Abstract

We consider an ensemble of identical semiconductor nanoparticles randomly embedded into dielectric matrix. The nanoparticles are polarized by the laser irradiation having linear polarization. The contribution of dipole–dipole interactions to third-order dielectric susceptibility is calculated by using mean random field method. It is shown that this contribution always has a negative sign, and it can be comparable with the values of optical nonlinearity observed experimentally.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. P. Shalaev, Phys. Rep. 272, 61 (1996).
    [CrossRef]
  2. G.-P. Banfi, V. Degiorgio, and D. Ricard, Adv. Phys. 47, 447 (1998).
    [CrossRef]
  3. W. J. C. Grant and M. W. P. Strandberg, Phys. Rev. 135, A715 (1964).
    [CrossRef]
  4. M. W. Klein, Phys. Rev. 173, 552 (1968).
    [CrossRef]
  5. V. P. Shcherbakov, Fiz. Met. Metalloved. 48, 1134 (1979).
  6. Y. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  7. A. Martucci, J. Fick, J. Schell, G. Battaglin, and M. Guglielmi, J. Appl. Phys. 86, 79 (1999).
    [CrossRef]
  8. X. Wan, X. Yao, M. Wang, and H. Hao, J. Electroceram. 21, 737 (2008).
    [CrossRef]
  9. H. S. Kim, M. H. Lee, N. C. Jeong, S. M. Lee, B. K. Rhee, and K. B. Yoon, J. Am. Chem. Soc. 128, 15070 (2006).
    [CrossRef] [PubMed]
  10. F. Wang, J. Shan, M. Islam, I. Herman, M. Bonn, and T. Heinz, Nat. Mater. 5, 861 (2006).
    [CrossRef] [PubMed]
  11. S. A. Empedocles and M. G. Bawendi, Science 278, 2114 (1997).
    [CrossRef]

2008

X. Wan, X. Yao, M. Wang, and H. Hao, J. Electroceram. 21, 737 (2008).
[CrossRef]

2006

H. S. Kim, M. H. Lee, N. C. Jeong, S. M. Lee, B. K. Rhee, and K. B. Yoon, J. Am. Chem. Soc. 128, 15070 (2006).
[CrossRef] [PubMed]

F. Wang, J. Shan, M. Islam, I. Herman, M. Bonn, and T. Heinz, Nat. Mater. 5, 861 (2006).
[CrossRef] [PubMed]

1999

A. Martucci, J. Fick, J. Schell, G. Battaglin, and M. Guglielmi, J. Appl. Phys. 86, 79 (1999).
[CrossRef]

1998

G.-P. Banfi, V. Degiorgio, and D. Ricard, Adv. Phys. 47, 447 (1998).
[CrossRef]

1997

S. A. Empedocles and M. G. Bawendi, Science 278, 2114 (1997).
[CrossRef]

1996

V. P. Shalaev, Phys. Rep. 272, 61 (1996).
[CrossRef]

1979

V. P. Shcherbakov, Fiz. Met. Metalloved. 48, 1134 (1979).

1968

M. W. Klein, Phys. Rev. 173, 552 (1968).
[CrossRef]

1964

W. J. C. Grant and M. W. P. Strandberg, Phys. Rev. 135, A715 (1964).
[CrossRef]

Banfi, G.-P.

G.-P. Banfi, V. Degiorgio, and D. Ricard, Adv. Phys. 47, 447 (1998).
[CrossRef]

Battaglin, G.

A. Martucci, J. Fick, J. Schell, G. Battaglin, and M. Guglielmi, J. Appl. Phys. 86, 79 (1999).
[CrossRef]

Bawendi, M. G.

S. A. Empedocles and M. G. Bawendi, Science 278, 2114 (1997).
[CrossRef]

Bonn, M.

F. Wang, J. Shan, M. Islam, I. Herman, M. Bonn, and T. Heinz, Nat. Mater. 5, 861 (2006).
[CrossRef] [PubMed]

Degiorgio, V.

G.-P. Banfi, V. Degiorgio, and D. Ricard, Adv. Phys. 47, 447 (1998).
[CrossRef]

Empedocles, S. A.

S. A. Empedocles and M. G. Bawendi, Science 278, 2114 (1997).
[CrossRef]

Fick, J.

A. Martucci, J. Fick, J. Schell, G. Battaglin, and M. Guglielmi, J. Appl. Phys. 86, 79 (1999).
[CrossRef]

Grant, W. J. C.

W. J. C. Grant and M. W. P. Strandberg, Phys. Rev. 135, A715 (1964).
[CrossRef]

Guglielmi, M.

A. Martucci, J. Fick, J. Schell, G. Battaglin, and M. Guglielmi, J. Appl. Phys. 86, 79 (1999).
[CrossRef]

Hao, H.

X. Wan, X. Yao, M. Wang, and H. Hao, J. Electroceram. 21, 737 (2008).
[CrossRef]

Heinz, T.

F. Wang, J. Shan, M. Islam, I. Herman, M. Bonn, and T. Heinz, Nat. Mater. 5, 861 (2006).
[CrossRef] [PubMed]

Herman, I.

F. Wang, J. Shan, M. Islam, I. Herman, M. Bonn, and T. Heinz, Nat. Mater. 5, 861 (2006).
[CrossRef] [PubMed]

Islam, M.

F. Wang, J. Shan, M. Islam, I. Herman, M. Bonn, and T. Heinz, Nat. Mater. 5, 861 (2006).
[CrossRef] [PubMed]

Jeong, N. C.

H. S. Kim, M. H. Lee, N. C. Jeong, S. M. Lee, B. K. Rhee, and K. B. Yoon, J. Am. Chem. Soc. 128, 15070 (2006).
[CrossRef] [PubMed]

Kim, H. S.

H. S. Kim, M. H. Lee, N. C. Jeong, S. M. Lee, B. K. Rhee, and K. B. Yoon, J. Am. Chem. Soc. 128, 15070 (2006).
[CrossRef] [PubMed]

Klein, M. W.

M. W. Klein, Phys. Rev. 173, 552 (1968).
[CrossRef]

Lee, M. H.

H. S. Kim, M. H. Lee, N. C. Jeong, S. M. Lee, B. K. Rhee, and K. B. Yoon, J. Am. Chem. Soc. 128, 15070 (2006).
[CrossRef] [PubMed]

Lee, S. M.

H. S. Kim, M. H. Lee, N. C. Jeong, S. M. Lee, B. K. Rhee, and K. B. Yoon, J. Am. Chem. Soc. 128, 15070 (2006).
[CrossRef] [PubMed]

Martucci, A.

A. Martucci, J. Fick, J. Schell, G. Battaglin, and M. Guglielmi, J. Appl. Phys. 86, 79 (1999).
[CrossRef]

Rhee, B. K.

H. S. Kim, M. H. Lee, N. C. Jeong, S. M. Lee, B. K. Rhee, and K. B. Yoon, J. Am. Chem. Soc. 128, 15070 (2006).
[CrossRef] [PubMed]

Ricard, D.

G.-P. Banfi, V. Degiorgio, and D. Ricard, Adv. Phys. 47, 447 (1998).
[CrossRef]

Schell, J.

A. Martucci, J. Fick, J. Schell, G. Battaglin, and M. Guglielmi, J. Appl. Phys. 86, 79 (1999).
[CrossRef]

Shalaev, V. P.

V. P. Shalaev, Phys. Rep. 272, 61 (1996).
[CrossRef]

Shan, J.

F. Wang, J. Shan, M. Islam, I. Herman, M. Bonn, and T. Heinz, Nat. Mater. 5, 861 (2006).
[CrossRef] [PubMed]

Shcherbakov, V. P.

V. P. Shcherbakov, Fiz. Met. Metalloved. 48, 1134 (1979).

Shen, Y.

Y. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Strandberg, M. W. P.

W. J. C. Grant and M. W. P. Strandberg, Phys. Rev. 135, A715 (1964).
[CrossRef]

Wan, X.

X. Wan, X. Yao, M. Wang, and H. Hao, J. Electroceram. 21, 737 (2008).
[CrossRef]

Wang, F.

F. Wang, J. Shan, M. Islam, I. Herman, M. Bonn, and T. Heinz, Nat. Mater. 5, 861 (2006).
[CrossRef] [PubMed]

Wang, M.

X. Wan, X. Yao, M. Wang, and H. Hao, J. Electroceram. 21, 737 (2008).
[CrossRef]

Yao, X.

X. Wan, X. Yao, M. Wang, and H. Hao, J. Electroceram. 21, 737 (2008).
[CrossRef]

Yoon, K. B.

H. S. Kim, M. H. Lee, N. C. Jeong, S. M. Lee, B. K. Rhee, and K. B. Yoon, J. Am. Chem. Soc. 128, 15070 (2006).
[CrossRef] [PubMed]

Adv. Phys.

G.-P. Banfi, V. Degiorgio, and D. Ricard, Adv. Phys. 47, 447 (1998).
[CrossRef]

Fiz. Met. Metalloved.

V. P. Shcherbakov, Fiz. Met. Metalloved. 48, 1134 (1979).

J. Am. Chem. Soc.

H. S. Kim, M. H. Lee, N. C. Jeong, S. M. Lee, B. K. Rhee, and K. B. Yoon, J. Am. Chem. Soc. 128, 15070 (2006).
[CrossRef] [PubMed]

J. Appl. Phys.

A. Martucci, J. Fick, J. Schell, G. Battaglin, and M. Guglielmi, J. Appl. Phys. 86, 79 (1999).
[CrossRef]

J. Electroceram.

X. Wan, X. Yao, M. Wang, and H. Hao, J. Electroceram. 21, 737 (2008).
[CrossRef]

Nat. Mater.

F. Wang, J. Shan, M. Islam, I. Herman, M. Bonn, and T. Heinz, Nat. Mater. 5, 861 (2006).
[CrossRef] [PubMed]

Phys. Rep.

V. P. Shalaev, Phys. Rep. 272, 61 (1996).
[CrossRef]

Phys. Rev.

W. J. C. Grant and M. W. P. Strandberg, Phys. Rev. 135, A715 (1964).
[CrossRef]

M. W. Klein, Phys. Rev. 173, 552 (1968).
[CrossRef]

Science

S. A. Empedocles and M. G. Bawendi, Science 278, 2114 (1997).
[CrossRef]

Other

Y. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Reduced dipolar contribution to third-order susceptibility of ensemble versus volume concentration of spherical nanoparticles calculated using Lorentzian and Gaussian distribution functions [Eqs. (12, 14)].

Equations (17)

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

p = ε m α v E in ,
α = 3 4 π ε p ε m ε p + 2 ε m ,
E l = 3 ( R l · p ) R l p R l 2 ε m R l 5 .
W L = B L π ( B L 2 + E 2 ) ,
B L = 8 π 2 9 3 c v α E in .
W G = exp ( ( E / B G ) 2 ) π B G
B G = 32 π c v 15 ( 2 r ) 3 α E in ,
Z = exp ( p E / k B T ) W ( E ) d E ,
F = k B T c v ln Z .
P = χ ( 1 ) E in + χ ( 3 ) | E in | 2 E in ,
P = F t E in ,
E max = 2 p / ε m ( 2 r ) 3 ,
Z = i 2 π { [ Ei 1 ( a + i b ) Ei 1 ( a i b ) ] e i b + [ Ei 1 ( a + i b ) Ei 1 ( a i b ) ] e i b } , a = α 2 v 2 E in 2 4 r 3 k B T , b = α 2 v E in 2 k B T ,
χ ( 3 ) = 8 π 2 ε m 2 α 4 v c 2 27 k B T { 16 c π 2 9 + 3 v ( 2 arctan 32 π 2 c r 3 9 3 v π ) r 3 } .
χ ( 3 ) = 8 π ε m 2 v 2 α 4 c 2 9 3 r 3 k B T .
χ ( 3 ) = 4 π ε m 2 v 2 α 4 c 2 15 r 3 k B T .
n 2 = 4 π n 0 χ ( 3 ) ,

Metrics