We report on the thermal treatment of photodarkened Yb-doped fiber samples. The method of non-isothermal bleaching at different temperature ramp rates can be used to determine the thermal energy distribution of photodarkening induced color centers. A distributed activation energy with a mean value of about 1.3 eV and a FWHM of 0.5 eV was found. Spectral changes during thermal treatment were observed and could be interpreted, e.g. as an enhancement of the absorption cross section.
© 2009 OSA
Photodarkening (PD) in Yb-doped fibers is a main limiting factor for the long-term stability of fiber lasers and amplifiers. The origin of this pump-induced loss mechanism is still under discussion. But it is well-known that PD strongly depends on the chemical composition of the active core material . Different mechanisms are discussed to be responsible for the formation of the assumed color centers, e.g. oxygen deficiency centers  and a charge transfer process . To characterize PD, various methods have been suggested, especially acceleration of the process and standardization of the measurement technique on short fiber samples . An important aspect of these measurement techniques is the pumping concept. Cladding-pumping is proposed to characterize PD at different Yb inversion levels, which significantly depend on the pump power and the pump wavelength. This technique is also suitable to LMA fibers. Core-pumping with sufficient power delivers a saturated inversion level, which is only dependent on the pump wavelength and hence improves the repeatability of PD measurements at a defined fiber type .
Several methods for complete or partial bleaching of PD are known. One possibility is optical bleaching, which has already been presented at wavelengths ranging from the ultraviolet (UV)  up to the visible (VIS) range . Another important mechanism is the thermal bleaching. Jasapara et al.  demonstrated the complete removal of PD loss, heating up a pre-darkened Yb fiber to 773 K, by spectral investigations. Shubin et al.  observed thermal bleaching between 573 and 673 K. Moreover, it was shown by experiments at room temperature that the pump-induced PD itself is a relaxation process leading to an equilibrium between generation and annihilation of color centers . An isothermal method to determine the energy distribution of optically induced color centers based on the thermally induced decay of fiber Bragg gratings was presented by Erdogan et al. . Using this isothermal approach Söderlund et al.  recently published a thermal binding energy of 1.28 eV for PD-induced color centers in Yb-doped fibers.
In this work we investigate the non-isothermal bleaching of pre-induced color centers by temporal and spectral measurements. The results will contribute to the understanding of the PD process and deliver a distribution of the thermal activation energy of induced color centers.
Our experimental setup can be used for the measurement of PD and the thermal bleaching of photodarkened fibers at different temperature ramp rates (non-isothermal bleaching). For this purpose, the transmission of probe light is measured temporally at 633 nm or spectrally at different times in the course of pumping or heating treatment. The combined setup is shown in Fig. 1 ; the single-clad fiber (SCF) connections of the type SMF-28 are marked as solid lines for the spectral analysis and as dashed lines for the temporal measurements. A commercial single mode pump diode stabilized by a fiber Bragg grating at 975 nm with an output power of 250 mW is used to perform core-pumping of the Yb fibers under test. The probe light is delivered by a stabilized halogen lamp. The fiber under test is fed through a tube furnace with a protecting glass pipe and can be heated up in a controlled regime. A thermoelectric sensor is set next to the fiber sample to measure its ambient air temperature.
All data are recorded by means of a data logger. For the temporal measurements, the transmission of probe light around 633 nm (spectral width 25 nm) is analyzed with a lock-in amplifier technique which has already been presented in  for cladding-pumping experiments. For spectral measurements, the halogen lamp spectrum is used as probe light suppressing the UV light below 350 nm by an edge filter to avoid optical annealing. The transmission spectra are taken by an optical spectrum analyzer (OSA).
All experiments have been performed independently at 1 to 2 cm short, pristine samples of a fiber with a 10 µm Yb-doped core and 125 µm cladding diameter. The fiber was fabricated by MCVD (Modified Chemical Vapor Deposition) and solution doping. The dopant concentrations of the fiber core are 0.6 mol% Yb2O3, 3.9 mol% Al2O3 and 0.6 mol% P2O5. All fibers located within the tube furnace were uncoated to avoid burning off.
For the experiments on thermal bleaching, a fiber sample was pre-darkened by pumping in a water bath to ensure room temperature. After reaching the PD saturation, the pump light was switched off and the fiber sample was heated up with a selected temperature ramp rate and the probe light was measured until the transmission value before PD was restored. The temporal experiments have been accompanied by spectral measurements.
It is known from earlier investigations on the used fiber type , that the PD loss in the mentioned state is stable at least during several days. Therefore, a change of the number of PD color centers near room temperature was not expected. However, from the measurement at 633 nm we found an increase of the PD loss up to a temperature of about 470 K depending on the temperature ramp rate (Fig. 3(a) ). A similar heat-induced loss enhancement has also been described in [12,13]. Further heating results in a drop of loss until the level of the un-darkened (pristine) fiber is completely restored up to 770 K. The maximum loss value and its corresponding temperature as well as the temperature of complete bleaching are influenced by the selected ramp rate (Fig. 3(a)). Experiments on a new un-darkened fiber delivered no change of loss during heating and ensure that PD induced color centers are responsible for the effects discussed in this paper.
In order to get a deeper insight in the phenomenon, we have repeated the thermal bleaching experiment taking transmission spectra at different temperatures. The PD loss spectra in Fig. 2 were calculated with regard to the spectrum of the pristine fiber. By enhancing the temperature, the spectral loss is reduced at short wavelengths, but at longer wavelengths the loss spectra cross the spectrum observed for room temperature. The results of the temporal and spectral measurement show a good agreement in regard to the probe wavelength of 633 nm.
To model the bleaching process, we denote the proportion of non-bleached color centers by p(T), with 0 ≤ p ≤ 1. The temperature T is a linear function of time t. The loss enhancement at the probe wavelength (Fig. 3(a)) indicates a superposition of bleaching and other processes, e.g. the change of the absorption cross section of the color centers or the formation of additional color centers due to the increase of temperature. These processes are under discussion  and a theoretical description is not yet available. Therefore, we use an empirical approach to determine p from the PD loss α:
(a) We suppose a multiplicative superposition of bleaching and other processes
(b) The known long term stability of the PD loss near room temperature and the negligible effect of bleaching at low temperatures in Fig. 3(a) suggest p(T < 400 K) ≈1. In this range Eq. (1) yields α = f(T). The factor f is nearly independent on the ramp rate (there are some deviations at the beginning of the annealing process and small level differences due to the measurement error of the sample length). The linear behavior of f(T) can be approved up to 440 K (see ramp rate r = 20 K/min) and expressed by a linear function of T ().
(c) We assume that the linear behavior of f(T) extends to higher temperatures, and note that in our discussion this factor has the most important influence at the beginning of the bleaching process (from 400 to 550 K). Taking this into account, Eq. (1) yields the proportion of non-bleached color centers p(T) as shown in Fig. 3(b).
To obtain information on the thermal activation energy, we model the bleaching of the color centers at a constant ramp rate r by a simple kinetic model. The time and temperature dependent decrease of p(T) follows the rate equationFig. 3(b). In Eq. (2), we assumed a first order reaction, but the result (Eq. (3)) holds also for higher order reactions.
In Fig. 4 , activation energies were calculated using three different combinations of p(T), measured at different ramp rates r: (A) 10 K/min and 20 K/min, (B) 5 K/min and 15 K/min, (C) 5 K/min and 20 K/min. The results show a broad distribution of activation energies similar to a Gaussian cumulative distribution function. Therefore, we tried a least squares fit using the model function:Fig. 4). The resulting fit parameters a and b are 1.03 eV and 0.20 eV for (A), 1.35 eV and 0.22 eV for (B) and 1.27 eV and 0.24 eV for (C), respectively. The corresponding Gaussian distributions can be visualized by their probability density functions σ(E A), shown in Fig. 5(a) . The broadness of the symmetrical energy distributions is nearly equal for the three combinations of p(T). The deviations of the average activation energies are caused by measurement errors, primarily by the error of the temperature difference ΔT = T 2 – T 1 in Eq. (3). An estimation of the relative error δE A/E A with T 2 ≈T 1 and (dp/dT)1 ≈(dp/dT)2 yields:Fig. 4 and 5(a): The most sensitive combination of ramp rates is (A), because the relative factor of their rates is only two. The case of (B) with a relative factor of three is better suited, but the best combination to determine the activation energy distribution is case (C), whose resulting distribution is placed between the others. In the case of (C) the Gaussian fit shown in Fig. 5(a) delivers a mean value of 1.27 eV and a FWHM of 0.47 eV.
In analogy to Eq. (3), but restricted to the first order reaction Eq. (2), we have also calculated the pre-exponential factor k 0 for the case (C). It is not constant but varies remarkably during the bleaching process between 107 to 1010 Hz (Fig. 5(b)). It should be noted that the pre-exponential factor – in contrast to the activation energy – depends on the assumed concentration function of the reaction rate, i.e. the reaction order.
We have presented a useful method to determine the thermal activation energy of PD induced color centers in Yb-doped fibers. In our bleaching experiments at fibers, which have been photodarkened at room temperature, we observed complete thermal annealing of the induced PD loss in the temperature range up to 770 K similar to previously published measurements [7,8]. But additionally, we could show that the thermal progression of the annealing process is accompanied by spectral changes. An enhancement of the PD loss at the used probe wavelength of 633 nm in the temperature range up to 470 K was recovered, and the whole loss spectrum shows thermal broadening as it has also been described in . At higher temperatures, the relative shape of the spectrum remains unchanged. Thus, we can use the method of non-isothermal bleaching measuring at one selected wavelength ensuring the consistence to other probe wavelengths. Differences of the above mentioned temperatures with respect to  could partially be reasoned by much larger ramp rates used there, but also by the special composition of the fiber investigated in  that is unknown.
On the basis of our bleaching experiments at different temperature ramp rates, we determined the thermal activation energy distribution in the framework of a kinetic model. This distribution is relatively broad and can be well fitted by a Gaussian distribution, which delivers a mean value at 1.3 eV and a FWHM of 0.5 eV. These values are very similar to the results obtained by an isothermal measuring method described in . The pre-exponential factor k0 in the range of 107 to 1010 Hz was determined with the assumption of a first order reaction. A more detailed investigation of the reaction mechanism, however, in combination with a microscopic model of the bleaching process, is beyond the scope of this paper.
Whereas the photodarkening process in Yb doped samples requires an energetic activation by 5 to 6 eV (UV photons  or 4 to 5 excited Yb ions ), thermal annealing is generally possible at even lower activation energies around 1.3 eV.
References and links
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