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

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Variance estimation of radiation intensity on laser amplifier output

Dmitry V. Zaitsev

Published Dec 22, 1998• 0 citations
Publisher

Abstract

On the basis of Markov processes theory the equations for variation of universal population number and variation of atoms number of radiating coherency due to external laser radiation are deduced. Derived analytical expressions allow us to estimate relative error of output laser intensity in dependence on input laser intensity.
DOI
10.1117/12.334411

Related papers

Mathematical model of laser generation on the basis of Markov processes theory

Dmitry V. Zaitsev

The discrete nature of active media atoms, laser light photons and their Poisson distribution law allow us to apply correctly Markov processes theory with discrete states and continuous time to the description of laser generation process. The equations of photons quantity in laser resonator and population inversion are deduced. The results coincide with known equations. Equations of photons quantity dispersion and population inversion dispersion are deduced also. The analysis of these equations permits us to explain the operation of spiking pulsed multimode lasers.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 1, 1996•1 citation

Intensity Fluctuations in the Output of cw Laser Oscillators. I

D. E. McCumber

Using linearized rate equations, we have calculated the intensity fluctuations expected in the output of four-level cw laser oscillators. Intrinsic quantum effects have been included by restricting the eigenvalues of photon and atomic population operators to discrete integral values and by using equivalent noise sources. The total output fluctuations increase monotonically with output power; the relative fluctuations decrease monotonically, and at high output levels inversely as the output power squared. The low-frequency fluctuations differ in that the relative fluctuations increase with output below threshold (noise amplifier region) but decrease sharply above threshold (dynamic saturation region). Curves typical of gas, solid, and diode lasers are illustrated. The theory agrees well with preliminary experimental results.

Physical Review•Jan 7, 1966•357 citations

Laser generation with coloured input: II. Photon-number fluctuations of laser radiation in the presence of squeezed vacuum input

Игорь Евгеньевич Проценко, Luigi A. Lugiato

We apply the laser quantum Langevin equations derived in part I of this paper to the description of the laser intensity fluctuations when the external field entering the input - output port is in a squeezed vacuum state with finite bandwidth. We focus on the two opposite limits in which the detection time is much longer, or much shorter, than the inverse of the cavity linewidth. When there is detuning between the squeezed input and the laser frequency, the variance of the intensity fluctuations displays regular oscillations with frequency equal to the detuning. In the limit of small detection times there is the possibility of substantial reduction of the photon-number fluctuations using a squeezed input.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Oct 1, 1996•0 citations

Stochastic and probabilistic equations for three- and four-level lasers: tutorial

Colin J. McKinstrie

In this tutorial, Langevin stochastic equations and Markov probability equations are used to model electron- and photon-number fluctuations in three- and four-level lasers. Equations are derived for the moments of the electron and photon numbers (means, variances and correlations). Both approaches produce the same moment equations. In the Langevin approach, the moments of the noise terms must be specified by other means, whereas in the Markov approach, they are determined self-consistently and satisfy the shot-noise rule: For each process that is modeled by the rate equations, the driving terms in the variance equations equal the moduli of the associated terms in the mean equations. The driving terms in the correlation equations have the same magnitudes as the variance terms, but can be positive or negative, depending on whether the changes in the electron and photon numbers are correlated or anti-correlated, respectively. Formulas are derived for the relative intensity noise and its spectrum. The consequences of these results for three- and four-level lasers are discussed.

Journal of the Optical Society of America B•Feb 3, 2020•7 citations

Laser amplification of incoherent radiation

Lionel N. Menegozzi, Willis E. Lamb

The amplification of noise in a laser amplifier is treated theoretically. The model for the active medium and its description using density-matrix techniques, are taken from the theory of laser operation. The fundamental concern of this investigation is the spectral behavior of the radiation in the nonlinear regime; hence, the formalism is written from the onset in the frequency domain. The statistics of the light are gradually modified by the nonlinear amplification process, and expressions are derived for the rate of change of fluctuations in intensity as a measure of statistical changes. These expressions should be easily susceptible to detailed experimental observations. In addition, the range of validity of Litvak's Gaussian-statistics approximation is discussed with some detail. In the homogeneous-broadening case, the evolution of initially broadband Gaussian radiation toward quasimonochromatic oscillations with laserlike statistics is extensively explored in several numerical examples. The connections of this study with the time-domain work of Risken and Nummedal, on self-pulsing in a ring-laser configuration, are clearly established. Finally, spectral-narrowing and -rebroadening effects in Doppler-broadened media are discussed both analytically and with numerical examples. These examples show the distinct contribution of pulsations in the population ("Raman-type terms"), and saturation phenomena. The predicted narrowing-rebroadening rate is compared with expressions found in previous literature.

Physical Review A•Feb 1, 1978•30 citations

Intensity noise of injection-locked lasers: Quantum theory using a linearized input-output method

Timothy C. Ralph, C. C. Harb, Hans‐A. Bachor

We derive analytical expressions for the quantum-noise spectra of an atomic laser using a linearized input-output method. We generalize the method to the problem of injection-locked lasers. We identify three distinct spectral noise regimes in the solution, unifying previous results. The approach offers insights into the physical processes and is especially suited for comparison with experiment. The quantum spectral noise properties of the pump laser and the injected laser appear explicitly in the solution. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Nov 1, 1996•62 citations
The discrete nature of active media atoms, laser light photons and their Poisson distribution law allow us to apply correctly Markov processes theory with discrete states and continuous time to the description of laser generation process. The equations of photons quantity in laser resonator and population inversion are deduced. The results coincide with known equations. Equations of photons quantity dispersion and population inversion dispersion are deduced also. The analysis of these equations permits us to explain the operation of spiking pulsed multimode lasers.
Using linearized rate equations, we have calculated the intensity fluctuations expected in the output of four-level cw laser oscillators. Intrinsic quantum effects have been included by restricting the eigenvalues of photon and atomic population operators to discrete integral values and by using equivalent noise sources. The total output fluctuations increase monotonically with output power; the relative fluctuations decrease monotonically, and at high output levels inversely as the output power squared. The low-frequency fluctuations differ in that the relative fluctuations increase with output below threshold (noise amplifier region) but decrease sharply above threshold (dynamic saturation region). Curves typical of gas, solid, and diode lasers are illustrated. The theory agrees well with preliminary experimental results.
We apply the laser quantum Langevin equations derived in part I of this paper to the description of the laser intensity fluctuations when the external field entering the input - output port is in a squeezed vacuum state with finite bandwidth. We focus on the two opposite limits in which the detection time is much longer, or much shorter, than the inverse of the cavity linewidth. When there is detuning between the squeezed input and the laser frequency, the variance of the intensity fluctuations displays regular oscillations with frequency equal to the detuning. In the limit of small detection times there is the possibility of substantial reduction of the photon-number fluctuations using a squeezed input.
In this tutorial, Langevin stochastic equations and Markov probability equations are used to model electron- and photon-number fluctuations in three- and four-level lasers. Equations are derived for the moments of the electron and photon numbers (means, variances and correlations). Both approaches produce the same moment equations. In the Langevin approach, the moments of the noise terms must be specified by other means, whereas in the Markov approach, they are determined self-consistently and satisfy the shot-noise rule: For each process that is modeled by the rate equations, the driving terms in the variance equations equal the moduli of the associated terms in the mean equations. The driving terms in the correlation equations have the same magnitudes as the variance terms, but can be positive or negative, depending on whether the changes in the electron and photon numbers are correlated or anti-correlated, respectively. Formulas are derived for the relative intensity noise and its spectrum. The consequences of these results for three- and four-level lasers are discussed.
The amplification of noise in a laser amplifier is treated theoretically. The model for the active medium and its description using density-matrix techniques, are taken from the theory of laser operation. The fundamental concern of this investigation is the spectral behavior of the radiation in the nonlinear regime; hence, the formalism is written from the onset in the frequency domain. The statistics of the light are gradually modified by the nonlinear amplification process, and expressions are derived for the rate of change of fluctuations in intensity as a measure of statistical changes. These expressions should be easily susceptible to detailed experimental observations. In addition, the range of validity of Litvak's Gaussian-statistics approximation is discussed with some detail. In the homogeneous-broadening case, the evolution of initially broadband Gaussian radiation toward quasimonochromatic oscillations with laserlike statistics is extensively explored in several numerical examples. The connections of this study with the time-domain work of Risken and Nummedal, on self-pulsing in a ring-laser configuration, are clearly established. Finally, spectral-narrowing and -rebroadening effects in Doppler-broadened media are discussed both analytically and with numerical examples. These examples show the distinct contribution of pulsations in the population ("Raman-type terms"), and saturation phenomena. The predicted narrowing-rebroadening rate is compared with expressions found in previous literature.
We derive analytical expressions for the quantum-noise spectra of an atomic laser using a linearized input-output method. We generalize the method to the problem of injection-locked lasers. We identify three distinct spectral noise regimes in the solution, unifying previous results. The approach offers insights into the physical processes and is especially suited for comparison with experiment. The quantum spectral noise properties of the pump laser and the injected laser appear explicitly in the solution. \textcopyright{} 1996 The American Physical Society.