Intensity correlation functions of dye lasers: Comparison of colored-gain-noise and colored-loss-noise models

Abstract

The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times~larger than the deterministic relaxation time td, we show with the use of the adiabatic approximation that C(t ) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously shortand long-time behaviors. Cornparison with numerical simulations shows excellent results simultaneously for shortand long-time regimes. It is found that, when the correlation time of the noise increases, difFerences between the gainand loss-noise models tend to disappear. The decay of C(t ) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.

Decay of Intensity Correlation Function near Instability Point for the Model of Resonant Tunneling

“…The expression for the calculation of the correlation function of the non-Markovian process was obtained in [8,9]. In the short-time regime, it has the form…”

“…In the case of intensity fluctuations with a finite small correlation time , the Fokker-Planck equation for the probability density ( , ) connected with the Langevin equation (7) will be given by the following expression [8,10]:…”

“…In the non-Markovian case, the dependence of the correlation function on noise parameters may have some specific features, as compared to the Markovian limit [2,6,7,8]. The generalization of the DE method to the case of a Gaussian colored noise in the first approximation with respect to the noise correlation time has been done in [2,9].…”

Dynamical properties of a mutualism system in the presence of noise and time delay

“…In this paper, we are interested in the stationary correlation function and associated relaxation time, which are used to describe the fluctuation decay of dynamical variable x. The normalized correlation function is [25,26]…”

“…The stationary normalized correlation function and the associated relaxation time can be respectively expressed as [25,26]…”