In some Brillouin-based distributed sensing applications, a measurement of strain, but not temperature, is required. However, as both environmental conditions influence the Brillouin frequency, distinguishing the effects of temperature from strain can be challenging. In general, with respect to the Brillouin gain spectrum (BGS), distinguishing strain from temperature in a measurement requires that at least two Brillouin spectral components be present in the system, in the form of a pair of fibers [1], cores [2], fiber core layers [3], acoustic modes [4], polarizations [5], etc. Clearly, these spectral components must have peak frequencies $(\nu )$ that differ in some way in their responses to changes in temperature and/or strain.

An alternate approach would be to design the optical fiber to somehow be immune to temperature (or “athermal”), but not to strain. In that case, the Brillouin frequency measured at some optical wavelength would then be fully independent of the temperature of the fiber. It has recently been shown [6,7] that a number of possible glass compositions give rise to precisely this condition. From a system-level perspective, these fibers have two features that may be considered undesirable, namely highly multimode operation (core $\mathrm{\Delta }n\approx 0.1$ and $\sim 20\mathrm{\mu m}$ diameters) and a greatly reduced sensitivity to strain that has thus far accompanied a reduction in thermal sensitivity. Reduced sensitivity to the strain of the sensing fiber obviously then deleteriously reduces the sensitivity of the whole measurement system.

It was later shown that a large value of thermal expansion for the core is a beneficial attribute in helping to reduce thermal sensitivity [8]. In short, the acoustic velocity of the glass system (and not its refractive index) dominates its (Brillouin) thermal response. Silica is widely understood to possess an acoustic velocity that increases with increasing temperature (i.e., a positive bulk thermal response). Its acoustic velocity, “anomalously,” also decreases as a strong function of any applied pressure [8]. Therefore, when in fiber form, if the core has a thermal expansion coefficient (CTE) larger than that of the cladding, elevating the fiber temperature will impart a positive pressure on the core, causing a relative decrease in the acoustic velocity of its silica constituent. Such a configuration is realized when dopants or constituents with CTEs larger than silica, such as alumina or lanthana [7] or group I oxides [9], are utilized in the core glass. This offsets the increased velocity due to the simple bulk thermal response of silica.

Here, through the use of a lithium aluminosilicate glass composition, a two-moded (with a $\sim 5\mathrm{\mu m}$ core diameter) optical fiber with very low, and negative, thermal coefficient, $\mathrm{d}\nu /\mathrm{d}T$ ($-0.26\mathrm{MHz}/\mathrm{K}$), is demonstrated. Simultaneously, the strain sensitivity is reduced by only 20% relative to standard Corning SMF-28. These results suggest that the thermal response of silica has been slightly overcompensated for and that less lithia–alumina in the core would lead to an athermal fiber ($\mathrm{d}\nu /\mathrm{d}T\sim 0\mathrm{MHz}/\mathrm{K}$). Increasing the silica content will also improve the strain sensitivity of the fiber and lower the $V$ number, thus outlining a path toward a single-mode fiber. While the present fiber is not optimized, it is a solid demonstration of the powerful potential of considering novel glass compositions when designing optical fibers for distributed sensing and other applications. There is little doubt that novel fiber compositions such as these will drive the future of a number of lightwave systems.

Lithium oxide bonds into the silica glass structure as a network modifier without significant expansion of it, thereby densifying the glass. The large relative thermal expansion of lithia can be utilized as a design parameter in achieving a Brillouin-athermal single-mode fiber. In order to fabricate the fiber, a starting $50:50$ mol. % mixture of ${\mathrm{Li}}_2\mathrm{O}$ and ${\mathrm{Al}}_2{\mathrm{O}}_3$ powders was pressed into 3 mm pellets. These pellets were utilized in a powder-in-tube molten core fabrication process [6]. A fiber was drawn down to a $\sim 5\mathrm{\mu m}$ core with standard $\sim 125\mathrm{\mu m}$ cladding diameters from an initial 3 mm (inner diameter) $\times 30\mathrm{mm}$ (outer diameter) silica capillary tube preform. The fiber was drawn at 1950°C, well above the 1625°C melting point for the ${\mathrm{Li}}_2\mathrm{O}\text{-}{\mathrm{Al}}_2{\mathrm{O}}_3$ composition, to a length of 800 m, with the cladding diameter varying by less than 1% over the length. The purity of the precursors led to a somewhat large background loss ($\sim 1.75\mathrm{dB}/\mathrm{m}$ at 1550 nm) in this proof-of-concept fiber. Reliable splicing of standard step-index telecom fiber (10 μm mode-field diameter at 1550 nm; standard Corning SMF-28) to the fiber was accomplished using a built-in program on a Fitel telecom-grade portable fusion splicer. Splice losses were in the vicinity of 1 dB, mainly due to the mode-field diameter (MFD) mismatch between the fibers. Due to its low mass, lithium cannot be detected using energy dispersive x-ray spectroscopy (EDX), and instead, secondary ion mass spectroscopy (SIMS) was used; initial measurements suggest $\sim 6.5$ mol. % each of lithia and alumina in the fiber core (at core center), with the remainder being silica. Figure 1 provides the SIMS image of the fiber core while sampling ${}^6\mathrm{Li}+$. From the SIMS data, the aluminum and lithium components were found to be homogeneously mixed in the final glass.

 

Fig. 1. SIMS image of the fiber core. Relative lithium counts are on the vertical density scale on the right-hand side.

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The refractive index profile (RIP) was measured transversely through the side of the fiber using a spatially resolved Fourier transform interferometer [10] and is provided in Fig. 2. The RIP was measured at both 950 and 1550 nm, since the shorter wavelength afforded much finer spatial resolution, thereby elucidating the fine details of the core structure. Most of the RIP difference between the two wavelengths is attributable to the poor spatial resolution of the small core at 1550 nm, rather than actual core $\mathrm{\Delta }n$ differences. Previous investigations have suggested that the core $\mathrm{\Delta }n$ wavelength dependence is particularly small in the near-IR between 950 and 1550 nm [11]. A comparison of the total integrated phase delay of the core relative to the cladding at both wavelengths (Fig. 3) is much less sensitive to the spatial resolution and shows that the total integrated optical path length delay measured at 1550 nm was about $98.6\%\pm 1.1\%$ of the total integrated optical path length delay measured at 950 nm. Therefore, we may safely conclude that the core $\mathrm{\Delta }n$ at 1550 nm was about $98.6\%\pm 1.1\%$ of the core $\mathrm{\Delta }n$ measured at 950 nm.

 

Fig. 2. Refractive index profile of the fiber, measured at 950 and 1550 nm.

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Fig. 3. Comparison of the core optical path delay (m) at 950 and 1550 nm for the prototype fiber. The results suggest that the RIP at 1550 nm is 98.6% of that at 950 nm.

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With the results and conclusions of the previous paragraph in mind, the RIP at 950 nm is utilized as a high-resolution approximation to the RIP at the (Brillouin) measurement wavelength of 1534 nm. A multilayer approximation to the RIP was made, and two optical modes of the waveguide were identified: ${\mathrm{LP}}_{01}$ (mode index, or MI, of 1.462) and ${\mathrm{LP}}_{11}$ (MI of 1.450). The MFD for the fundamental mode was calculated, using the Petermann II method, to be 5.17 μm. Table 1 lists several parameters (either measured or calculated) associated with the fiber (fundamental optical mode where relevant). For the same core diameter, a lower numerical aperture (NA) (less alumina and/or lithia) will give rise to a single-mode fiber, and this may be accomplished by adding ${\mathrm{SiO}}_2$ powder to the starting core mixture of the present study. Alternatively, the fiber may be drawn to a smaller size. In that case, since smaller diameter cores typically possess more cladding silica (as dilution of the starting core mixture by silica decreases with increasing core size in the molten core method) [12], there will also be a reduction in the NA. Finally, other materials may be incorporated into the original core mixture, such as boria (${\mathrm{B}}_2{\mathrm{O}}_3$), which lowers the refractive index.

Table 1. Summary of Optical Fiber Properties^a

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Figure 4 shows the normalized BGS with the fiber at room (23°C) temperature and at an elevated (95°C) temperature, utilizing a 5 m length of fiber. Interestingly, the BGS is found to have a peak frequency that decreases with increasing temperature (at a rate of $-0.26\mathrm{MHz}/°\mathrm{C}$). This is in contrast to what is typically observed for SMF-28–like single-mode telecommunications fibers ($+1.1\mathrm{MHz}/°\mathrm{C}$). The negative dependence of the Brillouin frequency on temperature suggests that overcompensation for the bulk thermal response of silica has occurred, leading to the unique result presented here. Indeed typical high-silica fibers have thermal responses that are positive valued. More importantly, one can logically conclude that by decreasing the lithia and alumina content in the fiber, a purely athermal fiber composition can be realized. Furthermore, as discussed in the previous paragraph, this will also reduce the $V$ number of the fiber, opening a path to the development of a truly single-mode fiber. Work is currently underway with this target in mind. A simple linear extrapolation can be used to estimate this composition: with $\sim 6.5$ mol. % of each of lithia and alumina, $\mathrm{d}\nu /\mathrm{d}T$ has been reduced by 1.36 MHz/K. This gives a molar response of about $-0.21\mathrm{MHz}$/(K-mol. %), and therefore an athermal fiber at a molar quantity of $\sim 5.3$ mol. % of each of lithia and alumina. If for a given system a range of acceptable $\mathrm{d}\nu /\mathrm{d}T$ values can be identified, this will dictate a set of tolerances on the fiber composition.

 

Fig. 4. Brillouin gain spectrum shown at two temperatures (labeled in the graph). The dashed lines are Lorentzian fits to the data. The Brillouin frequency decreases with increasing temperature. An end image of the cleaved fiber is provided in the inset.

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Figure 5 shows the dependence of the Brillouin frequency on strain. A 2 m segment of fiber was utilized for this test. The observed slope, 406 MHz/%, is only about 20% lower than what is observed for standard Corning SMF-28 at the same wavelength [13]. In light of the conclusions in the previous paragraph, reducing the alumina and lithia content in the fiber will also beneficially lead to an enhancement of the slope of the strain curve and improve the relative strain sensitivity of the fiber. Finally, an end-of-life failure test was performed on the fiber, and it was found to break at $\sim 5.7\%$ tension.

 

Fig. 5. Brillouin frequency versus applied strain (stretch).

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Finally, the BGS for the fiber is extremely well represented by a single Lorentzian function. At elevated temperatures, the spectrum narrows somewhat (from 169 to about 162 MHz), as is typical of high–silica-content optical fiber cores [14]. The small change suggests that acoustic waveguide attenuation (due to the fiber being an acoustic-wave antiguide), which is not a strong function of temperature, is a significant contributor to the spectral width. Utilizing the simple model found in [15], along with a five-layer step approximation to the core with central acoustic velocity 6166 m/s (see Table 1), the waveguide contribution to the spectral width is estimated to be $\sim 79\mathrm{MHz}$, leading to an estimate of $\sim 90\mathrm{MHz}$ for the intrinsic Brillouin linewidth (assuming a two-Lorentzian convolution), which is driven by acoustic-wave damping by the material. This is still relatively broad, suggesting a reduced Brillouin gain coefficient (BGC) in group I-aluminosilicate–core fibers relative to more conventional fibers [14]. Utilizing the modeling methodologies outlined elsewhere [6], a few of the characteristics of the lithia component in the core glass are outlined in Table 2. These values were determined using data found in Table 1.

Table 2. Summary of Some Relevant Physical Characteristics of Lithia^a

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The optical fiber of the present study has a longitudinal acoustic velocity that is larger than that of the surrounding cladding. This renders the fiber an acoustic antiguide, leading to a BGS that is broadened by waveguide attenuation [18]. However, interestingly, it is found that lithia increases the acoustic velocity only slightly when added to silica. This could have significant advantages for realizing acoustically antiguiding fibers for Brillouin scattering suppression, since a large core-clad acoustic velocity contrast, if in the acoustically antiguiding configuration, will still have waveguide loss that is insignificant relative to that of material damping [19]. In addition, it is deduced from [16] that the photoelastic coefficient $p_{12}$ (the BGC is proportional to the square of $p_{12}$ [20]) is reduced when lithia is added to silica. While both of these features are clearly desirable for the suppression of Brillouin scattering, they may be clear disadvantages when using Brillouin scattering in these fibers for sensing applications.

A drawback to this fiber is its reduced BGC ($>10\mathrm{dB}$ reduced relative to the standard step-index Corning SMF-28 fiber described above). However, the sizeable NA of the fiber leads to a calculated (Petermann II method) MFD of about 5.1 μm. Depending on the system architecture, fiber length, etc., this may offer some compensatory recovery of the strength of Brillouin scattering, but with careful attention paid to the potential presence of other nonlinear parasitics. For the benefit of the reader, the nonlinear refractive index, $n_2$, is estimated next. Given the similarity of $n_2$ for quartz [21] and sapphire [22], to the first order, it is assumed that the addition of lithia dominates any changes to $n_2$ in the present glass composition. In [23] it was found that a ${\mathrm{Li}}_2\mathrm{O}\text{-}{\mathrm{SiO}}_2$ glass with 25% lithia content (molar) has a value of $n_2$ that is about 22% larger than that of fused silica (at 800 nm). Thus, utilizing a simple linear interpolation to the present 6.5 mol. % ${\mathrm{Li}}_2\mathrm{O}$, $n_2$ at the core center is estimated to be about 6% larger than that of pure silica. The value seen by the optical mode will be somewhat closer to the pure silica value, given the gradient nature of the dopant distribution in the core.

To the best of our knowledge, for the very first time, through a proof-of-concept fiber, a path toward a true single-mode fiber for athermal Brillouin-based distributed strain sensing has been identified and demonstrated through compositional tailoring of the fiber core. We have uniquely demonstrated, for a high-silica-content fiber, a Brillouin frequency shift that decreases with increasing temperature. This suggests overcompensation of the Brillouin response of silica and that less lithia–alumina is required to achieve a truly athermal fiber. The proof-of-concept fiber was two moded, so an increase in the silica content will also serve to lower the $V$ number.

The enhanced CTE of the core is a major contributor to the reduction in the thermal response of the fiber. While silica is known to have an acoustic velocity that increases with increasing temperature, it decreases with applied pressure. When the core has a thermal expansion larger than that of the surrounding (and much larger) cladding, its expansion becomes constricted relative to an unclad, freely expanding material. This can be construed as a positive pressure on the core and its silica constituent, this pressure off-setting the bulk thermal response of silica.

Lithia is found to increase the acoustic velocity when added to silica, but with a magnitude less than alumina. The resulting acoustic antiguidance, in addition to the reduced value of the photoelastic constant ($p_{12}$), causes a significant decrease in the BGC, which may be a disadvantage in distributed sensor systems due to a reduction in the signal-to-noise ratio if optical power is an issue. The use of higher-purity materials is expected to significantly lower the optical attenuation. ${\mathrm{Na}}_2\mathrm{O}$ and ${\mathrm{K}}_2\mathrm{O}$ are both expected to act in a fashion similar to that observed here for ${\mathrm{Li}}_2\mathrm{O}$, but both should have a greater impact on the thermal response since they influence the CTE more strongly than ${\mathrm{Li}}_2\mathrm{O}$ [9]. They may also possess a lower acoustic velocity, which could render an acoustic waveguide. Coupled with that, these materials may also prove to possess narrower intrinsic Brillouin spectral widths (lower acoustic material damping coefficients), thus greatly enhancing the BGC relative to that of the lithium aluminosilicate fiber presented here. As such, the other group I oxide silicates are very much worth investigating, as are compositional ratios other than the $1{\mathrm{Al}}_2{\mathrm{O}}_3\text{:}1{\mathrm{Li}}_2\mathrm{O}$ utilized here.