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Applied Physics Letters

Role of excited-impurity quasiparticles for amplification of radiation in an erbium-doped glass fiber amplifier

Karl Friedrich Renk

Published Mar 29, 2010• 1 citation
Publisher

Abstract

In this paper, I will show that excited-impurity quasiparticles may play an essential role for the amplification of radiation in an erbium-doped glass fiber amplifier. A quasiparticle consists of an excited state of an erbium ion interacting with other erbium ions and with the thermal bath via phonon-assisted energy transfer processes. The quasiparticles populate energy levels of a quasiband. Fermi’s statistics determines the average occupation numbers of the levels. The quasiparticle model leads to an analytical expression for the gain coefficient of an erbium-doped glass fiber amplifier, or generally, of a fiber amplifier or fiber laser.

DOI
10.1063/1.3372630

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Journal of the Optical Society of America B•Aug 1, 2005•4 citations
In this paper, I will show that excited-impurity quasiparticles may play an essential role for the amplification of radiation in an erbium-doped glass fiber amplifier. A quasiparticle consists of an excited state of an erbium ion interacting with other erbium ions and with the thermal bath via phonon-assisted energy transfer processes. The quasiparticles populate energy levels of a quasiband. Fermi’s statistics determines the average occupation numbers of the levels. The quasiparticle model leads to an analytical expression for the gain coefficient of an erbium-doped glass fiber amplifier, or generally, of a fiber amplifier or fiber laser.
"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.
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.
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.
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.>
A study on the dynamics of gain spectral hole burning (GSHB) in a silica-based erbium-doped fiber amplifier at 77 K was performed. When a saturation signal was input into an Er3+-doped fiber, a multigain spectral hole structure that consisted of nine gain spectral holes, was observed in the wavelength region from 1510 to 1640 nm at 77 K. As for the Er3+ ion concentration dependence of these gain spectral holes, the depth of the gain spectral hole at around 1530 nm was found to become shallower in the silica-based erbium-doped fiber that had higher Er3+ ion content. This Er3+ ion concentration dependence of the gain spectral hole depth suggests that the contribution of the energy-transfer interaction between Er3+ ions excited to the Stark levels within the ^4 I_13/2 manifold plays an important role in the gain spectral hole formation at 77 K. As far as we know, this is the first report of the Er3+ ion concentration effect on the GSHB in the Er3+-doped fiber. The dynamics of GSHB is discussed in relation to the effect of energy transfer between Er3+ ions. In addition, the relation between gain spectral hole structure and the Stark energy structure of Er3+ ion is also discussed.