Colored Pump Noise Research Articles

Dye laser with pump and quantum noise

Department of Physics and Center of Complex Systems Research, Beckman Institute,University of Illinois at Urbana–Champaign, Urbana, Illinois 61801~Received 1 August 1995!We consider a single-mode dye laser with colored pump noise and white quantum noise. An analyticalapproach is applied to study the statistics of the intensity fluctuations for arbitrary correlation times of thepump noise. Full numerical solutions are compared with our approximation and previous approximationsschemes. The present approximation scheme compares favorably over wide regimes in parameter space withthe numerical data.PACS number~s!: 42.55.Mv, 05.40.1j, 82.20.Mj, 42.50.LcI. INTRODUCTION

First-order-like transition for colored saturation models of dye lasers: Effects of quantum noise.

A multidimensional form of the unified colored-noise approximation is applied to obtain the Fokker-Planck equation for intensity distributions of dye-laser models simultaneously driven by colored pump noise and quantum noise. The stationary intensity distributions (SID's) of these models are calculated. The first-order-like transitions (FOLT's) of the models are studied and compared. With the help of the combination of Sturm's theorem and Descarte's rule of signs, the following conclusions on the FOLT are obtained. (1) In the limit of white pump noise (the correlation time of the pump noise \ensuremath{\tau}=0), the FOLT disappears for the colored loss-noise model with saturation whereas it does not disappear for the colored gain-noise model. (2) The dependence of the FOLT on \ensuremath{\tau} is intensely affected by the quantum noise. If quantum noise is neglected, the first critical curve which separates the regions of single extremum and double extrema of the SID does not change with \ensuremath{\tau}. However, when the quantum noise is considered, the first critical curve does change with \ensuremath{\tau}. (3) When \ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\infty}, the area of region II in which the SID varies monotonically contracts and tends to zero. Therefore the FOLT disappears in the models. (4) It is found that when the strength of the quantum noise P varies (\ensuremath{\tau} is fixed), the critical curves also change.

First-order-like transition for colored-noise saturation models of dye lasers.

A unified colored-noise approximation is applied to calculate the stationary intensity probabilities of colored-gain-noise and colored-loss-noise models for dye lasers with saturation effects. We compare the results of the unified colored-noise approximation with the predictions of the best Fokker-Planck equation for the stationary intensity probability of a colored-gain-noise model, and find that the results of the unified colored-noise approximation agree better with simulation results than the results of the best Fokker-Planck equation. The first-order-like transition of colored-gain-noise and colored-loss-noise models with saturation effects is discussed and compared. It is found that the emergence of the first-order-like transition is related to the saturation element in the fluctuation term of the dye-laser model for white pump noise, and the occurrence of the first-order-like transition is only due to the existence of colored pump noise in the loss-noise models for dye lasers with saturation effects.

Intensity Correlation, Relaxation Time, Intensity Fluctuation and First-Order-Like Transition of Dye Laser

Statistical properties of dye laser are studied by using the colored gain-noise model which has been presented recently. We calculate the intensity correlation function and relaxation time driven by colored pump noise and white spontaneous-emission noise simultaneously. Intensity fluctuation and first-order-like transition are analyzed too in this paper. It is found that the colored gain-noise model can describe well the anomalous statistical properties of dye laser.

Effects of colored pump noise on intensity correlations of a single-mode dye laser.

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.

Dye laser model with pump and quantum fluctuations; White noise

A single mode dye laser model with two stochastically fluctuating forces representing pump and quantum fluctuations is discussed. In extension to a previous paper we investigate the different influences ofcolored pump noise andwhite quantum fluctuations on the laser light statistics. The corresponding two-variable Fokker-Planck equation is solved by means ofmatrix continued fractions. A comparison to the model with two white noise forces is also included. We focus especially on the intensity correlation time enhancement observed for low noise strengths which seems to be the result of a competition between (multiplicative) pump noise and (additive) quantum noise. An increase in correlation time of the colored pump noise causes the intensity correlation time enhancement to disappear.