Abstract

It is shown that the lineshapes of inhomogeneously broadened spectra, due to the statistical nature of their formation, exhibit spectral fluctuations. Formulas are obtained that allow one, based on correlation analysis of different realizations of the inhomogeneously broadened line, to reconstruct its homogeneous lineshape and to evaluate the number of centers involved in its formation. The magnitude of these spectral fluctuations is estimated and it is shown that the proposed method can be efficiently used in practice.

© 2001 Optical Society of America

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References

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  1. J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, Springer series in Solid-State Sciences, (Springer-Verlag, Heidelberg, 1996).
  2. A. Zrenner, L. V. Butov, M. Hagn, and G. Abstreiter,“Quantum dots formed by interface fluctuations in AlAs/GaAs coupled quantum well structures,”G. Böhm and G. Weimann. Phys. Rev. Lett. 72, 3382 (1994).
    [Crossref] [PubMed]
  3. K. Brunner, G. Abstreiter, G. Böhm, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138 (1994).
    [Crossref] [PubMed]
  4. H. F. Hess, E. Betzig, T. D. Harris, L. N. Pfeiffer, and K. W. West, Science264, 1740 (1994).
    [Crossref] [PubMed]
  5. D. Gammon, E. S. Snow, B. V. Shanobrook, D. S. Katzer, and D. Park, “Fine Structure Splitting in the Optical Spectra of Single GaAs Quantum Dots,” Phys. Rev. Lett. 76, 3005 (1996).
    [Crossref] [PubMed]
  6. Q. Wu, R. D. Grober, D. Gammon, and D. S. Katzer, “Imaging Spectroscopy of Two-Dimensional Excitons in a Narrow GaAs/AlGaAs Quantum Well,” Phys. Rev. Lett. 83, 2652 (1999).
    [Crossref]
  7. A. van der Ziel, Noise in Measurements (John Wiley & Sons, New York, 1976).

1999 (1)

Q. Wu, R. D. Grober, D. Gammon, and D. S. Katzer, “Imaging Spectroscopy of Two-Dimensional Excitons in a Narrow GaAs/AlGaAs Quantum Well,” Phys. Rev. Lett. 83, 2652 (1999).
[Crossref]

1996 (1)

D. Gammon, E. S. Snow, B. V. Shanobrook, D. S. Katzer, and D. Park, “Fine Structure Splitting in the Optical Spectra of Single GaAs Quantum Dots,” Phys. Rev. Lett. 76, 3005 (1996).
[Crossref] [PubMed]

1994 (2)

A. Zrenner, L. V. Butov, M. Hagn, and G. Abstreiter,“Quantum dots formed by interface fluctuations in AlAs/GaAs coupled quantum well structures,”G. Böhm and G. Weimann. Phys. Rev. Lett. 72, 3382 (1994).
[Crossref] [PubMed]

A. Zrenner, L. V. Butov, M. Hagn, and G. Abstreiter,“Quantum dots formed by interface fluctuations in AlAs/GaAs coupled quantum well structures,”G. Böhm and G. Weimann. Phys. Rev. Lett. 72, 3382 (1994).
[Crossref] [PubMed]

K. Brunner, G. Abstreiter, G. Böhm, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138 (1994).
[Crossref] [PubMed]

Abstreiter, G.

K. Brunner, G. Abstreiter, G. Böhm, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138 (1994).
[Crossref] [PubMed]

A. Zrenner, L. V. Butov, M. Hagn, and G. Abstreiter,“Quantum dots formed by interface fluctuations in AlAs/GaAs coupled quantum well structures,”G. Böhm and G. Weimann. Phys. Rev. Lett. 72, 3382 (1994).
[Crossref] [PubMed]

Betzig, E.

H. F. Hess, E. Betzig, T. D. Harris, L. N. Pfeiffer, and K. W. West, Science264, 1740 (1994).
[Crossref] [PubMed]

Böhm, G.

A. Zrenner, L. V. Butov, M. Hagn, and G. Abstreiter,“Quantum dots formed by interface fluctuations in AlAs/GaAs coupled quantum well structures,”G. Böhm and G. Weimann. Phys. Rev. Lett. 72, 3382 (1994).
[Crossref] [PubMed]

K. Brunner, G. Abstreiter, G. Böhm, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138 (1994).
[Crossref] [PubMed]

Brunner, K.

K. Brunner, G. Abstreiter, G. Böhm, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138 (1994).
[Crossref] [PubMed]

Butov, L. V.

A. Zrenner, L. V. Butov, M. Hagn, and G. Abstreiter,“Quantum dots formed by interface fluctuations in AlAs/GaAs coupled quantum well structures,”G. Böhm and G. Weimann. Phys. Rev. Lett. 72, 3382 (1994).
[Crossref] [PubMed]

Gammon, D.

Q. Wu, R. D. Grober, D. Gammon, and D. S. Katzer, “Imaging Spectroscopy of Two-Dimensional Excitons in a Narrow GaAs/AlGaAs Quantum Well,” Phys. Rev. Lett. 83, 2652 (1999).
[Crossref]

D. Gammon, E. S. Snow, B. V. Shanobrook, D. S. Katzer, and D. Park, “Fine Structure Splitting in the Optical Spectra of Single GaAs Quantum Dots,” Phys. Rev. Lett. 76, 3005 (1996).
[Crossref] [PubMed]

Grober, R. D.

Q. Wu, R. D. Grober, D. Gammon, and D. S. Katzer, “Imaging Spectroscopy of Two-Dimensional Excitons in a Narrow GaAs/AlGaAs Quantum Well,” Phys. Rev. Lett. 83, 2652 (1999).
[Crossref]

Hagn, M.

A. Zrenner, L. V. Butov, M. Hagn, and G. Abstreiter,“Quantum dots formed by interface fluctuations in AlAs/GaAs coupled quantum well structures,”G. Böhm and G. Weimann. Phys. Rev. Lett. 72, 3382 (1994).
[Crossref] [PubMed]

Harris, T. D.

H. F. Hess, E. Betzig, T. D. Harris, L. N. Pfeiffer, and K. W. West, Science264, 1740 (1994).
[Crossref] [PubMed]

Hess, H. F.

H. F. Hess, E. Betzig, T. D. Harris, L. N. Pfeiffer, and K. W. West, Science264, 1740 (1994).
[Crossref] [PubMed]

Katzer, D. S.

Q. Wu, R. D. Grober, D. Gammon, and D. S. Katzer, “Imaging Spectroscopy of Two-Dimensional Excitons in a Narrow GaAs/AlGaAs Quantum Well,” Phys. Rev. Lett. 83, 2652 (1999).
[Crossref]

D. Gammon, E. S. Snow, B. V. Shanobrook, D. S. Katzer, and D. Park, “Fine Structure Splitting in the Optical Spectra of Single GaAs Quantum Dots,” Phys. Rev. Lett. 76, 3005 (1996).
[Crossref] [PubMed]

Park, D.

D. Gammon, E. S. Snow, B. V. Shanobrook, D. S. Katzer, and D. Park, “Fine Structure Splitting in the Optical Spectra of Single GaAs Quantum Dots,” Phys. Rev. Lett. 76, 3005 (1996).
[Crossref] [PubMed]

Pfeiffer, L. N.

H. F. Hess, E. Betzig, T. D. Harris, L. N. Pfeiffer, and K. W. West, Science264, 1740 (1994).
[Crossref] [PubMed]

Shah, J.

J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, Springer series in Solid-State Sciences, (Springer-Verlag, Heidelberg, 1996).

Shanobrook, B. V.

D. Gammon, E. S. Snow, B. V. Shanobrook, D. S. Katzer, and D. Park, “Fine Structure Splitting in the Optical Spectra of Single GaAs Quantum Dots,” Phys. Rev. Lett. 76, 3005 (1996).
[Crossref] [PubMed]

Snow, E. S.

D. Gammon, E. S. Snow, B. V. Shanobrook, D. S. Katzer, and D. Park, “Fine Structure Splitting in the Optical Spectra of Single GaAs Quantum Dots,” Phys. Rev. Lett. 76, 3005 (1996).
[Crossref] [PubMed]

Tränkle, G.

K. Brunner, G. Abstreiter, G. Böhm, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138 (1994).
[Crossref] [PubMed]

van der Ziel, A.

A. van der Ziel, Noise in Measurements (John Wiley & Sons, New York, 1976).

Weimann, G.

K. Brunner, G. Abstreiter, G. Böhm, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138 (1994).
[Crossref] [PubMed]

A. Zrenner, L. V. Butov, M. Hagn, and G. Abstreiter,“Quantum dots formed by interface fluctuations in AlAs/GaAs coupled quantum well structures,”G. Böhm and G. Weimann. Phys. Rev. Lett. 72, 3382 (1994).
[Crossref] [PubMed]

West, K. W.

H. F. Hess, E. Betzig, T. D. Harris, L. N. Pfeiffer, and K. W. West, Science264, 1740 (1994).
[Crossref] [PubMed]

Wu, Q.

Q. Wu, R. D. Grober, D. Gammon, and D. S. Katzer, “Imaging Spectroscopy of Two-Dimensional Excitons in a Narrow GaAs/AlGaAs Quantum Well,” Phys. Rev. Lett. 83, 2652 (1999).
[Crossref]

Zrenner, A.

A. Zrenner, L. V. Butov, M. Hagn, and G. Abstreiter,“Quantum dots formed by interface fluctuations in AlAs/GaAs coupled quantum well structures,”G. Böhm and G. Weimann. Phys. Rev. Lett. 72, 3382 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

A. Zrenner, L. V. Butov, M. Hagn, and G. Abstreiter,“Quantum dots formed by interface fluctuations in AlAs/GaAs coupled quantum well structures,”G. Böhm and G. Weimann. Phys. Rev. Lett. 72, 3382 (1994).
[Crossref] [PubMed]

K. Brunner, G. Abstreiter, G. Böhm, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138 (1994).
[Crossref] [PubMed]

D. Gammon, E. S. Snow, B. V. Shanobrook, D. S. Katzer, and D. Park, “Fine Structure Splitting in the Optical Spectra of Single GaAs Quantum Dots,” Phys. Rev. Lett. 76, 3005 (1996).
[Crossref] [PubMed]

Q. Wu, R. D. Grober, D. Gammon, and D. S. Katzer, “Imaging Spectroscopy of Two-Dimensional Excitons in a Narrow GaAs/AlGaAs Quantum Well,” Phys. Rev. Lett. 83, 2652 (1999).
[Crossref]

Other (3)

A. van der Ziel, Noise in Measurements (John Wiley & Sons, New York, 1976).

H. F. Hess, E. Betzig, T. D. Harris, L. N. Pfeiffer, and K. W. West, Science264, 1740 (1994).
[Crossref] [PubMed]

J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, Springer series in Solid-State Sciences, (Springer-Verlag, Heidelberg, 1996).

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Figures (2)

Fig. 1.
Fig. 1.

Results of correlation analysis of an inhomogeneously broadened line obtained by computer simulation. Correlation functions of the line profile (narrow peak, solid curve) are compared with auto-convolution of the homogeneously broadened line (dashed curve) for several numbers of realizations NR (NR =3, 30 and 300). The inhomogeneous/homogeneous linewidth ratio α=20. Broad spectrum in each figure is a realization of the inhomogeneously broadened line.

Fig. 2.
Fig. 2.

Computer-simulated realizations of an inhomogeneously broadened line for total number of emitters N=103, 104, and 105 and for the inhomogeneous/ homogeneous linewidth ratio α=10, 30, and 100.

Equations (12)

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

A ( ω ) = i = 1 N a ( ω ω i )
< A ( ω ) > = N ρ ( x ) a ( ω x ) d x N ρ ( ω )
a ( ω ) = 1 π δ δ 2 + ω 2
< A ( ω ) A ( ω ) > < A ( ω ) > < A ( ω ) > < A ( ω + ω 2 ) > =
a ( ω x ) a ( ω x ) dx = 1 π 2 δ ( ω ω ) 2 + 4 δ 2
r = 1 N R A r ( ω ) A r ( ω ) N R 1 r r ' = 1 N R A r ( ω ) A r ' ( ω ) r = 1 N R A r ( ω + ω 2 )
a ( ω x ) a ( ω x ) dx = 1 π 2 δ ( ω ω ) 2 + 4 δ 2
D ( ω ) < A 2 ( ω ) > < A ( ω ) > 2
d = 1 N ρ ( x ) a 2 ( ω x ) dx ( ρ ( x ) a ( ω x ) dx ) 2 ρ ( x ) a ( ω x ) dx
d 1 2 π N ρ ( ω ) δ
S N α N R
n 1 d ,

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