Measurement and analysis of pump-dependent refractive index and dispersion effects in erbium-doped fiber amplifiers

In a doped fiber, at wavelengths close to an absorption, the refractive index, and hence the dispersion, is expected to be a strong function of wavelength, as described by the Kramers-Kronig relationship. Furthermore, this spectral variation itself will be a function of pumping. This paper describes an accurate and sensitive experimental determination of the pump dependence of the refractive index in an erbium-doped fiber amplifier. A Mach-Zehnder interferometric measurement is described where only one arm is comprised of doped fiber. Particular attention is paid to accounting for the significant difference in power levels in the two arms and the effects of polarization and incoherent light. The measured refractive-index change matches well with that theoretically predicted. The pumped and unpumped dispersion of the amplifier are calculated. While the extra dispersion is of similar magnitude to that of silica fiber, the impact on long telecommunications systems is likely to be negligible. However, this extra dispersion may be important in shorter systems such as soliton lasers. Given the good agreement between theory and experiment, the variation of dispersion with fractional inversion is calculated from absorption and gain measurements. The presence of codopants is known to alter the absorption and emission spectra; the effect on the dispersion is calculated, and a near linear dependence on germanium concentration is observed.