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Journal of the Optical Society of America B

Resonance-enhanced refractive index and its dynamics in rare-earth-doped fibers

Yan Xue, P. L. Chu, Weiping Zhang

Published Oct 1, 1993• 16 citations
Publisher

Abstract

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.

DOI
10.1364/josab.10.001840

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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.
A novel measurement system provides determination of pump induced phase shifts in erbium doped fibers with an accuracy of /spl sim//spl pi//20. Using this system, a systematical analysis of the pump induced modulation of the refractive index and dispersions for a signal at 1550 nm and a pump at 980 nm is reported. The analysis contains measurements of pump induced refractive index changes as function of wavelength, pump power, and doping concentration. A model taking account of the contribution to the refractive index changes from optical transitions between /sup 4/I/sub 15/2/ states and /sup 4/I/sub 13/2/ states in Er/sup 3+/ yields good agreement to experimental results apart from a wavelength independent offset. The offset is interpreted to originate from high energetic optical transitions. The results show that for a large refractive index modulation, a short and highly doped fiber should be used with limited amplified spontaneous emission effect. In optical communication systems comprising erbium doped fiber amplifiers, a tradeoff between dispersion and amplification must be made.
Resonance properties of the all-fiber ring cavity filled with nonlinear material - saturable rare-earth-doped fiber are analyzed and experimentally investigated. Unlike the earlier investigated erbium-doped fiber at 1550nm where the optical absorption photo-induced change (saturation) is observed only, the ytterbium-doped fiber at 1064nm demonstrates the saturation of the refractive index mainly. For this configuration we report experimental observation of the optical bistability and hysteresis in the transmitted output light at the 10mW-scale incident light power. The experimental results are in qualitative agreement with the theoretical analysis that takes into account the saturation of both parameters: the optical absorption and the refractive index of the doped fiber. The reported results seem promising for applications in high-sensitivity interferometric configurations at 1064nm operation wavelength.
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.
We quantify the refractive index changes (RIC) in single-mode ytterbium-doped optical fibers induced by optical pulses at 980 nm and, for the first time, report details of the effect dynamics. The RIC dynamics is shown to follow that of the population of the excited/unexcited ion states with a factor proportional to their polarizability difference (PD). The absolute PD value is evaluated in the spectral range of 1460-1620 nm for different fiber samples and is found to be independent on the fiber geometry and on the ion concentration. The PD dispersion profile indicates to a predominant far-resonance UV rather than near-resonant IR transitions contribution to the RIC.
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.