Abstract

Three-photon-induced four-photon absorption via excited-state absorption and self-defocusing nonlinear refraction are reported for the first time, to our knowledge, in ZnO quantum dots with average sizes of 2.0±0.1  nm with 1064 nm radiation from a Q-switched Nd:YAG laser at a peak intensity of 2.5  GW/cm2. By employing the three-level two-step model, the experimental results can be explained quite satisfactorily.

© 2009 Optical Society of America

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  1. A. Penzkofer and W. Falkenstein, Opt. Commun. 16, 247 (1976).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  19. B. Gu, X.-Q. Huang, S.-Q. Tan, M. Wang, and W. Ji, Appl. Phys. B 95, 375 (2009).
    [CrossRef]

2009

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, R. Sarkar, A. K. Mitra, and U. Chatterjee, J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

X. B. Feng, G. C. Xing, and W. Ji, J. Opt. A 11, 024004 (2009).
[CrossRef]

B. Gu, X.-Q. Huang, S.-Q. Tan, M. Wang, and W. Ji, Appl. Phys. B 95, 375 (2009).
[CrossRef]

2008

G. Xing, W. Ji, Y. Zheng, and J. Ying, Appl. Phys. Lett. 93, 241114 (2008).
[CrossRef]

G. S. He, L. Tan, Q. Zheng, and P. N. Prasad, Chem. Rev. 108, 1245 (2008).
[CrossRef] [PubMed]

B. Gu, J. He, W. Ji, and H. T. Wang, J. Appl. Phys. 103, 073105 (2008).
[CrossRef]

B. Gu and W. Ji, Opt. Express 16, 10208 (2008).
[CrossRef] [PubMed]

P. Kumbhakar, D. Singh, C. S. Tiwary, and A. K. Mitra, Chalcogenide Let. 5, 387 (2008).

L. Irimpan, V. P. N. Nampoori, and P. Radhakrishnan, J. Appl. Phys. 103, 094914 (2008).
[CrossRef]

2005

2004

S. Polyakov, F. Yoshino, M. Liu, and G. Stegeman, Phys. Rev. B 69, 115421 (2004).
[CrossRef]

2003

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

1998

R. Wang, X. Wu, B. Zou, L. Wang, P. Wu, S. Liu, J. Wang, and J. Xu, Chin. Phys. Lett. 15, 27 (1998).
[CrossRef]

1997

1993

T. Kobayashi, Optoelectron., Devices Technol. 8, 309 (1993).

1990

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

1976

A. Penzkofer and W. Falkenstein, Opt. Commun. 16, 247 (1976).
[CrossRef]

Brant, M. C.

Chatterjee, U.

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, R. Sarkar, A. K. Mitra, and U. Chatterjee, J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

Chattopadhyay, M.

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, R. Sarkar, A. K. Mitra, and U. Chatterjee, J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

Chen, J.

Ding, J.

Falkenstein, W.

A. Penzkofer and W. Falkenstein, Opt. Commun. 16, 247 (1976).
[CrossRef]

Fan, Y.

Feng, X. B.

X. B. Feng, G. C. Xing, and W. Ji, J. Opt. A 11, 024004 (2009).
[CrossRef]

Fleitz, P. A.

Ganeev, R. A.

R. A. Ganeev, J. Opt. A 7, 717 (2005).
[CrossRef]

Gu, B.

B. Gu, X.-Q. Huang, S.-Q. Tan, M. Wang, and W. Ji, Appl. Phys. B 95, 375 (2009).
[CrossRef]

B. Gu and W. Ji, Opt. Express 16, 10208 (2008).
[CrossRef] [PubMed]

B. Gu, J. He, W. Ji, and H. T. Wang, J. Appl. Phys. 103, 073105 (2008).
[CrossRef]

B. Gu, J. Wang, J. Chen, Y. Fan, J. Ding, and H. Wang, Opt. Express 13, 9230 (2005).
[CrossRef] [PubMed]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

He, G. S.

G. S. He, L. Tan, Q. Zheng, and P. N. Prasad, Chem. Rev. 108, 1245 (2008).
[CrossRef] [PubMed]

He, J.

B. Gu, J. He, W. Ji, and H. T. Wang, J. Appl. Phys. 103, 073105 (2008).
[CrossRef]

Huang, X. -Q.

B. Gu, X.-Q. Huang, S.-Q. Tan, M. Wang, and W. Ji, Appl. Phys. B 95, 375 (2009).
[CrossRef]

Irimpan, L.

L. Irimpan, V. P. N. Nampoori, and P. Radhakrishnan, J. Appl. Phys. 103, 094914 (2008).
[CrossRef]

Ji, W.

X. B. Feng, G. C. Xing, and W. Ji, J. Opt. A 11, 024004 (2009).
[CrossRef]

B. Gu, X.-Q. Huang, S.-Q. Tan, M. Wang, and W. Ji, Appl. Phys. B 95, 375 (2009).
[CrossRef]

G. Xing, W. Ji, Y. Zheng, and J. Ying, Appl. Phys. Lett. 93, 241114 (2008).
[CrossRef]

B. Gu, J. He, W. Ji, and H. T. Wang, J. Appl. Phys. 103, 073105 (2008).
[CrossRef]

B. Gu and W. Ji, Opt. Express 16, 10208 (2008).
[CrossRef] [PubMed]

X. J. Zhang, W. Ji, and S. H. Tang, J. Opt. Soc. Am. B 14, 1951 (1997).
[CrossRef]

Kobayashi, T.

T. Kobayashi, Optoelectron., Devices Technol. 8, 309 (1993).

Kumbhakar, P.

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, R. Sarkar, A. K. Mitra, and U. Chatterjee, J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

P. Kumbhakar, D. Singh, C. S. Tiwary, and A. K. Mitra, Chalcogenide Let. 5, 387 (2008).

Liu, M.

S. Polyakov, F. Yoshino, M. Liu, and G. Stegeman, Phys. Rev. B 69, 115421 (2004).
[CrossRef]

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

Liu, S.

R. Wang, X. Wu, B. Zou, L. Wang, P. Wu, S. Liu, J. Wang, and J. Xu, Chin. Phys. Lett. 15, 27 (1998).
[CrossRef]

Maclean, D. G.

Mitra, A. K.

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, R. Sarkar, A. K. Mitra, and U. Chatterjee, J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

P. Kumbhakar, D. Singh, C. S. Tiwary, and A. K. Mitra, Chalcogenide Let. 5, 387 (2008).

Nampoori, V. P. N.

L. Irimpan, V. P. N. Nampoori, and P. Radhakrishnan, J. Appl. Phys. 103, 094914 (2008).
[CrossRef]

Penzkofer, A.

A. Penzkofer and W. Falkenstein, Opt. Commun. 16, 247 (1976).
[CrossRef]

Polyakov, S.

S. Polyakov, F. Yoshino, M. Liu, and G. Stegeman, Phys. Rev. B 69, 115421 (2004).
[CrossRef]

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

Prasad, P. N.

G. S. He, L. Tan, Q. Zheng, and P. N. Prasad, Chem. Rev. 108, 1245 (2008).
[CrossRef] [PubMed]

Radhakrishnan, P.

L. Irimpan, V. P. N. Nampoori, and P. Radhakrishnan, J. Appl. Phys. 103, 094914 (2008).
[CrossRef]

Rogers, J. E.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Sarkar, R.

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, R. Sarkar, A. K. Mitra, and U. Chatterjee, J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Singh, D.

P. Kumbhakar, D. Singh, C. S. Tiwary, and A. K. Mitra, Chalcogenide Let. 5, 387 (2008).

Slagle, J. E.

Stegeman, G.

S. Polyakov, F. Yoshino, M. Liu, and G. Stegeman, Phys. Rev. B 69, 115421 (2004).
[CrossRef]

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

Sutherland, R. L.

Tan, L.

G. S. He, L. Tan, Q. Zheng, and P. N. Prasad, Chem. Rev. 108, 1245 (2008).
[CrossRef] [PubMed]

Tan, S. -Q.

B. Gu, X.-Q. Huang, S.-Q. Tan, M. Wang, and W. Ji, Appl. Phys. B 95, 375 (2009).
[CrossRef]

Tang, S. H.

Tiwary, C. S.

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, R. Sarkar, A. K. Mitra, and U. Chatterjee, J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

P. Kumbhakar, D. Singh, C. S. Tiwary, and A. K. Mitra, Chalcogenide Let. 5, 387 (2008).

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Wang, H.

Wang, H. T.

B. Gu, J. He, W. Ji, and H. T. Wang, J. Appl. Phys. 103, 073105 (2008).
[CrossRef]

Wang, J.

B. Gu, J. Wang, J. Chen, Y. Fan, J. Ding, and H. Wang, Opt. Express 13, 9230 (2005).
[CrossRef] [PubMed]

R. Wang, X. Wu, B. Zou, L. Wang, P. Wu, S. Liu, J. Wang, and J. Xu, Chin. Phys. Lett. 15, 27 (1998).
[CrossRef]

Wang, L.

R. Wang, X. Wu, B. Zou, L. Wang, P. Wu, S. Liu, J. Wang, and J. Xu, Chin. Phys. Lett. 15, 27 (1998).
[CrossRef]

Wang, M.

B. Gu, X.-Q. Huang, S.-Q. Tan, M. Wang, and W. Ji, Appl. Phys. B 95, 375 (2009).
[CrossRef]

Wang, R.

R. Wang, X. Wu, B. Zou, L. Wang, P. Wu, S. Liu, J. Wang, and J. Xu, Chin. Phys. Lett. 15, 27 (1998).
[CrossRef]

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Wu, P.

R. Wang, X. Wu, B. Zou, L. Wang, P. Wu, S. Liu, J. Wang, and J. Xu, Chin. Phys. Lett. 15, 27 (1998).
[CrossRef]

Wu, X.

R. Wang, X. Wu, B. Zou, L. Wang, P. Wu, S. Liu, J. Wang, and J. Xu, Chin. Phys. Lett. 15, 27 (1998).
[CrossRef]

Xing, G.

G. Xing, W. Ji, Y. Zheng, and J. Ying, Appl. Phys. Lett. 93, 241114 (2008).
[CrossRef]

Xing, G. C.

X. B. Feng, G. C. Xing, and W. Ji, J. Opt. A 11, 024004 (2009).
[CrossRef]

Xu, J.

R. Wang, X. Wu, B. Zou, L. Wang, P. Wu, S. Liu, J. Wang, and J. Xu, Chin. Phys. Lett. 15, 27 (1998).
[CrossRef]

Ying, J.

G. Xing, W. Ji, Y. Zheng, and J. Ying, Appl. Phys. Lett. 93, 241114 (2008).
[CrossRef]

Yoshino, F.

S. Polyakov, F. Yoshino, M. Liu, and G. Stegeman, Phys. Rev. B 69, 115421 (2004).
[CrossRef]

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

Zhang, X. J.

Zheng, Q.

G. S. He, L. Tan, Q. Zheng, and P. N. Prasad, Chem. Rev. 108, 1245 (2008).
[CrossRef] [PubMed]

Zheng, Y.

G. Xing, W. Ji, Y. Zheng, and J. Ying, Appl. Phys. Lett. 93, 241114 (2008).
[CrossRef]

Zou, B.

R. Wang, X. Wu, B. Zou, L. Wang, P. Wu, S. Liu, J. Wang, and J. Xu, Chin. Phys. Lett. 15, 27 (1998).
[CrossRef]

Appl. Phys. B

B. Gu, X.-Q. Huang, S.-Q. Tan, M. Wang, and W. Ji, Appl. Phys. B 95, 375 (2009).
[CrossRef]

Appl. Phys. Lett.

G. Xing, W. Ji, Y. Zheng, and J. Ying, Appl. Phys. Lett. 93, 241114 (2008).
[CrossRef]

Chalcogenide Let.

P. Kumbhakar, D. Singh, C. S. Tiwary, and A. K. Mitra, Chalcogenide Let. 5, 387 (2008).

Chem. Rev.

G. S. He, L. Tan, Q. Zheng, and P. N. Prasad, Chem. Rev. 108, 1245 (2008).
[CrossRef] [PubMed]

Chin. Phys. Lett.

R. Wang, X. Wu, B. Zou, L. Wang, P. Wu, S. Liu, J. Wang, and J. Xu, Chin. Phys. Lett. 15, 27 (1998).
[CrossRef]

IEEE J. Quantum Electron.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

J. Appl. Phys.

B. Gu, J. He, W. Ji, and H. T. Wang, J. Appl. Phys. 103, 073105 (2008).
[CrossRef]

M. Chattopadhyay, P. Kumbhakar, C. S. Tiwary, R. Sarkar, A. K. Mitra, and U. Chatterjee, J. Appl. Phys. 105, 024313 (2009).
[CrossRef]

L. Irimpan, V. P. N. Nampoori, and P. Radhakrishnan, J. Appl. Phys. 103, 094914 (2008).
[CrossRef]

J. Opt. A

R. A. Ganeev, J. Opt. A 7, 717 (2005).
[CrossRef]

X. B. Feng, G. C. Xing, and W. Ji, J. Opt. A 11, 024004 (2009).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

A. Penzkofer and W. Falkenstein, Opt. Commun. 16, 247 (1976).
[CrossRef]

Opt. Express

Optoelectron., Devices Technol.

T. Kobayashi, Optoelectron., Devices Technol. 8, 309 (1993).

Phys. Rev. B

S. Polyakov, F. Yoshino, M. Liu, and G. Stegeman, Phys. Rev. B 69, 115421 (2004).
[CrossRef]

Phys. Rev. Lett.

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

UV–VIS absorption characteristics of ZnO nanoparticles. Insets (a) and (b) show pure 4PA and 3PA-induced 4PA via ESA, respectively.

Fig. 2
Fig. 2

Dashed-dotted (red), short dashed (black), dotted (green), solid (blue), and dashed (magenta) curves are the theoretical normalized OA z-scan transmittance traces obtained for pure 2PA (with α 2 = 2.86   cm / GW ), concurrence of 2PA and 3PA (with α 2 = 1.2   cm / GW and α 3 = 2.2 cm 3 / GW 2 ), pure 3PA (with α 3 = 0.71 cm 3 / GW 2 ), 3PA-induced effective 4PA (with α 3 = 0.058 cm 3 / GW 2 and α 4 = 0.013 cm 5 / GW 3 ), and pure 4PA (with α 4 = 0.36 cm 5 / GW 3 ) OA z-scan traces, respectively. Circles are the experimental points. Inset (top) shows XRD pattern of the same QDs. Inset (bottom) shows pulse duration dependence of normalized effective 4PA coefficients [4].

Fig. 3
Fig. 3

Normalized transmittance trace for CA z scan taking contribution from pure NLR. The contribution from pure NLR is calculated from the experimental CA and OA transmittance traces and following the method described in [13].

Tables (1)

Tables Icon

Table 1 3PA-Induced Effective 4PA and NLR Coefficients of ZnO QDs

Equations (3)

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

d I d z = α 0 I α m I m ,
I z = σ 3 p 0 I 3 σ e p 1 I ,
T ( z , p , q ) = r = 0 4 s = 0 4 a r s p r q s ,

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