Abstract

Because of the existence of an exciton–biexciton transition inside an optically excited semiconductor, the dielectric constant is modified to be a wave-vector-dependent function. The spatial dispersion relation leads to three propagating modes of polariton, for which two additional boundary conditions will be required. In the vicinity of a resonance, the mathematical study shows that two modes among the three dominate, and the third wave with a large imaginary part can be neglected without affecting the essential physics. Based on the study, a criterion is developed for selecting the appropriate modes. Numerical results are presented for a thin semiconducting film.

© 2009 Optical Society of America

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  1. J. Frenkel, Phys. Rev. 37, 17 (1931).
    [CrossRef]
  2. W. Liang, Phys. Educ. 5, 226 (1970).
    [CrossRef]
  3. C. Klingshirn, Semiconductor Optics (Springer-Verlag, 2007).
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    [CrossRef]
  5. P. Zory, Jr., Quantum Well Lasers (Academic, 1993).
  6. F. Bassania, G. La Roccaa, and M. Artonib, J. Lumin. 110, 174 (2004).
    [CrossRef]
  7. P. Borri, W. Langbein, U. Woggon, A. Esser, J. Jensen, and J. Hvam, Semicond. Sci. Technol. 18, S351 (2003).
    [CrossRef]
  8. S. Chesi, M. Artoni, G. La Rocca, F. Bassani, and A. Mysyrowicz, Phys. Status Solidi 1, 497 (2004).
    [CrossRef]
  9. M. Phillips and H. Wang, Phys. Rev. Lett. 89, 186401 (2002).
    [CrossRef] [PubMed]
  10. X. Li, Y. Wu, D. Steel, D. Grammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, Science 301, 809 (2003).
    [CrossRef] [PubMed]
  11. J. Luther, M. Beard, Q. Song, M. Law, R. Ellingson, and A. Nozik, Nano Lett. 7, 1779 (2007).
    [CrossRef] [PubMed]
  12. A. Nozik, Annu. Rev. Phys. Chem. 52, 193 (2001).
    [CrossRef] [PubMed]
  13. K. Cho, Optical Response of Nanostructures: Microscopic Nonlocal Theory (Springer-Verlag, 2003).
  14. O. Keller, Phys. Rep. 268, 85 (1996).
    [CrossRef]
  15. L. Silvrestri, G. Czajkowski, and F. Bassani, Phys. Status Solidi A 175, 383 (1999).
    [CrossRef]
  16. A. Stahl and I. Balslev, Electrodynamics of the Semiconductor Band Edge, Vol. 110 of Springer Tracts in Modern Physics (Springer-Verlag, 1987).
    [CrossRef]
  17. Y. Sun, H. Ajiki, and G. Bao, Commun. Comp. Phys. 4, 1051 (2008).
  18. G. Bao and Y. Sun, Contemp. Math. 494, 27 (2009).
  19. I. Abramt, A. Maruani, and S. Schmitt-Rink, J. Phys. C 17, 5163 (1984).
    [CrossRef]

2009 (1)

G. Bao and Y. Sun, Contemp. Math. 494, 27 (2009).

2008 (1)

Y. Sun, H. Ajiki, and G. Bao, Commun. Comp. Phys. 4, 1051 (2008).

2007 (1)

J. Luther, M. Beard, Q. Song, M. Law, R. Ellingson, and A. Nozik, Nano Lett. 7, 1779 (2007).
[CrossRef] [PubMed]

2004 (2)

F. Bassania, G. La Roccaa, and M. Artonib, J. Lumin. 110, 174 (2004).
[CrossRef]

S. Chesi, M. Artoni, G. La Rocca, F. Bassani, and A. Mysyrowicz, Phys. Status Solidi 1, 497 (2004).
[CrossRef]

2003 (2)

X. Li, Y. Wu, D. Steel, D. Grammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, Science 301, 809 (2003).
[CrossRef] [PubMed]

P. Borri, W. Langbein, U. Woggon, A. Esser, J. Jensen, and J. Hvam, Semicond. Sci. Technol. 18, S351 (2003).
[CrossRef]

2002 (1)

M. Phillips and H. Wang, Phys. Rev. Lett. 89, 186401 (2002).
[CrossRef] [PubMed]

2001 (1)

A. Nozik, Annu. Rev. Phys. Chem. 52, 193 (2001).
[CrossRef] [PubMed]

1999 (1)

L. Silvrestri, G. Czajkowski, and F. Bassani, Phys. Status Solidi A 175, 383 (1999).
[CrossRef]

1996 (1)

O. Keller, Phys. Rep. 268, 85 (1996).
[CrossRef]

1993 (1)

M. Reed, Sci. Am. 268, 118 (1993).
[CrossRef]

1984 (1)

I. Abramt, A. Maruani, and S. Schmitt-Rink, J. Phys. C 17, 5163 (1984).
[CrossRef]

1970 (1)

W. Liang, Phys. Educ. 5, 226 (1970).
[CrossRef]

1931 (1)

J. Frenkel, Phys. Rev. 37, 17 (1931).
[CrossRef]

Abramt, I.

I. Abramt, A. Maruani, and S. Schmitt-Rink, J. Phys. C 17, 5163 (1984).
[CrossRef]

Ajiki, H.

Y. Sun, H. Ajiki, and G. Bao, Commun. Comp. Phys. 4, 1051 (2008).

Artoni, M.

S. Chesi, M. Artoni, G. La Rocca, F. Bassani, and A. Mysyrowicz, Phys. Status Solidi 1, 497 (2004).
[CrossRef]

Artonib, M.

F. Bassania, G. La Roccaa, and M. Artonib, J. Lumin. 110, 174 (2004).
[CrossRef]

Balslev, I.

A. Stahl and I. Balslev, Electrodynamics of the Semiconductor Band Edge, Vol. 110 of Springer Tracts in Modern Physics (Springer-Verlag, 1987).
[CrossRef]

Bao, G.

G. Bao and Y. Sun, Contemp. Math. 494, 27 (2009).

Y. Sun, H. Ajiki, and G. Bao, Commun. Comp. Phys. 4, 1051 (2008).

Bassani, F.

S. Chesi, M. Artoni, G. La Rocca, F. Bassani, and A. Mysyrowicz, Phys. Status Solidi 1, 497 (2004).
[CrossRef]

L. Silvrestri, G. Czajkowski, and F. Bassani, Phys. Status Solidi A 175, 383 (1999).
[CrossRef]

Bassania, F.

F. Bassania, G. La Roccaa, and M. Artonib, J. Lumin. 110, 174 (2004).
[CrossRef]

Beard, M.

J. Luther, M. Beard, Q. Song, M. Law, R. Ellingson, and A. Nozik, Nano Lett. 7, 1779 (2007).
[CrossRef] [PubMed]

Borri, P.

P. Borri, W. Langbein, U. Woggon, A. Esser, J. Jensen, and J. Hvam, Semicond. Sci. Technol. 18, S351 (2003).
[CrossRef]

Chesi, S.

S. Chesi, M. Artoni, G. La Rocca, F. Bassani, and A. Mysyrowicz, Phys. Status Solidi 1, 497 (2004).
[CrossRef]

Cho, K.

K. Cho, Optical Response of Nanostructures: Microscopic Nonlocal Theory (Springer-Verlag, 2003).

Czajkowski, G.

L. Silvrestri, G. Czajkowski, and F. Bassani, Phys. Status Solidi A 175, 383 (1999).
[CrossRef]

Ellingson, R.

J. Luther, M. Beard, Q. Song, M. Law, R. Ellingson, and A. Nozik, Nano Lett. 7, 1779 (2007).
[CrossRef] [PubMed]

Esser, A.

P. Borri, W. Langbein, U. Woggon, A. Esser, J. Jensen, and J. Hvam, Semicond. Sci. Technol. 18, S351 (2003).
[CrossRef]

Frenkel, J.

J. Frenkel, Phys. Rev. 37, 17 (1931).
[CrossRef]

Grammon, D.

X. Li, Y. Wu, D. Steel, D. Grammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, Science 301, 809 (2003).
[CrossRef] [PubMed]

Hvam, J.

P. Borri, W. Langbein, U. Woggon, A. Esser, J. Jensen, and J. Hvam, Semicond. Sci. Technol. 18, S351 (2003).
[CrossRef]

Jensen, J.

P. Borri, W. Langbein, U. Woggon, A. Esser, J. Jensen, and J. Hvam, Semicond. Sci. Technol. 18, S351 (2003).
[CrossRef]

Katzer, D.

X. Li, Y. Wu, D. Steel, D. Grammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, Science 301, 809 (2003).
[CrossRef] [PubMed]

Keller, O.

O. Keller, Phys. Rep. 268, 85 (1996).
[CrossRef]

Klingshirn, C.

C. Klingshirn, Semiconductor Optics (Springer-Verlag, 2007).

La Rocca, G.

S. Chesi, M. Artoni, G. La Rocca, F. Bassani, and A. Mysyrowicz, Phys. Status Solidi 1, 497 (2004).
[CrossRef]

La Roccaa, G.

F. Bassania, G. La Roccaa, and M. Artonib, J. Lumin. 110, 174 (2004).
[CrossRef]

Langbein, W.

P. Borri, W. Langbein, U. Woggon, A. Esser, J. Jensen, and J. Hvam, Semicond. Sci. Technol. 18, S351 (2003).
[CrossRef]

Law, M.

J. Luther, M. Beard, Q. Song, M. Law, R. Ellingson, and A. Nozik, Nano Lett. 7, 1779 (2007).
[CrossRef] [PubMed]

Li, X.

X. Li, Y. Wu, D. Steel, D. Grammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, Science 301, 809 (2003).
[CrossRef] [PubMed]

Liang, W.

W. Liang, Phys. Educ. 5, 226 (1970).
[CrossRef]

Luther, J.

J. Luther, M. Beard, Q. Song, M. Law, R. Ellingson, and A. Nozik, Nano Lett. 7, 1779 (2007).
[CrossRef] [PubMed]

Maruani, A.

I. Abramt, A. Maruani, and S. Schmitt-Rink, J. Phys. C 17, 5163 (1984).
[CrossRef]

Mysyrowicz, A.

S. Chesi, M. Artoni, G. La Rocca, F. Bassani, and A. Mysyrowicz, Phys. Status Solidi 1, 497 (2004).
[CrossRef]

Nozik, A.

J. Luther, M. Beard, Q. Song, M. Law, R. Ellingson, and A. Nozik, Nano Lett. 7, 1779 (2007).
[CrossRef] [PubMed]

A. Nozik, Annu. Rev. Phys. Chem. 52, 193 (2001).
[CrossRef] [PubMed]

Park, D.

X. Li, Y. Wu, D. Steel, D. Grammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, Science 301, 809 (2003).
[CrossRef] [PubMed]

Phillips, M.

M. Phillips and H. Wang, Phys. Rev. Lett. 89, 186401 (2002).
[CrossRef] [PubMed]

Piermarocchi, C.

X. Li, Y. Wu, D. Steel, D. Grammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, Science 301, 809 (2003).
[CrossRef] [PubMed]

Reed, M.

M. Reed, Sci. Am. 268, 118 (1993).
[CrossRef]

Schmitt-Rink, S.

I. Abramt, A. Maruani, and S. Schmitt-Rink, J. Phys. C 17, 5163 (1984).
[CrossRef]

Sham, L.

X. Li, Y. Wu, D. Steel, D. Grammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, Science 301, 809 (2003).
[CrossRef] [PubMed]

Silvrestri, L.

L. Silvrestri, G. Czajkowski, and F. Bassani, Phys. Status Solidi A 175, 383 (1999).
[CrossRef]

Song, Q.

J. Luther, M. Beard, Q. Song, M. Law, R. Ellingson, and A. Nozik, Nano Lett. 7, 1779 (2007).
[CrossRef] [PubMed]

Stahl, A.

A. Stahl and I. Balslev, Electrodynamics of the Semiconductor Band Edge, Vol. 110 of Springer Tracts in Modern Physics (Springer-Verlag, 1987).
[CrossRef]

Steel, D.

X. Li, Y. Wu, D. Steel, D. Grammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, Science 301, 809 (2003).
[CrossRef] [PubMed]

Stievater, T.

X. Li, Y. Wu, D. Steel, D. Grammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, Science 301, 809 (2003).
[CrossRef] [PubMed]

Sun, Y.

G. Bao and Y. Sun, Contemp. Math. 494, 27 (2009).

Y. Sun, H. Ajiki, and G. Bao, Commun. Comp. Phys. 4, 1051 (2008).

Wang, H.

M. Phillips and H. Wang, Phys. Rev. Lett. 89, 186401 (2002).
[CrossRef] [PubMed]

Woggon, U.

P. Borri, W. Langbein, U. Woggon, A. Esser, J. Jensen, and J. Hvam, Semicond. Sci. Technol. 18, S351 (2003).
[CrossRef]

Wu, Y.

X. Li, Y. Wu, D. Steel, D. Grammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, Science 301, 809 (2003).
[CrossRef] [PubMed]

Zory, P.

P. Zory, Jr., Quantum Well Lasers (Academic, 1993).

Annu. Rev. Phys. Chem. (1)

A. Nozik, Annu. Rev. Phys. Chem. 52, 193 (2001).
[CrossRef] [PubMed]

Commun. Comp. Phys. (1)

Y. Sun, H. Ajiki, and G. Bao, Commun. Comp. Phys. 4, 1051 (2008).

Contemp. Math. (1)

G. Bao and Y. Sun, Contemp. Math. 494, 27 (2009).

J. Lumin. (1)

F. Bassania, G. La Roccaa, and M. Artonib, J. Lumin. 110, 174 (2004).
[CrossRef]

J. Phys. C (1)

I. Abramt, A. Maruani, and S. Schmitt-Rink, J. Phys. C 17, 5163 (1984).
[CrossRef]

Nano Lett. (1)

J. Luther, M. Beard, Q. Song, M. Law, R. Ellingson, and A. Nozik, Nano Lett. 7, 1779 (2007).
[CrossRef] [PubMed]

Phys. Educ. (1)

W. Liang, Phys. Educ. 5, 226 (1970).
[CrossRef]

Phys. Rep. (1)

O. Keller, Phys. Rep. 268, 85 (1996).
[CrossRef]

Phys. Rev. (1)

J. Frenkel, Phys. Rev. 37, 17 (1931).
[CrossRef]

Phys. Rev. Lett. (1)

M. Phillips and H. Wang, Phys. Rev. Lett. 89, 186401 (2002).
[CrossRef] [PubMed]

Phys. Status Solidi (1)

S. Chesi, M. Artoni, G. La Rocca, F. Bassani, and A. Mysyrowicz, Phys. Status Solidi 1, 497 (2004).
[CrossRef]

Phys. Status Solidi A (1)

L. Silvrestri, G. Czajkowski, and F. Bassani, Phys. Status Solidi A 175, 383 (1999).
[CrossRef]

Sci. Am. (1)

M. Reed, Sci. Am. 268, 118 (1993).
[CrossRef]

Science (1)

X. Li, Y. Wu, D. Steel, D. Grammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, Science 301, 809 (2003).
[CrossRef] [PubMed]

Semicond. Sci. Technol. (1)

P. Borri, W. Langbein, U. Woggon, A. Esser, J. Jensen, and J. Hvam, Semicond. Sci. Technol. 18, S351 (2003).
[CrossRef]

Other (4)

P. Zory, Jr., Quantum Well Lasers (Academic, 1993).

C. Klingshirn, Semiconductor Optics (Springer-Verlag, 2007).

K. Cho, Optical Response of Nanostructures: Microscopic Nonlocal Theory (Springer-Verlag, 2003).

A. Stahl and I. Balslev, Electrodynamics of the Semiconductor Band Edge, Vol. 110 of Springer Tracts in Modern Physics (Springer-Verlag, 1987).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Plot (a) illustrates the light scattering by a CuCl film for an incident plane wave, where three polariton waves are produced inside the film. A sketch of the wavenumbers in the vicinity of a resonance ω = ω ex with very small damping constants is shown in (b).

Fig. 2
Fig. 2

(a) Transmission and (b) reflection spectra of a CuCl film 340 nm thick. The solid curves are obtained from the two-mode approximation; the dashed curves result from the three-mode computations.

Equations (6)

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

ε ( k , ω ) = ε b + 4 π μ gx 2 ω ex ω + k 2 2 M ex + i γ + Σ ,
( ω c ) 2 ε ( k , ω ) = k 2 or k 6 + a ( ω ) k 4 + b ( ω ) k 2 + c ( ω ) = 0
a ( ω ) = M ( ω bi ω pu + 2 ω ex 3 ω i β i 2 γ ) ( ω c ) 2 ε b ,
b ( ω ) = M ( ω bi ω pu ω i β ) [ ( ω c ) 2 ε b + 2 M ( ω ex ω i γ ) ] 8 π M 2 μ gx 2 ( ω c ) 2 2 M ( ω c ) 2 ε b ( ω ex ω i γ ) + μ xb 2 | E 0 | 2 2 M 2 4 ,
c ( ω ) = 2 M 2 2 [ μ xb 2 | E 0 | 2 2 + ( ω bi ω pu ω i β ) ( 4 π μ gx 2 + ε b ( ω ex ω i γ ) ) ] ( ω c ) 2 ,
d 2 E i d x 2 + k i 2 E i = 0 , i = 1 , 3 ,

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