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IEEE Journal of Quantum Electronics

A numerical model for the complex susceptibility of saturated erbium-doped amplifiers

Kamal Alameh, Robert A. Minasian

Published May 1, 1997• 7 citations
Publisher

Abstract

A detailed model for the complex susceptibility behavior of erbium-doped amplifiers, which applies in the saturation regime of operation, is presented. The model takes into account the effective individual laser transitions between the upper and lower manifolds. The model is based on a curve fitting algorithm that fits the emission and absorption cross section with Voigt lineshapes, which correspond to the effects of both homogeneous and inhomogeneous line broadenings. Experimental measurements show that the model accurately predicts the susceptibility in the saturation regime. The sensitivity of the model susceptibility predictions to the Stark-split energy level data is shown to be minor, as long as the number of transition wavelengths used is high. Results show the full spectral behavior of the complex susceptibility of an integrated optical erbium-doped amplifier in the saturation regime and show that signal-induced changes in refractive index of up to around 1.6/spl times/10/sup -6/ can be obtained with a few milliwatts of signal change by driving the amplifier into saturation.

DOI
10.1109/3.572161

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A detailed model for the complex susceptibility behavior of erbium-doped amplifiers, which applies in the saturation regime of operation, is presented. The model takes into account the effective individual laser transitions between the upper and lower manifolds. The model is based on a curve fitting algorithm that fits the emission and absorption cross section with Voigt lineshapes, which correspond to the effects of both homogeneous and inhomogeneous line broadenings. Experimental measurements show that the model accurately predicts the susceptibility in the saturation regime. The sensitivity of the model susceptibility predictions to the Stark-split energy level data is shown to be minor, as long as the number of transition wavelengths used is high. Results show the full spectral behavior of the complex susceptibility of an integrated optical erbium-doped amplifier in the saturation regime and show that signal-induced changes in refractive index of up to around 1.6/spl times/10/sup -6/ can be obtained with a few milliwatts of signal change by driving the amplifier into saturation.
A study of the complex atomic susceptibility of erbium-doped fiber amplifiers operating near the 1.53- mu m transition (/sup 4/I/sub 13/2/-/sup 4/I/sub 15/2/) developed from a semiclassical theoretical description is presented. Expressions for the emission cross section sigma /sub e/( lambda ) and absorption cross section sigma /sub a/( lambda ) of erbium:glass as a quasi-three-level laser system with Stark-split sublevel manifolds are derived. The results are used to calculate the cross sections of aluminosilicate erbium-doped fibers at low temperatures (T=4.2, 77 K) and at room temperature. It is demonstrated that an expression for the gain coefficient of the fiber amplifier can be derived from the expression of the susceptibility. Using Kramers-Kronig relations, an expression for the refractive index change in the fiber is derived. The theoretical spectral gain profile of the fiber amplifier and concurrent refractive index changes are analyzed for different pumping regimes.>
A basic understanding of the susceptibility of fiber amplifiers (SOFA) is required to undertake device optimization, e.g., for uses in optical communications systems. In recent work Desurvire1 has developed a semiclassical treatment of the SOFA for erbium-doped fiber amplifiers (EDFAs) taking account of the Stark splitting of the energy levels in the Er-doped glass. That work, which utilized the standard Kramers-Kronig relationships, was applicable to the unsaturated regime of operation. In this contribution, generalized Kramers-Kronig relations2 are utilized to obtain analytical expressions for the SOFA valid even in the saturation regime. It is then shown how, given experimentally measurable absorption cross-sections, the SOFA may be calculated in any operating conditions. In this way gain and refractive-index changes occurring in EDFAs may be deduced, again having universal validity.
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.
Rapid development of optical fiber amplifiers, and more especially of the erbium-doped fiber amplifiers (EDFA) during the last decade, has benefited from extensive work on the configuration of the system itself: determination of pump wavelength, pumping configuration, improvement of noise performance, etc. However, less effort have been dedicated to study the interaction that influences the spectral profile of the gain bandwidth and particularly the relation between the glass composition and the spectroscopy of erbium. Here, we report a systematic determination of key parameters responsible for the global profile of the gain bandwidth: stark splitting, homogeneous broadening, and inhomogeneous broadening. The correlation between these parameters and the glass structure from one part and the behavior of the EDFA in amplification regime from another part is discussed. The quasiregular crystal-field splitting of tellurite and fluoride glasses is found to correlate well with the flatness of the gain profile. Moreover, the low-temperature homogeneous bandwidths extrapolated to room temperature can be correlated to the saturation spectral hole widths measured in the amplification regime.
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.