Abstract

Photoelectron counting distributions are obtained for sources which obey compound Poisson statistics. Various cases are considered in which the sources (semiconductor lasers) emit coherent light and their intensity fluctuates in accordance with a Gaussian distribution of operating temperatures. The lasers are otherwise assumed to be ideal, and the quantum efficiency of the detector is assumed to be unity. This paper represents an ideal situation where the source is the only concern in the calculation of the photoelectron counting distributions. It is found that for large temperature fluctuations (σ > 10 K), a substantial downward shift of the peak of the photon probability density function is observed. The function becomes more asymmetric and the mean value decreases as the standard deviation of the temperature increases.

© 1983 Optical Society of America

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References

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  1. G. J. Troup, Photon Counting and Photon Statistics, Congress in Quantum Electronics (Pergamon, London, 1972).
  2. P. Diament, M. C. Teich, Appl. Opt. 10, 1664 (1971).
    [CrossRef] [PubMed]
  3. P. Diament, M. C. Teich, J. Opt. Soc. Am. 60, 682 (1970).
    [CrossRef]
  4. P. R. Prucnal, M. C. Teich, J. Opt. Soc. Am. 69, 539 (1979).
    [CrossRef]
  5. T. L. Paoli, IEEE J. Quantum Electron. QE-11, 276 (1975).
    [CrossRef]
  6. T. L. Paoli, Appl. Phys. Lett. 24, 187 (1974).
    [CrossRef]
  7. H. C. Casey, M. B. Panish, Heterostructure Lasers, Part A: Fundamental Principles (Academic, New York, 1978), pp. 177–178.
  8. S. M. Sze, Physics of Semiconductor Devices (Wiley-Interscience, New York, 1981), pp. 731.
  9. L. Mandel, Proc. Phys. Soc. London 72, 1037 (1958).
    [CrossRef]
  10. W. T. Tsang, R. A. Logan, J. P. Van der Ziel, Appl. Phys. Lett. 34, 644 (1979).
    [CrossRef]
  11. N. K. Dutta, R. J. Nelson, IEEE J. Quantum Electron. QE-18, 871 (1982).
    [CrossRef]
  12. Y. Horikoshi, Y. Furukawa, Jpn. J. Appl. Phys. 18, 809 (1979).
    [CrossRef]
  13. G. H. B. Thompson, G. D. Henshall, Electron. Lett. 16, 42 (1980).
    [CrossRef]
  14. N. K. Dutta, R. J. Nelson, “Temperature Dependence of the Threshold of InGaAsP DH Lasers and Auger Recombination,” in Proceedings, International Symposium on GaAs and Related Compounds, Vienna, Austria, 22–24 Sept. 1980, Inst. Phys. Conf. Ser. 56, pp. 193.
  15. N. K. Dutta, R. J. Nelson, Appl. Phys. Lett. 38, 407 (1981).
    [CrossRef]
  16. A. Sugimura, IEEE J. Quantum Electron. QE-17, 627 (1981).
    [CrossRef]
  17. T. U. K. Iwamoto, R. Lang, Appl. Phys. Lett. 38, 193 (1981).
    [CrossRef]
  18. N. K. Dutta, J. Appl. Phys. 52, 70 (1981).
    [CrossRef]
  19. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), pp. 65, 98–111.
  20. M. H. Lean, “Electromagnetic Field Solution with the Boundary Element Method,” Ph.D. Thesis, Department of Electrical Engineering, U. Manitoba (1981), pp. 22–17.

1982 (1)

N. K. Dutta, R. J. Nelson, IEEE J. Quantum Electron. QE-18, 871 (1982).
[CrossRef]

1981 (4)

N. K. Dutta, R. J. Nelson, Appl. Phys. Lett. 38, 407 (1981).
[CrossRef]

A. Sugimura, IEEE J. Quantum Electron. QE-17, 627 (1981).
[CrossRef]

T. U. K. Iwamoto, R. Lang, Appl. Phys. Lett. 38, 193 (1981).
[CrossRef]

N. K. Dutta, J. Appl. Phys. 52, 70 (1981).
[CrossRef]

1980 (1)

G. H. B. Thompson, G. D. Henshall, Electron. Lett. 16, 42 (1980).
[CrossRef]

1979 (3)

W. T. Tsang, R. A. Logan, J. P. Van der Ziel, Appl. Phys. Lett. 34, 644 (1979).
[CrossRef]

P. R. Prucnal, M. C. Teich, J. Opt. Soc. Am. 69, 539 (1979).
[CrossRef]

Y. Horikoshi, Y. Furukawa, Jpn. J. Appl. Phys. 18, 809 (1979).
[CrossRef]

1975 (1)

T. L. Paoli, IEEE J. Quantum Electron. QE-11, 276 (1975).
[CrossRef]

1974 (1)

T. L. Paoli, Appl. Phys. Lett. 24, 187 (1974).
[CrossRef]

1971 (1)

1970 (1)

1958 (1)

L. Mandel, Proc. Phys. Soc. London 72, 1037 (1958).
[CrossRef]

Casey, H. C.

H. C. Casey, M. B. Panish, Heterostructure Lasers, Part A: Fundamental Principles (Academic, New York, 1978), pp. 177–178.

Diament, P.

Dutta, N. K.

N. K. Dutta, R. J. Nelson, IEEE J. Quantum Electron. QE-18, 871 (1982).
[CrossRef]

N. K. Dutta, J. Appl. Phys. 52, 70 (1981).
[CrossRef]

N. K. Dutta, R. J. Nelson, Appl. Phys. Lett. 38, 407 (1981).
[CrossRef]

N. K. Dutta, R. J. Nelson, “Temperature Dependence of the Threshold of InGaAsP DH Lasers and Auger Recombination,” in Proceedings, International Symposium on GaAs and Related Compounds, Vienna, Austria, 22–24 Sept. 1980, Inst. Phys. Conf. Ser. 56, pp. 193.

Furukawa, Y.

Y. Horikoshi, Y. Furukawa, Jpn. J. Appl. Phys. 18, 809 (1979).
[CrossRef]

Henshall, G. D.

G. H. B. Thompson, G. D. Henshall, Electron. Lett. 16, 42 (1980).
[CrossRef]

Horikoshi, Y.

Y. Horikoshi, Y. Furukawa, Jpn. J. Appl. Phys. 18, 809 (1979).
[CrossRef]

Iwamoto, T. U. K.

T. U. K. Iwamoto, R. Lang, Appl. Phys. Lett. 38, 193 (1981).
[CrossRef]

Lang, R.

T. U. K. Iwamoto, R. Lang, Appl. Phys. Lett. 38, 193 (1981).
[CrossRef]

Lean, M. H.

M. H. Lean, “Electromagnetic Field Solution with the Boundary Element Method,” Ph.D. Thesis, Department of Electrical Engineering, U. Manitoba (1981), pp. 22–17.

Logan, R. A.

W. T. Tsang, R. A. Logan, J. P. Van der Ziel, Appl. Phys. Lett. 34, 644 (1979).
[CrossRef]

Mandel, L.

L. Mandel, Proc. Phys. Soc. London 72, 1037 (1958).
[CrossRef]

Nelson, R. J.

N. K. Dutta, R. J. Nelson, IEEE J. Quantum Electron. QE-18, 871 (1982).
[CrossRef]

N. K. Dutta, R. J. Nelson, Appl. Phys. Lett. 38, 407 (1981).
[CrossRef]

N. K. Dutta, R. J. Nelson, “Temperature Dependence of the Threshold of InGaAsP DH Lasers and Auger Recombination,” in Proceedings, International Symposium on GaAs and Related Compounds, Vienna, Austria, 22–24 Sept. 1980, Inst. Phys. Conf. Ser. 56, pp. 193.

Panish, M. B.

H. C. Casey, M. B. Panish, Heterostructure Lasers, Part A: Fundamental Principles (Academic, New York, 1978), pp. 177–178.

Paoli, T. L.

T. L. Paoli, IEEE J. Quantum Electron. QE-11, 276 (1975).
[CrossRef]

T. L. Paoli, Appl. Phys. Lett. 24, 187 (1974).
[CrossRef]

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), pp. 65, 98–111.

Prucnal, P. R.

Sugimura, A.

A. Sugimura, IEEE J. Quantum Electron. QE-17, 627 (1981).
[CrossRef]

Sze, S. M.

S. M. Sze, Physics of Semiconductor Devices (Wiley-Interscience, New York, 1981), pp. 731.

Teich, M. C.

Thompson, G. H. B.

G. H. B. Thompson, G. D. Henshall, Electron. Lett. 16, 42 (1980).
[CrossRef]

Troup, G. J.

G. J. Troup, Photon Counting and Photon Statistics, Congress in Quantum Electronics (Pergamon, London, 1972).

Tsang, W. T.

W. T. Tsang, R. A. Logan, J. P. Van der Ziel, Appl. Phys. Lett. 34, 644 (1979).
[CrossRef]

Van der Ziel, J. P.

W. T. Tsang, R. A. Logan, J. P. Van der Ziel, Appl. Phys. Lett. 34, 644 (1979).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

N. K. Dutta, R. J. Nelson, Appl. Phys. Lett. 38, 407 (1981).
[CrossRef]

T. U. K. Iwamoto, R. Lang, Appl. Phys. Lett. 38, 193 (1981).
[CrossRef]

T. L. Paoli, Appl. Phys. Lett. 24, 187 (1974).
[CrossRef]

W. T. Tsang, R. A. Logan, J. P. Van der Ziel, Appl. Phys. Lett. 34, 644 (1979).
[CrossRef]

Electron. Lett. (1)

G. H. B. Thompson, G. D. Henshall, Electron. Lett. 16, 42 (1980).
[CrossRef]

IEEE J. Quantum Electron. (3)

N. K. Dutta, R. J. Nelson, IEEE J. Quantum Electron. QE-18, 871 (1982).
[CrossRef]

T. L. Paoli, IEEE J. Quantum Electron. QE-11, 276 (1975).
[CrossRef]

A. Sugimura, IEEE J. Quantum Electron. QE-17, 627 (1981).
[CrossRef]

J. Appl. Phys. (1)

N. K. Dutta, J. Appl. Phys. 52, 70 (1981).
[CrossRef]

J. Opt. Soc. Am. (2)

Jpn. J. Appl. Phys. (1)

Y. Horikoshi, Y. Furukawa, Jpn. J. Appl. Phys. 18, 809 (1979).
[CrossRef]

Proc. Phys. Soc. London (1)

L. Mandel, Proc. Phys. Soc. London 72, 1037 (1958).
[CrossRef]

Other (6)

H. C. Casey, M. B. Panish, Heterostructure Lasers, Part A: Fundamental Principles (Academic, New York, 1978), pp. 177–178.

S. M. Sze, Physics of Semiconductor Devices (Wiley-Interscience, New York, 1981), pp. 731.

N. K. Dutta, R. J. Nelson, “Temperature Dependence of the Threshold of InGaAsP DH Lasers and Auger Recombination,” in Proceedings, International Symposium on GaAs and Related Compounds, Vienna, Austria, 22–24 Sept. 1980, Inst. Phys. Conf. Ser. 56, pp. 193.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), pp. 65, 98–111.

M. H. Lean, “Electromagnetic Field Solution with the Boundary Element Method,” Ph.D. Thesis, Department of Electrical Engineering, U. Manitoba (1981), pp. 22–17.

G. J. Troup, Photon Counting and Photon Statistics, Congress in Quantum Electronics (Pergamon, London, 1972).

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Figures (1)

Fig. 1
Fig. 1

Photon counting probability density function for Gaussian temperature fluctuations with indicated standard deviation.

Equations (13)

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p ( n / λ 0 ) = λ 0 n exp ( λ 0 ) n ! ,
λ 0 = τ τ + Δ I ( τ ) d τ ,
λ = k 1 J ,
J th = k 2 exp ( T / T 0 ) ,
λ = k exp ( T / T 0 ) ,
P T ( t ) = 0 t < 0 , = 1 2 erfc ( t 0 2 σ ) δ ( t ) t = 0 , = 1 2 π σ exp [ ( t t 0 ) 2 2 σ 2 ] t > 0 ,
p I ( λ ) = 0 λ < k , = T 0 2 k erfc ( t 0 2 σ ) δ ( λ k ) λ = k , = T 0 2 π σ 1 λ exp { [ T 0 ln ( λ k t 0 ) ] 2 2 σ 2 } λ > k ,
λ ¯ = λ 0 = E ( λ ) = λ p I ( λ ) d λ = k exp ( t 0 T 0 ) ,
k = λ 0 / exp ( t 0 T 0 ) .
p I ( λ ) = 0 λ < k , = T 0 2 λ 0 exp ( t 0 T 0 ) erfc ( t 0 2 σ ) δ ( λ k ) λ = k , = 1 2 π σ 1 1 λ exp { [ ln ( λ / λ 0 ) 2 ] 2 σ 1 2 } λ > k ,
p I ( n ) = 0 p ( n | λ ) p I ( λ ) d λ .
0 p I ( n ) d n = 1.
p I ( n ) = 0 λ n exp ( λ ) n ! 1 2 π σ 1 1 λ exp [ ( ln λ λ 0 ) 2 2 σ 1 2 ] d λ .

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