Chinese Physics Letters

Correlation Between Additive Noises Induced First-Order Phase Transition in a Two-Mode Laser

Quan Long, Cao Li, Wu Da-Jin, Zaiguang Li

Published Nov 1, 1996• 0 citations

Abstract

A phenomenological theory about the correlation between additive noises, in a two-mode laser arising from scattering of photons by the medium in the laser cavity is presented. It is applied to an inhomogeneously broadened two-mode ring laser. We have obtained an approximate expression for the steady-state intensity distribution, in which a first-order phase transition is found.

DOI: 10.1088/0256-307x/13/11/009

Related papers

Steady-state analysis of a two-mode laser with multiplicative white noise

Shiqun Zhu

Physical Review AJun 1, 199223 citations

Macroscopic Quantum Fluctuations and First-Order Phase Transition in a Laser

Paul D. Lett, William R. Christian, Surendra Singh +1 more

A homogeneously broadened two-mode ring laser has two metastable states in which one or the other mode intensity is zero. Quantum fluctuations cause the system to switch spontaneously, and at random times, between these states. The probability distribution of the light intensity of one laser mode has been measured, and found to exhibit two completely resolved peaks at zero and nonzero intensities, as predicted. This confirms the existence of a first-order laser phase transition.

Physical Review LettersDec 28, 198156 citations

Quantum statistical theory of the ring laser

Surendra Singh

Physical Review AFeb 1, 198114 citations

Steady-State Analysis of a Two-Mode Laser System with Cross-Correlation Between Real and Imaginary Parts of Quantum Noise

Dai Zu-cheng, Xiang You-Lin, Mei Dong-Cheng

Communications in Theoretical PhysicsMay 1, 20100 citations

Quantum theory of a two-mode laser with coupled transitions

Surendra Singh, Muhammad Suhail Zubairy

Physical Review AJan 1, 198038 citations

Statistical properties of gas ring lasers with backscattering

Luis Pesquera, R. Blanco, M. A. Rodrguez

Physical Review AJun 1, 198918 citations

Chinese Physics Letters

Correlation Between Additive Noises Induced First-Order Phase Transition in a Two-Mode Laser

Quan Long, Cao Li, Wu Da-Jin, Zaiguang Li

Published Nov 1, 1996• 0 citations

Publisher

Abstract

DOI: 10.1088/0256-307x/13/11/009

Related papers

Steady-state analysis of a two-mode laser with multiplicative white noise

Shiqun Zhu

The steady-state fluctuations of an inhomogeneously broadened two-mode laser with both additive and multiplicative white noise are investigated theoretically. A Fokker-Planck equation of the intensity-distribution function is presented. Analytic expressions of the autocorrelation and cross correlation of the steady-state two-mode intensities are derived for equal pump parameters of the two modes. Large intensity fluctuations occur when the laser is operated below threshold. However, when the laser is operated far above threshold, there is almost no difference between the laser models with and without multiplicative noise.The steady-state fluctuations of an inhomogeneously broadened two-mode laser with both additive and multiplicative white noise are investigated theoretically. A Fokker-Planck equation of the intensity-distribution function is presented. Analytic expressions of the autocorrelation and cross correlation of the steady-state two-mode intensities are derived for equal pump parameters of the two modes. Large intensity fluctuations occur when the laser is operated below threshold. However, when the laser is operated far above threshold, there is almost no difference between the laser models with and without multiplicative noise.

Physical Review AJun 1, 199223 citations

Macroscopic Quantum Fluctuations and First-Order Phase Transition in a Laser

Paul D. Lett, William R. Christian, Surendra Singh +1 more

Physical Review LettersDec 28, 198156 citations

Quantum statistical theory of the ring laser

Surendra Singh

A unified quantum treatment is presented for bidirectional two-mode ring lasers using the approach of Haken and co-workers. Equations of motion for the reduced density matrix of the field have been derived and used to study the fluctuation properties of the radiation field in different kinds of active media. The steady-state photon number distribution for an inhomogeneously broadened gas ring laser is derived. It is shown that for equal losses the relative fluctuations and normalized cross correlation of the photon numbers approach values $\frac{1}{3}$ and $\ensuremath{-}\frac{1}{3}$, respectively, for large excitations. For unequal losses the laser may emit typical single-mode laser radiation in the direction of the favored mode and typical equilibrium blackbody radiation in the direction of the weaker mode. Our results generally agree with the predictions of earlier treatments when the losses are equal. However, for unequal losses we predict different behavior for large excitations. Effects of detuning, spatial, and temporal variation of atomic inversion on the fluctuation properties have been investigated in the coherent-state diagonal representation of the density matrix, and steady-state intensity distributions have been derived for various kinds of active atoms. It is shown that for inhomogeneously broadened solid-state ring lasers spatial inhomogeneities may couple the modes strongly and the statistical properties of such lasers, characterized by a double-peaked intensity distribution and large relative-intensity fluctuations, may be similar to those of a homogeneously broadened ring laser. Curves are presented to illustrate the behavior.A unified quantum treatment is presented for bidirectional two-mode ring lasers using the approach of Haken and co-workers. Equations of motion for the reduced density matrix of the field have been derived and used to study the fluctuation properties of the radiation field in different kinds of active media. The steady-state photon number distribution for an inhomogeneously broadened gas ring laser is derived. It is shown that for equal losses the relative fluctuations and normalized cross correlation of the photon numbers approach values $\frac{1}{3}$ and $\ensuremath{-}\frac{1}{3}$, respectively, for large excitations. For unequal losses the laser may emit typical single-mode laser radiation in the direction of the favored mode and typical equilibrium blackbody radiation in the direction of the weaker mode. Our results generally agree with the predictions of earlier treatments when the losses are equal. However, for unequal losses we predict different behavior for large excitations. Effects of detuning, spatial, and temporal variation of atomic inversion on the fluctuation properties have been investigated in the coherent-state diagonal representation of the density matrix, and steady-state intensity distributions have been derived for various kinds of active atoms. It is shown that for inhomogeneously broadened solid-state ring lasers spatial inhomogeneities may couple the modes strongly and the statistical properties of such lasers, characterized by a double-peaked intensity distribution and large relative-intensity fluctuations, may be similar to those of a homogeneously broadened ring laser. Curves are presented to illustrate the behavior.

Physical Review AFeb 1, 198114 citations

Steady-State Analysis of a Two-Mode Laser System with Cross-Correlation Between Real and Imaginary Parts of Quantum Noise

Dai Zu-cheng, Xiang You-Lin, Mei Dong-Cheng

An inhomogeneously broadened two-mode laser system with cross-correlations between the real and imaginary parts of quantum noise is considered. The Fokker–Planck equation of the system is derived by the phase-locking method. The steady-state probability distribution, the mean light intensity, the normalization autocorrelation function, and cross correlation function are calculated. The results indicate that: (i) The cross-correlation between the real and imaginary parts of quantum noise can cause the stationary probability distribution from one peak structure to two extrema structure when the laser system is operated above threshold; (ii) The cross-correlation between the real and imaginary parts of quantum noise enhance the light intensity fluctuation and decrease the laser output when the laser system is operated below or near threshold; (iii) The effect of the cross-correlation between the real and imaginary parts of quantum noise is very weak on the stationary properties when the laser system is operated far above threshold.An inhomogeneously broadened two-mode laser system with cross-correlations between the real and imaginary parts of quantum noise is considered. The Fokker–Planck equation of the system is derived by the phase-locking method. The steady-state probability distribution, the mean light intensity, the normalization autocorrelation function, and cross correlation function are calculated. The results indicate that: (i) The cross-correlation between the real and imaginary parts of quantum noise can cause the stationary probability distribution from one peak structure to two extrema structure when the laser system is operated above threshold; (ii) The cross-correlation between the real and imaginary parts of quantum noise enhance the light intensity fluctuation and decrease the laser output when the laser system is operated below or near threshold; (iii) The effect of the cross-correlation between the real and imaginary parts of quantum noise is very weak on the stationary properties when the laser system is operated far above threshold.

Communications in Theoretical PhysicsMay 1, 20100 citations

Quantum theory of a two-mode laser with coupled transitions

Surendra Singh, Muhammad Suhail Zubairy

The quantum-statistical properties of the optical field of a two-mode laser with two coupled transitions have been studied by means of a generalization of the Scully and Lamb theory. The photon number distribution and the mode intensity distribution are obtained in the steady state for a system of homogeneously broadened atoms in resonance with the laser field. It is shown that the mode-coupling constant $\ensuremath{\xi}$ is unity and that near threshold the results of earlier treatments are recovered. Furthermore, it is shown that certain limit measures for the relative intensity fluctuations predicted by the semiclassical Fokker-Planck treatments based on the third-order theory are valid even in the limit of arbitrarily high gain levels.The quantum-statistical properties of the optical field of a two-mode laser with two coupled transitions have been studied by means of a generalization of the Scully and Lamb theory. The photon number distribution and the mode intensity distribution are obtained in the steady state for a system of homogeneously broadened atoms in resonance with the laser field. It is shown that the mode-coupling constant $\ensuremath{\xi}$ is unity and that near threshold the results of earlier treatments are recovered. Furthermore, it is shown that certain limit measures for the relative intensity fluctuations predicted by the semiclassical Fokker-Planck treatments based on the third-order theory are valid even in the limit of arbitrarily high gain levels.

Physical Review AJan 1, 198038 citations

Statistical properties of gas ring lasers with backscattering

Luis Pesquera, R. Blanco, M. A. Rodrguez

The two-mode inhomogeneously broadened ring laser with spontaneous-emission noise is investigated in the presence of backscattering. Using a linear transformation it is shown that this problem in the absence of detuning is equivalent to that of the ring laser without backscattering in the two following cases: (i) in-phase backcoupling case ( ${R}_{1}$ = ${R}_{2}^{\mathrm{*}}$ ), (ii) equal pump parameters and ``symmetric'' backscattering (\ensuremath{\Vert} ${R}_{1}$ \ensuremath{\Vert}=\ensuremath{\Vert} ${R}_{2}$ \ensuremath{\Vert}), where ${R}_{1}$ and ${R}_{2}$ are complex backscattering coefficients. We recover in this way the stationary probability density obtained by Christian and Mandel [Phys. Rev. A 34, 3932 (1986)]. Exact expressions for the mean values, fluctuations, and correlations of the two-mode intensities are derived. Our results show that the relative intensity fluctuations of both modes die out well above threshold. Mode-competition effects are reduced by symmetric backscattering. Exact formulas for the effective eigenvalue characterizing the initial decay of intensity correlation functions are given. These results are compared with the experimental data measured by Singh [Phys. Rep. 108, 217 (1984)].The two-mode inhomogeneously broadened ring laser with spontaneous-emission noise is investigated in the presence of backscattering. Using a linear transformation it is shown that this problem in the absence of detuning is equivalent to that of the ring laser without backscattering in the two following cases: (i) in-phase backcoupling case (${R}_{1}$=${R}_{2}^{\mathrm{*}}$), (ii) equal pump parameters and ``symmetric'' backscattering (\ensuremath{\Vert}${R}_{1}$\ensuremath{\Vert}=\ensuremath{\Vert}${R}_{2}$\ensuremath{\Vert}), where ${R}_{1}$ and ${R}_{2}$ are complex backscattering coefficients. We recover in this way the stationary probability density obtained by Christian and Mandel [Phys. Rev. A 34, 3932 (1986)]. Exact expressions for the mean values, fluctuations, and correlations of the two-mode intensities are derived. Our results show that the relative intensity fluctuations of both modes die out well above threshold. Mode-competition effects are reduced by symmetric backscattering. Exact formulas for the effective eigenvalue characterizing the initial decay of intensity correlation functions are given. These results are compared with the experimental data measured by Singh [Phys. Rep. 108, 217 (1984)].

Physical Review AJun 1, 198918 citations

\frac{1}{3}

and $\ensuremath{-}\frac{1}{3}$, respectively, for large excitations. For unequal losses the laser may emit typical single-mode laser radiation in the direction of the favored mode and typical equilibrium blackbody radiation in the direction of the weaker mode. Our results generally agree with the predictions of earlier treatments when the losses are equal. However, for unequal losses we predict different behavior for large excitations. Effects of detuning, spatial, and temporal variation of atomic inversion on the fluctuation properties have been investigated in the coherent-state diagonal representation of the density matrix, and steady-state intensity distributions have been derived for various kinds of active atoms. It is shown that for inhomogeneously broadened solid-state ring lasers spatial inhomogeneities may couple the modes strongly and the statistical properties of such lasers, characterized by a double-peaked intensity distribution and large relative-intensity fluctuations, may be similar to those of a homogeneously broadened ring laser. Curves are presented to illustrate the behavior.

{R}_{1}

{R}_{2}^{\mathrm{*}}

), (ii) equal pump parameters and ``symmetric'' backscattering (\ensuremath{\Vert}

{R}_{1}

\ensuremath{\Vert}=\ensuremath{\Vert}

{R}_{2}

\ensuremath{\Vert}), where

{R}_{1}

and

{R}_{2}

are complex backscattering coefficients. We recover in this way the stationary probability density obtained by Christian and Mandel [Phys. Rev. A 34, 3932 (1986)]. Exact expressions for the mean values, fluctuations, and correlations of the two-mode intensities are derived. Our results show that the relative intensity fluctuations of both modes die out well above threshold. Mode-competition effects are reduced by symmetric backscattering. Exact formulas for the effective eigenvalue characterizing the initial decay of intensity correlation functions are given. These results are compared with the experimental data measured by Singh [Phys. Rep. 108, 217 (1984)].