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

IEEE Journal of Quantum Electronics

Closed-form expressions for the gain in three- and four-level laser fibers

Michel J. F. Digonnet

Published Jan 1, 1990• 79 citations
Publisher

Abstract

Exact and approximate theoretical models of the small-signal single-pass gain in single-mode three-level laser fibers are presented. These models are relevant to the behavior of rare-earth-doped (in particular Er/sup 3+/) silica-based fibers. They account for the effects of both the pump and signal-mode structures and pump excited-state absorption (ESA), the latter being present for some pump wavelengths in Er-doped silica fibers. By relying on the modal overlap integral formalism for four-level lasers, relatively simple closed-form expressions for the pump absorption and the gain are derived. These expressions are also applicable to four level laser fibers by a simple adjustment of some of the model parameters.>

DOI
10.1109/3.60903

Related papers

Gain and noise in rare-earth-doped optical fibers

Marco Montecchi, Antonio Mecozzi, M. Settembre +2 more

Two pumping schemes are considered for optical amplifiers based on rare-earth-doped optical fibers in which pump light is fed either along with the signal light (copropagating) or through the opposite end of the fiber (counterpropagating), including the effects of the excited-state absorption (ESA) process. A rate-equation analysis shows that when ESA is absent the signal gain is the same in both pumping schemes, even under gain saturation, whereas when ESA is present the saturated signal gain is larger in the counterpropagating scheme. Independently of ESA the optical signal-to-noise ratio at the amplifier output is the same in both pumping schemes if the dopant behaves as a four-level laser system, and it is larger in the copropagating scheme for a three-level dopant.

Journal of the Optical Society of America B•Jan 1, 1991•10 citations

Signal amplification in strongly pumped fiber amplifiers

Amos A. Hardy, Ram Oron

Signal amplification is analyzed in strongly pumped fiber amplifiers both for three-level and four-level transitions, including scattering loss and excited state absorption. Simple analytic expressions are derived for the signal amplification and pump attenuation, along the fiber length, when either the signal and the pump are injected at the same fiber end (forward pumping) or when they are injected at the two opposite ends (backward pumping). Numerical examples for rare-earth doped fibers show excellent agreement between the analytical solution and the exact numerical solutions of the rate-equations for practical operating conditions.

IEEE Journal of Quantum Electronics•Mar 1, 1997•124 citations

The Gain Characteristics and the Optimum Fiber Length of Erbium-doped Fiber Amplifiers

Huang De, Li Zai

An apporoximative theoretical of an erbium-doped fiber amplifier (EDFA) has been proposed in this paper by the rate equation of three-level system. The optimum fiber length is obtained with different pump wavelength by considering the excited-stated-absorption(ESA) in EDFA. The relations between the gain and signal light intensity and pump light intensity are analyzed. It is found that the gain spectrum shape can be changed with the fiber length, which provides the evidence that EDFA is of great potential use in wavelength division multiplexed telecommunication systems.

Optical Communication Technology•Jan 1, 1994•0 citations

Er3+ excited-state absorption in an erbium-doped silica fiber at the wavelengths 1490–1580 and 978 nm

Alexander V. Kir’yanov, Yuri O. Barmenkov, ANA DINORA GUZMAN CHAVEZ

The spectral features of Er 3+ excited-state absorption (ESA) in an erbium-doped silica fiber (EF) at the telecom wavelengths 1490–1580 nm and at the wavelength 978 nm are reported. The measurement of the EF nonlinear transmission coefficient upon pumping the fiber in these spectral ranges, supplied with a theoretical background, allows one to obtain the spectrally dependent ESA parameter for the EF, which is defined as the ratio of the ESA to the ground-state absorption cross section.

Laser Physics•Nov 1, 2008•7 citations

Numerical simulation of laser pulse propagation in rare-earth-doped materials

Karl W. Beeson, Evgueni Parilov, Mary J. Potasek

We describe a general numerical method for calculating short-pulse laser propagation in rare-earth-doped materials, which are very important as gain materials for solid-state lasers, fiber lasers and optical amplifiers. The split-step, finite difference method simultaneously calculates changes in the laser pulse as it propagates through the material and calculates the dynamic populations of the rare-earth energy levels at any position within the material and for times during and after the laser pulse has passed through the material. Many traditional theoretical and numerical analyses of laser pulse propagation involve approximations and assumptions that limit their applicability to a narrow range of problems. Our numerical method, however, is more comprehensive and includes the processes of single- and multi-photon absorption, excited state absorption (ESA), energy transfer, upconversion, stimulated emission, cross relaxation, radiative relaxation and non-radiative relaxation. In the models, the rare-earth dopants can have an arbitrary number of energy levels. We are able to calculate the electron population density of every electronic level as a function of, for example, pulse energy, dopant concentration and sample thickness. We compare our theoretical results to published experimental results for rare-earth ions such as Er3+, Yb3+, Tm3+ and Ho3+.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 1, 2012•2 citations

Study of the complex atomic susceptibility of erbium-doped fiber amplifiers

E. Desurvire

A study of the complex atomic susceptibility of erbium-doped fiber amplifiers operating near the 1.53- mu m transition (/sup 4/I/sub 13/2/-/sup 4/I/sub 15/2/) developed from a semiclassical theoretical description is presented. Expressions for the emission cross section sigma /sub e/( lambda ) and absorption cross section sigma /sub a/( lambda ) of erbium:glass as a quasi-three-level laser system with Stark-split sublevel manifolds are derived. The results are used to calculate the cross sections of aluminosilicate erbium-doped fibers at low temperatures (T=4.2, 77 K) and at room temperature. It is demonstrated that an expression for the gain coefficient of the fiber amplifier can be derived from the expression of the susceptibility. Using Kramers-Kronig relations, an expression for the refractive index change in the fiber is derived. The theoretical spectral gain profile of the fiber amplifier and concurrent refractive index changes are analyzed for different pumping regimes.>

Journal of Lightwave Technology•Jan 1, 1990•138 citations
Exact and approximate theoretical models of the small-signal single-pass gain in single-mode three-level laser fibers are presented. These models are relevant to the behavior of rare-earth-doped (in particular Er/sup 3+/) silica-based fibers. They account for the effects of both the pump and signal-mode structures and pump excited-state absorption (ESA), the latter being present for some pump wavelengths in Er-doped silica fibers. By relying on the modal overlap integral formalism for four-level lasers, relatively simple closed-form expressions for the pump absorption and the gain are derived. These expressions are also applicable to four level laser fibers by a simple adjustment of some of the model parameters.>
Two pumping schemes are considered for optical amplifiers based on rare-earth-doped optical fibers in which pump light is fed either along with the signal light (copropagating) or through the opposite end of the fiber (counterpropagating), including the effects of the excited-state absorption (ESA) process. A rate-equation analysis shows that when ESA is absent the signal gain is the same in both pumping schemes, even under gain saturation, whereas when ESA is present the saturated signal gain is larger in the counterpropagating scheme. Independently of ESA the optical signal-to-noise ratio at the amplifier output is the same in both pumping schemes if the dopant behaves as a four-level laser system, and it is larger in the copropagating scheme for a three-level dopant.
Signal amplification is analyzed in strongly pumped fiber amplifiers both for three-level and four-level transitions, including scattering loss and excited state absorption. Simple analytic expressions are derived for the signal amplification and pump attenuation, along the fiber length, when either the signal and the pump are injected at the same fiber end (forward pumping) or when they are injected at the two opposite ends (backward pumping). Numerical examples for rare-earth doped fibers show excellent agreement between the analytical solution and the exact numerical solutions of the rate-equations for practical operating conditions.
An apporoximative theoretical of an erbium-doped fiber amplifier (EDFA) has been proposed in this paper by the rate equation of three-level system. The optimum fiber length is obtained with different pump wavelength by considering the excited-stated-absorption(ESA) in EDFA. The relations between the gain and signal light intensity and pump light intensity are analyzed. It is found that the gain spectrum shape can be changed with the fiber length, which provides the evidence that EDFA is of great potential use in wavelength division multiplexed telecommunication systems.
We describe a general numerical method for calculating short-pulse laser propagation in rare-earth-doped materials, which are very important as gain materials for solid-state lasers, fiber lasers and optical amplifiers. The split-step, finite difference method simultaneously calculates changes in the laser pulse as it propagates through the material and calculates the dynamic populations of the rare-earth energy levels at any position within the material and for times during and after the laser pulse has passed through the material. Many traditional theoretical and numerical analyses of laser pulse propagation involve approximations and assumptions that limit their applicability to a narrow range of problems. Our numerical method, however, is more comprehensive and includes the processes of single- and multi-photon absorption, excited state absorption (ESA), energy transfer, upconversion, stimulated emission, cross relaxation, radiative relaxation and non-radiative relaxation. In the models, the rare-earth dopants can have an arbitrary number of energy levels. We are able to calculate the electron population density of every electronic level as a function of, for example, pulse energy, dopant concentration and sample thickness. We compare our theoretical results to published experimental results for rare-earth ions such as Er3+, Yb3+, Tm3+ and Ho3+.
A study of the complex atomic susceptibility of erbium-doped fiber amplifiers operating near the 1.53- mu m transition (/sup 4/I/sub 13/2/-/sup 4/I/sub 15/2/) developed from a semiclassical theoretical description is presented. Expressions for the emission cross section sigma /sub e/( lambda ) and absorption cross section sigma /sub a/( lambda ) of erbium:glass as a quasi-three-level laser system with Stark-split sublevel manifolds are derived. The results are used to calculate the cross sections of aluminosilicate erbium-doped fibers at low temperatures (T=4.2, 77 K) and at room temperature. It is demonstrated that an expression for the gain coefficient of the fiber amplifier can be derived from the expression of the susceptibility. Using Kramers-Kronig relations, an expression for the refractive index change in the fiber is derived. The theoretical spectral gain profile of the fiber amplifier and concurrent refractive index changes are analyzed for different pumping regimes.>