienau, Ch.

A. Richter, M. Stüptitz, Ch. Lienau, T. Elsaesser, M. Ramsteiner, R. Nötzel, and K. H. Ploog, “Carrier trapping into single GaAs quantum wires studied by variable temperature near-field spectroscopy,” Ultramicroscopy 71, 205–212 (1998).
[CrossRef]

Martin, Y. C.

Y. C. Martin, H. F. Hamann, and H. K. Wickramasinghe, “Strength of the electric field in apertureless optical near-field microscopy,” J. Appl. Phys. 89, 5774–5778 (2001).
[CrossRef]

Mauritz, O.

O. Mauritz, G. Goldoni, F. Rossi, and E. Molinari, “Local optical spectroscopy in quantum confined systems: a theoretical description,” Phys. Rev. Lett. 82, 847–850 (1999).
[CrossRef]

Molinari, E.

O. Mauritz, G. Goldoni, F. Rossi, and E. Molinari, “Local optical spectroscopy in quantum confined systems: a theoretical description,” Phys. Rev. Lett. 82, 847–850 (1999).
[CrossRef]

Nesbitt, D. J.

H. F. Hamann, M. Kuno, A. Gallagher, and D. J. Nesbitt, “Molecular fluorescence in the vicinity of a nanoscopic probe,” J. Chem. Phys. 114, 8596–8609 (2001).
[CrossRef]

Nikitin, V.

J. Levy, V. Nikitin, J. M. Kikkawa, A. Cohen, N. Samarth, R. Garcia, and D. D. Awschalom, “Spatiotemporal near-field spin microscopy in patterned magnetic heterostructures,” Phys. Rev. Lett. 76, 1948–1951 (1996).
[CrossRef] [PubMed]

Nötzel, R.

A. Richter, M. Stüptitz, Ch. Lienau, T. Elsaesser, M. Ramsteiner, R. Nötzel, and K. H. Ploog, “Carrier trapping into single GaAs quantum wires studied by variable temperature near-field spectroscopy,” Ultramicroscopy 71, 205–212 (1998).
[CrossRef]

Novotny, L.

E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014–4017 (1999), and references therein.
[CrossRef]

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79, 645–648 (1997).
[CrossRef]

Pfeiffer, L.

R. D. Grober, T. D. Harris, J. K. Trautman, E. Betzig, W. Wegscheider, L. Pfeiffer, and K. W. West, “Optical spectros-copy of GaAs/AlGaAs quantum wire structure using near-field scanning optical microscopy,” Appl. Phys. Lett. 64, 1421–1423 (1994).
[CrossRef]

Ploog, K. H.

A. Richter, M. Stüptitz, Ch. Lienau, T. Elsaesser, M. Ramsteiner, R. Nötzel, and K. H. Ploog, “Carrier trapping into single GaAs quantum wires studied by variable temperature near-field spectroscopy,” Ultramicroscopy 71, 205–212 (1998).
[CrossRef]

Ramsteiner, M.

A. Richter, M. Stüptitz, Ch. Lienau, T. Elsaesser, M. Ramsteiner, R. Nötzel, and K. H. Ploog, “Carrier trapping into single GaAs quantum wires studied by variable temperature near-field spectroscopy,” Ultramicroscopy 71, 205–212 (1998).
[CrossRef]

Richter, A.

A. Richter, M. Stüptitz, Ch. Lienau, T. Elsaesser, M. Ramsteiner, R. Nötzel, and K. H. Ploog, “Carrier trapping into single GaAs quantum wires studied by variable temperature near-field spectroscopy,” Ultramicroscopy 71, 205–212 (1998).
[CrossRef]

Rossi, F.

O. Mauritz, G. Goldoni, F. Rossi, and E. Molinari, “Local optical spectroscopy in quantum confined systems: a theoretical description,” Phys. Rev. Lett. 82, 847–850 (1999).
[CrossRef]

Samarth, N.

J. Levy, V. Nikitin, J. M. Kikkawa, A. Cohen, N. Samarth, R. Garcia, and D. D. Awschalom, “Spatiotemporal near-field spin microscopy in patterned magnetic heterostructures,” Phys. Rev. Lett. 76, 1948–1951 (1996).
[CrossRef] [PubMed]

Sánchez, E. J.

E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014–4017 (1999), and references therein.
[CrossRef]

Stüptitz, M.

A. Richter, M. Stüptitz, Ch. Lienau, T. Elsaesser, M. Ramsteiner, R. Nötzel, and K. H. Ploog, “Carrier trapping into single GaAs quantum wires studied by variable temperature near-field spectroscopy,” Ultramicroscopy 71, 205–212 (1998).
[CrossRef]

Thomas, P.

B. Hanewinkel, A. Knorr, P. Thomas, and S. W. Koch, “Optical near-field response of semiconductor quantum dots,” Phys. Rev. B 55, 13,715–13,725 (1997).
[CrossRef]

Trautman, J. K.

R. D. Grober, T. D. Harris, J. K. Trautman, E. Betzig, W. Wegscheider, L. Pfeiffer, and K. W. West, “Optical spectros-copy of GaAs/AlGaAs quantum wire structure using near-field scanning optical microscopy,” Appl. Phys. Lett. 64, 1421–1423 (1994).
[CrossRef]

van Hulst, N.

N. van Hulst, ed., Proceedings of the 6th International Near-field Optics Conference, J. Microsc. (Oxford) 202, 1–450 (2001).
[CrossRef]

von der Heydt, A.

A. von der Heydt, A. Knorr, B. Hanewinkel, and S. W. Koch, “Optical near-field excitation at the semiconductor band edge: field distributions, anisotropic transitions and quadrupole enhancement,” J. Chem. Phys. 112, 7831–7838 (2000).
[CrossRef]

Wegscheider, W.

R. D. Grober, T. D. Harris, J. K. Trautman, E. Betzig, W. Wegscheider, L. Pfeiffer, and K. W. West, “Optical spectros-copy of GaAs/AlGaAs quantum wire structure using near-field scanning optical microscopy,” Appl. Phys. Lett. 64, 1421–1423 (1994).
[CrossRef]

West, K. W.

R. D. Grober, T. D. Harris, J. K. Trautman, E. Betzig, W. Wegscheider, L. Pfeiffer, and K. W. West, “Optical spectros-copy of GaAs/AlGaAs quantum wire structure using near-field scanning optical microscopy,” Appl. Phys. Lett. 64, 1421–1423 (1994).
[CrossRef]

Wickramasinghe, H. K.

Y. C. Martin, H. F. Hamann, and H. K. Wickramasinghe, “Strength of the electric field in apertureless optical near-field microscopy,” J. Appl. Phys. 89, 5774–5778 (2001).
[CrossRef]

Woolley, R. G.

R. G. Woolley, “A comment on ‘The multiple Hamiltonian for time dependent fields,’” J. Phys. B 6, L97–L99 (1973).
[CrossRef]

Xie, X. S.

E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014–4017 (1999), and references therein.
[CrossRef]

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79, 645–648 (1997).
[CrossRef]

Appl. Phys. Lett. (3)

R. D. Grober, T. D. Harris, J. K. Trautman, E. Betzig, W. Wegscheider, L. Pfeiffer, and K. W. West, “Optical spectros-copy of GaAs/AlGaAs quantum wire structure using near-field scanning optical microscopy,” Appl. Phys. Lett. 64, 1421–1423 (1994).
[CrossRef]

G. W. Bryant, “Probing quantum nanostructures with near-field microscopy and vice versa,” Appl. Phys. Lett. 72, 768–770 (1998).
[CrossRef]

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

Chem. Rev. (1)

For a recent review, see, R. C. Dunn, “Near-field scanning optical microscopy,” Chem. Rev. 99, 2891–2927 (1999).
[CrossRef]

J. Appl. Phys. (1)

Y. C. Martin, H. F. Hamann, and H. K. Wickramasinghe, “Strength of the electric field in apertureless optical near-field microscopy,” J. Appl. Phys. 89, 5774–5778 (2001).
[CrossRef]

J. Chem. Phys. (2)

H. F. Hamann, M. Kuno, A. Gallagher, and D. J. Nesbitt, “Molecular fluorescence in the vicinity of a nanoscopic probe,” J. Chem. Phys. 114, 8596–8609 (2001).
[CrossRef]

A. von der Heydt, A. Knorr, B. Hanewinkel, and S. W. Koch, “Optical near-field excitation at the semiconductor band edge: field distributions, anisotropic transitions and quadrupole enhancement,” J. Chem. Phys. 112, 7831–7838 (2000).
[CrossRef]

J. Microsc. (Oxford) (1)

N. van Hulst, ed., Proceedings of the 6th International Near-field Optics Conference, J. Microsc. (Oxford) 202, 1–450 (2001).
[CrossRef]

J. Phys. A (1)

L. D. Barron and C. G. Gray, “The multiple interaction Hamiltonian for time dependent fields,” J. Phys. A 6, 59–61 (1973).
[CrossRef]

J. Phys. B (1)

R. G. Woolley, “A comment on ‘The multiple Hamiltonian for time dependent fields,’” J. Phys. B 6, L97–L99 (1973).
[CrossRef]

Opt. Commun. (1)

A. Knorr, S. W. Koch, and W. W. Chow, “Optics in the multipole approximation: from atomic systems to solids,” Opt. Commun. 179, 167–178 (2000).
[CrossRef]

Phys. Rev. B (1)

B. Hanewinkel, A. Knorr, P. Thomas, and S. W. Koch, “Optical near-field response of semiconductor quantum dots,” Phys. Rev. B 55, 13,715–13,725 (1997).
[CrossRef]

Phys. Rev. Lett. (4)

O. Mauritz, G. Goldoni, F. Rossi, and E. Molinari, “Local optical spectroscopy in quantum confined systems: a theoretical description,” Phys. Rev. Lett. 82, 847–850 (1999).
[CrossRef]

J. Levy, V. Nikitin, J. M. Kikkawa, A. Cohen, N. Samarth, R. Garcia, and D. D. Awschalom, “Spatiotemporal near-field spin microscopy in patterned magnetic heterostructures,” Phys. Rev. Lett. 76, 1948–1951 (1996).
[CrossRef] [PubMed]

E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014–4017 (1999), and references therein.
[CrossRef]

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79, 645–648 (1997).
[CrossRef]

Ultramicroscopy (1)

A. Richter, M. Stüptitz, Ch. Lienau, T. Elsaesser, M. Ramsteiner, R. Nötzel, and K. H. Ploog, “Carrier trapping into single GaAs quantum wires studied by variable temperature near-field spectroscopy,” Ultramicroscopy 71, 205–212 (1998).
[CrossRef]

Other (6)

L. Novotny, “Forces in optical near-fields,” in Near-Field Optics and Surface Plasmon Polaritons, S. Kawata, ed. (Springer-Verlag, Berlin, 2001), pp. 123–141.

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1993).

L. Bányai and S. W. Koch, Semiconductor Quantum Dots (World Scientific, Singapore, 1993).

Ch. Hafner, The Generalized Multiple Multipole Technique for Computational Electromagnetics (Artech House, Norwood, Mass., 1990).

C. T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1993).

P. Yu and M. Cardona, Fundamentals of Semiconductors (Springer-Verlag, Berlin, 1996).

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Figures (7)

Fig. 1
Fig. 1

Energy-level diagram of a spherical quantum dot according to Eqs. (14) and (15). Each energy level is characterized by quantum numbers n and l, and its degeneracy corresponds to quantum number m. Differently from the case of a hydrogen atom, quantum number n does not restrict the number of suborbitals l.

Fig. 2
Fig. 2

Diagram of the allowed electric quadrupole transitions in a spherical quantum dot. The energy levels are labeled by the quantum numbers nlm (electron) and rst (hole). The selection rules are [l-s=±1 and (m-t=±1 or m-t=0)]. The allowed electric quadrupole transitions exclude the allowed electric dipole transitions.

Fig. 3
Fig. 3

(a) Computed field distribution (|E|2) near a gold tip irradiated by a plane wave polarized along the tip’s axis. Logarithmic scaling with a factor of 2 between successive contour lines. (b) Comparison of the computed field (|E|2, solid curve) with the corresponding field of a dipole (|E|2, dashed curve) oriented along the tip’s axis and located inside the tip. Both fields are evaluated along tip axis z, where z=0 coincides with the tip’s surface.

Fig. 4
Fig. 4

Simplified configuration of a quantum dot (r=xnx+yny) interacting with a laser-illuminated metal tip. The tip is replaced with a vertical dipole (ro=zonz) with moment po and oriented along the z axis.

Fig. 5
Fig. 5

Ratio of electric quadrupole absorption rate αQ and electric dipole absorption rate αE as a function of normalized distance (zo/λo) between excitation dipole (ro=zonz) and quantum dot center (r=0). The quantum dot radius is (a) a=5 nm and (b) a=10 nm. Vertical dashed lines: minimum physical separation between the center of the quantum dot and the exciting dipole. This separation corresponds to at+a, where at=5 nm is the radius of curvature of the metal tip.

Fig. 6
Fig. 6

Electric dipole absorption rate αE as a function of normalized lateral coordinates (x/λ, y/λ). The height of the excitation dipole is zo=0.025λ. e, d, and po denote the elementary charge, the lattice constant, and the dipole moment, respectively.

Fig. 7
Fig. 7

Electric dipole absorption rate αQ as a function of normalized lateral coordinates (x/λ, y/λ). The height of the excitation dipole is zo=0.025λ. e, d, and po denote the elementary charge, the lattice constant, and the dipole moment, respectively. The quantum dot radius is (a) a=0.01λ and (b) a=0.02λ. The width of the curve is roughly the same as in Fig. 6, which indicates that no improvement of resolution can be achieved by quadrupole transitions.

Equations (48)

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Hˆ=Hˆo+HˆI,
Hˆo=12m pˆ2+V(r),
HˆI=-em pˆ·A(r, t)+e22m A2(r, t)+eϕ(r, t),
z=P˜(r)·A(r, t)d3r0,
A(r, t)=n=0 1(n+2)n![(r-R)·]nB(R, t)×(r-R),
ϕ(r, t)=n=0 -1(n+1)!(r-R)[(r-R)·]n·E(R, t),
HˆI=HˆE+HˆM+HˆQ+.
HˆE=-d·E(r, t)|r=R,
HˆM=-m·B(r, t)|r=R,
HˆQ=-1·QE(r1, t)|r1=R.
V(r)=0rar>a,
Ψe(r)=1Vouc,0(r)ζe(r).
Ψh(r)=1Vouv,0(r)ζh(r),
ζn,l,me(h)(r, θ, ϕ)=Λnl(r)Yl,m(θ, ϕ).
Λnl(r)=2a3 1jl+1(βnl)jlβnl ra.
Ee=Eg+22me βnla2,
Eh=22mh βnla2,
Ψˆ(r)=n,l,m1Vouc,0(r)ζnlme(r)fˆnlm+1Vouv,0(r)ζnlmh(r)gˆnlm.
E(r, t)=E˜(r)exp(-iωt)+c.c.
αE=Ke nmlrst δ˜nrδ˜lsδ˜mtδ[ω-(Enle+Ersh)],
Ke=2πe2|E˜(0)·Pcv|2,
Pcv=1Vo UC uc,0*(r)ruv,0(r)d3r=-moω mcv.
mcv1V0 UC uc,0*(r)uv,0(r)d3r,
n=r,l=s,m=t.
HˆQ= Ψˆ(r)HQ(r)Ψˆ(r)d3r,
HQ(r)=-1·Q(r)E(r1, t)|r1=0,
Q(r)=(1/2)err.
HˆQ=-1·nlmrst fˆnlmgˆrst  uc,0*(r)ζnlme*(r)×Q(r)uv,0(r)ζrsth(r)d3rE(r1, t)r1=0+h.c.,
HˆQ=-1·enlmrstq fˆnlmgˆrst UC uc,0*(r+Rq)×ζnlme*(r+Rq)Q(r+Rq)uv,0(r+Rq)×ζrsth(r+Rq)d3rE(r1, t)r1=0+h.c.
HˆQ-1·e nlmrstq fˆnlmgˆrstζnlme*(Rq)ζrsth(Rq)×(½RqPcv+½PcvRq+Qcv)E(r1, t)r1=0+h.c.
Qcv=12Vo UC uc,0*(r)rruv,0(r)d3r.
HˆQ=-1·enlmrst fˆnlmgˆrst[½PcvDnmlrst+½DnmlrstPcv]E(r1, t)|r1=0+h.c.
Dnmlrst ζnlme*(R)Rζrsth(R)d3R,
Dnmlrst=AnlrsBlmBstCst2(2l+1)(nx±iny)×{δ˜(m+1)t[δ˜l(s-1)+δ˜l(s+1)]+δ˜(m-1)t[(l-m+1)(l-m+2)δ˜l(s-1)-(1+m)(l+m-1)δ˜l(s+1)]}+nzClmδ˜mtl+m+12l+3δ˜l(s-1)+l-m2l-1δ˜l(s+1),
Anlrs2π 0a R3Λnl(R)Λrs(R)dR,
Blm(2l+1)4π (l-m)!(l+m)!1/2,
Clm2(l+m)!(2l+1)(l-m)!.
αQ=2π nlmrst|nml; rst|HˆintQ|0|2δ[ω-(Enle+Ersh)].
αQ=2πe2 nlmrst|1·(½PcvDnmlrst+½DnmlrstPcv)E˜(r1)|r1=0|2δ[ω-(Enle+Ersh)].
m-t=±1,l-s=±1
m-t=0,l-s=±1.
E˜(r)=ko2εo G(r, ro, ω)po.
αE=Keδ[ω-(E10e+E10h)],
Ke=2πe2|E˜(0)|2|P|2
|P|=|Pcv1|=|Pcv2|=|Pcv3|.
αQ=KQδ[ω-(E10e+E10h)].
KQ=2π e22|P|2|D|2×i,jxiE˜j(0)2+xiE˜j(0) xjE˜i*(0).
|D|=|D100110|=|D100111|=|D10011-1|.

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