Abstract

Optical-field fluctuations due to fluctuations of the number of active emitters are predicted and the magnitude of the effect is calculated. The results indicate an observable effect, although the conditions for observation appear not to have been met in experiments in which light fluctuations have been measured. The magnitude of the effect is capable of yielding information about the thickness of an emitting layer or the product of line width and excited-state lifetime.

© 1972 Optical Society of America

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References

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  1. A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, Phys. Rev. 99, 1691 (1955).
    [Crossref]
  2. R. Hanbury Brown and R. Q. Twiss, Nature 177, 27 (1956).
    [Crossref]
  3. H. Nieuwenhuijzen, Bull. Astron. Inst. Netherlands 19, 391 (1968).
  4. L. Mandel, in Progress in Optics II, edited by E. Wolf (North–Holland, Amsterdam, 1963), p. 181.
    [Crossref]
  5. I. R. Senitzky, Phys. Rev. 128, 2864 (1962).
    [Crossref]
  6. L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
    [Crossref]
  7. R. J. J. Zijlstra and C. Th. J. Alkemade, Physica 31, 1486 (1965).
    [Crossref]
  8. H. M. Fijnat and R. J. Zijlstra, J. Phys. D 3, 45 (1970).
    [Crossref]
  9. This can be proven by means of the Carson theorem. See A. van der Ziel, Noise (Prentice–Hall, Englewood Cliffs, N. J., 1970), pp. 13–16.
  10. A. Theodore Forrester, J. Opt. Soc. Am. 51, 253 (1961).
    [Crossref]
  11. C. Th. J. Alkemade, Physica 25, 1145 (1959).
    [Crossref]
  12. This condition will be relaxed in Sec. IV.
  13. There exists some confusion concerning terminology. I use the term heterodyne as a general term denoting beating between different-frequency waves, including, for example, the components of a single spectral line, as in low-level detection. Superheterodyne is used here to imply the use of an intense local oscillator.
  14. A. Maitland and M. H. Dunn, Laser Physics (North–Holland, Amsterdam, 1969), Sec. 7.2.
  15. A. Yariv, Quantum Electronics (Wiley, New York, 1967), Sec. 14.2.
  16. A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, J. Opt. Soc. Am. 46, 339 (1956).
    [Crossref]
  17. A. C. G. Mitchell and E. J. Murphy, Phys. Rev. 46, 53 (1934).
    [Crossref]

1970 (1)

H. M. Fijnat and R. J. Zijlstra, J. Phys. D 3, 45 (1970).
[Crossref]

1968 (1)

H. Nieuwenhuijzen, Bull. Astron. Inst. Netherlands 19, 391 (1968).

1965 (1)

R. J. J. Zijlstra and C. Th. J. Alkemade, Physica 31, 1486 (1965).
[Crossref]

1964 (1)

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[Crossref]

1962 (1)

I. R. Senitzky, Phys. Rev. 128, 2864 (1962).
[Crossref]

1961 (1)

1959 (1)

C. Th. J. Alkemade, Physica 25, 1145 (1959).
[Crossref]

1956 (2)

1955 (1)

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, Phys. Rev. 99, 1691 (1955).
[Crossref]

1934 (1)

A. C. G. Mitchell and E. J. Murphy, Phys. Rev. 46, 53 (1934).
[Crossref]

Alkemade, C. Th. J.

R. J. J. Zijlstra and C. Th. J. Alkemade, Physica 31, 1486 (1965).
[Crossref]

C. Th. J. Alkemade, Physica 25, 1145 (1959).
[Crossref]

Dunn, M. H.

A. Maitland and M. H. Dunn, Laser Physics (North–Holland, Amsterdam, 1969), Sec. 7.2.

Fijnat, H. M.

H. M. Fijnat and R. J. Zijlstra, J. Phys. D 3, 45 (1970).
[Crossref]

Forrester, A. T.

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, J. Opt. Soc. Am. 46, 339 (1956).
[Crossref]

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, Phys. Rev. 99, 1691 (1955).
[Crossref]

Gudmundsen, R. A.

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, J. Opt. Soc. Am. 46, 339 (1956).
[Crossref]

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, Phys. Rev. 99, 1691 (1955).
[Crossref]

Hanbury Brown, R.

R. Hanbury Brown and R. Q. Twiss, Nature 177, 27 (1956).
[Crossref]

Johnson, P. O.

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, J. Opt. Soc. Am. 46, 339 (1956).
[Crossref]

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, Phys. Rev. 99, 1691 (1955).
[Crossref]

Maitland, A.

A. Maitland and M. H. Dunn, Laser Physics (North–Holland, Amsterdam, 1969), Sec. 7.2.

Mandel, L.

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[Crossref]

L. Mandel, in Progress in Optics II, edited by E. Wolf (North–Holland, Amsterdam, 1963), p. 181.
[Crossref]

Mitchell, A. C. G.

A. C. G. Mitchell and E. J. Murphy, Phys. Rev. 46, 53 (1934).
[Crossref]

Murphy, E. J.

A. C. G. Mitchell and E. J. Murphy, Phys. Rev. 46, 53 (1934).
[Crossref]

Nieuwenhuijzen, H.

H. Nieuwenhuijzen, Bull. Astron. Inst. Netherlands 19, 391 (1968).

Senitzky, I. R.

I. R. Senitzky, Phys. Rev. 128, 2864 (1962).
[Crossref]

Sudarshan, E. C. G.

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[Crossref]

Theodore Forrester, A.

Twiss, R. Q.

R. Hanbury Brown and R. Q. Twiss, Nature 177, 27 (1956).
[Crossref]

van der Ziel, A.

This can be proven by means of the Carson theorem. See A. van der Ziel, Noise (Prentice–Hall, Englewood Cliffs, N. J., 1970), pp. 13–16.

Wolf, E.

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[Crossref]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1967), Sec. 14.2.

Zijlstra, R. J.

H. M. Fijnat and R. J. Zijlstra, J. Phys. D 3, 45 (1970).
[Crossref]

Zijlstra, R. J. J.

R. J. J. Zijlstra and C. Th. J. Alkemade, Physica 31, 1486 (1965).
[Crossref]

Bull. Astron. Inst. Netherlands (1)

H. Nieuwenhuijzen, Bull. Astron. Inst. Netherlands 19, 391 (1968).

J. Opt. Soc. Am. (2)

J. Phys. D (1)

H. M. Fijnat and R. J. Zijlstra, J. Phys. D 3, 45 (1970).
[Crossref]

Nature (1)

R. Hanbury Brown and R. Q. Twiss, Nature 177, 27 (1956).
[Crossref]

Phys. Rev. (3)

A. T. Forrester, R. A. Gudmundsen, and P. O. Johnson, Phys. Rev. 99, 1691 (1955).
[Crossref]

I. R. Senitzky, Phys. Rev. 128, 2864 (1962).
[Crossref]

A. C. G. Mitchell and E. J. Murphy, Phys. Rev. 46, 53 (1934).
[Crossref]

Physica (2)

R. J. J. Zijlstra and C. Th. J. Alkemade, Physica 31, 1486 (1965).
[Crossref]

C. Th. J. Alkemade, Physica 25, 1145 (1959).
[Crossref]

Proc. Phys. Soc. (London) (1)

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[Crossref]

Other (6)

This can be proven by means of the Carson theorem. See A. van der Ziel, Noise (Prentice–Hall, Englewood Cliffs, N. J., 1970), pp. 13–16.

L. Mandel, in Progress in Optics II, edited by E. Wolf (North–Holland, Amsterdam, 1963), p. 181.
[Crossref]

This condition will be relaxed in Sec. IV.

There exists some confusion concerning terminology. I use the term heterodyne as a general term denoting beating between different-frequency waves, including, for example, the components of a single spectral line, as in low-level detection. Superheterodyne is used here to imply the use of an intense local oscillator.

A. Maitland and M. H. Dunn, Laser Physics (North–Holland, Amsterdam, 1969), Sec. 7.2.

A. Yariv, Quantum Electronics (Wiley, New York, 1967), Sec. 14.2.

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Figures (2)

Fig. 1
Fig. 1

Experimental configuration for observation of the effect of density fluctuation.

Fig. 2
Fig. 2

Expected results of a fluctuation vs distance experiment.

Equations (25)

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N 0 = ( 4 π A B τ / λ 2 ) [ exp ( h ν / k T ) - 1 ] - 1 .
f 2 / N 0 2 = ( λ 2 / 4 π A B τ ) [ exp ( h ν / k T ) - 1 ] .
F ( ω ) = ( 2 / π ) f 2 τ [ 1 + ( ω τ ) 2 ] - 1 ,
f 2 = 0 F ( ω ) d ω .
f ( t ) = p ( 2 F p Δ ω ) 1 2 cos ( ω p t + ϕ p ) ,
E = E 0 [ 1 + f ( t ) / N 0 ] 1 2 ,
E = ( 1 + p ( 2 F p Δ ω ) 1 2 N 0 cos ( ω p t + ϕ p ) ) 1 2 × m ( G m Δ ω ) 1 2 exp [ j ( ω m t + ϕ m ) ] .
I 0 2 ( Ω ) = 2 Δ Ω K G ( Ω ) ,
K G ( Ω ) = 0 G ( ω ) G ( ω + Ω ) d ω .
I F 2 ( Ω ) = Δ Ω N 0 2 0 [ F ( ω + Ω ) + F ( ω - Ω ) ] K G ( ω ) d ω .
I F 2 ( Ω ) / I 0 2 ( Ω ) = { 0 [ F ( ω + Ω ) + F ( ω - Ω ) ] K G ( ω ) d ω } / 2 N 0 2 K G ( Ω ) .
I F 2 ( 0 ) / I 0 2 ( 0 ) = [ 0 F ( ω ) K G ( ω ) d ω ] / N 0 2 K G ( 0 ) .
G ( ω ) = [ 1 + ( ω - ω 0 ) 2 / 4 B 2 ] - 1
K G ( ω ) = π B [ 1 + ( ω / 4 B ) 2 ] - 1 .
I F 2 / I 0 2 = ( f 2 / N 0 2 ) [ 4 B τ / ( 4 B τ + 1 ) ] .
I F 2 / I 0 2 = ( λ 2 / 4 π A B τ ) [ exp ( h ν / k T ) - 1 ] .
I 0 2 ( Ω ) = 2 L 2 Δ Ω [ G ( ω 0 + Ω ) + G ( ω 0 - Ω ) ]
I F 2 ( Ω ) = ( L 2 / N 0 2 ) Δ Ω × 0 G ( ω ) [ F ( ω - ω 0 + Ω ) + F ( ω - ω 0 - Ω ) ] d ω .
I F 2 ( 0 ) / I 0 2 ( 0 ) = [ 0 G ( ω ) F ( ω - ω 0 ) d ω ] / 2 N 0 2 G ( ω 0 ) .
I F 2 / I 0 2 = ( f 2 / N 0 2 ) 2 B τ / ( 2 B τ + 1 ) .
I F 2 / I 0 2 = ( Ψ / 4 π B τ ) [ exp ( h ν / k T ) - 1 ] .
I F 2 / I 0 2 = ( η Ψ / 4 π B τ ) I N 2 / I 0 2 ,
I F 2 / I 0 2 = Ψ h c / 2 τ λ 3 P ,
s = 2 λ / Ψ ,
I F 2 / I 0 2 = ( η λ / 2 π s B τ ) I N 2 / I 0 2 .