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

Chapman & Hall/CRC eBooks

Difference Equations for Photon-Number Distribution in the Stationary Regime of a Random Laser

Published Apr 29, 2005• 0 citations
Publisher

Abstract

Abstract The theory of a laser has provided many semiclassical and quantum models of the laser. Differential-difference equations play a prominent role in the description of the dynamics of the laser. Investigation of the steady state leads to a simplification of these equations to the difference equations. Recent studies of random lasers have aroused interest in the description of traditional lasers.

DOI
10.1201/9781420034905-30

Related papers

Difference Equations for Photon-Number Distribution in the Stationary Regime of a Random Laser

Vlasta Peřinová, A. Lukš

Chapman & Hall/CRC eBooks•Apr 29, 2005•0 citations

Quantum Fluctuations in Small Lasers

Kaushik Roy‐Choudhury, Stephan Haas, Anthony F. J. Levi

The dominant role of quantum fluctuations in determining the steady-state and transient response of a laser is demonstrated when there is a small number of particles in the system. In this regime, quantum fluctuations are found to suppress the lasing threshold and create a non-Poisson probability distribution for n discrete excited electronic states and s discrete photons. The correlation between n and s damps the averaged dynamic response of laser emission. Random walk calculations verify the master equation predictions and are used to connect to systems containing larger numbers of particles.

Physical Review Letters•Feb 5, 2009•32 citations

Regime of small number of photons in the cavity for a singleemitter laser

Ларионов Николай Владимирович

Abstract The model of a single-emitter laser generating in the regime of small number of photons in the cavity mode is theoretically investigated. Based on a system of equations for different moments of the field operators the analytical expressions for mean photon number and photon number variance are obtained. Using the master equation approach the differential equation for the phase-averaged quasi-probability Q is derived. For some limiting cases the exact solutions of this equation are found.

arXiv:2108.08664•Journal of Physics Conference Series•Nov 1, 2021•1 citation

Quantum Theory of Laser Radiation. II. Statistical Aspects of Laser Light

J. A. Fleck

We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with $N$ stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.

Physical Review•Sep 9, 1966•26 citations

Quantum Theory of Radiation. II. Statistical Aspects of Laser Light

J. A. Fleck

We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with $N$ stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.

Physical Review•Mar 10, 1967•4 citations

Exact steady-state solution of the quantum-mechanical single-mode laser model

V. Dohm

The fully quantum-mechanical model of a single-mode laser is examined. A previously introduced method of solution where both the pump and loss reservoirs are treated simultaneously as a weak perturbation of the atom-light system is employed. This method is similar to perturbation theory for degenerate systems in that the reservoirs remove the nonuniqueness (degeneracy) of the steady state of the unperturbed atom-light system. In the limit of weak reservoir coupling, the exact steady-state solution of the master equation is derived. This solution still contains the atomic variables explicitly and therefore remains valid even in situations where the conventional adiabatic elimination of the atomic variables is no longer possible. A compact discrete representation of the master equation in terms of atomic occupation numbers and photon numbers is developed which allows one to perform all calculations in an elementary manner, requiring only appropriate summations over photon and occupation numbers. General exact relations are obtained for the steady-state probability distribution function $p(n,m)$ to find $n$ photons in the light field and $m$ atoms in the excited state. Our solution constitutes the first steady-state laser distribution function that is valid for an arbitrary number of laser atoms and in the complete region from far below to far above threshold. It provides a quantitative criterion for the range of validity of approximate methods in laser theory.

Physical Review A•Jul 1, 1976•9 citations
Abstract The theory of a laser has provided many semiclassical and quantum models of the laser. Differential-difference equations play a prominent role in the description of the dynamics of the laser. Investigation of the steady state leads to a simplification of these equations to the difference equations. Recent studies of random lasers have aroused interest in the description of traditional lasers.
The dominant role of quantum fluctuations in determining the steady-state and transient response of a laser is demonstrated when there is a small number of particles in the system. In this regime, quantum fluctuations are found to suppress the lasing threshold and create a non-Poisson probability distribution for n discrete excited electronic states and s discrete photons. The correlation between n and s damps the averaged dynamic response of laser emission. Random walk calculations verify the master equation predictions and are used to connect to systems containing larger numbers of particles.
Abstract The model of a single-emitter laser generating in the regime of small number of photons in the cavity mode is theoretically investigated. Based on a system of equations for different moments of the field operators the analytical expressions for mean photon number and photon number variance are obtained. Using the master equation approach the differential equation for the phase-averaged quasi-probability Q is derived. For some limiting cases the exact solutions of this equation are found.
We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with NNN stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.
We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with NNN stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.
The fully quantum-mechanical model of a single-mode laser is examined. A previously introduced method of solution where both the pump and loss reservoirs are treated simultaneously as a weak perturbation of the atom-light system is employed. This method is similar to perturbation theory for degenerate systems in that the reservoirs remove the nonuniqueness (degeneracy) of the steady state of the unperturbed atom-light system. In the limit of weak reservoir coupling, the exact steady-state solution of the master equation is derived. This solution still contains the atomic variables explicitly and therefore remains valid even in situations where the conventional adiabatic elimination of the atomic variables is no longer possible. A compact discrete representation of the master equation in terms of atomic occupation numbers and photon numbers is developed which allows one to perform all calculations in an elementary manner, requiring only appropriate summations over photon and occupation numbers. General exact relations are obtained for the steady-state probability distribution function p(n,m)p(n,m)p(n,m) to find nnn photons in the light field and mmm atoms in the excited state. Our solution constitutes the first steady-state laser distribution function that is valid for an arbitrary number of laser atoms and in the complete region from far below to far above threshold. It provides a quantitative criterion for the range of validity of approximate methods in laser theory.