High concentration erbium amplifiers

Recently, much research and development has been devoted to the design of an efficient and short-length erbium-doped fiber amplifier (EDFA) with a high doping concentration of erbium ions 10²⁰ –10 ²¹ cm ⁻³ . Increased erbium concentration leads to degraded amplifier performance owing to migration-assisted up-conversion processes. To characterize the performance of a high concentration EDFA, models accounting for the upconversion of excitation on homogeneously distributed (homogeneous upconversion, or HUC) and clustered erbium ions (pair-induced quenching, or PIQ) have been exploited.

However, a detailed microscopic study of erbium-doped glasses by means of x-ray absorption fine structure spectroscopy has found no evidence of short-range pair clustering of Er³⁺ ions. Therefore more accurate physical models have to be used for fitting experimental results. Sergevev reported a model satisfying such criteria. Unlike HUC and PIQ models, this model takes into account only the variance in the distances between excited erbium ions. Averaging over the variance in the separations, we derived a system of macroscopic equations that was used successfully to fit experimental results for the EDFA’s gain as a function of the fiber length. However, the absence of some of the EDFA’s parameters, for example, emission and absorption cross sections, led to a lack of important theoretical results, for example, gain and noise figures as functions of signal power.

We have developed a complete model of the high-concentration EDFA accounting for the statistical nature of migration and upconversion processes and prove its reliability by fitting to published experimental data. We have shown that this statistical model exhibits better applicability for the characterization of high-concentration EDFAs than the model accounting for homogeneous upcon-version and PIQ.

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