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Presented here for the first time to the best of our knowledge is a detailed Brillouin spectroscopic study of novel, highly-BaO-doped silica glass optical fibers. The fibers were fabricated utilizing a molten-core method and exhibited baria (BaO) concentrations up to 18.4 mole %. Physical characteristics such as mass density, acoustic velocity, visco-elastic damping, and refractive index are determined for the baria component of the bariosilicate system. It is found that, of each of these parameters, only the acoustic velocity is less than that of pure silica. The effect of temperature and strain on the acoustic velocity also is determined by utilizing estimates of the strain- and thermo-optic coefficients. The dependencies are found to have signs opposite to those of silica, thus suggesting both Brillouin-frequency a-thermal and a-tensic binary compositions. Via the estimate of the strain-optic coefficient and data found in the literature, the Pockels’ photoelastic constant p12 is estimated, and both a calculation and measured estimate of the Brillouin gain versus baria content are presented. Such novel fibers incorporating the unique properties of baria could be of great utility for narrow linewidth fiber lasers, high power passive components (such as couplers and combiners), and Brillouin-based sensor systems.
©2013 Optical Society of America
Introduction
The doping of silica glass with other constituents to define the refractive index profile needed for wave-guiding in an optical fiber can also be used to control and tailor its acoustic properties as well [1]. While such acoustic designs can be utilized for the suppression of deleterious acoustic phenomena, such as stimulated Brillouin scattering (SBS) [2–4], or conversely the enhancement of certain Brillouin characteristics for applications such as distributed sensing [5–7], the literature regarding how dopants influence the various acoustic properties (sound velocity, visco-elastic damping, etc.) is surprisingly sparse. This is in contrast to the well-documented and broadly-characterized effect of dopants on the refractive index and optical attenuation of silica. As such, continued acoustic and Brillouin characterization of new materials can add significantly to the fiber designer’s toolbox, especially if some of these new materials possess interesting and unique properties. For completeness, however, it also is necessary to include in this toolbox the fiber fabrication methods [8–10] that enable novel yet still practical silica-based compositions needed to take advantage of such desirable material properties.
Consistent with the spirit of such exploration, here the Brillouin spectroscopy of baria (BaO)-doped silica fibers is presented for the first time to the best of our knowledge. The pure silica-clad fibers are derived from bulk polycrystalline baria; its fabrication being discussed in more detail in the next section. For use with a simplified additive model [11,12], the physical parameters of the bulk glassy baria component, including its refractive index, acoustic velocity, Brillouin spectral width, and mass density, are provided. Baria is known to have a refractive index and mass density that is much larger than those of silica, but it is also found to possess an acoustic velocity much lower than, and a visco-elastic damping coefficient much larger than, silica. Further, much like aluminosilicate glasses [7,13], baria possesses a dependence of the Brillouin frequency (due to the acoustic velocity) on the temperature and strain that is of opposite sign to that of silica. Hence, both Brillouin a-thermal and a-tensic fibers can also be realized [7] in the binary bariosilicate system; a finding heretofore reported only for one other glass system of practical significance to optical fiber-based applications: the aluminosilicates [7]. In homage to Robert Hooke's unscrambled anagram “Ut tensio sic vis” announcing his law of elasticity we use here the word “atensic” to represent a property (Brillouin frequency in the present case) that does not change with strain; analogous to ‘athermal’ for a property that does not change with temperature.
In addition, a comparison has previously been made between the physical characteristics of bulk crystalline materials and their glassy counterparts in the SiO2-Al2O3 system, where changes (reduction) in the mass density and refractive index for the amorphizing of SiO2 and Al2O3 were found to be nearly identical [7]. While a reduction in the magnitude of these properties in changing from the crystal to the glassy phase is neither surprising nor unexpected, their similarity suggests, at least, that some physical characteristics in the fabrication of optical fiber from crystalline precursors [9] can be predicted a priori. Here, it is shown that in terms of the mass density and refractive index, the transformation of baria from the crystalline precursor phase to a glassy in-silica phase is nearly identical to that of the case of fibers derived from sapphire (Al2O3), but with somewhat reduced relative acoustic velocity, providing compelling insight into the glass formation process in the fabrication of crystal-derived all-glass optical fibers.
Experimental
This section provides details on the fabrication of the BaO-doped silica fibers. The measurement methods utilized in investigating the BaO-doped silica fibers also are described. The measurements include determination of the refractive index profiles, attenuation spectra, compositional profiles, Brillouin spectra, and strain- and temperature-dependencies of the Brillouin scattering frequency. From these, the physical attributes of the bulk glassy baria were determined utilizing an additive model, which is described in a subsequent section.
Fiber fabrication
As-purchased BaO powder (99.99% purity; Sigma Aldrich, St. Louis, MO) was sleeved inside an HSQ (Heraeus) fused silica tube measuring about 3.5 mm inner diameter by 30 mm outer diameter. This preform was drawn on a Heathway draw tower (Clemson University, Clemson, SC) at a temperature of about 1975°C. This temperature was chosen because BaO possesses a melting temperature of about 1920°C [14] fulfilling the general requirement of the molten core technique that the core phase melt at a temperature below which the cladding glass draws into fiber [8]. Between 100 and 200 meters each of fiber at (uncoated) diameters of 125 μm, 150 μm, and 175 μm were collected. The fibers all were coated with a standard single acrylate coating (DSM Desotech, Elgin, IL). The three fibers of this study are designated ‘A,’ ‘B,’ and ‘C,’ in order of increasing baria content. In the present case, these are the 150 μm, 175 μm, and 125 μm fibers, respectively. While data for all the fibers were similar, where appropriate data for Fiber C will be shown as the illustrative example since it represents the highest baria content achieved in this work.
Refractive index profiles and attenuation spectra
The refractive index profiles (RIPs) were measured by Interfiber Analysis (Livingston, NJ) at a wavelength of about 1000 nm (with an uncertainty of ± 0.00005) using a spatially resolved Fourier transform technique [15]. For the calculations presented in the subsequent sections, the measured refractive index difference, Δn, at a wavelength of 1000 nm is assumed here to be the same as at the Brillouin probe wavelength of 1534 nm, since it could not be measured at the longer test wavelength. Thus the refractive index of silica is taken to be its value at 1534 nm (1.444) and Δn is assumed from the RIPs. Spectral attenuation measurements were performed on ~1 – 2 meter segments of the drawn fiber. Over the range from 700 – 950 nm, a tungsten light source was used along with a miniature spectrometer (Ocean Optics Inc.). For the longer-wavelength measurements (up to 1700 nm), the broadband light source option on a Hewlett-Packard 7095 series optical spectrum analyzer was used.
Compositional profiles
Compositional analyses of the BaO-derived fiber cross-sections 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% elemental uncertainty) at an operating voltage of 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. Throughout the remainder of this paper, [BaO] is defined to be the BaO concentration in units of mole percent.
Brillouin spectra
The procedures used to investigate the acoustic and Brillouin properties of the fibers can be found in [12,16,17] and will therefore not be repeated here in detail. Briefly, the Brillouin spectra of the fibers are recorded utilizing a heterodyne system, similar to that described in [18]. 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. Spectra are recorded for a number of applied strains (ε, defined here to be a fractional elongation), including the zero-strain case, and temperatures (T), also including room temperature. 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 linear translation stage possessing a calibrated micrometer, wherein a linear stretch could be applied. It is noted that the measurements of all Brillouin spectra were performed on < 1.5 meter segments of fiber in order to avoid any inhomogeneous spectral broadening due to any lengthwise variations in the fiber composition.
Thermo-optic and strain-optic coefficients
The measured Brillouin frequency ν is a function of the modal index (nm), acoustic velocity (V), and optical wavelength (λ0) as ν = 2nmV/λo and taking the derivative with respect to temperature or strain of this expression for ν yields
which possesses both optical (dn/d(T,ε)) and acoustic (dV/d(T,ε)) terms. The optical terms are proportional to the thermo-optic coefficient (TOC) and strain-optic coefficient (SOC), and the acoustic terms are the thermo-acoustic and strain-acoustic coefficients (TAC and SAC, respectively). 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 [19], requiring tight control of testing conditions.However, a simpler approach was introduced in [17], 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 [17]
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 = -½no3(SOC), with the SOC defined from the photoelastic constants and Poisson ratio (νp) to be SOC = p12 - νp(p11 + p12). 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 = no + εQ + ΔT(TOC) with n0 being the zero-strain room-temperature value. The test fiber length is similarly dependent on strain and temperature with l = lo + εlo + ΔT ξ lo 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 NL = (c/FSRo) – lono.Results and discussion
Figure 1 displays the measured compositional (EDX) and refractive index profiles (RIP) of Fiber C as a representative example. The shape and position of the RIP and EDX are in excellent agreement with each other recognizing that the spatial precision of the measurements are slightly different. The core exhibits a graded-index (GRIN) shape resulting from the dissolution of cladding silica into the core during the fiber drawing process.
Fig. 1 Refractive index profile, RIP, measured at a wavelength of 1000 nm, (open circles; right ordinate) and BaO content measured using energy dispersive x-ray spectroscopy, EDX (solid squares; left ordinate) measurements on Fiber C.
Glass formation in the BaO-SiO2 system has been studied at least as far back as 1922 [20]. By 1927 it was known that liquid-liquid immiscibility existed between SiO2 and the other alkaline earth oxides; i.e., MgO, CaO, and SrO; as well as with Al2O3 [21]. However, despite numerous other chemical commonalities with its alkaline earth counterparts, BaO was not initially determined to be immiscible with SiO2 though Greig [21] does note that the shape of the liquidus of cristobalite (SiO2) is “of a peculiar and distinctive shape not hitherto encountered in silicate studies” in the BaO-SiO2 phase diagram. Liquid-liquid immiscibility was subsequently identified in this binary system ranging from least 2 to 28 mole percent BaO with upper consolute point at about 10 mole percent BaO and 1460°C [22]. A critical cooling rate of about 103 K/sec was experimentally determined [23] which is in reasonable agreement with fiber draw quench rates. Despite these glass stability issues, the bariosilicate glass system possesses interesting features that are more opportune than in more conventional optical fiber glass systems. Two such important material factors are diffusivity and viscosity. The former being important because it defines the refractive index profile in the resulting fiber which governs many of its optical properties. The latter is important as it facilitates fiber formation during the molten core processing. Both diffusivity and viscosity will influence fusion splicing and therefore need to be considered in greater detail.
The diffusivity of barium in SiO2 at the 1975°C draw temperature can be calculated to be about 9.5 × 10−8 cm2/s [24]. It is worth noting that the diffusivity of barium in SiO2 is approximately 100 times larger than that for Al in SiO2 (i.e., Al2O3-doped SiO2). Given this diffusivity and the fiber core sizes, the diffusion of barium into the cladding SiO2 occurs quite rapidly: the barium traverses the 3 micron core radius of Fiber A in less than 1 s. Further, as the BaO core and SiO2 cladding begin to mix, the liquidus temperature reduces with a minimum achieved at a value of about 26 mole % BaO where the melting point is about 1647°C [14]. With respect to viscosity, BaO is considered a modifier to the glass network creating the number of non-bridging oxygens with its inclusion into SiO2. As this occurs, the viscosity of the BaO-SiO2 decreases with BaO content. Based on an extrapolation of the data in Ref. 21 the viscosity of the core melt during the molten core processing is about 10 poise and should facilitate the removal of bubbles remnant from the precursor powders and easily flow from preform into fiber. For completeness it is worth mentioning that the 10 poise viscosity is 102 larger than water at room temperature but about 103 times less than an equivalent amount of Al2O3 in SiO2. As will be discussed in more detail later, these high diffusivities coupled with low melt viscosities influence the splicing of the bariosilicate fibers.
Table 1 provides a compilation of the peak refractive index difference and baria concentrations (in both wt% and mol%) for all three fibers fabricated and studied in this work. The modal index for each fiber was calculated from its RIP, and these values also are provided in Table 1. Additionally, the measured attenuation coefficients at 1534 nm also can be found in Table 1. The attenuation spectrum for Fiber C is provided in Fig. 2 and the minimum observed value of about 1 dB/m was typical of all the baria-doped fibers studied. It is evident by the peak near 1390 nm that some OH is present in the fiber. The presence of OH is not surprising given the way in which the precursor BaO powder was processed. In addition, a broad absorption feature is observed near 1150 nm. The certificate of analysis for the precursor BaO powder testified to an overall purity of 99.7% (despite procuring 99.99% purity) with numerous trace transition metal and rare-earth impurities being present. While this absorption feature cannot be definitively ascribed to a specific impurity, its spectral location suggests it could be a combination of Sm3+, Dy3+, and/or Tm3+, all of which were present in the powder. In the future, both higher purity sources and controlled-atmosphere powder processing should reduce losses. However, for such an initial proof-of-concept as was conducted here, losses at or slightly below 1 dB/m are acceptable for the measurements undertaken. However a long-term goal is the reduction of the losses to the < 0.1 dB/m level, as is important for applications utilizing relatively short fiber, such as active fibers in fiber laser systems. Interestingly, much like for lightly GeO2-doped silica fibers, the minimum attenuation wavelength was found to be near 1550 nm.
Table 1. Summary of fiber characteristics. Fibers are listed in order of increasing baria content.
Fig. 2 Attenuation spectrum for Fiber C. The spectrum was typical of all the baria-doped fibers. An unobscured OH peak is found near 1390 nm but the peaks near 950 nm and 1250 nm are mostly hidden under the broad impurity absorption.
Figure 3 provides the room temperature and zero-strain Brillouin spectra for the three BaO-derived fibers. The solid (black) lines in the figure are Lorentzian fits to the measured spectra. The spectra each appear to be somewhat distinct and exhibit a number of spectral features. Since the acoustic velocity of baria is lower than that of silica, the bariosilicate core acts as an acoustic waveguide [25,26], and thus frequencies found above the strongest peak are due to scattering from higher-order acoustic modes (HOAMs). This is especially apparent in the Fiber A spectrum with several HOAMs appearing at frequencies above 10.5 GHz. The acoustic waveguide effect on the Brillouin spectrum has previously been described [27] and is well known. Table 1 summarizes the relevant details taken from the Brillouin spectra including the peak frequency (ν), spectral width (Δν), and the modal acoustic velocity (Vmode) calculated using the mode index for each fiber.
Fig. 3 Normalized Brillouin gain spectra measured at room temperature and zero-strain for the three BaO-doped fibers of the present study. Features to the blue of the main peaks are due to HOAMs and those to the red of the main peaks are due to HOMs.
Higher-order optical modes (HOMs) have a modal index that is lower than that of the fundamental and, as described in the previous section, the Brillouin frequency is found from νB = 2nmV/λo. Hence, HOMs also have associated Brillouin scattering frequencies that are lower than that of the fundamental mode. Previously, however, the spectral distribution of Brillouin scattering involving the HOMs was continuous [7], whereas in the present case, distinct peaks appear. Again, this is especially apparent in the Fiber A spectrum, where an additional peak near 10.3 GHz appears, rather than having a continuum-like distribution on the red side of the peak. Currently, this is believed to result from splicing conditions and selective mode excitation due to a mode-conversion effect in the vicinity of the splice, coupled with the use of a relatively short fiber in the measurement of the Brillouin spectra. Figure 4 shows an example splice from Fiber C to SMF-28TM fiber. It is found that baria readily diffuses at splice temperatures resulting in significant thermally-induced expansion of the core dimension in corroboration with the aforementioned comments on high diffusivity and low viscosity of the BaO-SiO2 system at the compositions treated in this work. Long splice times resulted in the complete apparent dissolution of the core. This is illustrated in Fig. 5 where a series of splices with identical splice power but differing splice times are shown. The taper that forms during splicing appears to act as an effective mode converter, with some random HOMs apparently being selected. While in the present case this effect results in some minor obscuring of the main peak centered at the fundamental optical-acoustic mode interaction, it may be possible to harness this intriguing property of baria for the fabrication of efficient mode converters and tapers. This is currently the subject of investigation.
Fig. 4 Example of a splice of Fiber C (left-side fiber) and SMF-28TM (right-side fiber). The splice duration was kept short (~2 s) due to the high diffusivity of bariosilicate glasses. The taper that forms during splicing seems to act as an effective mode converter. The diameter of the SMF-28 cladding is 125 μm.
Fig. 5 Evolution of the BaO-doped fiber core with increasing splice time, listed in green. The BaO-doped fiber is once again on the left-hand side.
Figure 6 provides the Brillouin spectra measured for Fiber C, as an example, at room temperature (22.0 °C) and at a temperature elevated by 58K. The Brillouin frequency has increased while there is a decrease in the spectral width by about 6 MHz. Strain measurements provided essentially identical results as those of the temperature measurements, but the spectral width did not appear to change with strain. It is found that the temperature- and strain-dependence of the Brillouin frequency are both very linear [28] 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 measured strain and thermal coefficients.
Fig. 6 Brillouin gain spectra for Fiber C measured at room temperature and at 80°C. The spectrum has blue-shifted and become somewhat narrower with heating.
Finally, as previously described, the measurement of the TOC and SOC for each fiber was facilitated with a ring laser configuration. The FSR of such a laser is c/ln, where l is the cavity length and n is the modal index, with the ring laser consisting of multiple fiber types, including the test fiber. When the fiber is heated or strained, its length increases, thereby causing a relative reduction in the FSR. In the case of increasing temperature, a positive TOC leads to an increasing modal index and therefore a relative reduction in the FSR. In the case of strain, a positive SOC leads to a decreasing modal index and therefore a relative increase in the FSR. In each of the fibers the SOC is less than that of silica (0.174 at the same wavelength [29]). This suggests that baria has a SOC less than silica. However, it is possible to achieve this effect in an alternative way. As the fiber is stretched, there may be a linear decrease in the optical mode number (or numbers) that are excited in the fiber. In this case, the effective mode index increases, resulting in a relative decrease in the FSR. While it seems unlikely that this would be manifested in each fiber simultaneously, it is not discounted as a possibility that obscures the data. Regardless of the causes of the reduced SOCs relative to pure silica, it has previously been shown that the optical terms in Eq. (1) are dominated by the acoustic terms [16,17], and thus the uncertainties in both the TOC and SOC contribute little error to the TAC and SAC deductions described in the next section. Furthermore, if there is indeed a mode transformation effect happening with changing strain, the SOC that is carried through to the SAC calculation will also carry the effects of this phenomenon with it, even if it is not a completely accurate SOC for the material itself. This is discussed in more detail in the next section.
Regarding the data, measurements of the change in FSR versus temperature were much more linear than those versus strain. This is currently believed to be due to the optical mode distribution in the fibers being different for both measurements (thermal and strain). If the distribution of optical modes excited in the multimode fiber changes with some measurement condition, then so does the effective modal index in the ring laser, thereby influencing the measurement of the FSR by obscuring the change in the material values. In the case of temperature, the fiber is coiled and kept firmly in a heated bath such that movement of the fiber was kept minimal. However, in the case of strain, the fiber was stretched linearly with one fiber end translated with respect to the other. Hence with the latter, due to the motion of a small quantity of fiber beyond the translation stage, the ring becomes somewhat distorted as the measurement progresses, and thus probably resulting in changes in the distribution of optical modes excited in the BaO-doped test fiber. This leads to a wide uncertainty range in the SOC measurements summarized in Table 1. By far, the worst-quality SOC data originated from Fiber A, which is consistent with the relative quality of the Brillouin spectra (see Fig. 3), and is probably related to the quality of splice achieved with this fiber. Figure 7 shows the change in FSR versus strain for Fiber A after an average of 10 individual measurements. The data appears to be super-linear (parabolic). Measurements on single mode fibers have always been very linear [29] without the need for averaging and thus work is underway to develop such a BaO-doped fiber in order to improve on the present SOC results.
Fig. 7 Measured change in FSR for Fiber A as a function of strain. Ten individual sets of data were acquired and averaged to obtain this graph. A fit to the data is also shown (dashed line).
Discussion
As noted based on the RIPs, it is evident that the BaO-doped fibers of this study have a GRIN-like profile. Therefore, to take this into account for the subsequent analysis, an eight-layer step-wise approximation was made to the fiber RIPs and compositional (EDX) profiles. Since each layer of the approximation has a unique composition, each layer also has unique material properties, such as acoustic velocity and mass density, which cooperate to give rise to a calculated optical and acoustic modes. These modes are then calculated using the methods outlined in [16–18]. In particular, the bulk parameters of baria (such as the acoustic velocity and Brillouin spectral width) are treated as fitting terms, and their values are iterated (thus consequently also iterating the materials values in each layer) until the calculated mode values match the measured ones. Pure silica values taken from the literature were used in this calculation, as specified in Table 2. The overall acoustic modal spectral width is found using [30]
where ΔνB(r) is the radial Brillouin spectral width profile and u(r) is the acoustic displacement. In the case of the present step-like approximation, the integral becomes a summation of eight terms.Table 2. Summary of the deduced baria characteristics for each fiber.
An additive model is utilized to calculate the value of acoustic velocity, Brillouin spectral width, etc., for each layer of the approximation. The model can be found in full detail elsewhere [11,31]. For the binary bariosilicate glass system, the refractive index can be determined by the following expression, with the subscripts ‘S’ and ‘B’ denoting silica and baria components, respectively
while the net acoustic velocity can be found fromwith m being defined asand ρ is the mass density and M the molar mass. The net mass density (and the material damping coefficient αm or αint in units of m−1) of the binary glass system can be found using an equation similar to Eq. (4) but with the refractive index, n, replaced by the density (or acoustic attenuation). For the case of the acoustic attenuation coefficient, and thereby the Brillouin spectral width, the equation possesses a scaling term that accounts for its frequency-dependence [31]. The results of these modeling calculations are summarized in Table 2 in the first four rows. For a final set of design parameters, the values from the three fibers are averaged, and the listed uncertainty is the maximum deviation of the measured data from the average value. Using the values at the center of the fiber (maximum baria content, [BaO], in each fiber), the refractive index and acoustic velocity are plotted versus [BaO] in Figs. 8(a) and 8(b), respectively, for each of the three fibers of this study. Also shown is the result for the additive model calculation utilizing the bulk values (averages) provided in Table 2. Both curves are somewhat non-linear and match the data very well.Fig. 8 (a) Refractive index difference versus baria content at fiber center (points) plotted with the additive model (solid line) and (b) Acoustic velocity versus baria content at fiber center (points) plotted with the additive model (solid line).
In order to determine the TOC and SOC for the baria component, the refractive index of bulk baria and silica are assumed to be linear functions of the temperature and strain, as described in the “Thermo-optic and strain-optic coefficients” subsection above using n0 → n as provided in Table 2. Then, while using silica values found elsewhere [16,29,30] (as summarized in Table 2) the TOC and SOC are set as fit parameters and the mode index is calculated as a function of temperature or strain. The TOC/SOC values for baria are iterated until the modal values match the measured ones. Similarly, to deduce the TAC and SAC, the acoustic velocity also is assumed, to first order, to be a linear function of the temperature and strain (). As with the TOC and SOC, the TAC and SAC are iterated until the calculated thermal and strain coefficients (which include contributions from both the acoustic velocity and optical modal index dependencies on temperature or strain) match the measured ones. For completeness, utilizing the additive model and the averaged baria values from Table 2 (last column), the thermal and strain coefficients (the dependence of the Brillouin frequency on temperature or strain respectively) for the binary bariosilicate material system are shown plotted in Figs. 9(a) and 9(b), respectively, along with the data obtained in the present work. The pure silica values are taken from [16,17]. Interestingly, the calculated a-thermal and a-tensic positions are at similar BaO concentrations: 27.3 mole% BaO and 34.3 mole%, respectively.
Fig. 9 (a) Modeled thermal coefficient of the binary bariosilicate system (solid line) plotted with the data of the present study (points). (b) Analogous plot for strain.
As done previously with sapphire-derived aluminosilicate glass fibers [7], a comparison is made between the glassy constituents of the binary bariosilicate glass and their bulk crystalline counterparts. Table 3 lists the values for the glassy phase determined here and various crystalline values found in the literature (as specified in the Table [26,32–36]). First, the glassy phase densities are for both silica and baria reduced by about 83% relative to their crystalline phase counterparts. This is in striking agreement with results for sapphire-derived aluminosilicate glass fibers [7], suggesting that the densities of the glassy phase components can be predicted a priori from the bulk crystal parameters. Similarly, the refractive index decreases to 93% and 92% of the crystalline values for silica and baria, respectively, also in agreement with previous results [7].
Table 3. Comparison of selected crystal- and glass-phase silica and baria bulk parameters.
It is of value to compare these results with those of others [20,24]. In Ref. 24, the refractive index of the binary BaO-SiO2 glass with baria concentration was found to be linear (n = 1.458 + 0.00467 × [BaO]), whereas it was found to be somewhat sub-linear in this work. Fitting the additive model to the data in [24], while moving to the visible HeNe wavelength 632 nm and retaining the mass density of silica as provided in Table 2, it is calculated that a reduction in both the mass density and refractive index relative to the crystalline case ([35] and [36], respectively) by exactly 2.8% gave rise to a match. In fact, utilizing these values, the additive model predicts that the refractive index versus baria content (mole%) dependence is almost purely linear since at this point the molar volumes of silica and baria are nearly matched. This is an increase in these values by about 17.8% relative to those provided in Table 3. Performing a similar analysis for the data in [20] at a wavelength of 589 nm, using density and refractive index values 72% and 92% of their bulk values gives rise to a sub-linear dependence with curvature identical to that in [20]. While the refractive index and density data presented here for the bariosilicate glass in optical fiber form is in very good agreement with [20], and less so with [24] (although the data in [24] is provided across a limited compositional range, such that the linear fit may not correctly extrapolate to 100% baria), this analysis suggests a wide variation in both refractive index and density with glass processing conditions, such as quenching rates, which would influence glass structure and, therefore properties such as fictive temperature that also influence selected optical properties including scattering losses.
Also, as with the case of the sapphire-derived aluminosilicate glass fibers, the acoustic velocity of the baria is reduced by a considerably larger quantity than is that of silica in going from the crystal to glassy phase. In the case of baria, it is reduced to 67% of its value, compared with 88% in the case of alumina [7]. The acoustic velocity is known to decrease with temperature for both alumina and baria [26] and this phenomenon may suggest that the (high-temperature) low-velocity values have been ‘frozen-in’ from rapid quenching of the melt.
Utilizing the deduced physical parameters for baria, the Brillouin gain coefficient (BGC) can be determined from the following equation [37]
where all parameters are defined as before and p12 is the Pockels’ photoelastic coefficient. A thorough search of the literature did not reveal a set of photoelastic constants for baria. A previous approach to deducing the Pockels’ coefficients included the SOC measurement presented above (which is a function of p11, p12, and the Poisson ratio νp), the use of fiber twist [29,38] to measure p44 ( = (p11 – p12)/2 for an isotropic system), and with knowledge of the Poisson ratio for baria (deduced to be 0.31 from [26,35]), p11 and p12 then can be determined. However, due to the wide range of uncertainty in the SOC measurement, and the multimoded nature of the fiber precluding measurement of p44, this method cannot be applied here. However, measurements of the SOC suggest that it is negative-valued.Second, data on binary systems (such as barioborate [39] and bariophosphate [40] glass) can be found in the literature. Simple linear extrapolation of the (p12 – p11) data from [39] and [40], gives rise to values of −0.036 and −0.038, respectively. While baria is expected to have a positive-valued stress-optic coefficient (p12 – p11) [41], based on the results in [39] and [40], it is expected to be both small and positive [41]. Utilizing the model found in [29], a fit-to-data found in [39] is performed. In [29], it was conjectured that the strain- and stress-optic coefficients (and thereby the Pockels’ coefficients) are additive and are carried through the model via the refractive index, giving rise to the following generalized expression for the stress-optic coefficient for a binary system
where n0 is the index of the mixed glass and the subscripted indices are those of the bulk materials. Starting with the bulk parameters for B2O3 found in [31] (ρ = 1820 kg/m3) and [39] (p12 - p11 = 0.102 and nB2O3 = 1.456) and those of BaO found in Table 2, the refractive index of baria determined here (Table 2) needed to be increased by exactly 12% to match the data in [39] (likely due to dispersion). The best-fit (p12 – p11) for baria was found to be + 0.005. The modeling results plotted with the data from [39] for both the refractive index and p44 are shown in Figs. 10(a) and 10(b), respectively, demonstrating very good agreement, albeit across a very small range of compositions. The result is as expected; a small and positive stress-optic coefficient and thus, as an approximation it is likely that, p11 ≈p12 for baria. Using the measured SOC from Table 2 (average value), we can estimate p12 to have a value of −0.33; a value that is large and negative. BaO appears to share the trait of a negative p12 with fellow alkali-earth metal oxide MgO [42]. This still needs confirmation and validation through measurements on (at least mostly) single mode fibers due to the uncertainties in the SOC measurements presented here.Fig. 10 (a) Modeled refractive index of the binary barioborate system (solid line) plotted with the data from [39] (points). (b) Analogous plot for photoelastic coefficient, p44.
Utilizing all of the data obtained up to this point, and again the model in [29] for determining p12 for a binary glass, Fig. 11 provides a calculation of the Brillouin gain coefficient as a function of [BaO]. The calculation has been done with respect to a typical SMF value of 2.5 × 10−11 m/W [11]. The acoustic attenuation coefficient helps to decrease the Brillouin gain while the relatively low acoustic velocity tends to enhance the Brillouin gain. Most interesting, however is that the assumed large negative Pockels’ coefficient contributes to a zero-p12 condition near 33.5 mole % of baria, resulting in a zero Brillouin gain condition [7,29]. This composition is roughly double in baria content relative to the existent Fiber C, and may be more reasonable to achieve that the requisite 88 mole % of alumina in the silicoaluminate (sapphire-derived) glass system [7]. If the SOC found here is in fact too large in magnitude (i.e. less negative), this will shift this zero-gain point to higher [BaO].
Fig. 11 Calculated Brillouin gain coefficient (BGC) relative to a typical SMF versus BaO concentration for the binary bariosilicate glasses. The open circles represent the locations, and computed BGC for the compositions treated in this work. A zero-p12 composition is calculated to be at a BaO concentration of about 33.5 mole %.
Finally, an attempt to estimate the Brillouin gain is made utilizing spontaneous scattering via a comparison with a reference fiber: Corning SMF-28TM. In order to calculate the Brillouin-scattering power, the analysis found in [43] was utilized where a Brillouin reflectivity, RB, was used to determine the total Brillouin signal appearing at the receiver,
where Im is the modified Bessel function of order m and and where P is the pump power launched into the fiber, A is the mode effective area (determined from the mode field diameter, MFD), L is the fiber length, νS is the frequency of the Stokes’ signal (approximately equal to that of the pump signal, at a wavelength of 1534 nm), and Γ is the decay rate (). The Brillouin frequency, νB, was selected to be the peak value from Fig. 3, and the remaining assumed values can be found in Table 1.Rather than measure absolute power, the strength of Brillouin scattering from the BaO-derived fiber is compared with a known conventional commercial fiber, SMF-28TM. A segment of SMF-28TM was spliced to the measurement apparatus, and a segment of the BaO-doped fiber was added to that. Fiber C was used in the present analysis since it can be spliced to SMF-28TM such that primarily the fundamental optical mode is excited most reliably, as is evident from Fig. 3. Figure 12 shows the result of the measurement for the lengths of fiber shown in the graph. The length the BaO-derived fiber was kept short due to optical attenuation.
Fig. 12 Relative Brillouin gain spectrum of a 0.33 m segment of BaO-derived fiber (Fiber C) spliced to 3.2 m of SMF-28TM.
From Fig. 12, it can be seen that the relative abundance of scattering from the SMF is about 14 times stronger than from the BaO-derived fiber. Calculating the ratio of the Brillouin reflectivities (using Eq. (9) and the requisite fiber parameters including length), and assuming that SMF-28TM has a Brillouin gain coefficient, gB, around 2.5 × 10−11 m/W [11], it can be determined that gB is about 0.21 × 10−11 m/W for Fiber C (including the effect of attenuation by simply applying a single-pass loss to the spontaneously-scattered Brillouin signal). This is about 1 dB higher than calculated in Fig. 11 for [BaO] = 18.4 mole%. Nevertheless, it is pointed out that due to the breadth of the optical mode and the GRIN-like distribution of baria, the optical mode overlaps some regions of the core with higher Brillouin gain, and so this relatively larger gB estimate is not unexpected. However, considering all of the uncertainties described throughout this paper, it is concluded that the gB measurement and its calculation are at least reasonably consistent with each other.
Offering a brief discussion of the Brillouin gain, the SMF fiber was about 10 times longer than the BaO-doped fiber, and the mode area about 4 times larger. Thus, all other physical parameters being the same (principally gB), one would have expected the two signals to be about 2.5 × different in magnitude. However, the Brillouin reflectivity is proportional to the product of the Brillouin gain with the spectral width (see Eq. (10)). Since a large part of the apparent reduction in gB is due to a negative Pockels’ coefficient, which does not broaden the spectral width, there is a relative reduction in the spontaneously scattered signal from the BaO fiber. In other words, low-p12 materials can have a far lower initiating Brillouin noise than in more conventional fibers.
Conclusions
For the first time to the best of our knowledge, both the fabrication of high BaO content silicate optical fibers and a detailed analysis of their Brillouin-related properties was presented. Baria concentrations up to 18.4 mole % were achieved in fibers with core diameters of less than 10 μm. From measurements of the Brillouin spectra, refractive index and compositional profiles, and the use of an additive model, physical parameters of baria including acoustic velocity, Brillouin spectral width, refractive index, and density were deduced. Measurements of the effect of temperature and strain on the acoustic velocity were presented, facilitated by estimates of the strain- and thermo-optic coefficients of BaO, with the former measurement possessing a wide uncertainty due to the multimoded nature of the fibers. It was found via a model that the bariosilicate binary system has both a-thermal and a-tensic (in the Brillouin frequency) compositions. Based on data found in the literature and the strain-optic coefficients measured here, an estimate of the Pockels’ coefficient p12 was provided, but again noting that the SOC measurement had a wide uncertainty range. The SOC measurements, including the resulting p12 estimate (negative-valued), remain to be verified and validated with a single mode BaO-doped fiber, which is part of on-going work. Using the parameters deduced here, a calculation of the Brillouin gain coefficient as a function of baria content for the binary system was presented. A zero Brillouin gain condition is predicted and remains to be validated. Finally, by measuring the relative spontaneous Brillouin scattering signal from the baria-doped fiber and a reference control fiber, gB was estimated and found to be in reasonable agreement with the calculated value. For the fiber with the largest baria content, the Brillouin gain coefficient was approximately 10 dB lower than that of a conventional telecommunications fiber.
Acknowledgments
The authors wish to acknowledge S. Morris (Clemson University) for the compositional analyses, Andrew Yablon (Interfiber Analysis) for the refractive index measurements, and Art Ballato for insightful and sound comments on acoustics. Author J. Guerrier was supported as a Charles Townes Fellow through the joint Clemson University / Furman University Charles Townes Optical Science and Engineering program. This work was supported by the Joint Technology Office through contract W911NF-12-1-0602. The splice machine utilized in this work was originally funded by DURIP award W911NF-07-1-0325.
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