| Summary: | In this thesis the theory of operation of single-mode erbium-doped fiber amplifiers
pumped at 980 nm is described. Details of the derivation of the general rate equation for the
propagation of signal, pump, and amplified spontaneous emission are provided. Based on this
equation, and McCumber's theory of phonon-terminated optical masers, two closed form
expressions are derived. In one of them, the fluorescence spectrum of an erbium-doped fiber is
related to its spectral absorption coefficient. Based on this expression, a rigorous basis for the
assessment of the applicability of McCumber's theory to the study of [sup 4]I[sub 13/2] ⇔ [sup 4]I[sub 15/2] transitions
in erbium-doped fibers has been established. For the cases of five silica-based erbiumdoped
fibers, experiments were performed and the results were used to validate this expression.
Another important benefit of this expression is that it does not require a measurement of
silica-based fiber's fluorescence spectrum, as it can be simply calculated from the spectral
absorption coefficient, simplifying fiber characterization. The other closed form expression,
provides a simple means for calculating absorption and emission cross-sections of erbiumdoped
fibers using the easily measured spectral absorption coefficient, the gain coefficient at
one particular wavelength, and the fluorescence lifetime. Also, based on this expression, an
analytical method for the simple determination of the erbium ion concentration inside the fiber
core is proposed.
Experiments were performed to evaluate the cross-sections of an erbium-doped fiber over
the wavelength range 1400-1650 nm. To check the accuracy of the calculated cross-sections,saturation powers at the wavelengths 1530 nm and 1550 nm were measured and results compared
with the ones calculated from the cross-sections, obtaining agreements within 6%.
Problems and difficulties associated with the conventional techniques for the measurement
of the spectral fluorescence and of the fluorescence lifetime are described. Also new experimental
setups were designed to simplify the measurement of these parameters. Furthermore,
experimental techniques for the measurement of other fiber parameters such as, spectral
absorption coefficient, gain coefficient, and signal saturation power are described.
The new theoretical and experimental techniques presented in this thesis can provide a
much simpler and more accurate means for characterizing erbium-doped fibers, improving the
accuracy of the numerical models commonly used for modeling erbium-doped fiber amplifiers.
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