Open Access
Add to BibSonomy
Abstract
A detailed investigation of concentration quenching and ion clustering effects in Er:YAG-derived all-glass optical fibers fabricated using the molten core method (MCM) is presented. Fibers are drawn from four precursor Er:YAG crystals, each possessing a different Er3+ concentration. The resulting fibers exhibited active ion densities ranging from 2.58 × 1025 m-3 to 19.5 × 1025 m-3. Compositional and refractive index profiles (RIPs) are shown to be uniformly graded across the fibers, for a given core diameter, facilitating the study of the impact of draw and host composition on rare earth spectroscopy, a first to the best of the Author’s knowledge. Measurements of the fluorescence lifetimes indicate some degree of clustering persists in all fibers; however, its reduction can clearly be correlated to an increase in sesquioxide (Al2O3 and Y2O3) concentration. Similarly, the critical quenching concentration is also revealed to increase with increasing sesquioxide concentration and ranged from 23.9 × 1025 m-3 to 40.4 × 1025 m-3 in the present fibers. Finally, emission and absorption spectra were found to be practically indistinguishable between the various fibers, with a zero-concentration radiative lifetime determined to be around 8.3 ms. Compared with other silica-based hosts, this lifetime is slightly lower, giving rise to proportionately higher cross-sections.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Rare-earth doped fibers have been widely studied for their utility as optical amplifiers and laser gain media [1]. Now ubiquitous, erbium-doped fibers (EDFs), utilizing the 4I13/2 $\to $ 4I15/2 transition, are of particular interest for amplifiers in the 1550 nm telecommunications band [2] and for ‘eye-safer’ fiber lasers [3]. Erbium-doped fiber optimization, both in terms of host material [4,5] and waveguide design [6,7], remains a notable research interest. While EDFs are conventionally made using chemical vapor deposition (CVD) methods based on a silica (SiO2) base glass, other, more specialty fabrication techniques have drawn significant attention since they offer vastly wider compositional spaces within which to enable enhanced performance [8]. One such example is the molten core method (MCM) [9], wherein a precursor core material is inserted into a cladding glass tube, often made of pure silica, and subsequently drawn into fiber at a temperature where the core is molten (hence the name).
Among the most studied MCM-derived all-glass fibers are those derived from crystalline YAG [10–14]. YAG (Y3Al5O12) melts at a temperature of ∼1940°C, making it suitable for MCM fiber fabrication using a pure silica cladding glass, which usually is drawn at about 2000°C. YAG can be doped with all the technologically useful rare-earth ions over broad concentration ranges, such that it is a valuable tool to explore such crystal-derived all-glass optical fibers and their properties. Further, the presence of the sesquioxide species in the resultant (silicate) core glass, particularly alumina, is known to aid in the doping of active ions by reducing clustering effects [15,16]. Therefore, YAG-derived active fibers, with their yttrium aluminosilicate (YAS) glass cores that arise from cladding SiO2 dissolution into the core melt during drawing [9], are expected to be a preferred host for realizing higher active ion concentrations than typically possible in more conventional silica-based, CVD-derived fibers [17].
Other benefits of YAG-derived all-glass fibers over their higher-silica-content counterparts include a broadened Brillouin linewidth and lower transverse photoelastic constant, p12. With respect to the latter, the precursor crystal has a value an order of magnitude smaller than that of silica [18], and this low-p12 characteristic is inherited by the glass through the sesquioxides. The combination of these two effects has been shown to reduce the Brillouin gain coefficient (BGC) by a factor of 6 times for a YAG-derived YAS glass fiber possessing 6 mol % Al2O3 + Y2O3 in silica [19]. Furthermore, these fibers have been shown to exhibit proportionally lower Raman scattering [20]. Since nonlinear gain depends upon fiber length, the threshold for stimulated Brillouin and Raman scattering can be further raised by using shorter lengths of more highly doped fibers. This could be realized if the YAS host can indeed incorporate more active ions prior to the onset of concentration quenching or clustering effects, which is the primary motivation for the present study. Additional operational benefits of YAG-derived all-glass fibers include reduced cooperative luminescence [21] and very low photodarkening [22].
While several rare-earth YAG-derived fibers have been produced [12,19,20,23–26], and there have been a wide range of demonstrations, including lasers and amplifiers, running the gamut of active ions, the effect of concentration has not yet been systematically investigated. Presented herein are the results of such a study for the case of Er:YAG-derived all-glass optical fibers. The core composition in MCM fibers is known to vary along the length [17], generally with highest silica concentrations nearing the end of the draw. By fabricating four fibers from four different Er:YAG precursor crystals, each with a unique Er3+ concentration, the effect of ion clustering and concentration quenching can be analyzed not only as a function of active ion content (ranging from 2.58 × 1025 m-3 to 19.5 × 1025 m-3), but also of sesquioxide concentration. Measurements of the fluorescence lifetimes indicate some degree of clustering persists across all fibers; however, its reduction can clearly be correlated to a decrease in relative silica concentration. Similarly, the critical quenching concentration is also revealed to increase with increasing sesquioxide concentration and ranged from 23.9 × 1025 m-3 to 40.4 × 1025 m-3 in the present fibers. Finally, also provided herein are what the Authors believe to be a definitive set of absorption and emission cross-section spectra for this fiber family, with a resulting zero-concentration radiative lifetime determined to be around 8.3 ms.
2. Fiber fabrication and base properties
2.1 Fiber fabrication
All-glass fibers were fabricated using the molten core method [9] with commercial grade single crystalline YAG (Scientific Materials, Bozeman MT, USA) as the core precursor and a telecommunications grade silica tube as the cladding. Four YAG rods, doped with nominal Er concentrations of 1, 2, 4, and 5 mole percent and measuring 3.0 mm in diameter and 10 mm in length, were each sleeved into the silica tube (Heraeus Tenevo, Buford, GA, US), which measured 3.0 mm in inner diameter and 30 mm in outer diameter and had one end heated and pre-sealed to hold the precursor YAG rods. Each Er:YAG / silica preform was then drawn at a temperature of approximately 2000°C into 125 μm (bare glass) diameter fiber and coated with a single layer of DSM Desolite 3471-3-14 UV curable polymer using a commercial Heathway fiber draw tower at Clemson University. The total coated fiber diameter was about 236 μm and in excess of 500 m was drawn. Fiber samples were collected at ∼150 m increments since, as noted, one hallmark of the core / clad dissolution and diffusion usually associated with the MCM is that composition changes along the draw length as the preform experiences more time at elevated temperatures.
2.2 Fiber composition
During the MCM process, the dissolution and diffusion of silica from the cladding into the core yields a graded profile in both the refractive index and YAS composition. Silica incorporation is greater the longer the core is molten, resulting in more dilute erbia (Er2O3), yttria (Y2O3), and alumina (Al2O3) concentrations towards the end of the draw. Consistent with the increased silica diffusion [17], the core diameter is also observed to decrease along the draw. Table 1 below provides core diameters for fibers taken from each of the 150 m increments that were collected. A compositional analysis using wavelength-dispersive X-ray spectroscopy (WDX, Geller MicroAnalytical, Topsfield MA, USA) for the 2% Er:YAG sample taken from a position of 425 meters (11 μm core diameter) is displayed in Fig. 1. Measured via the more expedient energy dispersive X-ray analysis (EDX), other than for the Er2O3, the relative weight percentages (wt. %) of oxide components were approximately the same between fibers of similar core diameter (575 m, 425 m, 450 m, and 450 m for the 1%, 2%, 4%, and 5% Er:YAG fiber draws, respectively). Therefore, more generally, this allows the Er3+ concentration to be treated as the only variable for a fixed host composition given fibers with approximately the same core size. To further cement this assertion, the refractive index profiles (RIPs) for the fibers with ∼ 10 μm core diameters (from all four different precursor crystals) are shown in Fig. 2. As expected, they all follow the same graded profile as shown representatively in Fig. 1. Further observations include a rather large index difference at their core centers and, while the RIPs are relatively similar, the 1% Er:YAG sample has an index somewhat lower than the rest. This is simply an indicator of slightly more silica in this fiber, as the sample was selected from later in the draw than the rest. Indeed, and as expected, the RIP is generally a good predictor of the relative silica content in the YAG-derived all-glass fiber where the ratio of the modifying Y2O3 and Al2O3 is constant. It should be noted that a larger core diameter implies less silica and higher numerical aperture, rendering an increasingly multimoded fiber. For broader system compatibility, higher-index cladding materials [27] and the use of pedestal layers [28] are currently being investigated.
Fig. 1. Compositional profile (in weight %) for the 2% Er:YAG-derived all-glass fiber measured using wavelength dispersive x-ray (WDX) spectroscopy. The sample was taken from a position of 425 m along the total fiber draw length. Note the peak erbia concentration was ∼ 0.8 wt % (7.0 × 1025 m-3 Er3+ concentration), while the average value was about 25% lower.
Fig. 2. Linescan of refractive index difference sampled at draw positions of 575 m, 425 m, 450 m, and 450 m for the 1%, 2%, 4%, and 5% Er-doped precursor YAG-derived fibers, respectively. The index values, relative to that for the pure silica cladding, were determined through a spatially resolved Fourier transform method [29]. The cladding extends to a position of ±62.5 μm (not shown).
Table 1. Fiber Properties
To estimate the remaining concentrations, namely for fibers with core diameters other than the ∼10 μm example, the WDX data was used as a benchmark. Since the fiber is highly multimoded even at these more conventional core sizes, an average Er3+ concentration for the 2% Er:YAG-derived sample was calculated from an overlap integral between its compositional profile and RIP. The compositional profile of Er2O3 was first converted to Er3+ number density, NEr(r), as
where ρ(r) is the glass mass density, NA is Avogadro’s number, and m is the summation of each oxide’s molar percentage multiplied by its molar mass. Like the compositional profile and RIP, the estimated glass density profile was graded, with the minimum density approaching that of amorphous silica (2200 kg/m3) and a peak at the center of the core of approximately 3460 kg/m3 [19]. The overlap integral was then calculated as3. Spectroscopy
3.1 Absorption cross-section
The first two ground state absorption (GSA) transitions associated with Er3+ are the 4I15/2 $\to $ 4I11/2 and 4I15/2 $\to $ 4I13/2, which correspond to wavelengths near 980 nm and 1530 nm, respectively (see Fig. 4). First, the absorption spectra in these two wavelength regions were recorded by inserting a fiber sample of known length between a white light source and an optical spectrum analyzer (OSA). These are provided in Fig. 5(a) and 5(b) for the fibers of Fig. 2, which show the constancy of the shape across the draws. The absorption cross-sections for these transitions were then calculated from the Beer-Lambert law for the transmittance, T(λ), as
where α(λ) is the loss spectrum in m-1 (which is equal to the absorption cross-section spectrum, σabs(λ), multiplied by the Er concentration, $\overline{\boldsymbol{N}}_{E r}$) and L is the length interrogated. The resulting cross-sections are displayed in Fig. 6, where the peak values at 978 nm and 1531 nm are approximately 0.25 pm2 and 0.63 pm2, respectively. In comparing the four fibers of Fig. 2, as expected, absorption at the two wavelength regions of interest increases in proportion to Er concentration in the fiber, as determined by the EDX measurements. This confirmed the uniformity and invariance of the absorption cross-section across the fibers of this study. The high erbium concentrations necessitated short sample lengths so that the absorption was within the dynamic range of the OSA. The slight ripple in Fig. 6(b) is the result of waveguide (modal) interference, which becomes stronger for shorter samples.Fig. 3. Silica content in weight % (solid lines) and mol % (dashed lines) versus longitudinal position, at core center, for each YAG-derived all-glass fiber draw. The silica content increases with position since the end-of-draw dwells longer in the furnace, promoting greater diffusion [17].
3.2 Emission cross-section
The fluorescence emission for the 4I11/2 $\to $ 4I15/2 transition was assumed to be negligible due to the short lifetime of the 4I11/2 state (∼ 10 μs) [30], so only the 4I13/2 $\to $ 4I15/2 transition was considered for determining the emission cross-section. The fiber samples were excited with a 976 nm laser diode pump, and a patch cable was positioned perpendicular to the fiber’s longitudinal axis and connected to an OSA. While perpendicular light collection (i.e., a side spectrum) does not provide as strong a signal as collecting directly from the fiber end, it avoids errors caused by reabsorption of waveguided emission. Normalized emission data is shown in Fig. 5(c), which vary insignificantly across the draws. After normalization, a form of the Füchtbauer-Ladenburg relationship [31,32] was used to convert the spectral data into cross-sections:
Fig. 4. Energy level diagram with transitions of interest for EDF noted. Dashed lines indicate absorption at pump and signal wavelengths, including excited state absorption (ESA) for 980 nm excitation, and solid lines represent radiative transitions. In most oxide glasses, the 4I13/2 level is populated by the pump through nonradiative relaxation from 4I11/2 (not shown).
Fig. 5. Ground state absorption spectra (in dB/m) for the 4I15/2 $\to $ (a) 4I11/2 and (b) 4I13/2 transitions, and (c) normalized fluorescence intensity (4I13/2 $\to $ 4I15/2) for the 4 fibers of Fig. 2.
Fig. 6. (a) Absorption cross-section near the 980 nm peak and (b) absorption and emission cross-sections near the 1530 nm peak.
4. Radiative lifetime
4.1 Pump dependence
The upper state lifetime for the 4I13/2 $\to $ 4I15/2 transition in Er3+ was measured by end-pumping ∼2 mm fiber lengths with a pulsed pump at 976 nm. The resulting output was sent through a pair of long-pass filters with 1400 nm cutoff wavelengths and focused onto an InGaAs avalanche photodiode (APD). The fluorescence decay kinetics of the Er:YAG-derived all-glass fibers were similar to those found in other Er-doped silica fibers where the decay is not well-characterized by a single exponential [34]. In particular, two distinct types of Er3+ sites were detected [35]. The first type represents relatively isolated ions in the glass with long metastable lifetimes, which are impacted by concentration quenching effects. The second type refers to clustered ions with shortened lifetimes due to multi-ion interactions typically attributed to homogeneous upconversion [35]. In the former case, the lifetime should be largely independent of pump power, while in the latter case, it is not [34,35]. This largely depends on the number of ions within the cluster that are excited, which decreases with decreasing pump power, minimizing the effects of the cluster. With a temporal resolution of 1 μs, inhomogeneous upconversion (i.e., a fast, sub-ms component) was not observed, indicating that sesquioxides in the host material prevent ion pair formation and therefore clusters from being as closely grouped as those in commercial silica-based fibers [35]. Interestingly, this is consistent with recent observations in Yb:YAG-derived optical fibers, namely a significant reduction in pair-induced cooperative luminescence [11] and resistance to photodarkening [22].
To confirm that both types of sites are present, the decay was recorded for multiple (peak) pump powers. The normalized decay is presented in Fig. 7(a) for a sample of fiber from the 5% Er:YAG precursor draw. If a single type of Er3+ site were responsible for the decay of the upper state, the data would follow a straight line whose slope would be independent of pump power. First, the curves indicate that a multi-exponential model is necessary (indeed, a two-exponential sum was deemed to be an excellent fit to all data). The figure also shows that the decay data evolves with pump power, indicating the presence of ion clusters [35]. The impact of the clusters becomes stronger as the pump power is increased but is seen to saturate near 137 mW where all ions within a cluster are excited. Therefore, all remaining lifetime measurements were made at this pump power. Note that beyond about 10 ms, each curve has approximately the same time constant.
Fig. 7. (a) Measured upper state decay in fiber taken from 450 m from 5% Er:YAG precursor draw over a range of pump powers. Note that in each case roughly the same asymptotic slope is reached. (b) Measured upper state lifetime with two-exponential fitting (dashed line) in the fiber samples from Fig. 2. As a reminder, those were the 10 μm core diameter fibers selected from each draw.
4.2 Er3+ concentration dependence
The upper state lifetime, τ, of the 4I13/2 state is dependent on individual radiative (τr), nonradiative (τnr), and quenching (τq) components [36]:
Quenching in an EDF takes place, for example, when an excited Er3+ ion loses energy to an impurity such as a transition metal or OH− group. Within one lifetime, energy can be transferred multiple times between multiple erbium ions. Some of these ions may be in the vicinity of an impurity, and the probability of energy transfer to this quenching ion increases with increasing dopant concentration. Upconversion processes play a similar deleterious role. The effect on the overall lifetime is given by [37]
The measured upper state temporal decays in the fiber samples with similar core sizes (fibers from Fig. 2) are shown in Fig. 7(b). The results confirm that the asymptotic lifetime is decreasing with increasing Er3+ concentration, indicative of concentration quenching. Also revealed in the Figure is an increased presence of ion clusters for higher concentrations. A two-exponential curve-fit was performed on the luminescence decay from several locations along each draw (see Table 1). Each exponential term was integrated to determine the relative abundance of the two Er3+ sites. For the samples in Fig. 7(b), it was determined that the lifetime of isolated ions decreased from 8.2 ms to 5.9 ms when the concentration was increased from 2.58 × 1025 m-3 to 15.2 × 1025 m-3. The relative contribution of ion clusters rose from 3.6% to 18.8%, which is consistent with observations in silica fibers possessing similar doping levels [35].
4.3 Draw position dependence
Position along the fiber draw was also investigated as a variable for the processes described above. From Table 1, the relative abundance of the two Er3+ sites remained approximately the same along each individual fiber draw albeit with a slight increase in clustering nearing the end-of-draw, despite the Er3+ concentration being least at that point. This is contradictory to a comparison of data across the separate fiber draws, which shows that site contribution is significantly affected by doping concentration. Stated another way, the proportion of clustering sites seems to increase as the erbium concentration in the precursor crystal increases rather than simply in accordance with the concentration in the fiber. Therefore, there is a separate correlation between the fiber draw location and the creation of ion clusters that is independent, at least to first order, of erbium concentration. It is likely that Er3+ clusters are more prone to form the longer the core is molten in the furnace, with more time for this phenomenon to take place later in the draw. The counterpoint to this assertion is that the system, when molten, is in a state of high miscibility. Another view is that the sesquioxides serve to reduce the impact of clustering. From the discussion in previous sections, the yttria and alumina levels remain proportional to the Er3+ content for a given doping level, and, therefore, their concentrations also decrease along the fiber draw (see Fig. 3 above). Simply put, with the increasing silica concentration there is a greater likelihood for Er3+ to cluster. To further illustrate this point, for a fixed Er3+ concentration, the proportion of clustering sites decreases near the beginning of the fiber draw, where there are greater sesquioxide concentrations. For example, the 5% Er:YAG precursor fiber, near a draw length of 900 m, the 4% case near 750 m, and the 2% case near the beginning-of-draw all have approximately the same Er3+ concentrations, but clustering decreases significantly in going from the former to the latter. This confirms the role of the host composition in the prevention of clustering, and further reinforces the importance of novel, enabling fabrication methods such as MCM.
Another interesting trend is that the lifetime of the isolated ions is higher at the ends of the draw and lowest near the middle for the more highly doped 4% and 5% Er:YAG precursor fibers. It is theorized that there are two competing processes acting on the upper state lifetime along the fiber draw: 1) a decrease in active ion concentration that lengthens the lifetime as according to Eqn. (6) and (2) the impact of yttria and alumina in increasing the quenching concentration. The latter is dominant at the beginning of the draw, and the former is dominant at the end of the draw. The ideal fiber location for maximizing efficiency in an MCM draw would therefore be the beginning-of-draw where Er3+, yttria, and alumina are present with greatest concentration, lifetime is longest, and there is least impact from ion clustering.
The significance of draw position (i.e., the concentrations of Al2O3 and Y2O3) is further demonstrated in Fig. 8. Lifetime values are grouped by positions spaced approximately 150 m apart, which correspond to similar core diameter fibers taken from across the four draws. The lifetimes of the two Er3+ sites are both seen to decrease with increasing dopant concentration. As stated before, the silica concentration increases with increasing draw position. Since the lifetime unexpectedly decreases along the draw, this confirms that the increased silica dilution of the core must play a significant role. The model from Eqn. (6) was fit to each dataset in Fig. 8(a), with Nc (provided below) and τ0 set to be fitting parameters. Quite interestingly, all of the fittings converge to τ0 = 8.3 ms in the zero concentration limit. Since Fig. 8(a) displays the lifetime after having removed the clustering contribution in Fig. 8(b), and the models account for quenching effects, the radiative lifetime can be confirmed to be 8.3 ms. Interestingly, this is consistent with previous measurements of the radiative lifetime in crystalline Er:YAG at low concentrations [38], suggesting the possibility of some “structural inheritance” in the molecular structure immediately around the Er3+ ions. By comparison, the lifetime has been shown to approach ∼5.9 ms at the power saturation limit for highly doped (3.9 × 1025 m-3) silica glass EDF [39]. This concentration is roughly 5 times lower than what is needed for Er:YAG-derived fibers, taken from a position of 150 m in the draw, to reach the same reduction in the lifetime.
Fig. 8. (a) Isolated Er3+ lifetimes for the 4I13/2 → 4I15/2 transition (squares) along with a fitted model (dashed lines) with Eqn. (6). The data show that the quenching concentration is higher near the beginning of draw, where there is less silica. (b) Clustered Er3+ lifetimes for similar draw positions as a function of Er3+ concentration.
The critical quenching concentrations for the four draw positions from beginning to end are determined from the fittings described above to be 40.4 × 1025 m-3, 30.4 × 1025 m-3, 27.0 × 1025 m-3, and 23.9 × 1025 m-3. In this range, Nc has an almost one-to-one dependence upon the total sesquioxide molar concentration (i.e., twice the amount, twice the Nc). This indicates that quenching of excited Er3+ ions is more likely at later points in the draw. In the case of cluster formation, as discussed above, it too is more likely towards the end of the draw. Previous studies performed on the effects of concentration in silicate glass fibers found that an erbium concentration of 6.2 × 1025 m-3 had a 12% contribution of paired/clustered ions to lifetime [40], with similar results observed in [35] (3.9 × 1025 m-3 had about 11%). As seen in Table 1, the beginning of an Er:YAG precursor MCM draw can accommodate more than twice as many ions before the same proportion is reached. As a result, at least in the range of compositions readily accessible via the MCM process, YAS glasses can accommodate roughly two to three times the Er3+ concentration relative to conventional high silica content glasses. This is important since Er3+ is widely understood to have both low solubility [15] and low absorption cross-sections [33] when doped into silica, hence the importance of Yb3+ sensitization [41]. The greater allowable erbium ion concentrations, coupled with the somewhat higher absorption cross sections described above, may obviate the need for sensitization while shortening the active fiber length with efficient resonant pumping [42]. These are particularly important when considering the management of nonlinearities at high power [19].
5. Conclusions
Highly-doped (2.58 × 1025–19.5 × 1025 m-3 average concentrations) Er:YAG-derived all-glass fibers fabricated via MCM have been characterized spectroscopically and the effects of clustering and concentration quenching thoroughly investigated. Fibers were fabricated from four crystalline precursors, each possessing a unique Er3+ content so that the impact of erbium concentration on the resulting fibers can be quantified. As a result of the longitudinally varying composition associated with MCM, the effect of host composition could also be investigated. From two independent measurements, the peak emission and absorption cross-sections for the 4I13/2 $\leftrightarrow $ 4I15/2 transition were found to be almost equal at 0.64 pm2 and 0.63 pm2, respectively. The peak absorption cross-section for the 4I15/2 $\to $ 4I11/2 transition was found to be 0.25 pm2. These were determined to be universal across all fibers investigated in this study.
The decay kinetics of the fibers were also investigated when pumping into the 980 nm band. Each fiber of the investigation exhibited at least some erbium ion clustering that seemed to increase in proportion to the Er3+ concentration in the precursor YAG crystal. Further analysis showed that the proportion of clustered ions decreases as the silica content decreases, or as the Al2O3 and Y2O3 concentrations increase. The critical quenching concentration is also revealed to increase with increasing sesquioxide concentration and ranged from 23.9 × 1025 m-3 to 40.4 × 1025 m-3 in the present fibers. Future investigations would include understanding the impact of impurities, namely transition metals, on the critical quenching concentrations. That said, at least in the range of fibers fabricated here, and with the available precursor crystals, YAS glasses can accommodate roughly two to three times the Er3+ concentration relative to conventional high silica content glasses, which may be of great consequence for power scaling in systems requiring the management of nonlinearities, namely stimulated Brillouin scattering for lidar applications [43]. Power and efficiency measurements in these fibers are forthcoming.
Funding
U.S. Department of Defense Energy Joint Transition Office (DE JTO) (N00014-17-1-2546); Air Force Office of Scientific Research (FA9550-16-1-0383).
Acknowledgement
Authors would like to thank Nanjie Yu and Alex Pietros for assistance with measurements.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. M. Norouzi, P. Badeka, P. Chahande, and B. Briley, “A survey on rare earth doped optical fiber amplifiers,” in Proceedings of IEEE International Conference on Electro-Information Technology (IEEE, 2013).
2. R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, “Low-noise erbium-doped fibre amplifier operating at 1.54μm,” Electron. Lett. 23(19), 1026–1028 (1987). [CrossRef]
3. P. F. Wysocki, M. J. F. Digonnet, and B. Y. Kim, “Electronically tunable, 1.55-μm erbium-doped fiber laser,” Opt. Lett. 15(5), 273–275 (1990). [CrossRef]
4. M. R. Babu, N. M. Rao, and A. M. Babu, “Effect of erbium ion concentration on structural and luminescence properties of lead borosilicate glasses for fiber amplifiers,” Lumin. 33(1), 71–78 (2018). [CrossRef]
5. A. M. Loconsole, M. C. Falconi, D. Laneve, V. Portosi, S. Taccheo, and F. Prudenzano, “Wideband optical amplifier based on Tm:Er:Yb:Ho co-doped germanate glass,” in Proceedings of 2020 Italian Conference on Optics and Photonics (IEEE, 2020), pp. 1–4.
6. Z. Zhang, C. Guo, L. Cui, Q. Mo, N. Zhao, C. Du, X. Li, and G. Li, “21 spatial mode erbium-doped fiber amplifier for mode division multiplexing transmission,” Opt. Lett. 43(7), 1550–1553 (2018). [CrossRef]
7. M. Wada, T. Sakamoto, T. Yamamoto, S. Aozasa, and K. Nakajima, “Low mode dependent gain few-mode EDFA with fiber based mode scrambler,” in Proceedings of 2019 24th OptoElectronics and Communications Conference and 2019 International Conference on Photonics in Switching and Computing (IEEE, 2019), paper MC2-4.
8. P. D. Dragic, M. Cavillon, and J. Ballato, “Materials for optical fiber lasers: a review,” Appl. Phys. Rev. 5(4), 041301 (2018). [CrossRef]
9. J. Ballato and A. C. Peacock, “Perspective: Molten core optical fiber fabrication—a route to new materials and applications,” APL Photon. 3, 120903 (2018). [CrossRef]
10. J.-C. Chen, Y.-S. Lin, C.-N. Tsai, K.-Y. Huang, C.-C. Lai, W.-Z. Su, R.-C. Shr, F.-J. Kao, T.-Y. Chang, and S.-L. Huang, “400-nm-bandwidth emission from a Cr-doped glass fiber,” IEEE Photon. Technol. Lett. 19(8), 595–597 (2007). [CrossRef]
11. P. D. Dragic, J. Ballato, T. Hawkins, and P. Foy, “Feasibility study of Yb:YAG-derived silicate fibers with large Yb content as gain media,” Opt. Mater. 34(8), 1294–1298 (2012). [CrossRef]
12. S. Yoo, A. S. Webb, R. J. Standish, T. C. May-Smith, and J. K. Sahu, “Q-switched neodymium-doped Y3Al5O12-based silica fiber laser,” Opt. Lett. 37(12), 2181–2183 (2012). [CrossRef]
13. X. Li, J. Li, T. Cheng, D. Chen, S. Zheng, W. Bi, W. Gao, Y. Ohishi, L. Hu, and M. Liao, “Silicate glass hybrid fiber with all-normal dispersion for coherent supercontinuum,” J. Lightwave Technol. 34(15), 3523–3528 (2016). [CrossRef]
14. C. Z. Li, Z. X. Jia, Z. H. Cong, Z. J. Liu, X. Y. Zhang, G. S. Qin, and W. P. Qin, “Gain characteristics of ytterbium-doped SiO2–Al2O3–Y2O3 fibers,” Laser Phys. 29(5), 055804 (2019). [CrossRef]
15. K. Arai, H. Namikawa, K. Kumata, T. Honda, Y. Ishii, and T. Handa, “Aluminum or phosphorus co-doping effects on the fluorescence and structural properties of neodymium-doped silica glasses,” J. Appl. Phys. 59(10), 3430–3436 (1986). [CrossRef]
16. J. Ballato and P. Dragic, “On the clustering of rare earth dopants in fiber lasers,” J. Directed Energy 6(2), 175–181 (2017).
17. M. Cavillon, P. Dragic, B. Faugas, T. W. Hawkins, and J. Ballato, “Insights and aspects to the modeling of the molten core method for optical fiber fabrication,” Materials 12(18), 2898 (2019). [CrossRef]
18. V. R. Johnson and F. A. Olson, “Photoelastic properties of YAG,” Proc. IEEE 55(5), 709–710 (1967). [CrossRef]
19. P. Dragic, P.-C. Law, J. Ballato, T. Hawkins, and P. Foy, “Brillouin spectroscopy of YAG-derived optical fibers,” Opt. Express 18(10), 10055–10067 (2010). [CrossRef]
20. P. D. Dragic and J. Ballato, “Characterisation of Raman gain spectra in Yb:YAG-derived optical fibres,” Electron. Lett. 49(14), 895–897 (2013). [CrossRef]
21. S. Morris and J. Ballato, “Molten-core fabrication of novel optical fibers,” Am. Ceram. Soc. Bulletin 92(4), 24–29 (2013).
22. M. Engholm, M. Tuggle, C. Kucera, T. Hawkins, P. Dragic, and J. Ballato, “On the origin of photodarkening resistance in Yb-doped silica fibers with high aluminum concentration,” Opt. Mater. Express 11(1), 115–126 (2021). [CrossRef]
23. Y.-C. Huang, J.-S. Wang, Y.-K. Lu, W.-K. Liu, K.-Y. Huang, S.-L. Huang, and W.-H. Cheng, “Preform fabrication and fiber drawing of 300 nm broadband Cr-doped fibers,” Opt. Express 15(22), 14382–14388 (2007). [CrossRef]
24. M. Jia, J. Wen, W. Luo, Y. Dong, F. Pang, Z. Chen, G. Peng, and T. Wang, “Improved scintillating properties in Ce:YAG derived silica fiber with the reduction from Ce4+ to Ce3+ ions,” J. Lumin. 221, 117063 (2020). [CrossRef]
25. G. Qian, W. Wang, G. Tang, X. Guan, W. Lin, Q. Qian, D. Chen, C. Yang, J. Liu, G. Zhou, S. Xu, and Z. Yang, “Tm:YAG ceramic derived multimaterial fiber with high gain per unit length for 2 μm laser applications,” Opt. Lett. 45(5), 1047–1050 (2020). [CrossRef]
26. G. Tang, G. Qian, W. Lin, W. Wang, Z. Shi, Y. Yang, N. Dai, Q. Qian, and Z. Yang, “Broadband 2 μm amplified spontaneous emission of Ho/Cr/Tm:YAG crystal derived all-glass fibers for mode-locked fiber laser applications,” Opt. Lett. 44(13), 3290–3293 (2019). [CrossRef]
27. D. Litzkendorf, S. Grimm, K. Schuster, J. Kobelke, A. Schwuchow, A. Ludwig, J. Kirchhof, M. Leich, S. Jetschke, J. Dellith, J.-L. Auguste, and G. Humbert, “Study of lanthanum aluminum silicate glasses for passive and active optical fibers,” Int. J. Appl. Glass Sci. 3(4), 321–331 (2012). [CrossRef]
28. P. Laperle, C. Paré, H. M. Zheng, A. Croteau, and Y. Taillon, “Yb-doped LMA triple-clad fiber laser,” Proc. SPIE 6343, 63430X (2006). [CrossRef]
29. A. D. Yablon, “Multi-wavelength optical fiber refractive index profiling by spatially resolved Fourier transform spectroscopy,” J. Lightwave Technol. 28(4), 360–364 (2010). [CrossRef]
30. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers Fundamentals and Technology (Academic Press, 1999).
31. W. F. Krupke, “Induced-emission cross sections in neodymium laser glasses,” IEEE J. Quantum Electron. 10(4), 450–457 (1974). [CrossRef]
32. J. Dong, M. Bass, Y. Mao, P. Deng, and F. Gan, “Dependence of the Yb3+ emission cross section and lifetime on temperature and concentration in yttrium aluminum garnet,” J. Opt. Soc. Am. B 20(9), 1975–1979 (2003). [CrossRef]
33. W. J. Miniscalco, “Erbium-doped glasses for fiber amplifiers at 1500 nm,” J. Lightwave Technol. 9(2), 234–250 (1991). [CrossRef]
34. G. Nykolak, P. C. Becker, J. Shmulovich, Y. H. Wong, D. J. DiGiovanni, and A. J. Bruce, “Concentration-dependent 4I13/2 lifetimes in Er3+-doped fibers and Er3+-doped planar waveguides,” IEEE Photon. Technol. Lett. 5(9), 1014–1016 (1993). [CrossRef]
35. A. V. Kir’yanov, Y. O. Barmenkov, G. E. Sandoval-Romero, and L. Escalante-Zarate, “Er3+ concentration effects in commercial erbium-doped silica fibers fabricated through the MCVD and DND technologies,” IEEE J. Quantum Electron. 49(6), 511–521 (2013). [CrossRef]
36. J. M. Knall, M. Esmaeelpour, and M. J. F. Digonnet, “Model of anti-Stokes fluorescence cooling in a single-mode optical fiber,” J. Lightwave Technol. 36(20), 4752–4760 (2018). [CrossRef]
37. F. Auzel, F. Bonfigli, S. Gagliari, and G. Baldacchini, “The interplay of self-trapping and self-quenching for resonant transitions in solids; role of a cavity,” J. Lumin. 94-95, 293–297 (2001). [CrossRef]
38. W. Q. Shi, M. Bass, and M. Birnbaum, “Effects of energy transfer among Er3+ ions on the fluorescence decay and lasing properties of heavily doped Er:Y3Al5O12,” J. Opt. Soc. Am. B 7(8), 1456–1462 (1990). [CrossRef]
39. K. Kuroda and Y. Yoshikuni, “Determination of metastable state lifetimes of a high-concentration erbium-doped fiber under population inversion conditions at 980 nm pump and 1.5 µm probe wavelengths,” Appl. Phys. B 126(8), 132 (2020). [CrossRef]
40. P. Myslinski, D. Nguyen, and J. Chrostowski, “Effects of concentration on the performance of erbium-doped fiber amplifiers,” J. Lightwave Technol. 15(1), 112–120 (1997). [CrossRef]
41. L. Dong, T. Matniyaz, M. T. Kalichevsky-Dong, J. Nilsson, and Y. Jeong, “Modeling Er/Yb fiber lasers at high powers,” Opt. Express 28(11), 16244–16255 (2020). [CrossRef]
42. M. Dubinskii, J. Zhang, and V. Ter-Mikirtychev, “Highly scalable, resonantly cladding-pumped, Er-doped fiber laser with record efficiency,” Opt. Lett. 34(10), 1507–1509 (2009). [CrossRef]
43. X. Yang, R. Lindberg, J. Larsson, J. Bood, M. Brydegaard, and F. Laurell, “1.57 μm fiber source for atmospheric CO2 continuous-wave differential absorption lidar,” Opt. Express 27(7), 10304–10310 (2019). [CrossRef]
