Provided herein is a detailed analysis of the Brillouin properties of alumina-doped silica optical fiber. The acoustic velocity of alumina in silica is shown to be a very strong function of its mass density, which can vary significantly from sample-to-sample and likely originates from the observed linear relationship between the longitudinal elastic modulus and the mass density. Further, the refractive index versus the alumina concentration provides a very sensitive probe of this mass density, and can be used to derive other structural details about the alumina. For example, for the first time to the best of our knowledge measurements of the thermo- and strain-acoustic coefficients (TAC and SAC, respectively) of the alumina dopant in silica-based fiber are presented and it is shown that these quantities are not strongly influenced by the density of alumina. Further, the material acoustic damping does not appear to be strongly influenced by the density. The TAC and SAC, or the dependence of the acoustic velocity on temperature or strain, respectively, are both found to be negative and large for alumina, in fact much larger than those for silica. Alumina thus represents a unique and potentially very useful material for the compositional tuning of the Brillouin scattering characteristics of optical fibers for distributed sensing and other applications. Conversely, these properties of alumina reduce the effectiveness of using applied temperature or strain gradients to fiber in order to suppress Brillouin scattering in fiber laser systems.
©2012 Optical Society of America
Aside from the rare earth elements themselves, alumina is arguably the most ubiquitous dopant found in active fiber laser applications that utilize silica-based materials [1–3]. Chiefly, alumina is known to improve the solubility of rare-earths in silica enabling concentrations up to a few oxide weight percent . This is of practical importance as such solubility permits the considerable shortening of fiber lengths which, in turn, lessens background loss restrictions on fiber fabrication. Additionally, shorter fiber lengths increase nonlinear thresholds thereby enabling larger power levels from fiber laser systems . As a co-dopant, alumina has also been shown to decrease the susceptibility of fiber to structural damage (so-called photodarkening) at high optical power levels [6,7].
In addition to the solvation capabilities of alumina in silica, it has also been shown to possess unique acoustic properties, giving rise to novel fiber designs utilized to partly suppress stimulated Brillouin scattering (SBS) [8,9]; a phenomenon that limits the power available from narrow-linewidth fiber systems. More specifically, for the past two decades, alumina has been recognized as the only dopant available that increases the acoustic velocity when added to silica , although yttria was recently shown to have a similar effect . Fiber designs based on the use of alumina can include tailored acoustic velocity profiles of the fiber core and cladding that spread the SBS interaction over multiple acoustic frequencies thereby decreasing the peak Brillouin gain coefficient (BGC) [8,9,12]. Additionally, since alumina increases the acoustic velocity when added to silica, alumina-doped silica core-pure silica-clad fibers are acoustic anti-guides. With careful fiber design, this can serve to increase the acoustic wave loss, thereby decreasing the nonlinear interaction time, decreasing the Brillouin gain coefficient [9,13–16].
Despite the useful acoustic characteristics possessed by alumina, and its use by several research groups in new fiber designs, there still exists a great deal of inconsistency in the literature in its absolute influence on silica; namely how it impacts the refractive index, acoustic velocity, and acoustic damping rate. The damping rate here is related to the visco-elastic properties of the material and is distinct from the waveguide properties that, for example, arise from the anti-guiding nature of a carefully designed acoustic waveguide. In this paper, it is conjectured that this aforementioned inconsistency has its origins in the ‘apparent’ mass density of the alumina constituent in the alumina-silica system, which is likely a very strong function of fiber processing conditions. Previous characterization of the properties of alumina-doped silica-based fibers have not included the mass density due to the difficulty in obtaining high-resolution density measurements of a fiber core, typically only comprising less than 1% the total mass of a fiber. Further, while mass density measurements on bulk samples of aluminosilicate glasses have been presented in the past [17,18], the final phase of fiber manufacture, the draw and rapid quenching of the glass, can have a significant impact on the observed optical and acoustic properties of a completed fiber [19–22].
Analyses of bulk aluminosilicate materials, in particular those by Nassau, et al. , suggest that measurements of the refractive index can be an excellent probe of the alumina glass density. Specifically, and as expected, the larger the mass density of the alumina constituent in a binary aluminosilicate glass, the greater is the increase in the refractive index upon adding it to silica. In other words, the change in refractive index with alumina molar content (Δn/[Al]) is larger when the apparent density of the alumina component is larger. As such, we interpret Δn/[Al] as potentially providing a very useful insight into the material properties of aluminosilicate fiber, and it is therefore utilized here as a very sensitive probe of the mass density of the fiber core.
More specifically, for the first time to the best of our knowledge, Brillouin spectroscopy measurements on three aluminosilicate fibers are provided and utilized in order to determine the impact of alumina on the acoustic and elastic properties of silica-based optical fibers. Three fibers from two independent fiber fabrication facilities, each with a unique Δn/[Al] are included in this work. A wide range in the apparent alumina density (2779 kg/m3 to 3470 kg/m3) is observed and shown to have a strong impact on several important properties of the fibers, though not on all of them. For completeness, included in this discussion are recent results on sapphire-derived optical fibers (SDOFs) , which are high-alumina-content all-glass aluminosilicate optical fibers drawn from a silica-clad crystalline sapphire core preform. The SDOF also possesses a Δn/[Al] distinct from the three fibers of this study.
In addition to analyses of the acoustic velocity and material acoustic damping, this work also reports for the first time the effect of strain and temperature on the observed Brillouin scattering frequency [24,25] in aluminosilicate fibers. These coefficients are important, as they can be used to calculate and frame sets of designer acoustic profiles for specialty optical fibers for distributed sensing applications based on stimulated  or spontaneous  Brillouin scattering (SBS and SpBS, respectively). Also, as described earlier, since alumina is used ubiquitously in active fiber laser applications, enumerating these parameters elucidates how alumina influences one’s ability to suppress SBS in high-power narrow linewidth fiber lasers via applied temperature  or strain  gradients.
Ultimately, the alumina component is found to have both a temperature- and strain-dependence of the acoustic velocity (TAC and SAC, respectively) that are opposite in sign to and much larger than that for silica. This may prove to be very useful in the design of optical fiber for distributed sensing applications, as this enables control of the temperature- and strain-dependent Brillouin scattering characteristics through compositional engineering of the fiber. However, this feature of alumina at the level of ‘typical’ doping concentrations in active rare earth-doped fibers decreases the effectiveness of SBS suppression via applied temperature or strain gradients.
2. Fiber fabrication and experimental configurations
Two fibers (Fibers 1 and 2) were produced at the Central Glass & Ceramic Research Institute (CGCRI) in India. These fibers were fabricated by the modified chemical vapor deposition (MCVD) process followed by the solution doping technique  using an alcohol solution of suitable strength of aluminum chloride as a source of Al2O3. The multiple porous silica layers deposited within the silica tube by the MCVD process were soaked in the solution for a period of one hour followed by air drying after removal of the solution. The whole composition of air-dried porous layers containing aluminum chloride was oxidized in the presence of oxygen to produce the aluminosilicate core. The whole porous medium was sintered by gradually increasing the heating temperature from 1300 °C to 1850 °C followed by collapsing at high temperature above 2000 °C for making of the final preform samples, which were finally drawn on a tower at 2025 °C and a tension of 25 g. The fibers were buffered with a standard coating.
An additional fiber was made at COMSET (Clemson University) using the MCVD process. The solution doping process used a mixture of aluminum chloride and water. The preform was allowed to soak in the solution for approximately one hour before draining. The doped core was allowed to dry under nitrogen then sintered to consolidate the core region. The entire preform was heated above 2200 °C on the MCVD lathe in order to fully collapse the doped tube into a solid rod for subsequent drawing. The glass rod was then drawn (Clemson University) at a temperature of approximately 1925 °C. Draw tensions were approximately 35 grams on the fiber. The fiber was coated using a standard single coating layer of Desolite 3471-3-14 (DSM Desotech). The average fiber diameter was 125.3 microns, and coated average diameter was 244.3 microns.
Compositional analyses were performed under high vacuum, using energy dispersive x-ray (EDX) spectroscopy in secondary electron (SE) mode on a Hitachi SU-6600 analytical variable pressure field emission scanning electron microscope (with ± 0.01% uncertainty). The operating voltage was 20kV. Prior to examination, the fibers were sleeved and UV epoxy cured into silica glass ferrules and their ends mechanically polished to a 1 micron finish. The fiber samples were sputter-coated with carbon prior to analysis in order to provide a conductive layer to mitigate charging effects from the glass. The refractive index profiles (RIPs) were measured at Interfiber Analysis at a wavelength of around 975 nm (with an uncertainty of ± 0.00005). The RIP measurement for one of the fibers was repeated at 632 nm, revealing marginal dispersion in the index difference (Δn) over the wavelength range. Thus, the measured RIP at 975 nm is assumed here to be the same at the Brillouin probe wavelength of 1534 nm. The measurements of the composition and RIP immediately give rise to measurements of Δn/[Al] (or the change in refractive index versus the change in alumina content [Al]) for each fiber.
The methods used to investigate the acoustic properties of the fibers can be found in [24,25,31], and will therefore not be reproduced here in detail. However, in short, the Brillouin spectra of the fibers are recorded for a number of applied strains (ε, defined here to be a fractional elongation), including the zero-strain case and temperatures (T), including room temperature. A heterodyne system, similar to that described in , was used to perform the Brillouin measurements on the fibers. Briefly, the system launches a narrow-linewidth signal at 1534 nm (λo = 1534 nm) through a circulator and into the test fiber. The Stokes’ signal generated in this fiber passes back through the circulator, is optically filtered and amplified, and finally is analyzed with a heterodyne receiver. In order to measure the temperature dependence of the Brillouin frequency, the test fibers were immersed in a heated water bath, controlled from room temperature (21.5 °C) up to the boiling point (100 °C), such that measurements over a temperature range of about 80K could be made. In order to measure the strain dependence, one end of the test fiber was affixed to a rigid plate via an epoxy and the other end to a strain gauge, wherein a linear stretch could be applied. It is noted that the measurements of all Brillouin spectra were performed on ~3 meter segments of fiber in order to avoid any inhomogeneous spectral broadening due to lengthwise variations in the fiber composition.
The measured Brillouin frequency is a function of the modal index (nm), acoustic velocity (V), and optical wavelength (λ0) as 2nmV/λo and taking the derivative with respect to temperature or strain yields33], requiring tight control of testing conditions.
However, a simpler approach was introduced in , wherein a fiber ring laser was constructed utilizing a segment (~2 m) of test fiber (for which determination of the TOC or SOC is desired). Since the laser is intentionally constructed to possess a plethora of longitudinal lasing modes, collecting the output of the laser with a detector and observing the resulting electrical output with an electrical spectrum analyzer (ESA) discloses the free spectral range (FSR) of the laser in addition to the presence higher order harmonics of the FSR at the ESA. The FSR of this laser is a function of any strain (ε) or change in temperature (ΔT) of the test fiber, and thus any changes in strain or temperature will result in a change in measured frequency given by Eq. (2), n is the mode index of the test fiber, which is a function of both temperature and strain, as with n0 being the zero-strain room-temperature value. The test fiber length is similarly dependent on strain and temperature with where ξ is the linear thermal expansion coefficient. Since the core is held rigidly in the fiber, the linear thermal expansion coefficient of silica (i.e., the cladding) is assumed for each fiber. Finally, the product NL is found from a measurement of the zero-strain, room-temperature FSR (FSR0) as .
3. Experimental data and analysis
Figure 1 presents the measured RIPs of the two fibers produced at CGCRI plotted with a normalized set of compositional profiles, demonstrating an excellent match between the two measurements. The normalization constants (Δn/[Al]s) were found to be 1.87 × 10−3 per mole% Al2O3 and 2.01 × 10−3 per mole% Al2O3 for Fibers 1 and 2, respectively. Figure 2 provides similar data for Fiber 3, which was produced at COMSET, with a normalization constant found to be 2.39 × 10−3 per mole% Al2O3. In summary, the three fibers employed in this study each have a unique Δn/[Al], with > 20% variation in the observed value that does not have an apparent dependence on the alumina concentration.
One of the authors (PD) previously has shown that utilizing an additive model (ADM) can be very accurate in modeling the acoustic velocity and refractive index (among some other parameters such as the Brillouin spectral width) of a binary system [31,34,35]. For a binary glass system, such as the aluminosilicate case of the present study, the refractive index can be determined by the following expression, with the subscripts ‘S’ and ‘A’ denoting silica and alumina, respectivelyEq. (3) but with the refractive index n replaced by the density (or acoustic attenuation). The molar mass value is fixed, but the selection of the density of alumina can possess a significant amount of uncertainty [17,18], and lead to vastly different dependencies of the observed aluminosilicate acoustic velocity on the molar content of alumina ([Al]) due to the nature of the additive model  being driven by the molar volume. Thus, as previously described, the Δn/[Al] is utilized as a probe of the alumina mass density ρA.
Specific reference to the two cases found in  is made; the density and refractive index measurements made by Nassau and those reproduced from  in  ( in this paper is Ref. 8 in ). In both cases, the density of pure silica is roughly 2200 kg/m3 (which will be assumed throughout the remainder of this paper), but the extrapolated bulk alumina mass densities, or stated a different way, the slopes of the density of the binary glass versus alumina content, are considerably different. Furthermore, there is also an observed difference in the dependence of the refractive index on [Al] in both cases. Fitting the additive model directly to the data found in  for the two cases adopted here, mass densities of 2845 kg/m3 and 3350 kg/m3 are obtained for Δn/[Al] values of 1.92 × 10−3 per mole% Al2O3 and 2.30 × 10−3 per mole% Al2O3, respectively. Since the relationship between Δn/[Al] and mass density for the two cases is approximately linear, a linear dependence of the density on the measured Δn/[Al] is assumed, thus giving rise to the extrapolated alumina mass densities provided in Table 2. Now, with the alumina mass density (and thereby the molar volume) for each glass becoming defined, we may proceed with the additive model to determine the remaining optical and mechanical properties of the alumina constituent.
First, however, for completeness and comparison a calculation of the refractive index difference as a function of [Al] is provided in Fig. 3 for each of the fibers of this study and the SDOF from . Also shown on these curves are the data points for the measured Δn for each fiber. These plots are meant to demonstrate that over a small [Al] range, the dependence of Δn on [Al] is approximately linear. Over a large [Al] range, however, the curves are all sub-linear (Δn/[Al] decreases with increasing [Al]). This results from the fact that (ρs/Ms)(MA/ρA) > 1 or that the molar volume of silica is less than that of alumina. This condition is satisfied for the alumina constituent in each fiber, however as the molar volumes of the two species (silica and alumina) approach each other (such as for the case of Fiber 3 and SDOF) the n([Al]) curves become much more linear. The slopes of the curves, or dn/d[Al] are each unique, resulting from the unique mass density and index of alumina in each fiber, and dn/d[Al] ≈Δn/[Al] for each of Fibers 1, 2, and 3 in the range [Al] = [0, 8 mole%]. The origin of the varying mass density from fiber-to-fiber is currently not fully understood, and may be a result of differing processing conditions (such as draw tension) between the fibers. A recent paper suggests that a root cause of the phenomenon may be differing admixtures of coordination numbers in the amorphous material, with low- (such as 4-) coordinated alumina possessing lower density than higher- (such as 6-) coordinated alumina .
In order to model the fiber system, the optical and acoustic mode properties are calculated from an eight-layer step-wise approximation to the RIPs. The optical mode calculations give rise to the modal index (nm), while the calculations of the acoustic mode give rise to a complex propagation constant [13,15], from which the mode velocity and waveguide attenuation coefficient (αwg) are determined. This attenuation results from the acoustic anti-guiding nature of the optical fiber. Each of the eight layers of the approximation has a unique acoustic velocity and refractive index, and concomitantly these parameters each possess unique dependencies on the local temperature and any applied strain due to each layer having a unique composition. Therefore, in order to model the strain- and temperature-dependencies of the system, it is assumed that both the acoustic velocity and refractive index possess a simple linear dependence on temperature and strain (over small temperature and applied strain ranges). A similar approach was taken in [24,25], giving rise to accurate modeling results.
Figure 4 shows the Brillouin spectra measured for Fiber 2, as an example, at room temperature (22.5 °C) and at a temperature elevated by 66K. Strain measurements provided essentially identical graphical results as those of the temperature measurements. It is found that the temperature- and strain-dependence of the Brillouin frequency are both very linear  and that the frequency increases with increasing temperature or strain. Therefore, this data will not be shown here, but the best-fit slope to the linear data is provided in Table 1 , as the strain and thermal coefficients. The remaining measured quantities also are summarized in Table 1.
In order to determine the intrinsic Brillouin linewidth of the fibers, one can assume that Δν = (αwg + αint)V/π and then subtract away the contribution of the waveguide term. The spectral width for each fiber is determined by fitting a Lorentzian function to the measured spectra. The acoustic mode(s) in all fibers is calculated to occupy approximately the inner part of the optical core, as exemplified by the Fiber 1 calculation that was shown in Fig. 1. The oscillatory nature of the mode profile away from the core center is due to the Hankel function solutions to the cylindrical symmetry of the fiber giving rise to radiation modes that result from the acoustically anti-guiding nature of the fiber. Therefore, the deduced Brillouin spectral width for the bulk core glass then is found utilizing the average [Al] as determined from a weighted average subject to the acoustic mode spatial distribution within the central lobe of the acoustic mode. These averages are found to be 5.2, 7.0, and 3.4 mole percent for Fibers 1, 2, and 3, respectively, which are not significantly different from the peak alumina values. All other alumina parameters are found by fitting to the 8-layer step-wise approximation to the RIP, from which an 8-layer step-wise compositional profile is determined utilizing the unique Δn/[Al] for each fiber. The bulk values (acoustic velocity, TAC and SAC) are each used as fitting parameters and are iterated until the calculated value matches the measurement.
As described above, determination of the TAC and SAC requires some knowledge of the TOC and SOC. Thus, these quantities were measured utilizing the ring laser setup described in Section 2. The SOC measurement had more uncertainty associated with it than did the measurement of the TOC, mainly since the temperature could be accurately controlled and characterized, while uncertainty as small as 10 μm in the absolute fiber stretch leads to an uncertainty of roughly 0.01 in the SOC, and therefore these values in Table 1 were rounded to the nearest hundredths position. In order to determine the pure silica values, a segment of Sumitomo Z-FiberTM (pure silica core and F-doped silica cladding) was previously analyzed, and the results taken from [24,25]. For completeness, Fig. 5 provides the data obtained for the TOC measurement of Fiber 2 at M = 202, normalized to the fundamental harmonic. The TOC for the Sumitomo fiber was found to be 10.4 × 10−3 K−1.
Upon inspection of Table 2 , it may be concluded that neither the TAC nor SAC, nor the Brillouin spectral width appears to be significantly impacted by the differing densities of the alumina in the fibers. Mainly, it is the refractive index and acoustic velocity that appear to be most strongly impacted by the density. The differing acoustic velocities, coupled with the differing mass densities, leads to significantly different influences of the dopant on the acoustic velocity of the binary system, and thereby the measured Brillouin frequency. Figure 6 plots the acoustic velocity (Eq. (4)) versus [Al] for Fibers 1, 2 and 3, showing some difference in the slopes of the curves, ranging from 26.6 m/s/mol% to 29.1 m/s/mol%. Finally, and even more interesting, the relationship between the longitudinal elastic modulus and the mass density may be deduced (included are the SDOF and Nassau  data in this final analysis). Strikingly, as shown in Fig. 7 , there is a linear relationship (R2 = 0.98) between the longitudinal modulus and mass density of glassy alumina.
The measured TAC and SAC for the alumina dopant are found to be very large when compared with silica, and negative. This feature may find great utility in the compositional tuning of the acoustic velocity profile for distributed sensor systems based on Brillouin scattering. Furthermore, since these values (at concentrations < 10 mole percent) result in reduced sensitivity of the Brillouin frequency to temperature and strain, the effectiveness of suppressing SBS via applied strain or temperature gradients is decreased as [Al] is increased, much like with P2O5 in silica [24,25]. However, this must still be validated at higher alumina concentrations, as pure alumina (or high-Al content silica glass) is expected to have a greater sensitivity to strain and temperature than has silica. The possibility of producing such glasses is believed to be fundamentally limited by the nucleation and growth of mullite (3Al2O3∙2SiO2) crystals which is facilitated by octahedral alumina coordination  at very high alumina concentrations (> 60 mole percent in light of ).
While the measured SAC of alumina is larger than (and of opposite sign to) that of silica, the relative magnitudes are not extraordinary, unlike those of the TACs. This warrants some additional discussion regarding the TAC. While the TAC for silica utilized here is in very good agreement with that found in the literature , the TAC determined for alumina is not. Therefore, in order to compare the results presented here with those of bulk Al2O3 found in the literature, Eq. (1) is first rewritten in a more generalized logarithmic form as
Next, several values of for Al2O3 from the literature are compared with the results obtained here; a summary of which is provided in Table 3 . Since the core-clad ratio suggests that the elastic properties of the fiber will be driven by the pure silica cladding, the thermal expansion coefficient of silica is assumed in the calculation provided in Table 3, although the thermal expansion term contributes less than 1% to . Very clearly, the TACs of alumina are extraordinarily large when compared with measurements on the bulk materials.
The origins of the very large values are currently not known, and work is underway to try to understand them. However, it is clear that there is no apparent consistency from fiber-to-fiber, thus these variations most likely result from the variations in fiber fabrication conditions, which could lead to residual stresses, strains, etc. that influence the results obtained here, which is difficult, if not impossible, to quantify at this time. Furthermore, since there is a large mismatch between the coefficient of thermal expansion between the silica and alumina constituents (with the alumina value being much larger ), expansion of alumina and the response to this expansion by the surrounding silica would also introduce new stresses/strains upon heating, further influencing the acoustic velocity. While there does seem to be a trend of decreasing with increasing alumina concentration, this may only be a coincidence, but one warranting further investigation.
Finally, for completeness an estimate of the Brillouin gain coefficient, gB, is presented for the three fibers. Since the fibers are each multimode, and due to some uncertainty in a perfect single-mode launch, a power transmission test was not used for this estimate. Rather, since all the relevant quantities needed to calculate gB are found in Table 1, except the photoelastic constant p12, the additive model is first used to estimate p12 for the fibers. Utilizing the additive model as found in  and photoelastic constant values of 0.253  and −0.03  for silica and alumina, respectively (the photoelastic constant of bulk sapphire is assumed for that of alumina), values for p12 of 0.234, 0.227, and 0.243 are obtained for fibers 1, 2, and 3, respectively. Then, utilizing the following equation for gB 34].
In conclusion, a very detailed Brillouin analysis of alumina doped into silica-based optical fiber has been presented. The dependence of the refractive index difference on alumina concentration has been shown to vary significantly from sample-to-sample. It is conjectured that this variation has its origins in the significant mass density variations of the alumina constituent, and showed how measurements of Δn/[Al] can be used to derive these densities, leading to accurate determination of other physical parameters of alumina. These include the SAC and TAC, both of which are much larger than those of silica, but with no apparent significant dependence on the mass density of alumina. Also shown was that the Brillouin spectral width (acoustic damping) coefficient is not a strong function of the mass density. The values of the SAC and TAC make alumina attractive for use in the tailoring of specialty optical fibers for distributed strain and temperature sensing, while these same features actually limit the ability to suppress SBS in fiber laser systems via the use of applied temperature or strain gradients. Finally, variations in the observed acoustic velocity of alumina in silica were found to stem from a linear dependence of the longitudinal elastic modulus on the mass density.
Authors would like to thank A. Yablon of Interfiber Analysis for the RIP measurements and Prof. M. John Matthewson of Rutgers University for fruitful discussions.
References and links
2. A. S. Webb, A. J. Boyland, R. J. Standish, S. Yoo, J. K. Sahu, and D. N. Payne, “MCVD in-situ solution doping process for the fabrication of complex design large core rare-earth doped fibers,” J. Non-Cryst. Solids 356(18-19), 848–851 (2010). [CrossRef]
3. T. Simo, M. Söderlund, J. Koponen, V. Philippov, and P. Stenius, “The potential of direct nanoparticle deposition for the next generation of optical fibers,” Proc. SPIE 6116, 94–102 (2006).
4. 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 glass,” J. Appl. Phys. 59(10), 3430–3436 (1986). [CrossRef]
6. B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J.-P. Martin, and J.-P. de Sandro, “Low photodarkening single cladding ytterbium fibre amplifier,” Proc. SPIE 6453, 64530H (2007). [CrossRef]
7. T. Kitabayashi, M. Ikeda, M. Nakai, T. Sakai, K. Himeno, and K. Ohashi, “Population inversion factor dependence of photodarkening of Yb-doped fibres and its suppression by highly aluminum doping,” in Conference of Lasers and Electro-Optics, CLEO Technical Digest (OSA, 2006), paper OThC5.
8. M.-J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, and L. A. Zenteno, “Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express 15(13), 8290–8299 (2007). [CrossRef] [PubMed]
9. P. Dragic, “SBS-suppressed, single mode Yb-doped fibre amplifiers,” in Proc. OFC/NFOEC (2009), paper J.Th.A.10.
10. C. Jen, C. Neron, A. Shang, K. Abe, L. Bonnell, and J. Kushibiki, “Acoustic characterization of silica glasses,” J. Am. Ceram. Soc. 76(3), 712–716 (1993). [CrossRef]
12. P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” in Proc. CLEO/QELS Tech. Dig. (2005), pp. 1984–1986.
13. P. Dragic, “Brillouin suppression by fiber design,” in IEEE Summer Top. Meet. Ser. (2010), pp. 151–152.
14. M. D. Mermelstein, “SBS threshold measurements and acoustic beam propagation modeling in guiding and anti-guiding single mode optical fibers,” Opt. Express 17(18), 16225–16237 (2009). [CrossRef] [PubMed]
15. L. Dong, “Formulation of a complex mode solver for arbitrary circular acoustic waveguides,” J. Lightwave Technol. 18, 3162–3175 (2010).
16. P. D. Dragic, P.-C. Law, and Y.-S. Liu, “Higher order modes in acoustically antiguiding optical fiber,” Microw. Opt. Technol. Lett. 54(10), 2347–2349 (2012). [CrossRef]
17. K. Nassau, J. W. Shiever, and J. T. Krause, “Preparation and properties of fused silica containing alumina,” J. Am. Ceram. Soc. 58(9-10), 461 (1975). [CrossRef]
18. M. Huggins and K. Sun, “Calculation of density and optical constants of a glass from its composition in weight percentage,” J. Am. Ceram. Soc. 26(1), 4–11 (1943). [CrossRef]
19. Y. Hibino, F. Hanawa, and M. Horiguchi, “Drawing-induced residual stress effects on optical characteristics in pure-silica-core single-mode fibers,” J. Appl. Phys. 65(1), 30–34 (1989). [CrossRef]
20. A. D. Yablon, “Optical and mechanical effects of frozen-in stresses and strains in optical fibers,” IEEE J. Sel. Top. Quantum Electron. 10(2), 300–311 (2004). [CrossRef]
21. W. Zou, Z. He, A. D. Yablon, and K. Hotate, “Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains,” IEEE Photon. Technol. Lett. 19(18), 1389–1391 (2007). [CrossRef]
22. J. W. Lee, G. H. Sigel Jr, and J. Li, “Processing-induced defects in optical waveguide materials,” J. Non-Cryst. Solids 239(1-3), 57–65 (1998). [CrossRef]
23. P. Dragic, T. Hawkins, P. Foy, S. Morris, and J. Ballato, “Sapphire-derived all-glass optical fibres,” Nat. Photonics 6(9), 629–635 (2012). [CrossRef]
24. P.-C. Law, Y.-S. Liu, A. Croteau, and P. Dragic, “Acoustic coefficients of P2O5-doped silica fiber: acoustic velocity, acoustic attenuation, and thermo-acoustic coefficient,” Opt. Mater. Express 1(4), 686–699 (2011). [CrossRef]
25. P.-C. Law, A. Croteau, and P. Dragic, “Acoustic coefficients of P2O5-doped silica fiber: the strain-optic and strain-acoustic coefficients,” Opt. Mater. Express 2(4), 391–404 (2012). [CrossRef]
26. D. Culverhouse, F. Farahi, C. N. Pannell, and D. A. Jackson, “Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensors,” Electron. Lett. 25(14), 913–915 (1989). [CrossRef]
27. T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76-B, 382–390 (1993).
28. Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007). [CrossRef]
29. J. E. Rothenberg, P. A. Thielen, M. Wickham, and C. P. Asman, “Suppression of stimulated Brillouin scattering in single-frequency multi-kilowatt fiber amplifiers,” Proc. SPIE 6873, 68730O (2008). [CrossRef]
30. J. E. Townsend, S. B. Poole, and D. N. Payne, “Solution doping technique for fabrication of rare-earth doped optical fibres,” Electron. Lett. 23(7), 329–331 (1987). [CrossRef]
31. P. D. Dragic, “The acoustic velocity of Ge-doped silica fibers: a comparison of two models,” Int. J. Appl. Glass Sci. 1(3), 330–337 (2010). [CrossRef]
32. P. Dragic, “Estimating the effect of Ge doping on the acoustic damping coefficient via a highly Ge-doped MCVD silica fiber,” J. Opt. Soc. Am. B 26(8), 1614–1620 (2009). [CrossRef]
33. A. Bertholds and R. Dändliker, “Determination of the individual strain-optic coefficients in single-mode optical fibers,” J. Lightwave Technol. 6(1), 17–20 (1988). [CrossRef]
34. P. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. 45(5), 256–257 (2009). [CrossRef]
35. P. Dragic, “Brillouin gain reduction via B2O3 doping,” J. Lightwave Technol. 29(7), 967–973 (2011). [CrossRef]
36. G. Gutiérrez and B. Johansson, “Molecular dynamics study of structural properties of amorphous Al2O3,” Phys. Rev. B 65(10), 104202 (2002). [CrossRef]
37. M. Niklès, L. Thévenaz, and P. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997). [CrossRef]
38. W. Taylor, “Structure of sillimanite and mullite,” Z. Kristallogr. 68, 503–521 (1928).
39. S. Spinner, “Temperature dependence of elastic constants of vitreous silica,” J. Am. Ceram. Soc. 45(8), 394–397 (1962). [CrossRef]
40. R. H. Wittstruck, N. W. Emanetoglu, Y. Lu, S. Laffey, and A. Ballato, “Properties of transducers and substrates for high frequency resonators and sensors,” J. Acoust. Soc. Am. 118(3), 1414–1423 (2005). [CrossRef]
41. S. V. Sinogeikin, D. L. Lakshtanov, J. D. Nicholas, J. M. Jackson, and J. D. Bass, “High temperature elasticity measurements on oxides by Brillouin spectroscopy with resistive and IR laser heating,” J. Eur. Ceram. Soc. 25(8), 1313–1324 (2005). [CrossRef]
42. B. Stern, (Cornell University), V. DeFilippo (New Jersey Institute of Technology), and A. Ballato (Clemson University) are preparing a manuscript to be called “Elasticity of alumina to 1825 K, computed from sapphire data by self-consistent averaging.”
43. R. G. Munro, “Evaluated material properties for a sintered α-alumina,” J. Am. Ceram. Soc. 80(8), 1919–1928 (1997). [CrossRef]