Mass density and the Brillouin spectroscopy of aluminosilicate optical fibers

P. Dragic; J. Ballato; A. Ballato; S. Morris; T. Hawkins; P.-C. Law; S. Ghosh; M.C. Paul

doi:10.1364/OME.2.001641

1. Introduction

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 [4]. 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 [5]. 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 [10], although yttria was recently shown to have a similar effect [11]. 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. [17], 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) [23], 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 [26] or spontaneous [27] 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 [28] or strain [29] 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 [30] 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 [32], was used to perform the Brillouin measurements on the fibers. Briefly, the system launches a narrow-linewidth signal at 1534 nm (λ_o = 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 (n_m), acoustic velocity (V), and optical wavelength (λ₀) as 2n_mV/λ_o and taking the derivative with respect to temperature or strain yields

\frac{d ν}{d (T, ε)} = \frac{2}{λ_{o}} (V \frac{d n}{d (T, ε)} + n \frac{d V}{d (T, ε)}),

which possesses both the optical (dn/d(T,ε)) and acoustic (dV/d(T,ε)) terms. The optical terms are related to the thermo-optic coefficient (TOC) and strain-optic coefficient (SOC), and the acoustic terms are the TAC and SAC, as defined in the Introduction. Hence, to estimate how the acoustic velocity is influenced by strain or temperature, some knowledge or estimates of the TOC or SOC are needed. Typically, these quantities are measured interferometrically [33], requiring tight control of testing conditions.

However, a simpler approach was introduced in [25], 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 [25]

Δ ν_{_{E S A}}^{M} = M Δ F S R = - M \frac{c}{{(n l + N L)}^{2}} (n (l_{0}, ξ l_{0}) + l Q) (ε, Δ T),

where M is the harmonic number on which the measurement is performed, c is the speed of light, and Q, in the case of strain, is defined to be

Q = - \frac{1}{2} n_{0}^{3} S O C

, with the SOC defined from the photoelastic constants and Poisson ratio (ν^p) to be

S O C = p_{12} - ν^{p} (p_{11} + p_{12})

. Q is simply the TOC in the case of temperature. Clearly, the larger the M value, the more accurate will be the measurement. In Eq. (2), n is the mode index of the test fiber, which is a function of both temperature and strain, as

n = n_{0} + ε Q + Δ T TOC

with n₀ being the zero-strain room-temperature value. The test fiber length is similarly dependent on strain and temperature with

l = l_{0} + ε l_{0} + Δ T ξ l_{0}

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

N L = \frac{c}{F S R_{0}} - l_{0} n_{0}

.

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.

Fig. 1 RIP and EDX measurements for the aluminosilicate fibers produced at the CGCRI. The RIP for Fiber 2 was measured at both 975 nm and 632 nm (both shown) and are nearly indistinguishable. A plot of the acoustic mode in Fiber 1 is also shown. The absolute composition is found by dividing the refractive index by Δn/[Al] for the fibers.

Download Full Size | PDF

Fig. 2 RIP and EDX measurements for the aluminosilicate fiber produced at COMSET. The absolute composition is found by dividing the refractive index by Δn/[Al] for the fiber (2.39 × 10⁻³ per mole% Al₂O₃ for Fiber 3).

Download Full Size | PDF

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, respectively

n = m n_{A} + (1 - m) n_{S}

while the net acoustic velocity can be found from

V = {(\frac{m}{V_{A}} + \frac{(1 - m)}{V_{S}})}^{- 1}

with m being defined as

m = \frac{\frac{ρ_{S}}{M_{S}} \frac{M_{A}}{ρ_{A}} [A l]}{1 + [A l] (\frac{ρ_{S}}{M_{S}} \frac{M_{A}}{ρ_{A}} - 1)}

and ρ the mass density and M the molar mass. The net mass density (and the material damping coefficient α_m or α_int in units of m⁻¹) of the binary system can be found using an equation similar to Eq. (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 [31] being driven by the molar volume. Thus, as previously described, the Δn/[Al] is utilized as a probe of the alumina mass density ρ_A.

Specific reference to the two cases found in [17] is made; the density and refractive index measurements made by Nassau and those reproduced from [18] in [17] ([18] in this paper is Ref. 8 in [17]). 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 [17] 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 [23]. 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 [36].

Fig. 3 Refractive index difference for the three fibers of the present study and two data points for the SDOF from [23]. The points are the measured data for the fibers.

Download Full Size | PDF

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 (n_m), 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 (α_wg) 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 [37] 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.

Fig. 4 Brillouin spectra measured for Fiber 2 at room temperature and an elevated temperature. One anti-guiding acoustic mode is observed.

Download Full Size | PDF

Table 1. Summary of the measured fiber characteristics. Fibers are listed in order of increasing Δn/[Al].

View Table | View all tables in this article

In order to determine the intrinsic Brillouin linewidth of the fibers, one can assume that Δν = (α_wg + α_int)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-Fiber^TM (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.

Fig. 5 Measurements of the change in free spectral range, ΔFSR, (Hz) versus temperature for the TOC measurement utilizing the ring fiber laser arrangement described in Section 2. The solid line is the model fit to the data.

Download Full Size | PDF

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 [17] 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.

Table 2. Deduced physical properties of the alumina constituent in each of the test fibers. Results for the SDOF are provided for comparison purposes.

View Table | View all tables in this article

Fig. 6 Acoustic velocity versus alumina content for the three fibers of this study.

Download Full Size | PDF

Fig. 7 Longitudinal elastic modulus plotted versus the mass density of pure alumina. There appears to be a very linear (R² = 0.98) relationship between the two quantities in the density range (linear fit shown as the red line).

Download Full Size | PDF

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 [38] at very high alumina concentrations (> 60 mole percent in light of [23]).

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 [39], 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

\frac{d}{d T} \ln (ν) = \frac{1}{ν} \frac{d ν}{d T} = T_{ν}^{(1)} = \frac{1}{n} \frac{d n}{d T} + \frac{1}{V} \frac{d V}{d T} = T_{n}^{(1)} + T_{V}^{(1)}

where the superscript (1) denotes a first-order approximation, i.e., that the temperature dependencies are essentially linear over the thermal range considered. Therefore, the units in this normalized form are expressed as 10⁻⁶/K, or ppm/K. The thermal dependence of the normalized stiffness coefficient c₁₁ (

T c_{11}^{(1)}

) can therefore be expressed in terms of

T_{V}^{(1)}

and the linear coefficient of thermal expansion (ξ) as

T c_{11}^{(1)} = - 3 ξ + 2 T_{V}^{(1)}

where the factor of 3 results from the conversion of a linear coefficient of thermal expansion to a volume expansion and the factor of 2 arises from the square-law dependence of the stiffness coefficient on the acoustic velocity (

c_{11} = λ + 2 μ = ρ V^{2}

, with λ and μ being the Lamé constants).

Next, several values of $T c_{11}^{(1)}$ 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 $T c_{11}^{(1)}$ . Very clearly, the TACs of alumina are extraordinarily large when compared with measurements on the bulk materials.

Table 3. $T c_{11}^{(1)}$ from several sources in the literature, in comparison with values deduced from the fibers of this study.

View Table | View all tables in this article

The origins of the very large $T c_{11}^{(1)}$ 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 [39]), 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 $T c_{11}^{(1)}$ 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, g_B, 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 g_B 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 [35] and photoelastic constant values of 0.253 [25] and −0.03 [44] 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 g_B [5]

g_{B} = \frac{2 π n^{7} p_{12}^{2}}{c λ_{o}^{2} ρ V_{a} Δ ν},

the calculated g_B values are approximately 1.1 × 10⁻¹¹ m/W, 0.8 × 10⁻¹¹ m/W, and 1.0 × 10⁻¹¹ m/W for fibers 1, 2, and 3, respectively at the test wavelength of 1534 nm. Due to the increase in acoustic velocity, Brillouin spectral width (including the waveguide loss term) and density, and decrease in photoelastic constant, the Brillouin gain coefficients are less than one-half the value of a standard Ge-doped single mode fiber, which is around 2.5 × 10⁻¹¹ m/W [34].

4. Conclusion

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.

Acknowledgment

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

1. Y. Jeong, J. K. Sahu, D. N. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12(25), 6088–6092 (2004). [CrossRef] [PubMed]

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]

5. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972). [CrossRef] [PubMed]

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]

11. 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] [PubMed]

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]

44. H. Eilers, E. Strauss, and W. M. Yen, “Photoelastic effect in Ti³⁺-doped sapphire,” Phys. Rev. B Condens. Matter 45(17), 9604–9610 (1992). [CrossRef] [PubMed]

Value	Fiber 1	Fiber 2	SDOF [23]	Fiber 3
ν (GHz)	11.549 ± 0.002	11.737 ± 0.002	> 13	11.496 ± 0.002
Δn ( × 10⁻³)	9.7	14.5	> 50	8.1
Mode Index, n_m (1534 nm); room temp. and zero strain	1.451	1.456	> 1.5	1.449
Attenuation Coefficient (dB/m) at 1534 nm	0.059	0.032	0.2	0.375
V (m/s)	6105	6183	> 6500	6087***
[Al] mole%	5.2	7.2	> 20 mole%	3.4
Thermal Coefficient (MHz/K)	0.931 ± 0.026	0.880 ± 0.026	< 0.5	1.009 ± 0.026
TOC (K⁻¹)	+ 10.5 ± 0.2 × 10⁻⁶	+ 10.5 ± 0.2 × 10⁻⁶	*	+ 10.4 ± 0.2 × 10⁻⁶
Strain Coefficient (GHz/ε)	49.2 ± 0.2	48.7 ± 0.2	*	51.2 ± 0.2
SOC	0.18 ± 0.1	0.17 ± 0.1	*	0.18 ± 0.1
Δν (MHz)	45.0 ± 0.5	55.5 ± 0.5	> 90	50.0 ± 0.5
α_wg ( × 10³ m⁻¹)	6.7	8.6	~0	13
Δν_int (MHz)	32.0	38.6	> 90	25.0
ρ (kg/m³)**	2240	2268	> 2400	2246

Value	SiO₂**	Fiber 1 Al₂O₃	Fiber 2 Al₂O₃	SDOF Al₂O₃	Fiber 3 Al₂O₃
Index (at 1534 nm)	1.444	1.586	1.606	1.653	1.667
Molar mass (g/mol)	60.08	101.96	101.96	101.96	101.96
Density (kg/m³)	2200	2779	2965	3350	3470
Δn/[Al] (10⁻³/mol% oxide)	-	1.87	2.01	2.30***	2.39
V (m/s)	5970	9190	9640	9790	10013
Δν (MHz at 11 GHz)	17.0	272	313	274	287
TAC (m/s/K)	+ 0.555	−3.61	−3.45	−2.41	−4.48
SAC (km/s/ε)	+ 29.2	−49.0	−43.6	*	−48.0

Reference	$T c_{11}^{(1)}$ (ppm/K)
Wittstruck et al.** [40]	−70.2
Sinogeikin, et al. [41]	−100
Stern, et al. [42]	−108
Munro** [43]	−105
Fiber 1	−788
Fiber 2	−714
SDOF	−494
Fiber 3	−896

Value	Fiber 1	Fiber 2	SDOF [23]	Fiber 3
ν (GHz)	11.549 ± 0.002	11.737 ± 0.002	> 13	11.496 ± 0.002
Δn ( × 10⁻³)	9.7	14.5	> 50	8.1
Mode Index, n_m (1534 nm); room temp. and zero strain	1.451	1.456	> 1.5	1.449
Attenuation Coefficient (dB/m) at 1534 nm	0.059	0.032	0.2	0.375
V (m/s)	6105	6183	> 6500	6087***
[Al] mole%	5.2	7.2	> 20 mole%	3.4
Thermal Coefficient (MHz/K)	0.931 ± 0.026	0.880 ± 0.026	< 0.5	1.009 ± 0.026
TOC (K⁻¹)	+ 10.5 ± 0.2 × 10⁻⁶	+ 10.5 ± 0.2 × 10⁻⁶	*	+ 10.4 ± 0.2 × 10⁻⁶
Strain Coefficient (GHz/ε)	49.2 ± 0.2	48.7 ± 0.2	*	51.2 ± 0.2
SOC	0.18 ± 0.1	0.17 ± 0.1	*	0.18 ± 0.1
Δν (MHz)	45.0 ± 0.5	55.5 ± 0.5	> 90	50.0 ± 0.5
α_wg ( × 10³ m⁻¹)	6.7	8.6	~0	13
Δν_int (MHz)	32.0	38.6	> 90	25.0
ρ (kg/m³)**	2240	2268	> 2400	2246

Value	SiO₂**	Fiber 1 Al₂O₃	Fiber 2 Al₂O₃	SDOF Al₂O₃	Fiber 3 Al₂O₃
Index (at 1534 nm)	1.444	1.586	1.606	1.653	1.667
Molar mass (g/mol)	60.08	101.96	101.96	101.96	101.96
Density (kg/m³)	2200	2779	2965	3350	3470
Δn/[Al] (10⁻³/mol% oxide)	-	1.87	2.01	2.30***	2.39
V (m/s)	5970	9190	9640	9790	10013
Δν (MHz at 11 GHz)	17.0	272	313	274	287
TAC (m/s/K)	+ 0.555	−3.61	−3.45	−2.41	−4.48
SAC (km/s/ε)	+ 29.2	−49.0	−43.6	*	−48.0

Mass density and the Brillouin spectroscopy of aluminosilicate optical fibers

Abstract

1. Introduction

2. Fiber fabrication and experimental configurations

3. Experimental data and analysis

4. Conclusion

Acknowledgment

References and links

Cited By

Figures (7)

Tables (3)

Equations (8)

Optical Materials Express