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Journal of the Optical Society of America B

Unified model for analysis of light amplification in rare-earth doped fibers

J. Bai, E. Towe

Published Oct 20, 2014• 4 citations
Publisher

Abstract

This paper discusses a unified method for modeling and simulating signal light amplification in rare-earth doped optical fiber amplifiers. The model accounts for gain saturation, spontaneous emission, dispersion, and nonlinear effects along the length of the distributed gain medium. Simulations based on the unified model are shown to compare favorably with experimental results. The new model can be used to provide guidance in the design and construction of a variety of fiber-based optical amplifiers. Furthermore, it is suitable for analyzing the performance of high-power amplifiers in a wide range of operating conditions.

DOI
10.1364/josab.31.002809

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This paper discusses a unified method for modeling and simulating signal light amplification in rare-earth doped optical fiber amplifiers. The model accounts for gain saturation, spontaneous emission, dispersion, and nonlinear effects along the length of the distributed gain medium. Simulations based on the unified model are shown to compare favorably with experimental results. The new model can be used to provide guidance in the design and construction of a variety of fiber-based optical amplifiers. Furthermore, it is suitable for analyzing the performance of high-power amplifiers in a wide range of operating conditions.
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.
"Doping a part of the optical fiber core by (Er3+ ) ions in presence of external pumping power will lead to form the erbium-doped fiber amplifier (EDFA).The performance of this optical amplifier depends on (the power and the wavelength of the pumping laser, the power and wavelength of the input signal, amplifier length, ion concentration). These parameters will affect the characteristics of EDFA such as amplifier gain, gain saturation, noise figure and output power. However, these characteristics can be determined by solving the EDFA propagation and rate equations. The solution of these equations of two-level laser medium can be done numerically. In this paper, we are proposed a novel method to solve these equations. The reconstructed results are perfectly coincided the well known numerical results.
We present a theoretical formalism to describe the amplification of two monochromatic waves counter-propagating in a rare-earth-doped optical fiber amplifier. Interaction of the waves through a dynamical population inversion grating inscribed in the active fiber by the waves during their amplification results in a strong power transfer from one wave to another providing a preferable amplification of one wave at the expense of another. In this sense, the effect is similar to stimulated Brillouin scattering and is expected to be observed with both pumped and unpumped rare-earth-doped fibers possessing a finite polarizability difference between the excited and ground states.
The effect of homogeneous upconversion on the performance of an erbium-doped fiber amplifier (EDFA) is analyzed numerically, by means of a set of rate equations model. In particular, the influence of pump power, signal power, and Er/sup 3+/ concentration on the degradation, due to upconversion, is examined. Forward pumping is considered and amplified spontaneous emission, as well as scattering loss are taken into account. In addition, approximate analytical solutions, for the rate equations, which include the effect of the cooperative upconversion, are presented. It is shown that under the considered conditions, these analytical solutions provide a good approximation to the exact numerical solution and thus may be used for the design of such amplifiers.
A complete experimental and theoretical study of rare earth doped fiber-optic amplifiers for the first tele-communication window has been made. The thulium doped fluoride fiber amplifier is shown to provide amplification in the 800nm-820nm signal region. A complete steady state theoretical model has been presented and the model has been experimentally verified. The model predicts the gain, noise figure and the amplified spontaneous emission in the 800nm, 1470nm, 1900nm and 2300nm bands. The effect of population trapping at the sp3Fsb4\\sp3F\\sb4sp3Fsb4 energy level of thulium ion is also shown with the help of the model. It has been shown that about 5-15%o of the population is trapped at the sp3Fsb4\\sp3F\\sb4sp3Fsb4 energy level. We have also shown theoretically, the expected gain and noise performance of Thulium doped fluoride fiber amplifiers pumped in the 680nm absorption band. The maximum gain at 806nm is slightly lower than with comparable 780 nm pumping. The gain bandwidth is however found to increase with 680nm pumping. The higher ASE at shorter wavelengths ($<$806nm) reduces the gain at the peak wavelength (806nm). This is a result of the better inversion with three level pumping at 680nm as compared to two level resonant pumping at 780nm. We report an efficient single mode erbium doped flouride fiber amplifier in the 850nm signal band for the first time. The amplification is through an up-conversion process. The erbium doped flouride fiber amplifier was pumped with an estimated pump power of 35mW at 792nm. We have also considered a theoretical model for a single mode erbium doped fluoride fiber amplifier. Efficient amplification occurs because of the strong excited state absorption at the pump wavelength from the sp4Isb13/2\\sp4I\\sb{13/2}sp4Isb13/2 energy level.
Doping a part of the optical fiber core by (Er3+ ) ions in presence of external pumping power will lead to form the erbium-doped fiber amplifier (EDFA).The performance of this optical amplifier depends on (the power and the wavelength of the pumping laser, the power and wavelength of the input signal, amplifier length, ion concentration). These parameters will affect the characteristics of EDFA such as amplifier gain, gain saturation, noise figure and output power. However, these characteristics can be determined by solving the EDFA propagation and rate equations. The solution of these equations of two-level laser medium can be done numerically. In this paper, we are proposed a novel method to solve these equations. The reconstructed results are perfectly coincided the well known numerical results.