Measurements of the Fine Structure of Laser Intensity Correlations near Threshold

The correlation function of the intensity fluctuations of a single mode laser in the threshold region has been measured with a 1'ast digital correlator. The various exponential components have been separated for the first time, by exploiting the nonlinear characteristics of the correlator. The results are in quantitative agreement with the theoretical predictions. It is well known that the electromagnetic field emitted by a single-mode laser near threshold can be described as a non-linear Markov process. The most remarkable consequence of non-lineafity is that the laser-field correlation functions depart from a single-exponential behaviour and are characterized by a series of relaxation rates.* By using a new technique, we have been able to measure for the first time relaxation rates of order higher than one in the intensity correlation function of a cw He-Ne laser near threshold. The intensity correlation function K(T) of a cw laser is defined bq * A detailed description of the statistical properties of the laser fluctuations can be found in the experimental paper by Arecchi and Degiorgio in ref. [ 1 ] and in the theoretical papers See Risken and Vollmer in ref. 121. The connection with the notation of other authors is discussed by Arecchi and Degiorgio in ref. 11 1. K(7) = U(t) Z(t + 7))-u(tp2, (1) where Z(t) is the laser intensity at time t. The operational meaning of the average denoted by angular brackets is discussed in ref. [ 11. The laser theory predicts that, in the threshold region, K(T) may by written as [2] K(T) = K(O) ,GMj exp (-Ai 7), (2) where CjIl Mj = 1. The weights M. are functions only of a dimensionless quantity a, ca led the pump param-I eter. ** The pump parameter is proportional to the difference between unsaturated gain and cavity losses, and is, therefore, negative below and positive above threshold. The relaxation rates Ai can be expressed as Aj-CXj, where the dimensionless quantities Ai are also functions of a only. The proportionality constant C depends on the particular laser under investigation, and will be discussed later on in this paper. The numerical results obtained in ref. [2] indicate that, for any value of the pump parameter a, Mj is decreasing with the order j, if the Xi 's are such that hi < Xi+t. The experimental verification of eq. (2) is 329