Abstract

The four-band model, derived under the effective-mass approximation for cubic semiconductor quantum dots (QDs), is compared with experimental measurements on frequency degenerate three-photon absorption (3PA) in CdSe QDs and ZnS QDs. Qualitatively, the model provides the correct prediction on the magnitude of the 3PA cross-sections, which are in the range from 10-79 to 10-77 cm6s2photon-2 in the light frequency region of interest. More noticeably, the theoretical conclusion of an increasing tendency in the 3PA cross-sections with increasing dot-size is in agreement with the experiment. The discrepancy is also found for smaller QDs (dot-radius is less than one-third of the exciton Bohr radius), which is attributed to neglecting the mixing among the three valence bands in the theory.

© 2008 Optical Society of America

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  1. X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
    [Crossref] [PubMed]
  2. D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, “Water-Soluble Quantum Dots for Multiphoton Fluorescence Imaging in Vivo,” Science 300, 1434 (2003).
    [Crossref] [PubMed]
  3. B. Dubertret, P. Skourides, D. J. Norris, V. Noireaux, A. H. Brivanlou, and A. Libchaber, “In Vivo Imaging of Quantum Dots Encapsulated in Phospholipid Micelles,” Science 298, 1759 (2002).
    [Crossref] [PubMed]
  4. G. S. He, K. T. Yong, Q. D. Zheng, Y. Sahoo, A. Baev, A. I. Ryasnyanskiy, and P. N. Prasad, “Multi-photon excitation properties of CdSe quantum dots solutions and optical limiting behavior in infrared range,” Opt. Express 15, 12818 (2007).
    [Crossref] [PubMed]
  5. F. E. Hernandez, K. D. Belfield, and I. Cohanoschi, “Three-photon absorption enhancement in a symmetrical charge transfer fluorene derivative,” Chem. Phys. Lett. 391, 22 (2004).
    [Crossref]
  6. F. E. Hernandez, K. D. Belfield, I. Cohanoschi, M. Balu, and K. J. Schafer, “Three- and Four-Photon Absorption of a Multiphoton absorbing Fluorescent Probe,” Appl. Opt. 43, 5394 (2004).
    [Crossref] [PubMed]
  7. A. V. Fedorov, A. V. Baranov, and K. Inoue, “Two-photon transitions in systems with semiconductor quantum dots,” Phys. Rev. B. 54, 8627 (1996).
    [Crossref]
  8. J. W. M. Chon, M. Gu, C. Bullen, and P. Mulvaney, “Three-photon excited band edge and trap emission of CdS semiconductor nanocrystals,” Appl. Phys. Lett. 84, 4472 (2004).
    [Crossref]
  9. J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
    [Crossref]
  10. A. D. Lad, P. P. Kiran, G. R. Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and ZnSe/ZnS quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
    [Crossref]
  11. I. M. Lifshits and V. V. Slezov, “The kinetics of diffusional decomposition of super-saturated solid solutions,” Zh. Eksp. Teor. Fiz 35, 479 (1958).
  12. P. Lawaetz, “Valence-band Parameters in Cubic Semiconductors,” Phys. Rev. B 4, 3460 (1971).
    [Crossref]
  13. D. J. Norris and M. G. Bawendi, “Measurement and assignment of the size-dependent optical spectrum in CdSe quantum dots,” Phys. Rev. B 53, 16338 (1996).
    [Crossref]
  14. L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B 75, 075325 (2007).
    [Crossref]
  15. L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, and C. H. B. Cruz, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460 (2004).
    [Crossref]
  16. Y. Nosaka, “Finite depth spherical well model for excited states of ultrasmall semiconductor particles: an application,” J. Phys. Chem. 95, 5054 (1991).
    [Crossref]
  17. R. Viswanatha, S. Sapra, T. Saha-Dasgupta, and D. D. Sarma, “Electronic structure of and quantum size effect in III–V and II–VI semiconducting nanocrystals using a realistic tight binding approach,” Phys. Rev. B 72, 045333 (2005).
    [Crossref]
  18. N. Kumbhojkar, V. V. Nikesh, A. Kshirsagar, and S. Mahamuni, “Photophysical properties of ZnS nanoclusters,” J. Appl. Phys. 88, 6260 (2000).
    [Crossref]
  19. S. Sapra, A. Prakash, A. Ghangrekar, N. Periasamy, and D. D. Sarma, “Emission Properties of Manganese-Doped ZnS Nanocrystals,” J. Phys. Chem. B 109, 1663 (2005).
    [Crossref]
  20. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
    [Crossref]
  21. R. L. Sutherland, Handbook of Nonlinear Optics, with contributions by D. G. McLean and S. Kirkpatrick, Second Edition, (New York, NY: Marcel Dekker, 2003).
    [Crossref]
  22. J. He, Y. L. Qu, H. P. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13, 9235 (2005).
    [Crossref] [PubMed]
  23. I. M. Catalano, A. Cingolani, and A. Minafra, “Multiphoton impurity luminescence in zinc sulphide,” Opt. Commun. 7, 270 (1973).
    [Crossref]

2007 (3)

G. S. He, K. T. Yong, Q. D. Zheng, Y. Sahoo, A. Baev, A. I. Ryasnyanskiy, and P. N. Prasad, “Multi-photon excitation properties of CdSe quantum dots solutions and optical limiting behavior in infrared range,” Opt. Express 15, 12818 (2007).
[Crossref] [PubMed]

A. D. Lad, P. P. Kiran, G. R. Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and ZnSe/ZnS quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
[Crossref]

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B 75, 075325 (2007).
[Crossref]

2006 (1)

J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
[Crossref]

2005 (4)

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
[Crossref] [PubMed]

R. Viswanatha, S. Sapra, T. Saha-Dasgupta, and D. D. Sarma, “Electronic structure of and quantum size effect in III–V and II–VI semiconducting nanocrystals using a realistic tight binding approach,” Phys. Rev. B 72, 045333 (2005).
[Crossref]

S. Sapra, A. Prakash, A. Ghangrekar, N. Periasamy, and D. D. Sarma, “Emission Properties of Manganese-Doped ZnS Nanocrystals,” J. Phys. Chem. B 109, 1663 (2005).
[Crossref]

J. He, Y. L. Qu, H. P. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13, 9235 (2005).
[Crossref] [PubMed]

2004 (4)

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, and C. H. B. Cruz, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460 (2004).
[Crossref]

J. W. M. Chon, M. Gu, C. Bullen, and P. Mulvaney, “Three-photon excited band edge and trap emission of CdS semiconductor nanocrystals,” Appl. Phys. Lett. 84, 4472 (2004).
[Crossref]

F. E. Hernandez, K. D. Belfield, and I. Cohanoschi, “Three-photon absorption enhancement in a symmetrical charge transfer fluorene derivative,” Chem. Phys. Lett. 391, 22 (2004).
[Crossref]

F. E. Hernandez, K. D. Belfield, I. Cohanoschi, M. Balu, and K. J. Schafer, “Three- and Four-Photon Absorption of a Multiphoton absorbing Fluorescent Probe,” Appl. Opt. 43, 5394 (2004).
[Crossref] [PubMed]

2003 (1)

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, “Water-Soluble Quantum Dots for Multiphoton Fluorescence Imaging in Vivo,” Science 300, 1434 (2003).
[Crossref] [PubMed]

2002 (1)

B. Dubertret, P. Skourides, D. J. Norris, V. Noireaux, A. H. Brivanlou, and A. Libchaber, “In Vivo Imaging of Quantum Dots Encapsulated in Phospholipid Micelles,” Science 298, 1759 (2002).
[Crossref] [PubMed]

2000 (1)

N. Kumbhojkar, V. V. Nikesh, A. Kshirsagar, and S. Mahamuni, “Photophysical properties of ZnS nanoclusters,” J. Appl. Phys. 88, 6260 (2000).
[Crossref]

1996 (2)

D. J. Norris and M. G. Bawendi, “Measurement and assignment of the size-dependent optical spectrum in CdSe quantum dots,” Phys. Rev. B 53, 16338 (1996).
[Crossref]

A. V. Fedorov, A. V. Baranov, and K. Inoue, “Two-photon transitions in systems with semiconductor quantum dots,” Phys. Rev. B. 54, 8627 (1996).
[Crossref]

1991 (1)

Y. Nosaka, “Finite depth spherical well model for excited states of ultrasmall semiconductor particles: an application,” J. Phys. Chem. 95, 5054 (1991).
[Crossref]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

1973 (1)

I. M. Catalano, A. Cingolani, and A. Minafra, “Multiphoton impurity luminescence in zinc sulphide,” Opt. Commun. 7, 270 (1973).
[Crossref]

1971 (1)

P. Lawaetz, “Valence-band Parameters in Cubic Semiconductors,” Phys. Rev. B 4, 3460 (1971).
[Crossref]

1958 (1)

I. M. Lifshits and V. V. Slezov, “The kinetics of diffusional decomposition of super-saturated solid solutions,” Zh. Eksp. Teor. Fiz 35, 479 (1958).

Baev, A.

Balu, M.

Baranov, A. V.

A. V. Fedorov, A. V. Baranov, and K. Inoue, “Two-photon transitions in systems with semiconductor quantum dots,” Phys. Rev. B. 54, 8627 (1996).
[Crossref]

Barbosa, L. C.

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B 75, 075325 (2007).
[Crossref]

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, and C. H. B. Cruz, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460 (2004).
[Crossref]

Bawendi, M. G.

D. J. Norris and M. G. Bawendi, “Measurement and assignment of the size-dependent optical spectrum in CdSe quantum dots,” Phys. Rev. B 53, 16338 (1996).
[Crossref]

Belfield, K. D.

F. E. Hernandez, K. D. Belfield, and I. Cohanoschi, “Three-photon absorption enhancement in a symmetrical charge transfer fluorene derivative,” Chem. Phys. Lett. 391, 22 (2004).
[Crossref]

F. E. Hernandez, K. D. Belfield, I. Cohanoschi, M. Balu, and K. J. Schafer, “Three- and Four-Photon Absorption of a Multiphoton absorbing Fluorescent Probe,” Appl. Opt. 43, 5394 (2004).
[Crossref] [PubMed]

Bentolila, L. A.

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
[Crossref] [PubMed]

Brivanlou, A. H.

B. Dubertret, P. Skourides, D. J. Norris, V. Noireaux, A. H. Brivanlou, and A. Libchaber, “In Vivo Imaging of Quantum Dots Encapsulated in Phospholipid Micelles,” Science 298, 1759 (2002).
[Crossref] [PubMed]

Bruchez, M. P.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, “Water-Soluble Quantum Dots for Multiphoton Fluorescence Imaging in Vivo,” Science 300, 1434 (2003).
[Crossref] [PubMed]

Bullen, C.

J. W. M. Chon, M. Gu, C. Bullen, and P. Mulvaney, “Three-photon excited band edge and trap emission of CdS semiconductor nanocrystals,” Appl. Phys. Lett. 84, 4472 (2004).
[Crossref]

Buso, D.

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B 75, 075325 (2007).
[Crossref]

Catalano, I. M.

I. M. Catalano, A. Cingolani, and A. Minafra, “Multiphoton impurity luminescence in zinc sulphide,” Opt. Commun. 7, 270 (1973).
[Crossref]

Cesar, C. L.

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B 75, 075325 (2007).
[Crossref]

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, and C. H. B. Cruz, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460 (2004).
[Crossref]

Chon, J. W. M.

J. W. M. Chon, M. Gu, C. Bullen, and P. Mulvaney, “Three-photon excited band edge and trap emission of CdS semiconductor nanocrystals,” Appl. Phys. Lett. 84, 4472 (2004).
[Crossref]

Cingolani, A.

I. M. Catalano, A. Cingolani, and A. Minafra, “Multiphoton impurity luminescence in zinc sulphide,” Opt. Commun. 7, 270 (1973).
[Crossref]

Clark, S. W.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, “Water-Soluble Quantum Dots for Multiphoton Fluorescence Imaging in Vivo,” Science 300, 1434 (2003).
[Crossref] [PubMed]

Cohanoschi, I.

F. E. Hernandez, K. D. Belfield, and I. Cohanoschi, “Three-photon absorption enhancement in a symmetrical charge transfer fluorene derivative,” Chem. Phys. Lett. 391, 22 (2004).
[Crossref]

F. E. Hernandez, K. D. Belfield, I. Cohanoschi, M. Balu, and K. J. Schafer, “Three- and Four-Photon Absorption of a Multiphoton absorbing Fluorescent Probe,” Appl. Opt. 43, 5394 (2004).
[Crossref] [PubMed]

Cruz, C. H. B.

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B 75, 075325 (2007).
[Crossref]

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, and C. H. B. Cruz, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460 (2004).
[Crossref]

Doose, S.

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
[Crossref] [PubMed]

Dubertret, B.

B. Dubertret, P. Skourides, D. J. Norris, V. Noireaux, A. H. Brivanlou, and A. Libchaber, “In Vivo Imaging of Quantum Dots Encapsulated in Phospholipid Micelles,” Science 298, 1759 (2002).
[Crossref] [PubMed]

Fedorov, A. V.

A. V. Fedorov, A. V. Baranov, and K. Inoue, “Two-photon transitions in systems with semiconductor quantum dots,” Phys. Rev. B. 54, 8627 (1996).
[Crossref]

Fu, J.

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B 75, 075325 (2007).
[Crossref]

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, and C. H. B. Cruz, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460 (2004).
[Crossref]

Gambhir, S. S.

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
[Crossref] [PubMed]

Ghangrekar, A.

S. Sapra, A. Prakash, A. Ghangrekar, N. Periasamy, and D. D. Sarma, “Emission Properties of Manganese-Doped ZnS Nanocrystals,” J. Phys. Chem. B 109, 1663 (2005).
[Crossref]

Gu, M.

J. W. M. Chon, M. Gu, C. Bullen, and P. Mulvaney, “Three-photon excited band edge and trap emission of CdS semiconductor nanocrystals,” Appl. Phys. Lett. 84, 4472 (2004).
[Crossref]

Hagan, D. J.

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B 75, 075325 (2007).
[Crossref]

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, and C. H. B. Cruz, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460 (2004).
[Crossref]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

He, G. S.

He, J.

J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
[Crossref]

J. He, Y. L. Qu, H. P. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13, 9235 (2005).
[Crossref] [PubMed]

Hernandez, F. E.

F. E. Hernandez, K. D. Belfield, and I. Cohanoschi, “Three-photon absorption enhancement in a symmetrical charge transfer fluorene derivative,” Chem. Phys. Lett. 391, 22 (2004).
[Crossref]

F. E. Hernandez, K. D. Belfield, I. Cohanoschi, M. Balu, and K. J. Schafer, “Three- and Four-Photon Absorption of a Multiphoton absorbing Fluorescent Probe,” Appl. Opt. 43, 5394 (2004).
[Crossref] [PubMed]

Inoue, K.

A. V. Fedorov, A. V. Baranov, and K. Inoue, “Two-photon transitions in systems with semiconductor quantum dots,” Phys. Rev. B. 54, 8627 (1996).
[Crossref]

Ji, W.

J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
[Crossref]

J. He, Y. L. Qu, H. P. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13, 9235 (2005).
[Crossref] [PubMed]

Kiran, P. P.

A. D. Lad, P. P. Kiran, G. R. Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and ZnSe/ZnS quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
[Crossref]

Kirkpatrick, S.

R. L. Sutherland, Handbook of Nonlinear Optics, with contributions by D. G. McLean and S. Kirkpatrick, Second Edition, (New York, NY: Marcel Dekker, 2003).
[Crossref]

Kshirsagar, A.

N. Kumbhojkar, V. V. Nikesh, A. Kshirsagar, and S. Mahamuni, “Photophysical properties of ZnS nanoclusters,” J. Appl. Phys. 88, 6260 (2000).
[Crossref]

Kumar, G. R.

A. D. Lad, P. P. Kiran, G. R. Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and ZnSe/ZnS quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
[Crossref]

Kumbhojkar, N.

N. Kumbhojkar, V. V. Nikesh, A. Kshirsagar, and S. Mahamuni, “Photophysical properties of ZnS nanoclusters,” J. Appl. Phys. 88, 6260 (2000).
[Crossref]

Lad, A. D.

A. D. Lad, P. P. Kiran, G. R. Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and ZnSe/ZnS quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
[Crossref]

Larson, D. R.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, “Water-Soluble Quantum Dots for Multiphoton Fluorescence Imaging in Vivo,” Science 300, 1434 (2003).
[Crossref] [PubMed]

Lawaetz, P.

P. Lawaetz, “Valence-band Parameters in Cubic Semiconductors,” Phys. Rev. B 4, 3460 (1971).
[Crossref]

Li, H. P.

Li, J. J.

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
[Crossref] [PubMed]

Libchaber, A.

B. Dubertret, P. Skourides, D. J. Norris, V. Noireaux, A. H. Brivanlou, and A. Libchaber, “In Vivo Imaging of Quantum Dots Encapsulated in Phospholipid Micelles,” Science 298, 1759 (2002).
[Crossref] [PubMed]

Lifshits, I. M.

I. M. Lifshits and V. V. Slezov, “The kinetics of diffusional decomposition of super-saturated solid solutions,” Zh. Eksp. Teor. Fiz 35, 479 (1958).

Mahamuni, S.

A. D. Lad, P. P. Kiran, G. R. Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and ZnSe/ZnS quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
[Crossref]

N. Kumbhojkar, V. V. Nikesh, A. Kshirsagar, and S. Mahamuni, “Photophysical properties of ZnS nanoclusters,” J. Appl. Phys. 88, 6260 (2000).
[Crossref]

Martucci, A.

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B 75, 075325 (2007).
[Crossref]

McLean, D. G.

R. L. Sutherland, Handbook of Nonlinear Optics, with contributions by D. G. McLean and S. Kirkpatrick, Second Edition, (New York, NY: Marcel Dekker, 2003).
[Crossref]

Mi, J.

J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
[Crossref]

J. He, Y. L. Qu, H. P. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13, 9235 (2005).
[Crossref] [PubMed]

Michalet, X.

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
[Crossref] [PubMed]

Minafra, A.

I. M. Catalano, A. Cingolani, and A. Minafra, “Multiphoton impurity luminescence in zinc sulphide,” Opt. Commun. 7, 270 (1973).
[Crossref]

Mulvaney, P.

J. W. M. Chon, M. Gu, C. Bullen, and P. Mulvaney, “Three-photon excited band edge and trap emission of CdS semiconductor nanocrystals,” Appl. Phys. Lett. 84, 4472 (2004).
[Crossref]

Nikesh, V. V.

N. Kumbhojkar, V. V. Nikesh, A. Kshirsagar, and S. Mahamuni, “Photophysical properties of ZnS nanoclusters,” J. Appl. Phys. 88, 6260 (2000).
[Crossref]

Noireaux, V.

B. Dubertret, P. Skourides, D. J. Norris, V. Noireaux, A. H. Brivanlou, and A. Libchaber, “In Vivo Imaging of Quantum Dots Encapsulated in Phospholipid Micelles,” Science 298, 1759 (2002).
[Crossref] [PubMed]

Norris, D. J.

B. Dubertret, P. Skourides, D. J. Norris, V. Noireaux, A. H. Brivanlou, and A. Libchaber, “In Vivo Imaging of Quantum Dots Encapsulated in Phospholipid Micelles,” Science 298, 1759 (2002).
[Crossref] [PubMed]

D. J. Norris and M. G. Bawendi, “Measurement and assignment of the size-dependent optical spectrum in CdSe quantum dots,” Phys. Rev. B 53, 16338 (1996).
[Crossref]

Nosaka, Y.

Y. Nosaka, “Finite depth spherical well model for excited states of ultrasmall semiconductor particles: an application,” J. Phys. Chem. 95, 5054 (1991).
[Crossref]

Padilha, L. A.

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B 75, 075325 (2007).
[Crossref]

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, and C. H. B. Cruz, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460 (2004).
[Crossref]

Periasamy, N.

S. Sapra, A. Prakash, A. Ghangrekar, N. Periasamy, and D. D. Sarma, “Emission Properties of Manganese-Doped ZnS Nanocrystals,” J. Phys. Chem. B 109, 1663 (2005).
[Crossref]

Pinaud, F. F.

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
[Crossref] [PubMed]

Prakash, A.

S. Sapra, A. Prakash, A. Ghangrekar, N. Periasamy, and D. D. Sarma, “Emission Properties of Manganese-Doped ZnS Nanocrystals,” J. Phys. Chem. B 109, 1663 (2005).
[Crossref]

Prasad, P. N.

Qu, Y. L.

Ryasnyanskiy, A. I.

Saha-Dasgupta, T.

R. Viswanatha, S. Sapra, T. Saha-Dasgupta, and D. D. Sarma, “Electronic structure of and quantum size effect in III–V and II–VI semiconducting nanocrystals using a realistic tight binding approach,” Phys. Rev. B 72, 045333 (2005).
[Crossref]

Sahoo, Y.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

Sapra, S.

R. Viswanatha, S. Sapra, T. Saha-Dasgupta, and D. D. Sarma, “Electronic structure of and quantum size effect in III–V and II–VI semiconducting nanocrystals using a realistic tight binding approach,” Phys. Rev. B 72, 045333 (2005).
[Crossref]

S. Sapra, A. Prakash, A. Ghangrekar, N. Periasamy, and D. D. Sarma, “Emission Properties of Manganese-Doped ZnS Nanocrystals,” J. Phys. Chem. B 109, 1663 (2005).
[Crossref]

Sarma, D. D.

S. Sapra, A. Prakash, A. Ghangrekar, N. Periasamy, and D. D. Sarma, “Emission Properties of Manganese-Doped ZnS Nanocrystals,” J. Phys. Chem. B 109, 1663 (2005).
[Crossref]

R. Viswanatha, S. Sapra, T. Saha-Dasgupta, and D. D. Sarma, “Electronic structure of and quantum size effect in III–V and II–VI semiconducting nanocrystals using a realistic tight binding approach,” Phys. Rev. B 72, 045333 (2005).
[Crossref]

Schafer, K. J.

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

Skourides, P.

B. Dubertret, P. Skourides, D. J. Norris, V. Noireaux, A. H. Brivanlou, and A. Libchaber, “In Vivo Imaging of Quantum Dots Encapsulated in Phospholipid Micelles,” Science 298, 1759 (2002).
[Crossref] [PubMed]

Slezov, V. V.

I. M. Lifshits and V. V. Slezov, “The kinetics of diffusional decomposition of super-saturated solid solutions,” Zh. Eksp. Teor. Fiz 35, 479 (1958).

Sundaresan, G.

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
[Crossref] [PubMed]

Sutherland, R. L.

R. L. Sutherland, Handbook of Nonlinear Optics, with contributions by D. G. McLean and S. Kirkpatrick, Second Edition, (New York, NY: Marcel Dekker, 2003).
[Crossref]

Tsay, J. M.

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
[Crossref] [PubMed]

Van Stryland, E. W.

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B 75, 075325 (2007).
[Crossref]

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, and C. H. B. Cruz, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460 (2004).
[Crossref]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

Viswanatha, R.

R. Viswanatha, S. Sapra, T. Saha-Dasgupta, and D. D. Sarma, “Electronic structure of and quantum size effect in III–V and II–VI semiconducting nanocrystals using a realistic tight binding approach,” Phys. Rev. B 72, 045333 (2005).
[Crossref]

Webb, W. W.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, “Water-Soluble Quantum Dots for Multiphoton Fluorescence Imaging in Vivo,” Science 300, 1434 (2003).
[Crossref] [PubMed]

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

Weiss, S

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
[Crossref] [PubMed]

Williams, R. M.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, “Water-Soluble Quantum Dots for Multiphoton Fluorescence Imaging in Vivo,” Science 300, 1434 (2003).
[Crossref] [PubMed]

Wise, F. W.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, “Water-Soluble Quantum Dots for Multiphoton Fluorescence Imaging in Vivo,” Science 300, 1434 (2003).
[Crossref] [PubMed]

Wu, A. M.

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
[Crossref] [PubMed]

Ying, J. Y.

J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
[Crossref]

Yong, K. T.

Zheng, Q. D.

Zheng, Y.

J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
[Crossref]

Zipfel, W. R.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, “Water-Soluble Quantum Dots for Multiphoton Fluorescence Imaging in Vivo,” Science 300, 1434 (2003).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

J. W. M. Chon, M. Gu, C. Bullen, and P. Mulvaney, “Three-photon excited band edge and trap emission of CdS semiconductor nanocrystals,” Appl. Phys. Lett. 84, 4472 (2004).
[Crossref]

J. He, W. Ji, J. Mi, Y. Zheng, and J. Y. Ying, “Three-photon absorption in water-soluble ZnS nanocrystals,” Appl. Phys. Lett. 88, 181114 (2006).
[Crossref]

A. D. Lad, P. P. Kiran, G. R. Kumar, and S. Mahamuni, “Three-photon absorption in ZnSe and ZnSe/ZnS quantum dots,” Appl. Phys. Lett. 90, 133113 (2007).
[Crossref]

Chem. Phys. Lett. (1)

F. E. Hernandez, K. D. Belfield, and I. Cohanoschi, “Three-photon absorption enhancement in a symmetrical charge transfer fluorene derivative,” Chem. Phys. Lett. 391, 22 (2004).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

J. Appl. Phys. (1)

N. Kumbhojkar, V. V. Nikesh, A. Kshirsagar, and S. Mahamuni, “Photophysical properties of ZnS nanoclusters,” J. Appl. Phys. 88, 6260 (2000).
[Crossref]

J. Phys. Chem. (1)

Y. Nosaka, “Finite depth spherical well model for excited states of ultrasmall semiconductor particles: an application,” J. Phys. Chem. 95, 5054 (1991).
[Crossref]

J. Phys. Chem. B (1)

S. Sapra, A. Prakash, A. Ghangrekar, N. Periasamy, and D. D. Sarma, “Emission Properties of Manganese-Doped ZnS Nanocrystals,” J. Phys. Chem. B 109, 1663 (2005).
[Crossref]

Opt. Commun. (1)

I. M. Catalano, A. Cingolani, and A. Minafra, “Multiphoton impurity luminescence in zinc sulphide,” Opt. Commun. 7, 270 (1973).
[Crossref]

Opt. Express (3)

Phys. Rev. B (4)

R. Viswanatha, S. Sapra, T. Saha-Dasgupta, and D. D. Sarma, “Electronic structure of and quantum size effect in III–V and II–VI semiconducting nanocrystals using a realistic tight binding approach,” Phys. Rev. B 72, 045333 (2005).
[Crossref]

P. Lawaetz, “Valence-band Parameters in Cubic Semiconductors,” Phys. Rev. B 4, 3460 (1971).
[Crossref]

D. J. Norris and M. G. Bawendi, “Measurement and assignment of the size-dependent optical spectrum in CdSe quantum dots,” Phys. Rev. B 53, 16338 (1996).
[Crossref]

L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, C. H. B. Cruz, D. Buso, and A. Martucci, “Frequency degenerate and nondegenerate two-photon absorption spectra of semiconductor quantum dots,” Phys. Rev. B 75, 075325 (2007).
[Crossref]

Phys. Rev. B. (1)

A. V. Fedorov, A. V. Baranov, and K. Inoue, “Two-photon transitions in systems with semiconductor quantum dots,” Phys. Rev. B. 54, 8627 (1996).
[Crossref]

Science (3)

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307, 538 (2005).
[Crossref] [PubMed]

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, “Water-Soluble Quantum Dots for Multiphoton Fluorescence Imaging in Vivo,” Science 300, 1434 (2003).
[Crossref] [PubMed]

B. Dubertret, P. Skourides, D. J. Norris, V. Noireaux, A. H. Brivanlou, and A. Libchaber, “In Vivo Imaging of Quantum Dots Encapsulated in Phospholipid Micelles,” Science 298, 1759 (2002).
[Crossref] [PubMed]

Zh. Eksp. Teor. Fiz (1)

I. M. Lifshits and V. V. Slezov, “The kinetics of diffusional decomposition of super-saturated solid solutions,” Zh. Eksp. Teor. Fiz 35, 479 (1958).

Other (1)

R. L. Sutherland, Handbook of Nonlinear Optics, with contributions by D. G. McLean and S. Kirkpatrick, Second Edition, (New York, NY: Marcel Dekker, 2003).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1.

The 3PA cross-section plotted as a function of the dot diameter for CdSe QDs with the three-photon excitation wavelength of ~1300 nm. The solid line is our theoretical calculation. The solid squares are the data measured by He, et al. [4].

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Fig. 2.
Fig. 2.

UV-VIS one-photon absorption (thick solid line:—) spectrum, together with the Gaussian fitting bands (dotted lines:⋯), of the ZnS QDs. The inset shows the PL (dashed line:---) spectrum excited at 230 nm.

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Fig. 3.
Fig. 3.

Typical open-aperture Z-scans at 700 nm for the ZnS QDs. The symbols denote the experimental data while the solid lines are theoretically fitted curves employing the Z-scan theory described in the text. The inset shows the Z-scan curves for the ZnS bulk crystal.

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Fig. 4.
Fig. 4.

3PA cross-sections calculated as a function of the wavelength for ZnS QDs. The solid squares are the experimental data.

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Tables (1)

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Table 1. Parameters used in the Calculations for the Investigated Materials

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Equations (4)

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σ 3 = 6 π ħ 2 ω 3 ε ω 3 2 ( 8 π e 2 3 ω 2 c ) 3 ( P ħ ) 2 ∑ j = 1 3 〈 F c , h j 〉 ,
〈 F c , h j 〉 = 1 2 Δ h j ∑ β 1 , β 2 , β 0 ( l 2 δ l 2 , l 0 + 1 + l 0 δ l 2 , l 0 − 1 ) ( l 1 δ l 1 , l 2 + 1 + l 2 δ l 1 , l 2 − 1 )
× T β 1 , β 2 , β 0 c , h j ( R β 1 ; β 0 ( h j ) ) ξ β 2 4 ξ β 0 2 ξ β 1 2 ( ξ β 2 2 − ξ β 0 2 ) 2 ( ξ β 1 2 − ξ β 2 2 ) 2 f ( R β 1 ; β 0 ( h j ) ) ( R β 1 ; β 0 ( h j ) ) 3 .
T OA = 1 π p 0 ∫ − ∞ ∞ ln ⁡ [ 1 + p 0 2 exp ( − 2 x 2 ) + p 0 exp ⁡ ( − x 2 ) ] dx

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