Dye Laser Statistics in the Presence of Colored Noise Pump Fluctuations
As has been demonstrated in recent experiments,1,2 the output of the dye laser excited near threshold exhibits very unusual statistical properties. The divergence of relative intensity fluctuations <(ΔI)2>/<I>2 as the excitation approaches the threshold, unexplained by the conventional laser theory that includes only additive fluctuations, can be understood as arising due to fluctuations in the pump parameter itself. A theory modeling the multiplicative pump fluctuations as Gaussian white noise,3 although successful in explaining some of the results of ref. 1, fails to agree with experiments for excitations away from threshold. Since fluctuations, arising due to physical processes, always have a finite correlation time associated with them, the approximation of setting this time to zero (white noise) would be expected to be inaccurate for laser excitations away from threshold. One must then take into account the colored noise character of the fluctuations. It is the purpose of this paper to present a theory that models the pump fluctuations on an Ornstein Uhlenbeck process. As we have shown elsewhere4, this model successfully explains the experimental results of Short et. al for excitations near to and away from threshold.
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