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Optics Express

Gain dynamics and refractive index changes in fiber amplifiers: a frequency domain approach

Henrik Tünnermann, Jörg Neumann, Dietmar Kracht, Peter W. Wessels

Published Jun 1, 2012• 71 citations
Publisher

Abstract

Gain dynamics and refractive index changes in fiber amplifiers are important in many areas. For example, the knowledge of the frequency responses for seed and pump power modulation are required to actively stabilize low noise fiber amplifiers. Slow and fast light via coherent population oscillations rely on the change of group index to delay or advance pulses, and refractive index changes in fiber amplifiers are a possible explanation for mode fluctuations in high power fiber amplifiers. Here, we analyze the frequency dependent influence of seed and pump power modulation on the fiber amplifier output power and the refractive index. We explain the observed power and refractive index modulation with an analytic model originally developed for telecom amplifiers and discuss a further simplification of the model.

DOI
10.1364/oe.20.013539

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IEEE Photonics Technology Letters•Sep 1, 1997•3 citations
Gain dynamics and refractive index changes in fiber amplifiers are important in many areas. For example, the knowledge of the frequency responses for seed and pump power modulation are required to actively stabilize low noise fiber amplifiers. Slow and fast light via coherent population oscillations rely on the change of group index to delay or advance pulses, and refractive index changes in fiber amplifiers are a possible explanation for mode fluctuations in high power fiber amplifiers. Here, we analyze the frequency dependent influence of seed and pump power modulation on the fiber amplifier output power and the refractive index. We explain the observed power and refractive index modulation with an analytic model originally developed for telecom amplifiers and discuss a further simplification of the model.
This paper reports the measurement and analysis of signal power-induced changes in the refractive index spectrum of an aluminosilicate erbium-doped fiber amplifier (EDFA). For a constant 980 nm pump power of 11 mW, a 1553 nm signal power of 4.6 mW caused a peak-to-trough change in refractive index of (3.8/spl plusmn/0.4)/spl times/10/sup -8/ across the EDFA gain spectrum. A Kramers-Kronig transform of the signal-induced change in absorption coefficient agreed well with the measured change in refractive index. This result conflicts with the behavior of the system predicted by a homogeneously broadened two-level model and suggests limitations in the representation of the Er/sup 3+/:glass system by a discrete set of homogeneously broadened transitions.
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.
We present a theory that enables us to account for the pump-induced change of refractive index in a rare-earth-doped fiber. Experimental results carried out on an erbium-doped fiber with cw pump and cw signal operation confirm the accuracy of this theory at the steady state. Both theoretical and experimental results show that significant index changes can be obtained for the order of 1–2 mW of cw optical pump or signal power. In addition we studied the transient dynamics of the resonance-enhanced refractive index in a wide range of pulse widths from millisecond to tens of femtoseconds. The result shows that a fast response of refractive-index changes is achievable since the effects of spontaneous emission and nonradiative decay are negligible in the short-pulse case.
The slow light effect in SOAs has many applications in microwave photonics such as phase shifting and filtering. Models are needed to predict slow light in SOAs and its dependence on the bias current, optical power and modulation index. In this paper we predict the slow light characteristics of a tensile-strained SOA by using a detailed time-domain model. The model includes full band-structure based calculations of the material gain, bimolecular recombination and spontaneous emission, a carrier density rate equation and travelling wave equations for the input signal and amplified spontaneous emission. The slow light effect is caused by coherent population oscillations, whereby beating between the spectral components of an amplitude modulated lightwave causes carrier density oscillations at the beat frequency, leading to changes in the group velocity. The resulting beat signal at the SOA output after photodetection, is phase shifted relative to the SOA input beat signal. The phase shift can be adjusted by controlling the optical power and bias current. However the beat signal gain is low at low frequencies, leading to a poor beat signal output signal-to-noise ratio. If the optical input and SOA drive current are simultaneously modulated, this leads to forced population oscillations that greatly enhance the low frequency beat signal gain. The model is used to determine the improvement in gain and phase response and its dependency on the optical power, bias current and modulation index. Model predictions show good agreement with experimental trends reported in the literature.
Frontiers in Guided Wave Optics and Optoelectronics 210 enable those who are not expert in the field to appreciate the subject of the research.We give a clear physical insight into the electronic and thermal RIC mechanisms, and present important estimations helping the reader to clearly understand the scientific context, motivation and aims of this work.The main body of the work is centered around two experimental studies (Fotiadi et al., 2008c; Fotiadi et al., 2009c), reproduced in parts 3 and 4. Part 3 is dedicated to the fundamental properties of the Yb-doped fibers sensitive to the diode pumping at 980 nm.In this part we show our original RIC experiments performed with different samples of aluminum-silicate fibers and report on the dynamical characteristics of the RIC effect measured in the spectral range 1460 -1620 nm.Detailed analysis of these experimental data has brought us to the conclusion that the process is predetermining by the electronic RIC mechanism that can be quantitatively described by a two-level population inversion model with the polarizability difference (PD) of the Yb-ion in the excited and ground states as the only material model parameter determined from the experimental data.The absolute PD value measured in the experiment is found to be independent on the testing wavelength and the fiber specification parameters, i.e. the cross-section profile, the size, the length and the Yb-ion concentration.Our results ensure a predominant contribution to the RIC effect from far-resonance UV electronic transitions rather than near-resonant IR transitions.Part 4 of the Chapter focuses on potential applications of the RIC effect in advanced fiber laser systems implemented through our original concept of all-fiber coherent beam combining.The concept employs Yb-doped fibers as optically controllable phase shifters to be conjugated with Er-doped fiber amplifiers operating at ~1.55 µm.The coherent combining of 500-mW Er-doped amplifiers successfully demonstrated in our experiment confirms the validity of the concept.The performance characteristics of the multichannel fiber laser system associated with the proposed power scaling method are also under discussion. RICs in Yb-doped optical fibers: the origins and fundamentalsIn this part we summarize fundamentals of the electronic and thermal mechanisms of the refractive index changes (RIC) in single-mode ytterbium-doped optical fibers induced by optical pulses at 980 nm and we report the general equations describing RIC evolution.In particular, the electronic RIC dynamics is shown to follow the dynamics of the population of the excited/unexcited ion states with a factor proportional to their polarizability difference (PD).The thermal contribution to the RICs induced in standard Yb-doped fibers is shown to be negligible under condition of all-fiber low-power experiments discussed in the Chapter. Electronic and thermal RIC mechanisms caused by nonlinear pump absorptionYtterbium-doped silicate glass fibers are widely used for high-power, high-beam-quality laser sources due to their impressing gain efficiency, single transverse mode quality, relaxed thermal management problems, and overall robustness to environmental disturbances.Resulting from the confined mode structure and typically long propagation distances, nonlinear phenomena such as stimulated Brillouin scattering, stimulated Raman scattering, optical Kerr effect, inter-mode four-wave mixing, soliton and supercontinuum generation are observed in fiber lasers at relatively low power due to the high field intensity in the fiber www.intechopen.comResonantly Induced Refractive Index Changes in
Presents an analytical model which describes the dynamics of the modulation instability in a nonlinear, dispersive, homogeneously broadened and nonsaturable fiber amplifiers. The general case of arbitrary detuning between the laser frequency and the resonance frequency and arbitrary bandwidth of the amplifying transition is treated. The model accounts both for the gain dispersion and for the gain-induced, near resonant refractive index dispersion, Simple closed form expressions for the combined gain coefficients of the Stokes and anti-Stokes frequencies are obtained.