Abstract

We report on the observation of spectral dependence of absorption anisotropy in a CdSe quantum rod (QR) ensemble, which is aligned in a polymer film with a nanocrystal concentration of 2×105M. The experimental data on the polarization direction and anisotropy factor were obtained for the lowest excitonic transition and the second group of transitions in the QR. The nonzero constant value of anisotropy was investigated for the high-energy transitions, and is evidence of the one-dimensional confinement in the QR.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. J. Hu, L.-W. Wang, L.-S. Li, W. Yang, and A. P. Alivisatos, J. Phys. Chem. B 106, 2447 (2002).
    [CrossRef]
  5. R. Krahne, L. Manna, G. Morello, A. Figuerola, C. George, and S. Deka, Physical Properties of Nanorods (Springer, 2013).
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    [CrossRef]
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    [CrossRef]
  8. W. W. Yu, L. Qu, W. Guo, and X. Peng, Chem. Mater. 15, 2854 (2003).
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  9. U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, Nat. Methods 5, 763 (2008).
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  10. Y. Chen and Z. Rosenzweig, Anal. Chem. 74, 5132 (2002).
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  11. P. Reiss, E. Couderc, J. De Girolamo, and A. Pron, Nanoscale 3, 446 (2011).
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    [CrossRef]
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    [CrossRef]
  18. X. Chen, A. Nazzal, D. Goorskey, and M. Xiao, Phys. Rev. B 64, 245304 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. D. Katz, T. Wizansky, O. Millo, E. Rothenberg, T. Mokari, and U. Banin, Phys. Rev. Lett. 89, 086801 (2002).
    [CrossRef]

2012 (2)

J. Kamal, R. Gomes, Z. Hens, M. Karvar, K. Neyts, S. Compernolle, and F. Vanhaecke, Phys. Rev. B 85, 035126 (2012).
[CrossRef]

A. S. Baimuratov, V. K. Turkov, I. D. Rukhlenko, and A. V. Fedorov, Opt. Lett. 37, 4645 (2012).
[CrossRef]

2011 (1)

P. Reiss, E. Couderc, J. De Girolamo, and A. Pron, Nanoscale 3, 446 (2011).
[CrossRef]

2009 (1)

C. de Mello Donega and R. Koole, J. Phys. Chem. C 113, 6511 (2009).
[CrossRef]

2008 (2)

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, Nat. Methods 5, 763 (2008).
[CrossRef]

C. C. Yang and S. Li, J. Phys. Chem. C 112, 2851 (2008).
[CrossRef]

2004 (1)

A. Shabaev and A. L. Efros, Nano Lett. 4, 1821 (2004).
[CrossRef]

2003 (3)

M. Artemyev, B. Moller, and U. Woggon, Nano Lett. 3, 509 (2003).
[CrossRef]

W. W. Yu, L. Qu, W. Guo, and X. Peng, Chem. Mater. 15, 2854 (2003).
[CrossRef]

J. Li and L.-W. Wang, Nano Lett. 3, 101 (2003).
[CrossRef]

2002 (5)

D. Katz, T. Wizansky, O. Millo, E. Rothenberg, T. Mokari, and U. Banin, Phys. Rev. Lett. 89, 086801 (2002).
[CrossRef]

Y. Chen and Z. Rosenzweig, Anal. Chem. 74, 5132 (2002).
[CrossRef]

L. Manna, E. Scher, L.-S. Li, and A. P. Alivisatos, J. Am. Chem. Soc. 124, 7136 (2002).
[CrossRef]

J. Hu, L.-W. Wang, L.-S. Li, W. Yang, and A. P. Alivisatos, J. Phys. Chem. B 106, 2447 (2002).
[CrossRef]

X. Chen, A. Y. Nazzal, M. Xiao, Z. A. Peng, and X. Peng, J. Lumin. 97, 205 (2002).
[CrossRef]

2001 (3)

J. Hu, L.-S. Li, Y. Weidong, L. Manna, L.-W. Wang, and A. P. Alivisatos, Science 292, 2060 (2001).
[CrossRef]

X. Chen, A. Nazzal, D. Goorskey, and M. Xiao, Phys. Rev. B 64, 245304 (2001).
[CrossRef]

I. Grabchev, I. Moneva, A. Kozlov, and G. Elyashevich, Mater. Res. Innovations 4, 301 (2001).
[CrossRef]

2000 (1)

X. Peng, L. Manna, W. Yang, J. Wickham, E. Scher, A. Kadavanich, and A. Alivisatos, Nature 404, 59 (2000).
[CrossRef]

1996 (1)

A. P. Alivisatos, Science 271, 933 (1996).
[CrossRef]

1992 (1)

A. L. Efros, Phys. Rev. B 46, 7448 (1992).
[CrossRef]

1981 (1)

H. Aoyama, Y. Yamazaki, N. Matsuura, H. Mada, and S. Kobayashi, Mol. Cryst. Liq. Cryst. 72, 127 (1981).
[CrossRef]

1970 (1)

E. W. Thulstrup, J. Michl, and J. H. Eggers, J. Phys. Chem. 74, 3868 (1970).
[CrossRef]

Alivisatos, A.

X. Peng, L. Manna, W. Yang, J. Wickham, E. Scher, A. Kadavanich, and A. Alivisatos, Nature 404, 59 (2000).
[CrossRef]

Alivisatos, A. P.

J. Hu, L.-W. Wang, L.-S. Li, W. Yang, and A. P. Alivisatos, J. Phys. Chem. B 106, 2447 (2002).
[CrossRef]

L. Manna, E. Scher, L.-S. Li, and A. P. Alivisatos, J. Am. Chem. Soc. 124, 7136 (2002).
[CrossRef]

J. Hu, L.-S. Li, Y. Weidong, L. Manna, L.-W. Wang, and A. P. Alivisatos, Science 292, 2060 (2001).
[CrossRef]

A. P. Alivisatos, Science 271, 933 (1996).
[CrossRef]

Aoyama, H.

H. Aoyama, Y. Yamazaki, N. Matsuura, H. Mada, and S. Kobayashi, Mol. Cryst. Liq. Cryst. 72, 127 (1981).
[CrossRef]

Artemyev, M.

M. Artemyev, B. Moller, and U. Woggon, Nano Lett. 3, 509 (2003).
[CrossRef]

Baimuratov, A. S.

Banin, U.

D. Katz, T. Wizansky, O. Millo, E. Rothenberg, T. Mokari, and U. Banin, Phys. Rev. Lett. 89, 086801 (2002).
[CrossRef]

Cavaliere-Jaricot, S.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, Nat. Methods 5, 763 (2008).
[CrossRef]

Chen, X.

X. Chen, A. Y. Nazzal, M. Xiao, Z. A. Peng, and X. Peng, J. Lumin. 97, 205 (2002).
[CrossRef]

X. Chen, A. Nazzal, D. Goorskey, and M. Xiao, Phys. Rev. B 64, 245304 (2001).
[CrossRef]

Chen, Y.

Y. Chen and Z. Rosenzweig, Anal. Chem. 74, 5132 (2002).
[CrossRef]

Compernolle, S.

J. Kamal, R. Gomes, Z. Hens, M. Karvar, K. Neyts, S. Compernolle, and F. Vanhaecke, Phys. Rev. B 85, 035126 (2012).
[CrossRef]

Couderc, E.

P. Reiss, E. Couderc, J. De Girolamo, and A. Pron, Nanoscale 3, 446 (2011).
[CrossRef]

De Girolamo, J.

P. Reiss, E. Couderc, J. De Girolamo, and A. Pron, Nanoscale 3, 446 (2011).
[CrossRef]

de Mello Donega, C.

C. de Mello Donega and R. Koole, J. Phys. Chem. C 113, 6511 (2009).
[CrossRef]

Deka, S.

R. Krahne, L. Manna, G. Morello, A. Figuerola, C. George, and S. Deka, Physical Properties of Nanorods (Springer, 2013).

Efros, A. L.

A. Shabaev and A. L. Efros, Nano Lett. 4, 1821 (2004).
[CrossRef]

A. L. Efros, Phys. Rev. B 46, 7448 (1992).
[CrossRef]

Eggers, J. H.

E. W. Thulstrup, J. Michl, and J. H. Eggers, J. Phys. Chem. 74, 3868 (1970).
[CrossRef]

Elyashevich, G.

I. Grabchev, I. Moneva, A. Kozlov, and G. Elyashevich, Mater. Res. Innovations 4, 301 (2001).
[CrossRef]

Fedorov, A. V.

Figuerola, A.

R. Krahne, L. Manna, G. Morello, A. Figuerola, C. George, and S. Deka, Physical Properties of Nanorods (Springer, 2013).

George, C.

R. Krahne, L. Manna, G. Morello, A. Figuerola, C. George, and S. Deka, Physical Properties of Nanorods (Springer, 2013).

Gomes, R.

J. Kamal, R. Gomes, Z. Hens, M. Karvar, K. Neyts, S. Compernolle, and F. Vanhaecke, Phys. Rev. B 85, 035126 (2012).
[CrossRef]

Goorskey, D.

X. Chen, A. Nazzal, D. Goorskey, and M. Xiao, Phys. Rev. B 64, 245304 (2001).
[CrossRef]

Grabchev, I.

I. Grabchev, I. Moneva, A. Kozlov, and G. Elyashevich, Mater. Res. Innovations 4, 301 (2001).
[CrossRef]

Grabolle, M.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, Nat. Methods 5, 763 (2008).
[CrossRef]

Guo, W.

W. W. Yu, L. Qu, W. Guo, and X. Peng, Chem. Mater. 15, 2854 (2003).
[CrossRef]

Hens, Z.

J. Kamal, R. Gomes, Z. Hens, M. Karvar, K. Neyts, S. Compernolle, and F. Vanhaecke, Phys. Rev. B 85, 035126 (2012).
[CrossRef]

Hu, J.

J. Hu, L.-W. Wang, L.-S. Li, W. Yang, and A. P. Alivisatos, J. Phys. Chem. B 106, 2447 (2002).
[CrossRef]

J. Hu, L.-S. Li, Y. Weidong, L. Manna, L.-W. Wang, and A. P. Alivisatos, Science 292, 2060 (2001).
[CrossRef]

Kadavanich, A.

X. Peng, L. Manna, W. Yang, J. Wickham, E. Scher, A. Kadavanich, and A. Alivisatos, Nature 404, 59 (2000).
[CrossRef]

Kamal, J.

J. Kamal, R. Gomes, Z. Hens, M. Karvar, K. Neyts, S. Compernolle, and F. Vanhaecke, Phys. Rev. B 85, 035126 (2012).
[CrossRef]

Karvar, M.

J. Kamal, R. Gomes, Z. Hens, M. Karvar, K. Neyts, S. Compernolle, and F. Vanhaecke, Phys. Rev. B 85, 035126 (2012).
[CrossRef]

Katz, D.

D. Katz, T. Wizansky, O. Millo, E. Rothenberg, T. Mokari, and U. Banin, Phys. Rev. Lett. 89, 086801 (2002).
[CrossRef]

Kobayashi, S.

H. Aoyama, Y. Yamazaki, N. Matsuura, H. Mada, and S. Kobayashi, Mol. Cryst. Liq. Cryst. 72, 127 (1981).
[CrossRef]

Koole, R.

C. de Mello Donega and R. Koole, J. Phys. Chem. C 113, 6511 (2009).
[CrossRef]

Kozlov, A.

I. Grabchev, I. Moneva, A. Kozlov, and G. Elyashevich, Mater. Res. Innovations 4, 301 (2001).
[CrossRef]

Krahne, R.

R. Krahne, L. Manna, G. Morello, A. Figuerola, C. George, and S. Deka, Physical Properties of Nanorods (Springer, 2013).

Li, J.

J. Li and L.-W. Wang, Nano Lett. 3, 101 (2003).
[CrossRef]

Li, L.-S.

L. Manna, E. Scher, L.-S. Li, and A. P. Alivisatos, J. Am. Chem. Soc. 124, 7136 (2002).
[CrossRef]

J. Hu, L.-W. Wang, L.-S. Li, W. Yang, and A. P. Alivisatos, J. Phys. Chem. B 106, 2447 (2002).
[CrossRef]

J. Hu, L.-S. Li, Y. Weidong, L. Manna, L.-W. Wang, and A. P. Alivisatos, Science 292, 2060 (2001).
[CrossRef]

Li, S.

C. C. Yang and S. Li, J. Phys. Chem. C 112, 2851 (2008).
[CrossRef]

Mada, H.

H. Aoyama, Y. Yamazaki, N. Matsuura, H. Mada, and S. Kobayashi, Mol. Cryst. Liq. Cryst. 72, 127 (1981).
[CrossRef]

Manna, L.

L. Manna, E. Scher, L.-S. Li, and A. P. Alivisatos, J. Am. Chem. Soc. 124, 7136 (2002).
[CrossRef]

J. Hu, L.-S. Li, Y. Weidong, L. Manna, L.-W. Wang, and A. P. Alivisatos, Science 292, 2060 (2001).
[CrossRef]

X. Peng, L. Manna, W. Yang, J. Wickham, E. Scher, A. Kadavanich, and A. Alivisatos, Nature 404, 59 (2000).
[CrossRef]

R. Krahne, L. Manna, G. Morello, A. Figuerola, C. George, and S. Deka, Physical Properties of Nanorods (Springer, 2013).

Matsuura, N.

H. Aoyama, Y. Yamazaki, N. Matsuura, H. Mada, and S. Kobayashi, Mol. Cryst. Liq. Cryst. 72, 127 (1981).
[CrossRef]

Michl, J.

E. W. Thulstrup, J. Michl, and J. H. Eggers, J. Phys. Chem. 74, 3868 (1970).
[CrossRef]

Millo, O.

D. Katz, T. Wizansky, O. Millo, E. Rothenberg, T. Mokari, and U. Banin, Phys. Rev. Lett. 89, 086801 (2002).
[CrossRef]

Mokari, T.

D. Katz, T. Wizansky, O. Millo, E. Rothenberg, T. Mokari, and U. Banin, Phys. Rev. Lett. 89, 086801 (2002).
[CrossRef]

Moller, B.

M. Artemyev, B. Moller, and U. Woggon, Nano Lett. 3, 509 (2003).
[CrossRef]

Moneva, I.

I. Grabchev, I. Moneva, A. Kozlov, and G. Elyashevich, Mater. Res. Innovations 4, 301 (2001).
[CrossRef]

Morello, G.

R. Krahne, L. Manna, G. Morello, A. Figuerola, C. George, and S. Deka, Physical Properties of Nanorods (Springer, 2013).

Nann, T.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, Nat. Methods 5, 763 (2008).
[CrossRef]

Nazzal, A.

X. Chen, A. Nazzal, D. Goorskey, and M. Xiao, Phys. Rev. B 64, 245304 (2001).
[CrossRef]

Nazzal, A. Y.

X. Chen, A. Y. Nazzal, M. Xiao, Z. A. Peng, and X. Peng, J. Lumin. 97, 205 (2002).
[CrossRef]

Neyts, K.

J. Kamal, R. Gomes, Z. Hens, M. Karvar, K. Neyts, S. Compernolle, and F. Vanhaecke, Phys. Rev. B 85, 035126 (2012).
[CrossRef]

Nitschke, R.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, Nat. Methods 5, 763 (2008).
[CrossRef]

Peng, X.

W. W. Yu, L. Qu, W. Guo, and X. Peng, Chem. Mater. 15, 2854 (2003).
[CrossRef]

X. Chen, A. Y. Nazzal, M. Xiao, Z. A. Peng, and X. Peng, J. Lumin. 97, 205 (2002).
[CrossRef]

X. Peng, L. Manna, W. Yang, J. Wickham, E. Scher, A. Kadavanich, and A. Alivisatos, Nature 404, 59 (2000).
[CrossRef]

Peng, Z. A.

X. Chen, A. Y. Nazzal, M. Xiao, Z. A. Peng, and X. Peng, J. Lumin. 97, 205 (2002).
[CrossRef]

Pron, A.

P. Reiss, E. Couderc, J. De Girolamo, and A. Pron, Nanoscale 3, 446 (2011).
[CrossRef]

Qu, L.

W. W. Yu, L. Qu, W. Guo, and X. Peng, Chem. Mater. 15, 2854 (2003).
[CrossRef]

Reiss, P.

P. Reiss, E. Couderc, J. De Girolamo, and A. Pron, Nanoscale 3, 446 (2011).
[CrossRef]

Resch-Genger, U.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, Nat. Methods 5, 763 (2008).
[CrossRef]

Rosenzweig, Z.

Y. Chen and Z. Rosenzweig, Anal. Chem. 74, 5132 (2002).
[CrossRef]

Rothenberg, E.

D. Katz, T. Wizansky, O. Millo, E. Rothenberg, T. Mokari, and U. Banin, Phys. Rev. Lett. 89, 086801 (2002).
[CrossRef]

Rukhlenko, I. D.

Scher, E.

L. Manna, E. Scher, L.-S. Li, and A. P. Alivisatos, J. Am. Chem. Soc. 124, 7136 (2002).
[CrossRef]

X. Peng, L. Manna, W. Yang, J. Wickham, E. Scher, A. Kadavanich, and A. Alivisatos, Nature 404, 59 (2000).
[CrossRef]

Schuler, N. W.

N. W. Schuler, “Iodine stained light polarizer,” U.S. Patent4,166,871 (April27, 1978).

Shabaev, A.

A. Shabaev and A. L. Efros, Nano Lett. 4, 1821 (2004).
[CrossRef]

Thulstrup, E. W.

E. W. Thulstrup, J. Michl, and J. H. Eggers, J. Phys. Chem. 74, 3868 (1970).
[CrossRef]

Turkov, V. K.

Vanhaecke, F.

J. Kamal, R. Gomes, Z. Hens, M. Karvar, K. Neyts, S. Compernolle, and F. Vanhaecke, Phys. Rev. B 85, 035126 (2012).
[CrossRef]

Wang, L.-W.

J. Li and L.-W. Wang, Nano Lett. 3, 101 (2003).
[CrossRef]

J. Hu, L.-W. Wang, L.-S. Li, W. Yang, and A. P. Alivisatos, J. Phys. Chem. B 106, 2447 (2002).
[CrossRef]

J. Hu, L.-S. Li, Y. Weidong, L. Manna, L.-W. Wang, and A. P. Alivisatos, Science 292, 2060 (2001).
[CrossRef]

Weidong, Y.

J. Hu, L.-S. Li, Y. Weidong, L. Manna, L.-W. Wang, and A. P. Alivisatos, Science 292, 2060 (2001).
[CrossRef]

Wickham, J.

X. Peng, L. Manna, W. Yang, J. Wickham, E. Scher, A. Kadavanich, and A. Alivisatos, Nature 404, 59 (2000).
[CrossRef]

Wizansky, T.

D. Katz, T. Wizansky, O. Millo, E. Rothenberg, T. Mokari, and U. Banin, Phys. Rev. Lett. 89, 086801 (2002).
[CrossRef]

Woggon, U.

M. Artemyev, B. Moller, and U. Woggon, Nano Lett. 3, 509 (2003).
[CrossRef]

Xiao, M.

X. Chen, A. Y. Nazzal, M. Xiao, Z. A. Peng, and X. Peng, J. Lumin. 97, 205 (2002).
[CrossRef]

X. Chen, A. Nazzal, D. Goorskey, and M. Xiao, Phys. Rev. B 64, 245304 (2001).
[CrossRef]

Yamazaki, Y.

H. Aoyama, Y. Yamazaki, N. Matsuura, H. Mada, and S. Kobayashi, Mol. Cryst. Liq. Cryst. 72, 127 (1981).
[CrossRef]

Yang, C. C.

C. C. Yang and S. Li, J. Phys. Chem. C 112, 2851 (2008).
[CrossRef]

Yang, W.

J. Hu, L.-W. Wang, L.-S. Li, W. Yang, and A. P. Alivisatos, J. Phys. Chem. B 106, 2447 (2002).
[CrossRef]

X. Peng, L. Manna, W. Yang, J. Wickham, E. Scher, A. Kadavanich, and A. Alivisatos, Nature 404, 59 (2000).
[CrossRef]

Yu, W. W.

W. W. Yu, L. Qu, W. Guo, and X. Peng, Chem. Mater. 15, 2854 (2003).
[CrossRef]

Anal. Chem. (1)

Y. Chen and Z. Rosenzweig, Anal. Chem. 74, 5132 (2002).
[CrossRef]

Chem. Mater. (1)

W. W. Yu, L. Qu, W. Guo, and X. Peng, Chem. Mater. 15, 2854 (2003).
[CrossRef]

J. Am. Chem. Soc. (1)

L. Manna, E. Scher, L.-S. Li, and A. P. Alivisatos, J. Am. Chem. Soc. 124, 7136 (2002).
[CrossRef]

J. Lumin. (1)

X. Chen, A. Y. Nazzal, M. Xiao, Z. A. Peng, and X. Peng, J. Lumin. 97, 205 (2002).
[CrossRef]

J. Phys. Chem. (1)

E. W. Thulstrup, J. Michl, and J. H. Eggers, J. Phys. Chem. 74, 3868 (1970).
[CrossRef]

J. Phys. Chem. B (1)

J. Hu, L.-W. Wang, L.-S. Li, W. Yang, and A. P. Alivisatos, J. Phys. Chem. B 106, 2447 (2002).
[CrossRef]

J. Phys. Chem. C (2)

C. C. Yang and S. Li, J. Phys. Chem. C 112, 2851 (2008).
[CrossRef]

C. de Mello Donega and R. Koole, J. Phys. Chem. C 113, 6511 (2009).
[CrossRef]

Mater. Res. Innovations (1)

I. Grabchev, I. Moneva, A. Kozlov, and G. Elyashevich, Mater. Res. Innovations 4, 301 (2001).
[CrossRef]

Mol. Cryst. Liq. Cryst. (1)

H. Aoyama, Y. Yamazaki, N. Matsuura, H. Mada, and S. Kobayashi, Mol. Cryst. Liq. Cryst. 72, 127 (1981).
[CrossRef]

Nano Lett. (3)

M. Artemyev, B. Moller, and U. Woggon, Nano Lett. 3, 509 (2003).
[CrossRef]

A. Shabaev and A. L. Efros, Nano Lett. 4, 1821 (2004).
[CrossRef]

J. Li and L.-W. Wang, Nano Lett. 3, 101 (2003).
[CrossRef]

Nanoscale (1)

P. Reiss, E. Couderc, J. De Girolamo, and A. Pron, Nanoscale 3, 446 (2011).
[CrossRef]

Nat. Methods (1)

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, Nat. Methods 5, 763 (2008).
[CrossRef]

Nature (1)

X. Peng, L. Manna, W. Yang, J. Wickham, E. Scher, A. Kadavanich, and A. Alivisatos, Nature 404, 59 (2000).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (3)

A. L. Efros, Phys. Rev. B 46, 7448 (1992).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Absorption spectra of the QR in (1) toluene solution and (2) embedded in PVB film; the spectrum of QR in solution was multiplied by a factor of 23. Inset shows the photograph of the sample of stretched polymer film with QRs. The double-ended arrow indicates the direction of stretching.

Fig. 2.
Fig. 2.

Schematic diagram of experimental setup for absorption measurements.

Fig. 3.
Fig. 3.

(1) Degree of absorption anisotropy in the ordered QR ensemble as function of energy of excitation quantum. Vertical lines show positions of V 1 z C 1 , V 2 x y C 2 , V 3 z C 1 and V 4 x y C 2 excitonic transitions with different spatial orientation [16]. QR energy gap is 1.92 eV. (2) Absorption spectrum of the QR embedded in PVB film. (3) Degree of absorption anisotropy in the disordered QR ensemble as function of energy of excitation quantum.

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