EDF “M5” / Er3+ parameters used in modeling
Erbium-doped fiber lasers (EDFLs) are contemporary sources of coherent radiation, attractive for numerous applications requiring both continuous-wave (CW) and pulsed operations, among which telecommunications in a wide wavelength range covering C and L bands ought to be emphasized. Pulsed operation, presenting big interest for practice, is attained in EDFLs by means of standard active and passive Q-switching and mode-locking techniques, capable of enforcing a laser to generate short pulses with durations ranged from hundreds fs to hundreds ns . In the meantime, transients to CW lasing and a laser’s relaxation frequency are also of close attention, e.g. when targeting the sensor applications [2, 3]. The detailed knowledge of the processes involved in Erbium-doped fibers (EDFs) to be used, when pumped, as a laser or amplifying medium in each of the referred regimes cannot be overestimated. The present work is a review of some of the most featuring nonlinear-optical effects that affect the oscillation regimes of EDFLs.
In spite of certain advantages (availability at the market, low cost, and easiness of handling), EDFLs demonstrate considerably lower efficiency as compared to the lasers based on Ytterbium-doped fibers. The basic cause is the multi-level energy scheme of Er3+ ions, which makes unavoidable absorption of photons at both the pump and laser wavelengths by the ions being at upper Er3+ levels, i.e. the “excited-state absorption” (ESA) [4, 5], including the state where 1.5-μm laser transition stems from. In other words, ESA presents a kind of “up-conversion” (UC) loss inherent to EDF; see section 2.
Another, nonlinear in nature, source of UC loss in EDFs and EDFLs on their base relates to so-called “collective” (concentration-related) effects arising in Er3+ ion pairs and in more complicate clusters (percentage of which grows with Er3+ concentration) ; see section 3. Appearance of the latter phenomenon is also associated with the multi-level energy scheme of Er3+ ions. Eventually, the cases of low-and heavily-doped EDFs are to be carefully segregated and properly addressed if one looks for optimization of an EDFL.
One more kind of optical nonlinearity that arises in actively Q-switched (AQS) EDFLs is stimulated Brillouin scattering (SBS). Depending of the EDF length and Q-cell’s modulation frequency EDFLs may operate in one of the two QS regimes: either in the “conventional” QS (CQS) one in which QS pulses are composed of several sub-pulses separated by a photon’s round-trip time (with negligible pulse jitter) [7, 8], or in the essentially stochastic SBS-induced QS (SBS-QS) one where pulse amplitude is bigger by an order of value as compared with CQS but where pulses suffer severe jitter . The results of an experimental study of the basins the CQS and SBS-QS regimes belong to and the basic spectral features of these regimes are discussed in section 4.
In section 5, the review’s conclusions are formulated.
2. ESA in EDF at the pump and laser wavelengths
In this section, we report a study aiming at determination of the ESA’s spectral dependence in EDF, covering the most important for applications spectral range, 1.48...1.59 μm, and at ~978 nm, the wavelength that usually is used for pumping EDFs by laser diodes (LDs). In the experiments discussed hereafter a low-doped silica EDF (
Figure 1 shows the fife level Er3+ ion energy scheme upon excitation at the pump (
The equations that describe functioning of the Er3+ system, in accord to the scheme shown in Figure 1, at excitation at sole or at both excitation wavelengths (
|Low-signal absorption at 1531 nm (experimental data)||cm-1|
|Low-signal absorption at 977 nm (experimental data)||cm-1|
|Relaxation time for 4I13/2 → 4I15/2 transition ||ms|
|Relaxation time for 4I11/2 → 4I13/2 transition||μs|
|Relaxation time for 4I9/2 → 4I11/2 transition ||ns|
|Relaxation time for (4F7/2/2H11/2/4S3/2) → 4I9/2 transition ||μs|
|Cross-section of 4I15/2 → 4I13/2 transition @ 1531 nm ||cm2|
|Cross-section of 4I15/2 → 4I11/2 transition @ 977 nm ||cm2|
2.1. Spectral features of ESA in low-doped EDF within the 1.48 to 1.59-μm range
The first experiment serves to reveal the existence of the ESA process in the EDF at pumping through 4I15/2→4I13/2 transition, refer to Figure 1. The UC emission (UCE) spectra were recorded in the wavelengths range near 980 nm (4I11/2→4I15/2 transition). The pump source was a 12-mW narrow-line LD (
The second experiment, allowing us to reveal the spectral dependence of ESA, was arranged through measurement of the integral lateral emission power collected from the EDF’s lateral surface, using a Si photo-detector directly placed above the fiber. Given Si is sensitive from the visible to near-IR (Si band-gap wavelength is ∼1.1 μm), the Si photo-detector (PD) does register the UCE signal (centered at ∼980 nm) and does not the spontaneous emission (SE) from level 4I13/2 (∼1.5 μm); a scattered pump-light component was found to be extremely weak. The results obtained at various pump powers are shown in Figure 2(b) (see curves 1–3). For comparison, we also plot in this figure (by curve 4) the integrated backward UCE power measured using OSA (from a 10-cm EDF sample). It is seen that the spectral dependence of the UCE signal is similar to the one of ESA power on the excitation wavelength. In fact, the shape of the presented dependencies is established by a convolution of the known GSA and yet unknown ESA spectra of Er3+ (notice that the latter depends on Er3+ ions population inversion).
Considering the simplified Er3+ ion’s model and the processes involved at excitation at
Apparently, UCE power depends on
The method to find the absolute values of the ESA parameter
Note that the contribution of amplified SE (ASE) to the output spectra was as low as 0.1–1.9% respectively to the overall transmitted power, provided a short (50 cm) EDF piece has been used.
The results of fitting of the experimental EDF transmission curves within the interval 1.48...1.59 μm are shown in Figure 3(a) by asterisks (see right scale). It is evident that these results, as the ones regarding the UCE experiments, almost coincide. The solid curve shown in this figure is the best fit of the experimental data by the polynomial regression.
The knowledge of the
2.2. ESA in low-doped EDF at 977 nm
We report here the results of a study of the other ESA process, 4I11/2→4F7/2 (see Figure 1), which takes the place when EDF is excited simultaneously at the two GSA wavelengths:
The first experiment was focused on the demonstration of the presence of “pump-ESA”, when EDF is pumped simultaneously at
The UCE spectra, obtained using a 5-cm EDF sample, are shown in Figure 4(c). The spectra were recorded for three signal powers (0, 25, and 260 mW) while fixed pump power (260 mW). One can see from the figure that even low-power (25 mW) signal radiation tremendously enhances UCE (compare curves 1 and 2) and that at further increasing signal power, up to
Figure 5 shows the dependence of “green” UCE signal (transition “5”→”3”, see Figure 1), detected from the EDF, on powers of pump and signal radiations launched into the fiber (in this case, again, the pump power was kept fixed,
Since UCE power is proportional to population of the 5th level of Er3+ ions, the experimental data can be fitted well by a simulated curve of normalized population inversion
where the normalized populations
We found that the best way to find the ESA parameter at the pump wavelength,
Actually, the coefficient adjacent to
Figure 6 shows the EDF transmissions measured for three different EDF lengths along with the best fits obtained using equations (7) at varying
2.3. Effect of ESA in EDF upon efficiency of CW EDFL.
We discuss hereafter the results of a theoretical study of influence of ESA inherent in Er3+ ions upon efficiency of an EDFL assembled in the linear (Fabry-Perot) configuration. The laser setup we shall deal with at modeling is shown in Figure 7. The low-doped EDF discussed above was considered to be an active medium and two fiber Bragg Gratings (FBGs) – to form selective couplers of the cavity, both centered at
We imply (see Figure 7) that the pump wave at 977 nm (absorption peak of 4I15/2→4I11/2 transition, see Figure 1) propagates rightward while the laser waves – rightward (marked by "+" superscript) and leftward (marked by "–" superscript), respectively. In the scheme, FBG1 plays the role of a rear 100% reflector (reflection
The laser is simulated by applying the two contra-propagating laser waves' model discussed in details in  with taking into account Gaussian distributions of the laser and pump waves. In this model, the pump wave is described by equation (11) and the signal waves – by equation (12) with a small modification being that powers of the two contra-propagating signal waves are assumed to be governed by the equation:
In equation (13) the superscripts "
where the second term on the right side is the SE power generated by a short fiber section
The boundary conditions are written as:
The EDFL’s efficiency as a function of FBG2’s reflectivity
The first important observation is that the optimal reflection of output FBG2, at which EDFL demonstrates the maximal efficiency, is drastically decreased when the ESA transitions are accounted for. For instance, the optimal reflection of FBG2 is ≈66% when only the EDF background loss (3.1 dB/km, see Table 1) is present (curve 1), whereas it is ≈11% when all kinds of the ESA loss are accounted for (curve 4). The other important fact is that the range of FBG2’s reflections, in which the output laser power varies within 10% (with respect to its maximum value if all the ESA transitions are considered), is relatively broad: ~2.5% to ~34%. At the optimal FBG2’s reflectivity (R2=11%) the laser efficiency reaches ~34% (implying all fiber splices are made lossless).
The fractions of pump and signal photons spent on the ESA transitions with respect to the absorbed by EDF pump photons are shown in Figure 8(b). It is seen that the contribution of the signal ESA loss is bigger when FBG2’s reflection is bigger (curve 2). Furthermore, if reflection of the output coupler approaches 100%, the absorbed pump power is spent entirely on the ESA transitions (see curves 2 and 3) and no photons at the laser output are produced (see curve 1). At optimal FBG2’s reflectivity (≈11%), about 23% of absorbed pump photons are spent on ESA at the laser wavelength and about 9.5% on ESA at the pump wavelength. Note that the sum of the relative photon numbers, as can be revealed from curves 1, 2 and 3, is approximately equal to 1 in the whole range of FBG2’s reflections.
The reader is advised here to refer to  for comparison of the developed theory with some of the experimental data on laser efficiency of EDFLs based on the EDF of M-type with relatively high Er3+ concentrations.
Finally, we conclude that the ESA processes at the laser and pump wavelengths strongly affect an EDFL’s efficiency and output coupler’s optimal reflectivity, at which the laser output power is maximal.
3. Er3+ concentration effects in EDF
In this part, we shall discuss the Er3+ concentration effects in EDFs resulting in a reduced efficiency of EDF based lasers and amplifiers, which is associated with the phenomenon of Er3+ ions’ clustering that leads, in turn, to non-saturable absorption (NSA) through inhomogeneous up-conversion (IUC).
For our experiments we selected the most representative commercial EDFs fabricated through the MCVD and direct nanoparticle deposition (DND) processes; all the fibers under scope in this section are similar in the sense of Er3+ doped core’s chemical composition being the most common alumino-silicate glass (in the case of MCVD-EDFs with addition of germanium). The first series of the EDFs (MCVD-based, "M"-series) includes two fibers: M5-125-980 and M12-125-980 (
3.1. Absorption and fluorescence spectra
The EDFs’ absorption spectra are shown in Figure 9(a) where Er3+ transitions 4I15/2 → 4I11/2 (within a 940...1020 nm range with a peak at 978 nm) and 4I15/2 → 4I13/2 (within a 1400...1600 nm range with a peak at 1.53 μm) are featured. The spectra were obtained using a white light source with fiber output and OSA with 1-nm resolution. It is seen that the absorption spectra of the EDFs of both series have a very similar shape (given by similarity of core glass chemical compositions), differing only in intensity. The ratio of the peaks’ magnitudes at 1.53 μm and at 978 nm was measured to be equal to ∼1.6, for the M and L EDFs.
Figure 9(b) demonstrates the normalized fluorescence spectra for L fibers (to simplify the picture the spectra for M fibers are not shown), measured at the maximal pump power at 978 nm,
To understand the origin of UCE and the dependence of UC intensity upon Er3+ concentration in the EDFs, let’s refer to Figure 10 in which the scheme of Er3+ energy levels and a sketch of the processes involved at the excitation at
3.2. Fluorescence decay kinetics
Like at the fluorescence spectra’ measurements discussed above, the kinetics of near-IR fluorescence at ∼1.53 μm was detected using the lateral geometry. However, the pump light at 978 nm was in this case switched on / off by applying a rectangular modulation of LD current at Hz-repetition rate. The launched into the EDF samples pump power was varied between zero and ∼400 mW. The fluorescence signal was detected either using an InGaAs PD with a Si filter placed between the fiber and a multimode patch cord delivering fluorescence to PD (being so the measurements above ~1.1 μm where the use of Si filter allows cutting off the pump light’s spectral component), or using a fast Si-PD with no spectral filtering applied (being in fact the measurements below ~1.1 μm), placed directly above a slit segregating a portion of fluorescence from the EDF’s surface. To diminish ASE and re-absorption on the results, we used short (∼0.5 cm) EDF pieces.
Typical kinetics of the fluorescence signal, recorded after switching pump light at 978 nm off, are presented in Figure 11 for the heavier doped EDFs M12 (a) and L110 (b); the data were acquired using InGaAs-PD with Si filtering (transmission band above 1.1 μm). We don’t present here the results for other, lower doped, EDFs as these showed similar but less featured trends in the decay kinetics.
It is seen from Figure 11 that for these two EDFs fluorescence power, corresponding to 1.53-μm spectral band, is saturated (as is saturated GSA of Er3+ ions) yet at a few mW of pump power. However the key feature is deviation from the exponential law in the fluorescence kinetics in EDF L110 (see Figure 11(b)). A similar trend occurs but is less expressed in the rest of L and M fibers with lower Er3+ concentration; see e.g. Figure 11(a). Another fact deserving attention is the presence of a sharp drop in the fluorescence signal in fiber L110 at high pump powers, which happens after switching pump off (refer to curves 4–6 in Figure 11(b)). Such a feature is present but in a smaller degree also in fibers L40, L20, and M12 (having substantially lower Er3+ contents) and almost vanishes in fiber M5 (having the lowest Er3+ content). Note that similar fluorescence kinetics were observed in some of the earlier reports, see e.g. [4, 10].
Overview of the fluorescence decays for all the EDFs under scope is provided in Figure 12 (points). These data were obtained at maximal pump power,
As seen from Figure 12, 1.53-μm fluorescence decays get more and more deviated from the single exponential law when Er3+ concentration increases: The fibers with smaller contents of Er3+ ions (M5, M12, and L20) demonstrate decays nearly a single-exponent law whereas fibers L40 and L110 – the decays, apparently different from this law. These features, associated to the Er3+ concentration effect, can be addressed in terms of the IUC process – see Section 3.3 where the results of modeling of Er3+ fluorescence kinetics are presented. The modeling of the fluorescence kinetics allowed us to get, for each EDF, lifetime
Furthermore, Figure 13 demonstrates the results of the fluorescence kinetics’ measurements in the optical band below 1.1 μm within a short (tens of μs) interval just after switching pump light off, for EDFs M12 (a), L40 (b), and L110 (c). The measurements were fulfilled using Si-PD without optical filtering at
We suggest that the found feature stems from a partial excitation relaxation in Er3+ clusters since it is present in the heavier doped EDFs but almost vanishes in the lower doped ones. The magnitude of the short-living component is a function of Er3+ concentration (and therefore of
3.3. Nonlinear absorption coefficient
The nonlinear absorption coefficient of a rare-earth doped fiber (e.g. EDF) as a function of pump power
In the study to be reported hereafter, pump light was delivered to an EDF sample from the same LD operated at 978 nm (used in the measurements of fluorescence spectra and lifetimes); pump power was varied from ≈0.5 to 400 mW. We measured first the nonlinear transmission coefficient of the EDF sample with length
The results obtained by applying the drawn procedure are shown in Figure 14(a) by symbols. Coefficients
Firstly, the kinetics of near-IR (∼1.53 μm) fluorescence decays obtained for the entire set of the EDF samples were modeled, which allows us to find Er3+ fluorescence lifetimes
For the normalized population density of single (index “s”) Er3+ ions being in the first excited (laser) state 4I13/2, the following rate equation holds :
where ; is the population density of single Er3+ ions in the excited state 2 (4I13/2), is their concentration, and
Assuming that pump power at 978 nm is high enough to achieve maximal populating of the excited state 4I13/2, i.e. at “infinite” pump power, the part of Er3+ ions being in the excited state is
Formula (21) is a worthy approximation for fitting of the whole of experimental near-IR fluorescence decay kinetics, reported above for
As seen from Figure 15, the parameter
The next step in modeling is simulation of Er3+ clusters’ contribution on the base of the experimental dependences of nonlinear absorption vs. pump power (see Figure 14(a)). A method to model nonlinear absorption of an EDF is based on the idea that ensemble of Er3+ ions in a fiber consists of two independent subsystems, assumed to be single (“s”) and clustered (“c”) ions. Considering this hypothesis, we generalize the model developed in  for propagation of a pump wave through the system of single and paired resonantly absorbing and fluorescing centers (pairs are the simplest case of clusters). The model’s generalization signifies here that the clusters’ subsystem is meant to comprise an arbitrary number of centers (Er3+ ions in our case) whereas the other subsystem – to consist of single species [6, 26].
We assume that a cluster of Er3+ ions can occupy only one of the two permitted states – the state <11>, where all ions forming the cluster are in the ground state, and the state <12>, where one excepted ion (an acceptor of energy transferred from the adjacent donor ions within the cluster) is in the excited state. The latter holds because if other cluster’s constituents absorb pump photons and move to the excited state, all them except one leave state 2 (down to state 1) immediately, whereas only this excepted one can stay in state 2.
We also take into account the presence of the short time
We consider that the populations of single ( ) and clustered ( ) Er3+ ions, satisfy the following relations:
The balance equations for pump power (
where majority of the quantities have been designated above, parameter
The modeling results are plotted by plain curves 1 to 5 in Figure 16(a). It is seen that they fit well the whole of the experimental data for the EDFs of both (M and L) types. Thus, the IUC process, treated by us as mostly non-radiative relaxation within Er3+ ion clusters, is justified as the key mechanism responsible for nonlinear absorption (attributed by coefficient
When making the numerical calculations, we found that, once searching for the best fit of the experiment by the theory, any
Notice that the presence in EDFs of NSA at increasing Er3+ concentration affects net gain in heavily-doped Er3+ fibers, which becomes more and more limited (saturated) as it stems from the presence of single Er3+ ions being in the excited state, whereas the clustered ions, in their big part, i.e. (
4. Effect of SBS upon operation of actively Q-switched EDFL
Actively Q-switched (AQS) EDFLs based on acousto-optics modulator (AOM), implemented in the Fabry-Perot geometry, usually produce Q-switch (QS) pulses with duration from a few to hundreds ns . The QS pulses are normally composed of a few sub-pulses separated by round-trip time of photon inside the cavity [31, 32]; this AQS regime will be called further "conventional" (CQS). In the meantime, it is known that in certain conditions FLs demonstrate stochastic QS pulsing, which stems, as it will be clearly demonstrated below, from intra-cavity stimulated Brillouin scattering (SBS) . Such pulses, referred further to as SBS-QS ones, are characterized by dramatic increasing of power as compared to CQS pulses but, at the same time, by perceptible jitters . In this section, we show that in certain circumstances SBS-QS pulsing is inherent in AOM-based AQS EDFLs. We also demonstrate that the areas (basins) where CQS and SBS-QS regimes exist are defined by definite values of EDF length and AOM’s repetition rate and that the most important condition for turning of the laser to one or another pulsing regime is absence or presence of spurious narrow-line continuous wave (CW) lasing in the intervals where the laser cavity is blocked (AOM is switched OFF).
4.1. Experimental setup
An experimental setup of the QS-EDFL is sketched in Figure 17. The laser cavity consists of a piece of a standard low-doped “M” EDF (
4.2. Properties of CQS and SBS-QS regimes
As well-known, AQS FLs operated in CQS regime usually generate pulses consisting of train of sub-pulses (ripples), separated by a time interval equal to a photon’s round-trip in the cavity. Such kind operation is fully described by the model of two contra-propagated waves in Fabry-Perot cavity, once considering the laser as a multi-pass amplifier of SE reflected several times by selective mirrors (FBGs) . CQS is observed at any
If the active fiber is long enough and AOM’s repetition rate is not too high the QS EDFL turns into the regime of SBS-induced pulsing. This kind of pulsing is quite different as compared with CQS. Typical SBS-QS pulses are shown in Figure 19(a) for
One more detail of SBS-QS is that pulses released in this regime suffer strong amplitude and timing jitters. Apparently, the presence of jittering is an indication of the stochastic nature of the SBS process involved. Furthermore, since the SBS-QS pulses are not composed of sub-pulses spaced by photon round-trip time, their RF (FFT) spectrum does not have peaks at the round-trip frequency (~10 MHz) and its harmonics (see Figure 19(b)).
4.3. Basins of CQS and SBS-QS regimes
To find basins of CQS and SBS-QS regimes existence, we measured the value of
The reason of the AQS-EDFL’s switching to CQS or SBS-QS regime is the existence or the absence of spurious narrow-line CW lasing when AOM is blocked. In the last case the cavity is formed by the output reflector FBG1 and by a small reflection from closed AOM (~ –40 dB) ("bad" cavity). The overall loss of this cavity is estimated to be ~45-47 dB, revealing its very low Q-factor. At long EDF and low AOM repetition rates (the area below the border line in Figure 20) the EDF charge is sufficient to provide fiber gain capable of overcoming the cavity loss, which results in arising CW lasing. After switching AOM on, the CW wave starts to propagate along the main laser cavity (formed by FBG1 and FBG2) with simultaneous amplification of its power by the EDF until the latter reaches SBS-threshold and produces a “giant” SBS-QS pulse. Thus, CW spurious lasing arising in the "bad" cavity is a startup mechanism for SBS-QS pulsing. In the area above the border line in Figure 20 the spurious CW lasing is not established since the EDF cannot accumulate gain sufficient to overcome the "bad" cavity’s loss.
To confirm the hypothesis that the mechanism “igniting” SBS-QS pulsing relates to arising of the narrow-line CW lasing in "bad" cavity (when AOM is closed), we fulfilled the experiments on measuring the laser’s optical spectra.
Firstly, we compared the optical spectra of the laser operated in CQS and SBS-QS regimes; see Figure 21. Comparing the lasing spectra at
To shade more light on the scenario drawn above, we also measured the spectral width of spurious CW lasing arising when AOM is closed by employing another technique that utilizes a modified delayed self-heterodyne interferometer (DSHI, see Figure 22), described in details in [35-37]. To carry out this, the laser output signal was split into two beams, one of which being passed through an optical frequency shifter (AOM) and then through a long recirculating fiber delay line made using SMF-28 fiber (
Figure 23 shows the spectral width of the signals at the frequencies multiplied by the AOM’s frequency shift, measured after fitting the DSHI signal by the Lorentzian law, in function of the delay-line length
Consequently, a narrow-line CW laser wave developing in “bad” cavity and being a prerequisite of SBS-QS pulsing is highly coherent. This explains why SBS is unavoidably boosted by spurious CW lasing in the “blocked” cavity after the moment of AOM’s opening, when the EDF is strongly inverted and thus strongly amplifying. Indeed, “unlimited” in length and therefore "uniform" Brillouin dynamic grating , induced in intra-cavity EDF (the fiber is always shorter than the estimated coherence length, ~20 km), is the main cause of SBS-QS pulsing.
In this Chapter, we reported some of the important nonlinear-optic features of EDFs, which, on one hand, impact efficiency of CW EDFLs on their base and, on the other hand, underlie the operation regimes established in EDFLs Q-switched using AOMs.
In particular, we showed that strong ESA transitions inherent in the Er3+ system at both the pump (~978 nm) and the laser (~1550 nm) wavelengths and ions’ clustering inherent in the EDFs heavily doped with Er3+ cause unavoidable nonlinear losses that, in turn, strongly reduce efficiency of EDFLs, as compared to efficiency of Ytterbium-doped fiber lasers. We demonstrated as well that for making a correct numerical modeling of an EDFL one needs to consider all kinds of the nonlinear losses intrinsic in EDFs.
We also discussed in details the peculiarities of EDFLs operated in actively Q-switched regime using AOM. We demonstrated that the operation regimes of these lasers strongly depend on EDF length and AOM’s repetition frequency. Specifically, at short EDF length or at high AOM’s repetition frequency the laser operates in “conventional” Q-switching regime (being in fact multi-pass amplification of Er3+ SE) where pulses with relatively moderate power and relatively long in duration are composed of several, stable in time, sub-pulses, separated by a photon’s round-trip time in the cavity. Furthermore, if EDF length is long enough and AOM’s repetition frequency is not too high, the laser turns to the completely different pulsing regime, characterized by much shorter and much powerful pulses; however, pulses of this type are subjected to noticeable timing and amplitude jitters, originated from the stochastic in nature SBS process, ignited by spurious narrow-line CW lasing in “bad” (at closed AOM) cavity.
Authors acknowledge support from the CONACyT, Mexico (Project No. 167945).
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