Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Theoretical Physics

Steady-State Analysis of Two Single-Mode Dye Laser Models with Multiplicative Colored Noise

Jian He, Cao Li, Wu Da-Jin

Published Dec 15, 1994• 2 citations
Publisher

Abstract

In this paper, a unified expansion theory that can be simultaneously applied to both large and small correlation times developed by Gang HU is established and applied to the systems driven by multiplicative colored noise. The stationary intensity probabilities are calculated for colored gain-noise and colored-loss-noise models. Comparing with the predictions of the best Fokker–Planck equation and the unified colored-noise approximation for the stationary intensity probability of the two models, it is found that the results of the unified expansion theory are in better agreement with simulations and experimental results than those of the best Fokker–Planck equation approximation and the unified colored-noise approximation.

DOI
10.1088/0253-6102/22/4/401

Related papers

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

Ling Lin, Cao Li, Wu Da-Jin

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.

Physical Review A•Jul 1, 1993•7 citations

Saturation Effects and the Colored Pump Noise in a Dye Laser

Jian He, Zhiyou Zhong, Wu Da-Jin +1 more

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.

Communications in Theoretical Physics•Mar 15, 1997•0 citations

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

Cao Li, Wu Da-Jin, Ling Lin

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.

Physical Review A•Jan 1, 1994•8 citations

Dye-laser equation with saturation and its best Fokker-Planck equation

Enrique Peacock-López, F. Javier de la Rubia, Bruce J. West +1 more

We carry out numerical simulations of the evolution and steady-state properties of a dye laser operating near resonance. The model we use is fully two dimensional (i.e., it includes the intensity and the phase of the radiation) and does not involve the usual low-intensity expansions commonly used in the literature. The equation for the complex electric field is driven by white additive noise (quantum fluctuations due to spontaneous emission) and by colored multiplicative noise (fluctuations of the gain parameter). We note that the simulations agree with the experimental results of Zhu, Yu, and Roy [Phys. Rev. A 34, 4333 (1986)] for parameter values used in their experiments. We compare the simulation results with predictions of the ``best Fokker-Planck equation'' (BFPE) for the steady-state distribution of the laser intensity and find remarkable quantitative agreement for large ranges of parameters values, even for values that are in principle beyond the range of validity of this equation. We conclude that the BFPE can be safely invoked to make predictions for this system.

Physical Review A•Apr 1, 1989•27 citations

Intensity correlation functions for the colored gain-noise model of dye lasers

Emilio Hernández-Garcı́a, Raúl Toral, Maxi San Miguel

Predictions for dye-laser intensity correlation functions of a stochastic model incorporating colored gain-noise fluctuations are discussed and compared with the predictions of the model incorporating loss-noise fluctuations. It is shown that differences between the two models are generally masked by the finite correlation time of the noise. Important differences are shown to exist well above threshold when the correlation time of the colored noise is of the same order or smaller than the cavity decay time. A new algorithm for the simulation of stochastic equations with colored noise is used and discussed.

Physical Review A•Dec 1, 1990•56 citations

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

J. M. Noriega, Luis Pesquera, M. A. Rodrguez +2 more

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 \ensuremath{\tau} larger than the deterministic relaxation time ${\mathit{t}}_{\mathit{d}}$, 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 short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and 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.

Physical Review A•Aug 1, 1991•20 citations
In this paper, a unified expansion theory that can be simultaneously applied to both large and small correlation times developed by Gang HU is established and applied to the systems driven by multiplicative colored noise. The stationary intensity probabilities are calculated for colored gain-noise and colored-loss-noise models. Comparing with the predictions of the best Fokker–Planck equation and the unified colored-noise approximation for the stationary intensity probability of the two models, it is found that the results of the unified expansion theory are in better agreement with simulations and experimental results than those of the best Fokker–Planck equation approximation and the unified colored-noise approximation.
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.
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.
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.
We carry out numerical simulations of the evolution and steady-state properties of a dye laser operating near resonance. The model we use is fully two dimensional (i.e., it includes the intensity and the phase of the radiation) and does not involve the usual low-intensity expansions commonly used in the literature. The equation for the complex electric field is driven by white additive noise (quantum fluctuations due to spontaneous emission) and by colored multiplicative noise (fluctuations of the gain parameter). We note that the simulations agree with the experimental results of Zhu, Yu, and Roy [Phys. Rev. A 34, 4333 (1986)] for parameter values used in their experiments. We compare the simulation results with predictions of the ``best Fokker-Planck equation'' (BFPE) for the steady-state distribution of the laser intensity and find remarkable quantitative agreement for large ranges of parameters values, even for values that are in principle beyond the range of validity of this equation. We conclude that the BFPE can be safely invoked to make predictions for this system.
Predictions for dye-laser intensity correlation functions of a stochastic model incorporating colored gain-noise fluctuations are discussed and compared with the predictions of the model incorporating loss-noise fluctuations. It is shown that differences between the two models are generally masked by the finite correlation time of the noise. Important differences are shown to exist well above threshold when the correlation time of the colored noise is of the same order or smaller than the cavity decay time. A new algorithm for the simulation of stochastic equations with colored noise is used and discussed.
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 \ensuremath{\tau} larger than the deterministic relaxation time td{\mathit{t}}_{\mathit{d}}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 short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and 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.