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Journal of Optical Communications

Investigation of Transient Response of Erbium-doped Fiber Lasers by Semi-classical Theory

A. R. Bahrampour, M. Mahjoei, P. Jamali

Published Jan 1, 2007• 0 citations
Publisher

Abstract

The transient response of all optical gain clamped multi channel erbium doped fiber amplifiers (EDFA's) and optical fiber inverter is studied by a semi-classical model. Using the semi-classical theory, the electric field interacting with mater is considered classical and the medium is quantized according to the equations of motion for density matrix. The rate equations and self consistency equations, which yield amplitude and phase of the electric fields of oscillator and amplifying channels are derived by considering Maxwell's equations and equation of motion of density matrix. The governing equations form a system of coupled partial differential equations. The relaxation oscillation behavior of stabilized multi channels erbium doped fiber amplifier and transient time response of an optical fiber inverter are simulated by the numerical solution of this system. The theoretical findings are in a good agreement with the previous experimental results that are reported.

DOI
10.1515/joc.2007.28.4.248

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The transient response of all optical gain clamped multi channel erbium doped fiber amplifiers (EDFA's) and optical fiber inverter is studied by a semi-classical model. Using the semi-classical theory, the electric field interacting with mater is considered classical and the medium is quantized according to the equations of motion for density matrix. The rate equations and self consistency equations, which yield amplitude and phase of the electric fields of oscillator and amplifying channels are derived by considering Maxwell's equations and equation of motion of density matrix. The governing equations form a system of coupled partial differential equations. The relaxation oscillation behavior of stabilized multi channels erbium doped fiber amplifier and transient time response of an optical fiber inverter are simulated by the numerical solution of this system. The theoretical findings are in a good agreement with the previous experimental results that are reported.
"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.
The time-frequency characteristics of the transient response of dynamic gratings in erbium-doped fiber are different from stable gratings, which make it has great application value in the fields of fiber laser and optical fiber sensing. In consideration of the time domain characteristics, a time domain response model was built, which was based on metastable Er3+ population rate equation and light field transmission equation. The model simulated the process of establishing dynamic gratings in erbium-doped fiber with time sequence. And the theoretical results showed that the formation time of the dynamic grating gets shorter with higher pump power and shorter Erbium-doped fiber length within the effective length limits, which was consistent with the experimental results obtained by the so called “Strong light and weak light alternation” method except that the measured formation time decay ranges obviously migrated to lower pump power relative to the theoretical results. In consideration of the frequency domain characteristics, the transient two-wave mixing process was approximately simulated by using four-wave mixing equation. The transient reflectance spectra obtained through numerical calculation reflected the evolution rule of the dynamic gratings, which were coincident with the experimental results gotten by the rapid optical frequency modulation method. Under the condition of 1.8m Erbium-doped fiber, the experimental results showed that the turning saturated pump light power from the absorption type dynamic gratings to the gain type ones is about 0.05mW, the maximum relative reflectance variation of the gain dynamic gratings (3%) is 3 times of the absorption types. The measurement results have important references to the practical application of Erbium-doped fiber dynamic gratings.
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.