Correlation Function of a Laser Beam Near Threshold

  • S. Chopra
  • L. Mandel


As is now well known, the rotating-wave van der Pol oscillator theories of the laser [1–4] lead to a precise prediction for the form of the intensity correlation function of the light. In the steady state, we may define the normalized intensity correlation function λ(τ) by the ratio
$$\lambda \left( \tau \right) \equiv <\Delta I\left( t \right)\Delta I\left( {t + \tau } \right)>/<I{>^2},$$
where I(t) is light intensity at time t and ΔI(t) is the difference between I(t) and its expectation value. The intensity may be treated as a classical random process, when the average in (1) is taken over the ensemble of realizations, or the intensity may be regarded as a Hilbert space operator, in which case the average denotes the quantum expectation, and it is understood that all operators are written in normal order.


Correlation Function Exponential Form Normal Order Break Curve Dimensionless Unit 


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  1. 1.
    H. Risken, Z. Phys. 186, 85 (1965) and 191, 302 (1966); Progress in Optics, Vol. 8, ed. E. Wolf ( North-Holland Publishing Co., Amsterdam, 1970 ) p. 239.Google Scholar
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    S. Chopra and L. Mandel, IEEE J. Quantum Electronics QE-8, 324 (1972).Google Scholar
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    For a description of the instrument and its operation, see S. Chopra and L. Mandel, Rev. Sci. Instru. 43, 1489 (1972).CrossRefGoogle Scholar
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    For details see D. Meitzer and L. Mandel, IEEE J. Quantum Electronics QE-6, 661 (1970) and D. Meitzer and L. Mandel, Phys. Rev. A 3S 1763 (1971).Google Scholar
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    See for example L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).CrossRefGoogle Scholar
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    For a comparison see F. Davidson and L. Mandel, J. Appl. Phys. 39, 62 (1968).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • S. Chopra
    • 1
  • L. Mandel
    • 1
  1. 1.University of RochesterRochesterUSA

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