Abstract

The frequency-degenerate two-photon absorption (TPA) in glutathione-capped colloidal CdTe quantum dots with a dot radius ranging from 1.5 to 2 nm, which belongs to the regime of very strong quantum confinement, is determined unambiguously by utilizing the Z-scan technique with femtosecond laser pulses. At laser wavelengths between 720 and 950 nm, the TPA cross sections are measured to be of the order of 10471046cm4  s  photon1, with precise values depending on both the laser wavelength and the dot size. The TPA measurements are in agreement with theoretical modeling based on a spherical eight-band Pidgen and Brown model. The quantitative modeling reveals underlying factors that contribute to both the TPA–size relationship and size dispersion effects.

© 2009 Optical Society of America

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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]

G. H. He, Q. D. Zheng, K. T. Yong, and A. Urbus, “Two-photon absorption based optical limiting and stabilization by using a CdTe quantum dot solution excited at optical communication wavelength of ~1300 nm,” Appl. Phys. Lett. 90, 181108 (2007).
[CrossRef]

Y. G. Zheng, S. G. Gao, and J. Y. Ying, “Synthesis and cell-imaging applications of glutathione-capped CdTe quantum dots,” Adv. Mater. 19, 376-380 (2007).
[CrossRef]

Y. L. Qu, W. Ji, Y. G. Zheng, and J. Y. Ying, “Auger recombination and intraband absorption of two-photon-excited carriers in colloidal CdSe quantum dots,” Appl. Phys. Lett. 90, 133112 (2007).
[CrossRef]

2006 (1)

S. C. Pu, M. J. Yang, C. C. Hsu, C. W. Lai, C. C. Hsieh, S. H. Lin, Y. M. Cheng, and P. T. Chou, “The empirical correlation between size and two-photon absorption cross section of CdSe and CdTe quantum dots,” Small 2, 1308-1313 (2006).
[CrossRef] [PubMed]

2005 (2)

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, 538-544 (2005), and references therein.
[CrossRef] [PubMed]

L. A. Padilha, J. Fu, D. J. Hagan, and E. W. V. Stryland, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460-6467 (2005).
[CrossRef] [PubMed]

2004 (1)

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, 4472-4474 (2004).
[CrossRef]

2003 (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, 1434-1436 (2003), and references therein.
[CrossRef] [PubMed]

W. W. Yu, L. Qu, W. Guo, and X. Peng, “Experimental determination of the extinction coefficient of CdTe, CdSe, and CdS nanocrystals,” Chem. Mater. 15, 2854-2860 (2003).
[CrossRef]

1999 (1)

P. C. Sercel, A. L. Efros, and M. Rose, “Intrinsic gap states in semiconductor nanocrystals,” Phys. Rev. Lett. 83, 2394-2397 (1999).
[CrossRef]

1998 (2)

U. Banin, C. J. Lee, A. A. Guzelian, A. V. Kadavanich, A. P. Alivisatos, W. Jaskolski, G. W. Bryant, A. L. Efros, and M. Rosen, “Size-dependent electronic level structure of InAs nanocrystal quantum dots: test of multiband effective mass theory,” J. Chem. Phys. 109, 2306-2309 (1998).
[CrossRef]

Al. L. Efros and M. Rosen, “Quantum size level structure of narrow-gap semiconductor nanocrystals: effect of band coupling,” Phys. Rev. B 58, 7120-7135 (1998).
[CrossRef]

1996 (1)

A. V. Fedorov, A. V. Baranov, and K. Inoue, “Two-photon transitions in systems with semiconductor quantum dots,” Phys. Rev. B 54, 8627-8732 (1996).
[CrossRef]

1992 (4)

K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement induced valence band mixing in CdS quantum dots observed by two photon spectroscopy,” Phys. Rev. B 45, 3465-3486 (1992).
[CrossRef]

Y. V. Vandyshev, V. S. Dneprovskii, and V. I. Klimov, “Nonlinear-transmission dynamics and nonlinear susceptibilities of semicoducting microcrystals (quantum dots),” Sov. Phys. JETP 74, 144-150 (1992).

H. Shinojima, J. Yumoto, and N. Uesugi, “Size dependence of optical nonlinearity of CdSSe microcrystallites doped in glass,” Appl. Phys. Lett. 60, 298-300 (1992).
[CrossRef]

D. C. Hutchings and E. W. Van Stryland, “Nondegenerate two photon absorption in zinc blende semicondcutors,” J. Opt. Soc. Am. B 9, 2065-2074 (1992).
[CrossRef]

1990 (2)

P. C. Sercel and K. J. Vahala, “Analytical formalism for determining quantum-wire and quantum-dot band structure in the multiband envelop-function approximation,” Phys. Rev. B 42, 3690-3711 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. V. Styland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

1985 (2)

1966 (1)

C. R. Pidgeon and R. N. Brown, “Interband magneto-absorption and Faraday rotation in InSb,” Phys. Rev. 146, 575-583 (1966).
[CrossRef]

Alivisatos, A. P.

U. Banin, C. J. Lee, A. A. Guzelian, A. V. Kadavanich, A. P. Alivisatos, W. Jaskolski, G. W. Bryant, A. L. Efros, and M. Rosen, “Size-dependent electronic level structure of InAs nanocrystal quantum dots: test of multiband effective mass theory,” J. Chem. Phys. 109, 2306-2309 (1998).
[CrossRef]

Banin, U.

U. Banin, C. J. Lee, A. A. Guzelian, A. V. Kadavanich, A. P. Alivisatos, W. Jaskolski, G. W. Bryant, A. L. Efros, and M. Rosen, “Size-dependent electronic level structure of InAs nanocrystal quantum dots: test of multiband effective mass theory,” J. Chem. Phys. 109, 2306-2309 (1998).
[CrossRef]

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, 8627-8732 (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]

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, 538-544 (2005), and references therein.
[CrossRef] [PubMed]

Brown, R. N.

C. R. Pidgeon and R. N. Brown, “Interband magneto-absorption and Faraday rotation in InSb,” Phys. Rev. 146, 575-583 (1966).
[CrossRef]

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, 1434-1436 (2003), and references therein.
[CrossRef] [PubMed]

Bryant, G. W.

U. Banin, C. J. Lee, A. A. Guzelian, A. V. Kadavanich, A. P. Alivisatos, W. Jaskolski, G. W. Bryant, A. L. Efros, and M. Rosen, “Size-dependent electronic level structure of InAs nanocrystal quantum dots: test of multiband effective mass theory,” J. Chem. Phys. 109, 2306-2309 (1998).
[CrossRef]

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, 4472-4474 (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]

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]

Cheng, Y. M.

S. C. Pu, M. J. Yang, C. C. Hsu, C. W. Lai, C. C. Hsieh, S. H. Lin, Y. M. Cheng, and P. T. Chou, “The empirical correlation between size and two-photon absorption cross section of CdSe and CdTe quantum dots,” Small 2, 1308-1313 (2006).
[CrossRef] [PubMed]

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, 4472-4474 (2004).
[CrossRef]

Chou, P. T.

S. C. Pu, M. J. Yang, C. C. Hsu, C. W. Lai, C. C. Hsieh, S. H. Lin, Y. M. Cheng, and P. T. Chou, “The empirical correlation between size and two-photon absorption cross section of CdSe and CdTe quantum dots,” Small 2, 1308-1313 (2006).
[CrossRef] [PubMed]

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, 1434-1436 (2003), and references therein.
[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]

Dneprovskii, V. S.

Y. V. Vandyshev, V. S. Dneprovskii, and V. I. Klimov, “Nonlinear-transmission dynamics and nonlinear susceptibilities of semicoducting microcrystals (quantum dots),” Sov. Phys. JETP 74, 144-150 (1992).

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, 538-544 (2005), and references therein.
[CrossRef] [PubMed]

Efros, A. L.

P. C. Sercel, A. L. Efros, and M. Rose, “Intrinsic gap states in semiconductor nanocrystals,” Phys. Rev. Lett. 83, 2394-2397 (1999).
[CrossRef]

U. Banin, C. J. Lee, A. A. Guzelian, A. V. Kadavanich, A. P. Alivisatos, W. Jaskolski, G. W. Bryant, A. L. Efros, and M. Rosen, “Size-dependent electronic level structure of InAs nanocrystal quantum dots: test of multiband effective mass theory,” J. Chem. Phys. 109, 2306-2309 (1998).
[CrossRef]

Efros, Al. L.

Al. L. Efros and M. Rosen, “Quantum size level structure of narrow-gap semiconductor nanocrystals: effect of band coupling,” Phys. Rev. B 58, 7120-7135 (1998).
[CrossRef]

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, 8627-8732 (1996).
[CrossRef]

Flytzanis, C.

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, and E. W. V. Stryland, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460-6467 (2005).
[CrossRef] [PubMed]

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, 538-544 (2005), and references therein.
[CrossRef] [PubMed]

Gao, S. G.

Y. G. Zheng, S. G. Gao, and J. Y. Ying, “Synthesis and cell-imaging applications of glutathione-capped CdTe quantum dots,” Adv. Mater. 19, 376-380 (2007).
[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, 4472-4474 (2004).
[CrossRef]

Guo, W.

W. W. Yu, L. Qu, W. Guo, and X. Peng, “Experimental determination of the extinction coefficient of CdTe, CdSe, and CdS nanocrystals,” Chem. Mater. 15, 2854-2860 (2003).
[CrossRef]

Guzelian, A. A.

U. Banin, C. J. Lee, A. A. Guzelian, A. V. Kadavanich, A. P. Alivisatos, W. Jaskolski, G. W. Bryant, A. L. Efros, and M. Rosen, “Size-dependent electronic level structure of InAs nanocrystal quantum dots: test of multiband effective mass theory,” J. Chem. Phys. 109, 2306-2309 (1998).
[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, and E. W. V. Stryland, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460-6467 (2005).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. V. Styland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

He, G. H.

G. H. He, Q. D. Zheng, K. T. Yong, and A. Urbus, “Two-photon absorption based optical limiting and stabilization by using a CdTe quantum dot solution excited at optical communication wavelength of ~1300 nm,” Appl. Phys. Lett. 90, 181108 (2007).
[CrossRef]

Hsieh, C. C.

S. C. Pu, M. J. Yang, C. C. Hsu, C. W. Lai, C. C. Hsieh, S. H. Lin, Y. M. Cheng, and P. T. Chou, “The empirical correlation between size and two-photon absorption cross section of CdSe and CdTe quantum dots,” Small 2, 1308-1313 (2006).
[CrossRef] [PubMed]

Hsu, C. C.

S. C. Pu, M. J. Yang, C. C. Hsu, C. W. Lai, C. C. Hsieh, S. H. Lin, Y. M. Cheng, and P. T. Chou, “The empirical correlation between size and two-photon absorption cross section of CdSe and CdTe quantum dots,” Small 2, 1308-1313 (2006).
[CrossRef] [PubMed]

Hu, Y. Z.

K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement induced valence band mixing in CdS quantum dots observed by two photon spectroscopy,” Phys. Rev. B 45, 3465-3486 (1992).
[CrossRef]

Hutchings, D. C.

Inoue, K.

A. V. Fedorov, A. V. Baranov, and K. Inoue, “Two-photon transitions in systems with semiconductor quantum dots,” Phys. Rev. B 54, 8627-8732 (1996).
[CrossRef]

Jaskolski, W.

U. Banin, C. J. Lee, A. A. Guzelian, A. V. Kadavanich, A. P. Alivisatos, W. Jaskolski, G. W. Bryant, A. L. Efros, and M. Rosen, “Size-dependent electronic level structure of InAs nanocrystal quantum dots: test of multiband effective mass theory,” J. Chem. Phys. 109, 2306-2309 (1998).
[CrossRef]

Ji, W.

Y. L. Qu, W. Ji, Y. G. Zheng, and J. Y. Ying, “Auger recombination and intraband absorption of two-photon-excited carriers in colloidal CdSe quantum dots,” Appl. Phys. Lett. 90, 133112 (2007).
[CrossRef]

Kadavanich, A. V.

U. Banin, C. J. Lee, A. A. Guzelian, A. V. Kadavanich, A. P. Alivisatos, W. Jaskolski, G. W. Bryant, A. L. Efros, and M. Rosen, “Size-dependent electronic level structure of InAs nanocrystal quantum dots: test of multiband effective mass theory,” J. Chem. Phys. 109, 2306-2309 (1998).
[CrossRef]

Kang, K. I.

K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement induced valence band mixing in CdS quantum dots observed by two photon spectroscopy,” Phys. Rev. B 45, 3465-3486 (1992).
[CrossRef]

Klimov, V. I.

Y. V. Vandyshev, V. S. Dneprovskii, and V. I. Klimov, “Nonlinear-transmission dynamics and nonlinear susceptibilities of semicoducting microcrystals (quantum dots),” Sov. Phys. JETP 74, 144-150 (1992).

Koch, S. W.

K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement induced valence band mixing in CdS quantum dots observed by two photon spectroscopy,” Phys. Rev. B 45, 3465-3486 (1992).
[CrossRef]

Lai, C. W.

S. C. Pu, M. J. Yang, C. C. Hsu, C. W. Lai, C. C. Hsieh, S. H. Lin, Y. M. Cheng, and P. T. Chou, “The empirical correlation between size and two-photon absorption cross section of CdSe and CdTe quantum dots,” Small 2, 1308-1313 (2006).
[CrossRef] [PubMed]

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, 1434-1436 (2003), and references therein.
[CrossRef] [PubMed]

Lee, C. J.

U. Banin, C. J. Lee, A. A. Guzelian, A. V. Kadavanich, A. P. Alivisatos, W. Jaskolski, G. W. Bryant, A. L. Efros, and M. Rosen, “Size-dependent electronic level structure of InAs nanocrystal quantum dots: test of multiband effective mass theory,” J. Chem. Phys. 109, 2306-2309 (1998).
[CrossRef]

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, 538-544 (2005), and references therein.
[CrossRef] [PubMed]

Lin, S. H.

S. C. Pu, M. J. Yang, C. C. Hsu, C. W. Lai, C. C. Hsieh, S. H. Lin, Y. M. Cheng, and P. T. Chou, “The empirical correlation between size and two-photon absorption cross section of CdSe and CdTe quantum dots,” Small 2, 1308-1313 (2006).
[CrossRef] [PubMed]

Liu, L. C.

K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement induced valence band mixing in CdS quantum dots observed by two photon spectroscopy,” Phys. Rev. B 45, 3465-3486 (1992).
[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]

McGinnis, B. P.

K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement induced valence band mixing in CdS quantum dots observed by two photon spectroscopy,” Phys. Rev. B 45, 3465-3486 (1992).
[CrossRef]

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, 538-544 (2005), and references therein.
[CrossRef] [PubMed]

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, 4472-4474 (2004).
[CrossRef]

Mysyrowicz, A.

K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement induced valence band mixing in CdS quantum dots observed by two photon spectroscopy,” Phys. Rev. B 45, 3465-3486 (1992).
[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, and E. W. V. Stryland, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13, 6460-6467 (2005).
[CrossRef] [PubMed]

Peng, X.

W. W. Yu, L. Qu, W. Guo, and X. Peng, “Experimental determination of the extinction coefficient of CdTe, CdSe, and CdS nanocrystals,” Chem. Mater. 15, 2854-2860 (2003).
[CrossRef]

Peyghambarian, N.

K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement induced valence band mixing in CdS quantum dots observed by two photon spectroscopy,” Phys. Rev. B 45, 3465-3486 (1992).
[CrossRef]

Pidgeon, C. R.

C. R. Pidgeon and R. N. Brown, “Interband magneto-absorption and Faraday rotation in InSb,” Phys. Rev. 146, 575-583 (1966).
[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, 538-544 (2005), and references therein.
[CrossRef] [PubMed]

Pu, S. C.

S. C. Pu, M. J. Yang, C. C. Hsu, C. W. Lai, C. C. Hsieh, S. H. Lin, Y. M. Cheng, and P. T. Chou, “The empirical correlation between size and two-photon absorption cross section of CdSe and CdTe quantum dots,” Small 2, 1308-1313 (2006).
[CrossRef] [PubMed]

Qu, L.

W. W. Yu, L. Qu, W. Guo, and X. Peng, “Experimental determination of the extinction coefficient of CdTe, CdSe, and CdS nanocrystals,” Chem. Mater. 15, 2854-2860 (2003).
[CrossRef]

Qu, Y. L.

Y. L. Qu, W. Ji, Y. G. Zheng, and J. Y. Ying, “Auger recombination and intraband absorption of two-photon-excited carriers in colloidal CdSe quantum dots,” Appl. Phys. Lett. 90, 133112 (2007).
[CrossRef]

Ricard, D.

Risbud, S. H.

K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement induced valence band mixing in CdS quantum dots observed by two photon spectroscopy,” Phys. Rev. B 45, 3465-3486 (1992).
[CrossRef]

Rose, M.

P. C. Sercel, A. L. Efros, and M. Rose, “Intrinsic gap states in semiconductor nanocrystals,” Phys. Rev. Lett. 83, 2394-2397 (1999).
[CrossRef]

Rosen, M.

U. Banin, C. J. Lee, A. A. Guzelian, A. V. Kadavanich, A. P. Alivisatos, W. Jaskolski, G. W. Bryant, A. L. Efros, and M. Rosen, “Size-dependent electronic level structure of InAs nanocrystal quantum dots: test of multiband effective mass theory,” J. Chem. Phys. 109, 2306-2309 (1998).
[CrossRef]

Al. L. Efros and M. Rosen, “Quantum size level structure of narrow-gap semiconductor nanocrystals: effect of band coupling,” Phys. Rev. B 58, 7120-7135 (1998).
[CrossRef]

Roussignol, P.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. V. Styland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Sandalphon,

K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement induced valence band mixing in CdS quantum dots observed by two photon spectroscopy,” Phys. Rev. B 45, 3465-3486 (1992).
[CrossRef]

Sercel, P. C.

P. C. Sercel, A. L. Efros, and M. Rose, “Intrinsic gap states in semiconductor nanocrystals,” Phys. Rev. Lett. 83, 2394-2397 (1999).
[CrossRef]

P. C. Sercel and K. J. Vahala, “Analytical formalism for determining quantum-wire and quantum-dot band structure in the multiband envelop-function approximation,” Phys. Rev. B 42, 3690-3711 (1990).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. V. Styland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Shinojima, H.

H. Shinojima, J. Yumoto, and N. Uesugi, “Size dependence of optical nonlinearity of CdSSe microcrystallites doped in glass,” Appl. Phys. Lett. 60, 298-300 (1992).
[CrossRef]

Singh, J.

J. Singh, Physics of Semiconductors and Their Heterostructures (McGraw Hill, 1993).

Soileau, M. J.

Stryland, E. W. V.

Styland, E. W. V.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. V. Styland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

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, 538-544 (2005), and references therein.
[CrossRef] [PubMed]

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, 538-544 (2005), and references therein.
[CrossRef] [PubMed]

Uesugi, N.

H. Shinojima, J. Yumoto, and N. Uesugi, “Size dependence of optical nonlinearity of CdSSe microcrystallites doped in glass,” Appl. Phys. Lett. 60, 298-300 (1992).
[CrossRef]

Urbus, A.

G. H. He, Q. D. Zheng, K. T. Yong, and A. Urbus, “Two-photon absorption based optical limiting and stabilization by using a CdTe quantum dot solution excited at optical communication wavelength of ~1300 nm,” Appl. Phys. Lett. 90, 181108 (2007).
[CrossRef]

Vahala, K. J.

P. C. Sercel and K. J. Vahala, “Analytical formalism for determining quantum-wire and quantum-dot band structure in the multiband envelop-function approximation,” Phys. Rev. B 42, 3690-3711 (1990).
[CrossRef]

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]

D. C. Hutchings and E. W. Van Stryland, “Nondegenerate two photon absorption in zinc blende semicondcutors,” J. Opt. Soc. Am. B 9, 2065-2074 (1992).
[CrossRef]

Vandyshev, Y. V.

Y. V. Vandyshev, V. S. Dneprovskii, and V. I. Klimov, “Nonlinear-transmission dynamics and nonlinear susceptibilities of semicoducting microcrystals (quantum dots),” Sov. Phys. JETP 74, 144-150 (1992).

Vanherzeele, H.

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, 1434-1436 (2003), and references therein.
[CrossRef] [PubMed]

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. V. Styland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (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, 538-544 (2005), and references therein.
[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, 1434-1436 (2003), and references therein.
[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, 1434-1436 (2003), and references therein.
[CrossRef] [PubMed]

Woodall, M. A.

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, 538-544 (2005), and references therein.
[CrossRef] [PubMed]

Yang, M. J.

S. C. Pu, M. J. Yang, C. C. Hsu, C. W. Lai, C. C. Hsieh, S. H. Lin, Y. M. Cheng, and P. T. Chou, “The empirical correlation between size and two-photon absorption cross section of CdSe and CdTe quantum dots,” Small 2, 1308-1313 (2006).
[CrossRef] [PubMed]

Ying, J. Y.

Y. G. Zheng, S. G. Gao, and J. Y. Ying, “Synthesis and cell-imaging applications of glutathione-capped CdTe quantum dots,” Adv. Mater. 19, 376-380 (2007).
[CrossRef]

Y. L. Qu, W. Ji, Y. G. Zheng, and J. Y. Ying, “Auger recombination and intraband absorption of two-photon-excited carriers in colloidal CdSe quantum dots,” Appl. Phys. Lett. 90, 133112 (2007).
[CrossRef]

Yong, K. T.

G. H. He, Q. D. Zheng, K. T. Yong, and A. Urbus, “Two-photon absorption based optical limiting and stabilization by using a CdTe quantum dot solution excited at optical communication wavelength of ~1300 nm,” Appl. Phys. Lett. 90, 181108 (2007).
[CrossRef]

Yu, W. W.

W. W. Yu, L. Qu, W. Guo, and X. Peng, “Experimental determination of the extinction coefficient of CdTe, CdSe, and CdS nanocrystals,” Chem. Mater. 15, 2854-2860 (2003).
[CrossRef]

Yumoto, J.

H. Shinojima, J. Yumoto, and N. Uesugi, “Size dependence of optical nonlinearity of CdSSe microcrystallites doped in glass,” Appl. Phys. Lett. 60, 298-300 (1992).
[CrossRef]

Zheng, Q. D.

G. H. He, Q. D. Zheng, K. T. Yong, and A. Urbus, “Two-photon absorption based optical limiting and stabilization by using a CdTe quantum dot solution excited at optical communication wavelength of ~1300 nm,” Appl. Phys. Lett. 90, 181108 (2007).
[CrossRef]

Zheng, Y. G.

Y. G. Zheng, S. G. Gao, and J. Y. Ying, “Synthesis and cell-imaging applications of glutathione-capped CdTe quantum dots,” Adv. Mater. 19, 376-380 (2007).
[CrossRef]

Y. L. Qu, W. Ji, Y. G. Zheng, and J. Y. Ying, “Auger recombination and intraband absorption of two-photon-excited carriers in colloidal CdSe quantum dots,” Appl. Phys. Lett. 90, 133112 (2007).
[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, 1434-1436 (2003), and references therein.
[CrossRef] [PubMed]

Adv. Mater. (1)

Y. G. Zheng, S. G. Gao, and J. Y. Ying, “Synthesis and cell-imaging applications of glutathione-capped CdTe quantum dots,” Adv. Mater. 19, 376-380 (2007).
[CrossRef]

Appl. Phys. Lett. (4)

G. H. He, Q. D. Zheng, K. T. Yong, and A. Urbus, “Two-photon absorption based optical limiting and stabilization by using a CdTe quantum dot solution excited at optical communication wavelength of ~1300 nm,” Appl. Phys. Lett. 90, 181108 (2007).
[CrossRef]

Y. L. Qu, W. Ji, Y. G. Zheng, and J. Y. Ying, “Auger recombination and intraband absorption of two-photon-excited carriers in colloidal CdSe quantum dots,” Appl. Phys. Lett. 90, 133112 (2007).
[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, 4472-4474 (2004).
[CrossRef]

H. Shinojima, J. Yumoto, and N. Uesugi, “Size dependence of optical nonlinearity of CdSSe microcrystallites doped in glass,” Appl. Phys. Lett. 60, 298-300 (1992).
[CrossRef]

Chem. Mater. (1)

W. W. Yu, L. Qu, W. Guo, and X. Peng, “Experimental determination of the extinction coefficient of CdTe, CdSe, and CdS nanocrystals,” Chem. Mater. 15, 2854-2860 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. V. Styland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

J. Chem. Phys. (1)

U. Banin, C. J. Lee, A. A. Guzelian, A. V. Kadavanich, A. P. Alivisatos, W. Jaskolski, G. W. Bryant, A. L. Efros, and M. Rosen, “Size-dependent electronic level structure of InAs nanocrystal quantum dots: test of multiband effective mass theory,” J. Chem. Phys. 109, 2306-2309 (1998).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. (1)

C. R. Pidgeon and R. N. Brown, “Interband magneto-absorption and Faraday rotation in InSb,” Phys. Rev. 146, 575-583 (1966).
[CrossRef]

Phys. Rev. B (5)

Al. L. Efros and M. Rosen, “Quantum size level structure of narrow-gap semiconductor nanocrystals: effect of band coupling,” Phys. Rev. B 58, 7120-7135 (1998).
[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]

A. V. Fedorov, A. V. Baranov, and K. Inoue, “Two-photon transitions in systems with semiconductor quantum dots,” Phys. Rev. B 54, 8627-8732 (1996).
[CrossRef]

K. I. Kang, B. P. McGinnis, Sandalphon, Y. Z. Hu, S. W. Koch, N. Peyghambarian, A. Mysyrowicz, L. C. Liu, and S. H. Risbud, “Confinement induced valence band mixing in CdS quantum dots observed by two photon spectroscopy,” Phys. Rev. B 45, 3465-3486 (1992).
[CrossRef]

P. C. Sercel and K. J. Vahala, “Analytical formalism for determining quantum-wire and quantum-dot band structure in the multiband envelop-function approximation,” Phys. Rev. B 42, 3690-3711 (1990).
[CrossRef]

Phys. Rev. Lett. (1)

P. C. Sercel, A. L. Efros, and M. Rose, “Intrinsic gap states in semiconductor nanocrystals,” Phys. Rev. Lett. 83, 2394-2397 (1999).
[CrossRef]

Science (2)

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, 538-544 (2005), and references therein.
[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, 1434-1436 (2003), and references therein.
[CrossRef] [PubMed]

Small (1)

S. C. Pu, M. J. Yang, C. C. Hsu, C. W. Lai, C. C. Hsieh, S. H. Lin, Y. M. Cheng, and P. T. Chou, “The empirical correlation between size and two-photon absorption cross section of CdSe and CdTe quantum dots,” Small 2, 1308-1313 (2006).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

Y. V. Vandyshev, V. S. Dneprovskii, and V. I. Klimov, “Nonlinear-transmission dynamics and nonlinear susceptibilities of semicoducting microcrystals (quantum dots),” Sov. Phys. JETP 74, 144-150 (1992).

Other (1)

J. Singh, Physics of Semiconductors and Their Heterostructures (McGraw Hill, 1993).

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Figures (9)

Fig. 1
Fig. 1

TEM photograph and size distribution (bottom inset) of the sample CdTe 510 (radius of 1.5 nm). In the top inset, the solid and the dashed curves are the measured one-photon absorption and one-photon-excited PL spectra, respectively.

Fig. 2
Fig. 2

TPA spectra measured for the CdTe QDs in aqueous solution. The CdTe QDs with radii of 1.5, 1.75, and 2.0 nm are denoted as CdTe 510, CdTe 555, and CdTe 615, respectively. Inset: typical open-aperture Z scans for CdTe 615. The solid curves are the fitting results. The laser intensities are 5.2, 4.8, 7.0, and 20   GW   cm 2 at 720, 780, 850, and 950 nm, respectively.

Fig. 3
Fig. 3

Bandgap energy of CdTe QDs calculated by the parabolic model (dashed-dotted curve) and the eight-band PB model (solid curve). The scattered values are experimental results from the UV-visible absorption spectra here (solid triangle) (see Fig. 1) as well as from [5] (hollow star) and [22] (black double cross), respectively.

Fig. 4
Fig. 4

(a) TPA coefficients from the Z scans (solid squares) compared with the calculated curves by the eight-band PB model (solid curves) and the parabolic model (dashed curves). The size dispersions are taken as 7% for all the calculations. (b) Comparison of the calculated TPA spectra based on eight-band PB modeling (solid curve), the modeling reported in [4] (dashed curve), and the parabolic approximation modeling (dashed-dotted curve), for CdTe QDs with bandgap energy at 600 nm (2.07 eV). The solid squares are the experimental data reported in [4]. HH and LH stand for heavy and light holes, respectively.

Fig. 5
Fig. 5

Calculated TPA cross section of CdTe QDs by the eight-band PB model as (a) a function of both size and wavelength and (b) as a function of dot diameter (solid curve) at 700 (hollow triangle), 780 (solid square), and 860 nm (hollow circle). The dashed curves are fitting curves with equation σ TPA = A ( 2 R ) B , where A is 38, 10, and 0.21 and B is 4.7, 5.28, and 7.7, for 700, 780, and 860 nm, respectively.

Fig. 6
Fig. 6

Calculated TPA cross sections of CdTe QDs at three maxima in the TPA spectra as a function of the dot size. The solid curves represent the calculated TPA cross sections, whereas the dashed and the dashed-dotted curves are the curves proportional to ( 2 R ) 2 and ( 2 R ) 3 , respectively.

Fig. 7
Fig. 7

Transition energies versus dot diameter in the transition energy range of 2.0–3.6 eV (corresponds to a wavelength range from 700 to 1200 nm). The first ten transitions are as follows: (1) 1 P 3 / 2 ( h ) 1 S 1 / 2 ( e ) , (2) 1 P 1 / 2 ( h ) 1 S 1 / 2 ( e ) , (3) 1 S 3 / 2 ( h ) 1 P 1 / 2 ( e ) , (4) 1 S 3 / 2 ( h ) 1 P 3 / 2 ( e ) , (5) 2 P 3 / 2 ( h ) 1 S 1 / 2 ( e ) , (6) 2 S 3 / 2 ( h ) 1 P 1 / 2 ( e ) , (7) 2 S 3 / 2 ( h ) 1 P 3 / 2 ( e ) , (8) 1 P 3 / 2 s ( h ) 1 S 1 / 2 ( e ) , (9) 1 P 3 / 2 ( h ) 1 D 5 / 2 ( e ) , and (10) 1 D 7 / 2 ( h ) 1 P 3 / 2 ( e ) .

Fig. 8
Fig. 8

(a) F c , h j and (b) σ TPA contributed from the first ten transitions as functions of the dot diameter.

Fig. 9
Fig. 9

Calculated TPA spectra by the eight-band PB model with different size dispersions for an average dot radius of 2 nm.

Tables (1)

Tables Icon

Table 1 Structural and Optical Parameters of CdTe QDs

Equations (6)

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

W ( 2 ) = 2 π j = 1 3 v 1 , v 0 | v 2 ψ v 1 c | A m c e P | ψ v 2 c   or   h j ψ v 2 c   or   h j | A m c e P | ψ v 0 h j E v 2 E v 0 ω i γ i | 2 δ ( E v 1 E v 0 2 ω ) ,
β = 4 ω N I 2 d R f ( R ) W ( 2 ) ,
β = 4 N ( 2 π ) 3 c 2 ε ω ω 3 j = 1 3 F c , h j ,
F c , h j = d R f ( R ) v 1 , v 0 | v 2 ψ v 1 c | 1 m c e P | ψ v 2 c   or   h j ψ v 2 c   or   h j | 1 m c e P | ψ v 0 h j E v 2 E v 0 ω i γ i | 2 δ ( E v 1 E v 0 2 ω ) .
σ TPA = 4 ( 2 π ) 3 c 2 ε ω ω 2 j = 1 3 F c , h j .
ψ ± ( r ) = i = 1 4 C ± ( k i ) j l ( k i r ) μ = a a Ω μ ± u a , μ c , v ,

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