Correlation Function of a Laser Beam Near Threshold

Abstract

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

$$\lambda \left( \tau \right) \equiv <\Delta I\left( t \right)\Delta I\left( {t + \tau } \right)>/<I{>^2},$$

(1)

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.

This work was supported by the Air Force Office of Scientific Research and by the National Science Foundation.