Analytic modeling of three level fibered amplifiers

Herve Coic; Frederic Leconte; Jean Francois Gleyze; Alain Jolly

doi:10.1117/12.474761

17 June 2003 Analytic modeling of three level fibered amplifiers

Herve Coic, Frederic Leconte, Jean Francois Gleyze, Alain Jolly

Proceedings Volume 4990, Rare-Earth-Doped Materials and Devices VII; (2003) https://doi.org/10.1117/12.474761
Event: Integrated Optoelectronics Devices, 2003, San Jose, CA, United States

Abstract

A new theoretical approach for modeling the saturated single pass gain in a three-level fiber amplifier is presented, relevant to the behavior of rare-earth-doped silica fibers. A basic approximation considering the stimulated emission rate W_s(z,ν) as a dimensionless parameter S, independent of the spatial and frequency variables z and ν, allows to obtain analytic expressions for input and output pump, ASE and signal powers inside the fiber core. We show that these expressions only depend on the S parameter, which is determined by solving the photon balance equation, and S is shown to be fully representative of the saturation in the medium. The main result of the model is that the pump repartition P(z) takes a simple analytical form, which can be separated into two parts, below and above the saturated absorption length L₀, which is a function of S. The first part 0⟨z⟨L₀ is the saturated absorption where the pump distribution is linear and the second part L₀⟨z⟨L is the non saturated absorption region with an exponentially decreasing pump distribution. Compared to other analytical models with the assumption of an averaged inversion population ⟨N₂(z)⟩, we obtain a good description of the difference between the co- and counter-propagating ASE behaviors accounting for the fiber length and the pumping level. The model, which is well suited to longitudinal pumping, can also describe a side pumped fiber amplifier by simple adjustment of some of the model parameters.

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Herve Coic, Frederic Leconte, Jean Francois Gleyze, and Alain Jolly "Analytic modeling of three level fibered amplifiers", Proc. SPIE 4990, Rare-Earth-Doped Materials and Devices VII, (17 June 2003); https://doi.org/10.1117/12.474761

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KEYWORDS

Absorption

Luminescence

Amplifiers

Fiber amplifiers

Ytterbium

Differential equations

Picosecond phenomena

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