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Physical Review A

Effective eigenvalue for the intensity correlations of single-mode and two-mode lasers

Maxi San Miguel, Luis Pesquera, Miguel A. Rodríguez, Aurora Hernández-Machado

Published Jan 1, 1987• 45 citations
Publisher

Abstract

Exact formulas for the effective eigenvalue characterizing the initial decay of intensity correlation functions are given in terms of stationary moments of the intensity. Spontaneous emission noise and nonwhite pump noise are considered. Our results are discussed in connection with earlier calculations, simulations, and experimental results for single-mode dye lasers, two-mode inhomogeneously broadened lasers, and two-mode dye ring lasers. The effective eigenvalue is seen to depend sensitively on noise characteristics and symmetry properties of the system. In particular, the effective eigenvalue associated with cross correlations of two-mode lasers is seen to vanish in the absence of pump noise as a consequence of detailed balance. In the presence of pump noise, the vanishing of this eigenvalue requires equal pump parameters for the two modes and statistical independence of spontaneous emission noise acting on each mode.

DOI
10.1103/physreva.35.208

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Exact formulas for the effective eigenvalue characterizing the initial decay of intensity correlation functions are given in terms of stationary moments of the intensity. Spontaneous emission noise and nonwhite pump noise are considered. Our results are discussed in connection with earlier calculations, simulations, and experimental results for single-mode dye lasers, two-mode inhomogeneously broadened lasers, and two-mode dye ring lasers. The effective eigenvalue is seen to depend sensitively on noise characteristics and symmetry properties of the system. In particular, the effective eigenvalue associated with cross correlations of two-mode lasers is seen to vanish in the absence of pump noise as a consequence of detailed balance. In the presence of pump noise, the vanishing of this eigenvalue requires equal pump parameters for the two modes and statistical independence of spontaneous emission noise acting on each mode.
Recent theoretical analyses of the single-mode laser with colored-noise pump fluctuations have allowed the detailed prediction of the short-time behavior of the intensity autocorrelations of such a laser. In particular, a rounding off of the intensity correlation function on the time scale of the correlation time of the pump fluctuations has been predicted. We present results from experiments performed on a single-mode dye-laser system that clearly confirm these predictions. Numerical simulations of the laser Langevin equations including the colored-noise pump fluctuations are used to fit the experimental results.
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A single-mode dye-laser model incorporating pump white noise through gain-parameter fluctuations is analyzed. It includes a fluctuating saturation term. Intensity fluctuations, a first-order-like transition, and intensity correlation functions are calculated and discussed. It is found that effects previously claimed to be a consequence of the presence of colored noise in the context of loss-noise models can be also explained by white gain noise, except for the existence of two time regimes in the early decay of intensity correlation functions.
We investigate the statistical properties of two single-mode dye-laser models—the colored-loss-noise model and the colored-gain-noise model. Analytic expressions of the probability, the mean and the variance of the steady-state laser intensity are obtained through the unified expansion theory [Phys. Rev. A43 (1991) 700]. By comparison we find that when the cavity decay rate for the electric field is large and the pump parameter is small, the differences of the results of the two laser models are small. Otherwise, the differences are large. And the correlation time of the noise has very obvious influence on the results of the two models.
We consider a single-mode dye-laser model with gain parameter fluctuations modeled by a white noise. The decay of the intensity correlation function C(t) is analyzed with the use of a method based on the combination of the low- and high-frequency expansions of the Laplace transform of C(t). The correlation function is approximated by a superposition of two decaying exponentials. Numerical simulations show that this approximation is accurate. We analyze the relaxation of C(t) in the domain of parameters, gain parameter close to the pump parameter, in which the white-gain-noise model reproduces the initial slow decay of C(t). It is found that the intensity correlation function does not show two separated time scales as observed experimentally.
The intensity and amplitude correlation functions of the optical field of a ring laser at line center are calculated, under conditions when the two pump parameters corresponding to the counter-rotating traveling wave modes are not necessarily equal. This represents a generalization of earlier treatments by M-Tehrani and Mandel (1978) and Hioe (1978). The laser is assumed to be at rest. A perturbative technique is used to express the correlation functions for a small difference $\ensuremath{\epsilon}$ of pump parameters in terms of the solutions for $\ensuremath{\epsilon}=0$. It is found that the cross correlations are unchanged to the first order in $\ensuremath{\epsilon}$, whereas the autocorrelations both of the light amplitude and of the light intensity are modified. Curves are presented to illustrate the behavior.