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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 9 — May. 6, 2013
  • pp: 10924–10941
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Brillouin spectroscopy of a novel baria-doped silica glass optical fiber

P. Dragic, C. Kucera, J. Furtick, J. Guerrier, T. Hawkins, and J. Ballato  »View Author Affiliations


Optics Express, Vol. 21, Issue 9, pp. 10924-10941 (2013)
http://dx.doi.org/10.1364/OE.21.010924


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Abstract

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 OSA

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

1. C. K. Jen, “Similarities and differences between fiber acoustics and fiber optics,” Proceedings of the IEEE Ultrasonics Symposium, (IEEE, 1985), pp. 1128 – 1133.

]. While such acoustic designs can be utilized for the suppression of deleterious acoustic phenomena, such as stimulated Brillouin scattering (SBS) [2

2. P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” CLEO/QELS Technical Digest, pp. 1984–1986, (2005), paper CThZ3.

4

4. A. Kobyakov, S. Kumar, D. Chowdhury, A. B. Ruffin, M. Sauer, S. Bickham, and R. Mishra, “Design concept for optical fibers with enhanced SBS threshold,” Opt. Express 13(14), 5338–5346 (2005). [CrossRef] [PubMed]

], or conversely the enhancement of certain Brillouin characteristics for applications such as distributed sensing [5

5. W. Zou, Z. He, M. Kishi, and K. Hotate, “Stimulated Brillouin scattering and its dependences on strain and temperature in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett. 32(6), 600–602 (2007). [CrossRef] [PubMed]

7

7. P. Dragic, T. Hawkins, P. Foy, S. Morris, and J. Ballato, “Sapphire-derived all-glass optical fibres,” Nat. Photonics 6(9), 629–633 (2012). [CrossRef]

], 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

8. J. Ballato and E. Snitzer, “Fabrication of fibers with high rare-earth concentrations for Faraday isolator applications,” Appl. Opt. 34(30), 6848–6854 (1995). [CrossRef] [PubMed]

10

10. S. Morris, T. Hawkins, P. Foy, C. McMillen, J. Fan, L. Zhu, R. Stolen, R. Rice, and J. Ballato, “Reactive molten core fabrication of silicon optical fiber,” Opt. Mater. Express 1(6), 1141–1149 (2011). [CrossRef]

] that enable novel yet still practical silica-based compositions needed to take advantage of such desirable material properties.

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

7. P. Dragic, T. Hawkins, P. Foy, S. Morris, and J. Ballato, “Sapphire-derived all-glass optical fibres,” Nat. Photonics 6(9), 629–633 (2012). [CrossRef]

]. 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

9. J. Ballato, T. Hawkins, P. Foy, B. Kokuoz, R. Stolen, C. McMillen, M. Daw, Z. Su, T. Tritt, M. Dubinskii, J. Zhang, T. Sanamyan, and M. J. Matthewson, “On the fabrication of all-glass optical fibers from crystals,” J. Appl. Phys. 105(5), 053110 (2009). [CrossRef]

] 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

14. M. Huntelaar and E. Cordfunke, “The ternary system BaSiO3-SrSiO3-SiO2,” J. Nucl. Mater. 201, 250–253 (1993). [CrossRef]

] 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

8. J. Ballato and E. Snitzer, “Fabrication of fibers with high rare-earth concentrations for Faraday isolator applications,” Appl. Opt. 34(30), 6848–6854 (1995). [CrossRef] [PubMed]

]. 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

15. A. Yablon, “Multi-wavelength optical fiber refractive index profiling by spatially resolved Fourier transform spectroscopy,” J. Lightwave Technol. 28(4), 360–364 (2010). [CrossRef]

]. 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

12. P. 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]

,16

16. 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]

,17

17. 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]

] 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

18. 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]

]. 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

However, a simpler approach was introduced in [17

17. 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]

], 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

17. 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]

]
ΔνESAM=MΔFSR=Mc(nl+NL)2(n(l0,ξl0)+lQ)(ε,ΔT),
(2)
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
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.
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.

Glass formation in the BaO-SiO2 system has been studied at least as far back as 1922 [20

20. P. Eskola, “The silicates of strontium and barium,” Am. J. Sci. 4(23), 331–375 (1922). [CrossRef]

]. 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

21. J. Greig, “Immiscibility in silicate melts,” Am. J. Sci. 13(73), 1–44 (1927). [CrossRef]

]. However, despite numerous other chemical commonalities with its alkaline earth counterparts, BaO was not initially determined to be immiscible with SiO2 though Greig [21

21. J. Greig, “Immiscibility in silicate melts,” Am. J. Sci. 13(73), 1–44 (1927). [CrossRef]

] 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

22. T. Seward, D. Uhlmann, and D. Turnbull, “Phase separation in the system BaO-SiO2,” J. Am. Ceram. Soc. 51(5), 278–285 (1968). [CrossRef]

]. A critical cooling rate of about 103 K/sec was experimentally determined [23

23. T. Seward, D. Uhlmann, and D. Turnbull, “Development of two-phase structure in glasses with special reference to the system BaO-SiO2,” J. Am. Ceram. Soc. 51(11), 634–642 (1968). [CrossRef]

] 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

24. H.-R. Wang, “Graded-index (GRIN) lenses by slurry-based three-dimensional printing (S-3DPTM),” PhD Dissertation, Massachusetts Institute of Technology (2005).

]. 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

14. M. Huntelaar and E. Cordfunke, “The ternary system BaSiO3-SrSiO3-SiO2,” J. Nucl. Mater. 201, 250–253 (1993). [CrossRef]

]. 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

21. J. Greig, “Immiscibility in silicate melts,” Am. J. Sci. 13(73), 1–44 (1927). [CrossRef]

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.

Figure 6
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.
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

28. 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]

] 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.

Discussion

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

11. P. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. 45(5), 256–257 (2009). [CrossRef]

,31

31. P. Dragic, “Brillouin gain reduction via B2O3 doping,” J. Lightwave Technol. 29(7), 967–973 (2011). [CrossRef]

]. 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
n=mnB+(1m)nS
(4)
while the net acoustic velocity can be found from
V=(mVB+(1m)VS)1
(5)
with m being defined as
m=ρSMSMBρB[BaO]1+[BaO](ρSMSMBρB1)
(6)
and 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

31. P. Dragic, “Brillouin gain reduction via B2O3 doping,” J. Lightwave Technol. 29(7), 967–973 (2011). [CrossRef]

]. 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)
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).
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.

It is of value to compare these results with those of others [20

20. P. Eskola, “The silicates of strontium and barium,” Am. J. Sci. 4(23), 331–375 (1922). [CrossRef]

,24

24. H.-R. Wang, “Graded-index (GRIN) lenses by slurry-based three-dimensional printing (S-3DPTM),” PhD Dissertation, Massachusetts Institute of Technology (2005).

]. In Ref. 24

24. H.-R. Wang, “Graded-index (GRIN) lenses by slurry-based three-dimensional printing (S-3DPTM),” PhD Dissertation, Massachusetts Institute of Technology (2005).

, 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

24. H.-R. Wang, “Graded-index (GRIN) lenses by slurry-based three-dimensional printing (S-3DPTM),” PhD Dissertation, Massachusetts Institute of Technology (2005).

], 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

35. Springer Materials, “The Landolt-Börnstein Database,” http://www.springermaterials.com/docs/pdfs/10681719_257.pdf

] and [36

36. C. J. Anderson and E. B. Hensley, “Index of refraction of barium oxide,” J. Appl. Phys. 46(1), 443 (1975). [CrossRef]

], 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

20. P. Eskola, “The silicates of strontium and barium,” Am. J. Sci. 4(23), 331–375 (1922). [CrossRef]

] 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

20. P. Eskola, “The silicates of strontium and barium,” Am. J. Sci. 4(23), 331–375 (1922). [CrossRef]

]. While the refractive index and density data presented here for the bariosilicate glass in optical fiber form is in very good agreement with [20

20. P. Eskola, “The silicates of strontium and barium,” Am. J. Sci. 4(23), 331–375 (1922). [CrossRef]

], and less so with [24

24. H.-R. Wang, “Graded-index (GRIN) lenses by slurry-based three-dimensional printing (S-3DPTM),” PhD Dissertation, Massachusetts Institute of Technology (2005).

] (although the data in [24

24. H.-R. Wang, “Graded-index (GRIN) lenses by slurry-based three-dimensional printing (S-3DPTM),” PhD Dissertation, Massachusetts Institute of Technology (2005).

] 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

7. P. Dragic, T. Hawkins, P. Foy, S. Morris, and J. Ballato, “Sapphire-derived all-glass optical fibres,” Nat. Photonics 6(9), 629–633 (2012). [CrossRef]

]. The acoustic velocity is known to decrease with temperature for both alumina and baria [26

26. K.-O. Park and J. M. Sivertsen, “Temperature dependence of the bulk modulus of BaO single crystals,” J. Am. Ceram. Soc. 60(11-12), 537–538 (1977). [CrossRef]

] and this phenomenon may suggest that the (high-temperature) low-velocity values have been ‘frozen-in’ from rapid quenching of the melt.

Second, data on binary systems (such as barioborate [39

39. K. Matusita, R. Yokota, T. Kimijima, T. Komatsu, and C. Ihara, “Compositional trends in photoelastic constants of borate glasses,” J. Am. Ceram. Soc. 67(4), 261–265 (1984). [CrossRef]

] and bariophosphate [40

40. K. Matusita, C. Ihara, T. Komatsu, and R. Yokota, “Photoelastic effects in phosphate glasses,” J. Am. Ceram. Soc. 68(7), 389–391 (1985). [CrossRef]

] glass) can be found in the literature. Simple linear extrapolation of the (p12 – p11) data from [39

39. K. Matusita, R. Yokota, T. Kimijima, T. Komatsu, and C. Ihara, “Compositional trends in photoelastic constants of borate glasses,” J. Am. Ceram. Soc. 67(4), 261–265 (1984). [CrossRef]

] and [40

40. K. Matusita, C. Ihara, T. Komatsu, and R. Yokota, “Photoelastic effects in phosphate glasses,” J. Am. Ceram. Soc. 68(7), 389–391 (1985). [CrossRef]

], 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

41. M. Guignard and J. W. Zwanziger, “Zero stress-optic barium tellurite glass,” J. Non-Cryst. Solids 353(16-17), 1662–1664 (2007). [CrossRef]

], based on the results in [39

39. K. Matusita, R. Yokota, T. Kimijima, T. Komatsu, and C. Ihara, “Compositional trends in photoelastic constants of borate glasses,” J. Am. Ceram. Soc. 67(4), 261–265 (1984). [CrossRef]

] and [40

40. K. Matusita, C. Ihara, T. Komatsu, and R. Yokota, “Photoelastic effects in phosphate glasses,” J. Am. Ceram. Soc. 68(7), 389–391 (1985). [CrossRef]

], it is expected to be both small and positive [41

41. M. Guignard and J. W. Zwanziger, “Zero stress-optic barium tellurite glass,” J. Non-Cryst. Solids 353(16-17), 1662–1664 (2007). [CrossRef]

]. Utilizing the model found in [29

29. P. Dragic, J. Ballato, S. Morris, and T. Hawkins, “Pockels’ coefficients of alumina in aluminosilicate optical fibers,” J. Opt. Soc. Am. B 30(2), 244–250 (2013). [CrossRef]

], a fit-to-data found in [39

39. K. Matusita, R. Yokota, T. Kimijima, T. Komatsu, and C. Ihara, “Compositional trends in photoelastic constants of borate glasses,” J. Am. Ceram. Soc. 67(4), 261–265 (1984). [CrossRef]

] is performed. In [29

29. P. Dragic, J. Ballato, S. Morris, and T. Hawkins, “Pockels’ coefficients of alumina in aluminosilicate optical fibers,” J. Opt. Soc. Am. B 30(2), 244–250 (2013). [CrossRef]

], 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
p44,eff=1n03(nBaO3m(p44,Al2O3)+nSiO23(1m)(p44,SiO2)),
(8)
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

31. P. Dragic, “Brillouin gain reduction via B2O3 doping,” J. Lightwave Technol. 29(7), 967–973 (2011). [CrossRef]

] (ρ = 1820 kg/m3) and [39

39. K. Matusita, R. Yokota, T. Kimijima, T. Komatsu, and C. Ihara, “Compositional trends in photoelastic constants of borate glasses,” J. Am. Ceram. Soc. 67(4), 261–265 (1984). [CrossRef]

] (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

39. K. Matusita, R. Yokota, T. Kimijima, T. Komatsu, and C. Ihara, “Compositional trends in photoelastic constants of borate glasses,” J. Am. Ceram. Soc. 67(4), 261–265 (1984). [CrossRef]

] (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

39. K. Matusita, R. Yokota, T. Kimijima, T. Komatsu, and C. Ihara, “Compositional trends in photoelastic constants of borate glasses,” J. Am. Ceram. Soc. 67(4), 261–265 (1984). [CrossRef]

] for both the refractive index and p44 are shown in Figs. 10(a)
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.
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

42. K. V. K. Rao and V. G. K. Murty, “Photoelastic constants of magnesium oxide,” Acta Crystallogr. 17(6), 788–789 (1964). [CrossRef]

]. 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.

Utilizing all of the data obtained up to this point, and again the model in [29

29. P. Dragic, J. Ballato, S. Morris, and T. Hawkins, “Pockels’ coefficients of alumina in aluminosilicate optical fibers,” J. Opt. Soc. Am. B 30(2), 244–250 (2013). [CrossRef]

] for determining p12 for a binary glass, Fig. 11
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 %.
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

11. P. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. 45(5), 256–257 (2009). [CrossRef]

]. 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

7. P. Dragic, T. Hawkins, P. Foy, S. Morris, and J. Ballato, “Sapphire-derived all-glass optical fibres,” Nat. Photonics 6(9), 629–633 (2012). [CrossRef]

,29

29. P. Dragic, J. Ballato, S. Morris, and T. Hawkins, “Pockels’ coefficients of alumina in aluminosilicate optical fibers,” J. Opt. Soc. Am. B 30(2), 244–250 (2013). [CrossRef]

]. 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

7. P. Dragic, T. Hawkins, P. Foy, S. Morris, and J. Ballato, “Sapphire-derived all-glass optical fibres,” Nat. Photonics 6(9), 629–633 (2012). [CrossRef]

]. 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].

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

43. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990). [CrossRef] [PubMed]

] was utilized where a Brillouin reflectivity, RB, was used to determine the total Brillouin signal appearing at the receiver,
RB=YeG'/2[I0(G'2)I1(G'2)],
(9)
where Im is the modified Bessel function of order m and
Y=(n¯+1)gBhνSΓL4A,
(10)
G'=gBPAL,
(11)
n¯=(exp(hνBkT)1)1,
(12)
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 (Γ=πΔν). 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
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.
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.

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

11. P. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. 45(5), 256–257 (2009). [CrossRef]

], 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

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.

References and links

1.

C. K. Jen, “Similarities and differences between fiber acoustics and fiber optics,” Proceedings of the IEEE Ultrasonics Symposium, (IEEE, 1985), pp. 1128 – 1133.

2.

P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” CLEO/QELS Technical Digest, pp. 1984–1986, (2005), paper CThZ3.

3.

M.-J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, D. A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” Optical Fiber Communication Conference, (Optical Society of America, 2006), paper OTuA4. [CrossRef]

4.

A. Kobyakov, S. Kumar, D. Chowdhury, A. B. Ruffin, M. Sauer, S. Bickham, and R. Mishra, “Design concept for optical fibers with enhanced SBS threshold,” Opt. Express 13(14), 5338–5346 (2005). [CrossRef] [PubMed]

5.

W. Zou, Z. He, M. Kishi, and K. Hotate, “Stimulated Brillouin scattering and its dependences on strain and temperature in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett. 32(6), 600–602 (2007). [CrossRef] [PubMed]

6.

P. Dragic, “Novel dual-Brillouin-frequency optical fiber for distributed temperature sensing,” Proc. SPIE 7197, 719710, 719710-10 (2009). [CrossRef]

7.

P. Dragic, T. Hawkins, P. Foy, S. Morris, and J. Ballato, “Sapphire-derived all-glass optical fibres,” Nat. Photonics 6(9), 629–633 (2012). [CrossRef]

8.

J. Ballato and E. Snitzer, “Fabrication of fibers with high rare-earth concentrations for Faraday isolator applications,” Appl. Opt. 34(30), 6848–6854 (1995). [CrossRef] [PubMed]

9.

J. Ballato, T. Hawkins, P. Foy, B. Kokuoz, R. Stolen, C. McMillen, M. Daw, Z. Su, T. Tritt, M. Dubinskii, J. Zhang, T. Sanamyan, and M. J. Matthewson, “On the fabrication of all-glass optical fibers from crystals,” J. Appl. Phys. 105(5), 053110 (2009). [CrossRef]

10.

S. Morris, T. Hawkins, P. Foy, C. McMillen, J. Fan, L. Zhu, R. Stolen, R. Rice, and J. Ballato, “Reactive molten core fabrication of silicon optical fiber,” Opt. Mater. Express 1(6), 1141–1149 (2011). [CrossRef]

11.

P. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. 45(5), 256–257 (2009). [CrossRef]

12.

P. 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]

13.

P. Dragic, J. Ballato, A. Ballato, S. Morris, T. Hawkins, P.-C. Law, S. Ghosh, and M. C. Paul, “Mass density and the Brillouin spectroscopy of aluminosilicate optical fibers,” Opt. Mater. Express 2(11), 1641–1654 (2012). [CrossRef]

14.

M. Huntelaar and E. Cordfunke, “The ternary system BaSiO3-SrSiO3-SiO2,” J. Nucl. Mater. 201, 250–253 (1993). [CrossRef]

15.

A. Yablon, “Multi-wavelength optical fiber refractive index profiling by spatially resolved Fourier transform spectroscopy,” J. Lightwave Technol. 28(4), 360–364 (2010). [CrossRef]

16.

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]

17.

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]

18.

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]

19.

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]

20.

P. Eskola, “The silicates of strontium and barium,” Am. J. Sci. 4(23), 331–375 (1922). [CrossRef]

21.

J. Greig, “Immiscibility in silicate melts,” Am. J. Sci. 13(73), 1–44 (1927). [CrossRef]

22.

T. Seward, D. Uhlmann, and D. Turnbull, “Phase separation in the system BaO-SiO2,” J. Am. Ceram. Soc. 51(5), 278–285 (1968). [CrossRef]

23.

T. Seward, D. Uhlmann, and D. Turnbull, “Development of two-phase structure in glasses with special reference to the system BaO-SiO2,” J. Am. Ceram. Soc. 51(11), 634–642 (1968). [CrossRef]

24.

H.-R. Wang, “Graded-index (GRIN) lenses by slurry-based three-dimensional printing (S-3DPTM),” PhD Dissertation, Massachusetts Institute of Technology (2005).

25.

C.-K. 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]

26.

K.-O. Park and J. M. Sivertsen, “Temperature dependence of the bulk modulus of BaO single crystals,” J. Am. Ceram. Soc. 60(11-12), 537–538 (1977). [CrossRef]

27.

N. Shibata, Y. Azuma, T. Horiguchi, and M. Tateda, “Identification of longitudinal acoustic modes guided in the core region of a single-mode optical fiber by Brillouin gain spectra measurements,” Opt. Lett. 13(7), 595–597 (1988). [CrossRef] [PubMed]

28.

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]

29.

P. Dragic, J. Ballato, S. Morris, and T. Hawkins, “Pockels’ coefficients of alumina in aluminosilicate optical fibers,” J. Opt. Soc. Am. B 30(2), 244–250 (2013). [CrossRef]

30.

P. Dragic and B. Ward, “Accurate modeling of the intrinsic Brillouin linewidth via finite element analysis,” IEEE Photon. Technol. Lett. 22(22), 1698–1700 (2010). [CrossRef]

31.

P. Dragic, “Brillouin gain reduction via B2O3 doping,” J. Lightwave Technol. 29(7), 967–973 (2011). [CrossRef]

32.

F. Langenhorst and A. Deutsch, “Shock experiments on pre-heated α- and β-quartz: I. Optical and density data,” Earth Planet. Sci. Lett. 125(1-4), 407–420 (1994). [CrossRef]

33.

Z. Shuang and W. Fuquan, “The study on dispersive equation and thermal refractive index coefficient of quartz crystal,” Acta Photon. Sin. 35, 1183–1186 (2006).

34.

J. Kushibiki, M. Ohtagawa, and I. Takanaga, “Comparison of acoustic properties between natural and synthetic α-quartz crystals,” J. Appl. Phys. 94(1), 295–300 (2003). [CrossRef]

35.

Springer Materials, “The Landolt-Börnstein Database,” http://www.springermaterials.com/docs/pdfs/10681719_257.pdf

36.

C. J. Anderson and E. B. Hensley, “Index of refraction of barium oxide,” J. Appl. Phys. 46(1), 443 (1975). [CrossRef]

37.

G. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

38.

R. Ulrich and A. Simon, “Polarization optics of twisted single-mode fibers,” Appl. Opt. 18(13), 2241–2251 (1979). [CrossRef] [PubMed]

39.

K. Matusita, R. Yokota, T. Kimijima, T. Komatsu, and C. Ihara, “Compositional trends in photoelastic constants of borate glasses,” J. Am. Ceram. Soc. 67(4), 261–265 (1984). [CrossRef]

40.

K. Matusita, C. Ihara, T. Komatsu, and R. Yokota, “Photoelastic effects in phosphate glasses,” J. Am. Ceram. Soc. 68(7), 389–391 (1985). [CrossRef]

41.

M. Guignard and J. W. Zwanziger, “Zero stress-optic barium tellurite glass,” J. Non-Cryst. Solids 353(16-17), 1662–1664 (2007). [CrossRef]

42.

K. V. K. Rao and V. G. K. Murty, “Photoelastic constants of magnesium oxide,” Acta Crystallogr. 17(6), 788–789 (1964). [CrossRef]

43.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990). [CrossRef] [PubMed]

OCIS Codes
(060.2290) Fiber optics and optical communications : Fiber materials
(060.2310) Fiber optics and optical communications : Fiber optics
(160.2290) Materials : Fiber materials
(290.5830) Scattering : Scattering, Brillouin

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: March 4, 2013
Revised Manuscript: April 16, 2013
Manuscript Accepted: April 23, 2013
Published: April 26, 2013

Citation
P. Dragic, C. Kucera, J. Furtick, J. Guerrier, T. Hawkins, and J. Ballato, "Brillouin spectroscopy of a novel baria-doped silica glass optical fiber," Opt. Express 21, 10924-10941 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-10924


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References

  1. C. K. Jen, “Similarities and differences between fiber acoustics and fiber optics,” Proceedings of the IEEE Ultrasonics Symposium, (IEEE, 1985), pp. 1128 – 1133.
  2. P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” CLEO/QELS Technical Digest, pp. 1984–1986, (2005), paper CThZ3.
  3. M.-J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, D. A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” Optical Fiber Communication Conference, (Optical Society of America, 2006), paper OTuA4. [CrossRef]
  4. A. Kobyakov, S. Kumar, D. Chowdhury, A. B. Ruffin, M. Sauer, S. Bickham, and R. Mishra, “Design concept for optical fibers with enhanced SBS threshold,” Opt. Express13(14), 5338–5346 (2005). [CrossRef] [PubMed]
  5. W. Zou, Z. He, M. Kishi, and K. Hotate, “Stimulated Brillouin scattering and its dependences on strain and temperature in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett.32(6), 600–602 (2007). [CrossRef] [PubMed]
  6. P. Dragic, “Novel dual-Brillouin-frequency optical fiber for distributed temperature sensing,” Proc. SPIE7197, 719710, 719710-10 (2009). [CrossRef]
  7. P. Dragic, T. Hawkins, P. Foy, S. Morris, and J. Ballato, “Sapphire-derived all-glass optical fibres,” Nat. Photonics6(9), 629–633 (2012). [CrossRef]
  8. J. Ballato and E. Snitzer, “Fabrication of fibers with high rare-earth concentrations for Faraday isolator applications,” Appl. Opt.34(30), 6848–6854 (1995). [CrossRef] [PubMed]
  9. J. Ballato, T. Hawkins, P. Foy, B. Kokuoz, R. Stolen, C. McMillen, M. Daw, Z. Su, T. Tritt, M. Dubinskii, J. Zhang, T. Sanamyan, and M. J. Matthewson, “On the fabrication of all-glass optical fibers from crystals,” J. Appl. Phys.105(5), 053110 (2009). [CrossRef]
  10. S. Morris, T. Hawkins, P. Foy, C. McMillen, J. Fan, L. Zhu, R. Stolen, R. Rice, and J. Ballato, “Reactive molten core fabrication of silicon optical fiber,” Opt. Mater. Express1(6), 1141–1149 (2011). [CrossRef]
  11. P. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett.45(5), 256–257 (2009). [CrossRef]
  12. P. 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]
  13. P. Dragic, J. Ballato, A. Ballato, S. Morris, T. Hawkins, P.-C. Law, S. Ghosh, and M. C. Paul, “Mass density and the Brillouin spectroscopy of aluminosilicate optical fibers,” Opt. Mater. Express2(11), 1641–1654 (2012). [CrossRef]
  14. M. Huntelaar and E. Cordfunke, “The ternary system BaSiO3-SrSiO3-SiO2,” J. Nucl. Mater.201, 250–253 (1993). [CrossRef]
  15. A. Yablon, “Multi-wavelength optical fiber refractive index profiling by spatially resolved Fourier transform spectroscopy,” J. Lightwave Technol.28(4), 360–364 (2010). [CrossRef]
  16. 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. Express1(4), 686–699 (2011). [CrossRef]
  17. P.-C. Law, A. Croteau, and P. Dragic, “Acoustic coefficients of P2O5-doped silica fiber: the strain-optic and strain-acoustic coefficients,” Opt. Mater. Express2(4), 391–404 (2012). [CrossRef]
  18. 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. B26(8), 1614–1620 (2009). [CrossRef]
  19. 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]
  20. P. Eskola, “The silicates of strontium and barium,” Am. J. Sci.4(23), 331–375 (1922). [CrossRef]
  21. J. Greig, “Immiscibility in silicate melts,” Am. J. Sci.13(73), 1–44 (1927). [CrossRef]
  22. T. Seward, D. Uhlmann, and D. Turnbull, “Phase separation in the system BaO-SiO2,” J. Am. Ceram. Soc.51(5), 278–285 (1968). [CrossRef]
  23. T. Seward, D. Uhlmann, and D. Turnbull, “Development of two-phase structure in glasses with special reference to the system BaO-SiO2,” J. Am. Ceram. Soc.51(11), 634–642 (1968). [CrossRef]
  24. H.-R. Wang, “Graded-index (GRIN) lenses by slurry-based three-dimensional printing (S-3DPTM),” PhD Dissertation, Massachusetts Institute of Technology (2005).
  25. C.-K. 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]
  26. K.-O. Park and J. M. Sivertsen, “Temperature dependence of the bulk modulus of BaO single crystals,” J. Am. Ceram. Soc.60(11-12), 537–538 (1977). [CrossRef]
  27. N. Shibata, Y. Azuma, T. Horiguchi, and M. Tateda, “Identification of longitudinal acoustic modes guided in the core region of a single-mode optical fiber by Brillouin gain spectra measurements,” Opt. Lett.13(7), 595–597 (1988). [CrossRef] [PubMed]
  28. 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]
  29. P. Dragic, J. Ballato, S. Morris, and T. Hawkins, “Pockels’ coefficients of alumina in aluminosilicate optical fibers,” J. Opt. Soc. Am. B30(2), 244–250 (2013). [CrossRef]
  30. P. Dragic and B. Ward, “Accurate modeling of the intrinsic Brillouin linewidth via finite element analysis,” IEEE Photon. Technol. Lett.22(22), 1698–1700 (2010). [CrossRef]
  31. P. Dragic, “Brillouin gain reduction via B2O3 doping,” J. Lightwave Technol.29(7), 967–973 (2011). [CrossRef]
  32. F. Langenhorst and A. Deutsch, “Shock experiments on pre-heated α- and β-quartz: I. Optical and density data,” Earth Planet. Sci. Lett.125(1-4), 407–420 (1994). [CrossRef]
  33. Z. Shuang and W. Fuquan, “The study on dispersive equation and thermal refractive index coefficient of quartz crystal,” Acta Photon. Sin.35, 1183–1186 (2006).
  34. J. Kushibiki, M. Ohtagawa, and I. Takanaga, “Comparison of acoustic properties between natural and synthetic α-quartz crystals,” J. Appl. Phys.94(1), 295–300 (2003). [CrossRef]
  35. Springer Materials, “The Landolt-Börnstein Database,” http://www.springermaterials.com/docs/pdfs/10681719_257.pdf
  36. C. J. Anderson and E. B. Hensley, “Index of refraction of barium oxide,” J. Appl. Phys.46(1), 443 (1975). [CrossRef]
  37. G. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
  38. R. Ulrich and A. Simon, “Polarization optics of twisted single-mode fibers,” Appl. Opt.18(13), 2241–2251 (1979). [CrossRef] [PubMed]
  39. K. Matusita, R. Yokota, T. Kimijima, T. Komatsu, and C. Ihara, “Compositional trends in photoelastic constants of borate glasses,” J. Am. Ceram. Soc.67(4), 261–265 (1984). [CrossRef]
  40. K. Matusita, C. Ihara, T. Komatsu, and R. Yokota, “Photoelastic effects in phosphate glasses,” J. Am. Ceram. Soc.68(7), 389–391 (1985). [CrossRef]
  41. M. Guignard and J. W. Zwanziger, “Zero stress-optic barium tellurite glass,” J. Non-Cryst. Solids353(16-17), 1662–1664 (2007). [CrossRef]
  42. K. V. K. Rao and V. G. K. Murty, “Photoelastic constants of magnesium oxide,” Acta Crystallogr.17(6), 788–789 (1964). [CrossRef]
  43. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42(9), 5514–5521 (1990). [CrossRef] [PubMed]

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