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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 18 — Aug. 30, 2010
  • pp: 18852–18865
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Wavelength dependence of the Brillouin spectral width of boron doped germanosilicate optical fibers

Pi-Cheng Law and Peter D. Dragic  »View Author Affiliations


Optics Express, Vol. 18, Issue 18, pp. 18852-18865 (2010)
http://dx.doi.org/10.1364/OE.18.018852


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Abstract

Boron co-doped germanosilicate fibers are investigated via the Brillouin light scattering technique using two wavelengths, 1534nm and 1064nm. Several fibers are investigated, including four drawn from the same preform but at different draw temperatures. The Stokes’ shifts and the Brillouin spectral widths are found to increase with increasing fiber draw temperature. A frequency-squared law has adequately described the wavelength dependence of the Brillouin spectral width of conventional Ge-doped fibers. However, it is found that unlike conventional Ge-doped fibers these fibers do not follow the frequency-squared law. This is explained through a frequency-dependent dynamic viscosity that modifies this law.

© 2010 OSA

1. Introduction

Brillouin scattering in optical fibers has been finding an increasing number of applications. More traditional of such applications are, for example, distributed sensing [1

1. D. Culverhouse, F. Farahi, C. N. Pannell, and D. A. Jackson, “Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensors,” Electron. Lett. 25(14), 913–915 (1989). [CrossRef]

,2

2. K. Shimizu, T. Horiguchi, and Y. Koyamada, “Measurement of distributed strain and temperature in a branched optical fiber network by using Brillouin OTDR,” Proc. SPIE 2360, 142–145 (1994). [CrossRef]

] and light amplification [3

3. D. Pohl, M. Maier, and W. Kaiser, “Transient and steady-state gain in stimulated Brillouin amplifiers,” IEEE J. Quantum Electron. 4(5), 320–321 (1968). [CrossRef]

], while newer applications include slow-light systems [4

4. Z. Zhu, M. D. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS slow light in an optical fiber,” J. Lightwave Technol. 25(1), 201–206 (2007). [CrossRef]

] and ultra-long coherence length lasers [5

5. A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: theoretical analysis,” Phys. Rev. A 62(2), 023803 (2000). [CrossRef]

], among others. Recently, novel fibers have been realized with the rationale that it is possible to tailor the acoustic properties, i.e. an acoustic index profile (AIP), of an optical fiber, sometimes largely independently of its optical properties [6

6. P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” in Conference on Lasers and Electro-Optics/Quantum Electronics and laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CTHZ3.

8

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

]. Undoubtedly, these and newer innovations will lead to an even broader range of applications for Brillouin scattering, both spontaneous (SpBS) and stimulated (SBS).

Effectively tailoring the AIP of an optical fiber necessitates a fairly accurate understanding of how fiber dopants influence a number of acoustic properties of the optical fiber, namely the acoustic velocity [9

9. 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]

] and viscosity [10

10. J. E. Masnik, J. Kieffer, and J. D. Bass, “Structural relaxations in alkali silicate systems by Brillouin light scattering,” J. Am. Ceram. Soc. 76(12), 3073–3080 (1993). [CrossRef]

,11

11. J. E. Masnik, J. Kieffer, and J. D. Bass, “The complex mechanical modulus as a structural probe: the case of alkali borate liquids and glasses,” J. Chem. Phys. 103(23), 9907–9917 (1995). [CrossRef]

] (or acoustic wave loss due to material damping). These parameters largely set the observed Brillouin frequency shift, νB, and Brillouin spectral width, ΔνB, respectively. The latter is important in designing fibers with Brillouin gain coefficients (BGC, units of m/W) of certain strength [12

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

], including maximizing or minimizing this value for a specific system or application.

This first order analysis, however, neglects the fact that there is an additional frequency-dependent dynamic viscosity term in the expression for the Brillouin spectral width [10

10. J. E. Masnik, J. Kieffer, and J. D. Bass, “Structural relaxations in alkali silicate systems by Brillouin light scattering,” J. Am. Ceram. Soc. 76(12), 3073–3080 (1993). [CrossRef]

]. This term has a maximum viscosity value at some glass temperature (or fictive temperature [15

15. T. M. Gross and M. Tomozawa, “Fictive temperature of GeO2 glass: its determination by IR method and its effects on density and refractive index,” J. Non-Cryst. Solids 353(52-54), 4762–4766 (2007). [CrossRef]

]), that is dependent on the acoustic frequency. We will show that when the temperature of the peak of the viscosity curve at hypersonic frequencies lies far from a fiber’s fictive temperature [16

16. A. S. Pine, “Brillouin scattering study of acoustic attenuation in fused quartz,” Phys. Rev. 185(3), 1187–1193 (1969). [CrossRef]

], ΔνB acquires a simple frequency-squared dependence. However, we will also show that when the peak of viscosity lies in the vicinity of a fiber’s fictive temperature, then a departure from this rule can be experienced. From [11

11. J. E. Masnik, J. Kieffer, and J. D. Bass, “The complex mechanical modulus as a structural probe: the case of alkali borate liquids and glasses,” J. Chem. Phys. 103(23), 9907–9917 (1995). [CrossRef]

], one may conclude that this is potentially the case with boric oxide as its peak viscosity at hypersonic acoustic frequencies lies around 1000 ~2000 K, warranting some further investigation.

In this paper, we investigate the wavelength dependence of ΔνB for boric oxide-doped germanosilicate fibers. A total of eight fibers are investigated at both 1534 nm and 1064 nm. Four of these are B + Ge-doped silica that were drawn from the same preform, but at different draw temperatures (1900 °C, 1950 °C, 2050 °C, and 2150 °C), while the remaining three B + Ge fibers include two different samples from Nufern of East Granby, CT and one purchased from Newport Corp. The latter three fibers are highly-B + Ge-doped photosensitive fibers. A sample of Corning SMF-28TM is included in the analysis as the eighth and a reference fiber. We find that each of the B-doped fibers follows a sub-wavelength-squared dependence of the Brillouin spectral width, while the Corning fiber appears to obey the wavelength-squared law. A possible explanation for this behavior is offered in some detail using the theory found in [10

10. J. E. Masnik, J. Kieffer, and J. D. Bass, “Structural relaxations in alkali silicate systems by Brillouin light scattering,” J. Am. Ceram. Soc. 76(12), 3073–3080 (1993). [CrossRef]

]. Understanding this phenomenon for other and less traditional dopants then becomes important for wavelength-specific applications.

2. Experimental setup

This experiment uses an optical heterodyne detection system to measure the Spontaneous Brillouin Scattering (SpBS) spectra [17

17. R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode fiber characterization,” Electron. Lett. 22, 1101–1113 (1986).

]. Since we are measuring at two wavelengths (1534 nm and 1064 nm), the systems we employed were both Er and Yb fiber amplifier-based. More details of the Er-based system can be found in [18

18. P. D. Dragic, “Brillouin spectroscopy of Nd-Ge co-doped silica fibers,” J. Non-Cryst. Solids 355(7), 403–413 (2009). [CrossRef]

], while Fig. 1
Fig. 1 Experimental apparatus for measurement of the Brillouin spectrum at 1064 nm. A narrow linewidth YAG laser operating at 1064 nm is boosted and passed through a circulator to the test fiber. The Stokes’ signal and local oscillator signal are then preamplified before being heterodyned with a fast detector.
illustrates the block diagram of the Yb-based experimental configuration which is described here. A Nd:YAG laser operating at 1064.263 nm and linewidth of less than 10 kHz works as a seed laser. The output light of the seed laser is isolated and then amplified by a first, in-house assembled, ytterbium doped fiber amplifier (YDFA#1) providing about 200mW of saturated output power. The amplified seed signal then passes through Port 2 of an optical circular. The optical circular is produced from HI-1060TM fiber which utilizes Ge dopant ions and has about 1.5m of this fiber at each of the three ports. Therefore, in addition to the signal from the fiber under test (FUT), the Brillouin frequency shifts from the HI-1060TM fiber are also observed. The amplified seed signal passes into the FUTs with an optical single mode launch generating the Brillouin scattered signals which pass back through port 3 of the circulator and into YDFA#2. The Brillouin scattered signals (reflected backward) are adequately amplified by YDFA#2 (small signal gain) before being heterodyned with a fast PiN detector (New Focus 1534). Finally, an Agilent PSA series electrical spectrum analyzer (ESA) measures the acoustic modes carried by the Brillouin scattered signals.

Due to adopting the heterodyne approach, the fundamental local oscillator (LO) signal is required for mixing. As such, we point out that the LO signal came from appropriately cleaving the output end of the FUT. The Fresnel reflection from the end of the FUT provides an adequate LO signal to achieve low-noise heterodyne detection, but was limited via a cleave angle so as to not saturate YDFA#2.

In the experiments, YDFA#1 works as a power amplifier to boost the seed laser output power. Meanwhile, YDFA#2 works as a detector preamplifier to increase the scattered and reflected signals, including both the SpBS and seed signals. In order to obtain trustworthy data, YDFA#1 should provide adequate power to generate SpBS signals, while not generating Stimulated Brillouin Scattering (SBS) with apparent gain. This may result in an observed linewidth that is narrower than the true spontaneous spectrum [19

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

]. Therefore, amplifier characteristics, including pump power, etc. were adjusted to avoid any spectral narrowing effects due to SBS gain.

YDFA#2 plays the very important role of amplifying the SpBS and seed signals to an adequate level for the fast PiN detector. We used 120cm of heavily-doped YDF and a 200mW pump laser diode in designing YDFA#2. Due to the lower signal power in this amplifier stage, we expect that significant ASE noise may come up and therefore the fiber length was selected in order to minimize this ASE noise. We also note that the reflected signals have different power levels. Apparently, the seed signal power can be multiple orders of magnitude larger than the SpBS signal power. Therefore, the seed signal could saturate YDFA#2 resulting in less gain being available to the SpBS signal. Therefore, as described above, we adjusted the cleave angle of the FUT to reduce the seed signal power reflected into YDFA#2 to that of small signal levels. Figure 2(a)
Fig. 2 a) Available YDFA#2 power for the Brillouin gain measurements and b) Gain vs. signal power for the heterodyne optical preamplifier showing the region of small signal gain.
and 2(b) are the output power and gain of YDFA#2 versus the input signal power at 1064nm at 221mW pumping power. It is found that YDFA#2 has a small signal gain in the range from 0dBm to −20dBm (or less) (insertion and splicing losses to the input power in the system makes these values seem large) with around 17dB net gain. Its performance allows the fast PiN to produce an adequate heterodyne signal.

3. Experimental results

Eight fibers are investigated in this study. Four of these (Fibers 1 – 4) were drawn from the same B-doped germanosilicate preform, but at different draw temperatures, as outlined in Table 1

Table 1. Fitted spectral widths and measured Stokes’ shifts for the various fibers at 1534 nm and 1064 nm.

table-icon
View This Table
. These fibers have core diameters of 10 μm and the concentrations of B2O3 and GeO2 were measured via Electron Probe Micro Analysis (EPMA) to be about 6.2 wt% and 10.8 wt%, respectively. The decreasing Stokes’ frequency with decreasing draw temperature (see Table 1) can largely be attributed to an increased required draw tension at lower temperatures resulting in a larger residual fiber strain, consistent with the results found in [20

20. C. Headley, J. B. Clayton, W. A. Reed, L. Eskildsen, and P. B. Hansen, “Technique for obtaining a 2.5 dB increase in the stimulated Brillouin scattering threshold of Ge-doped fibers by varying fiber draw tension,” in Optical Fiber Communication Conference, Technical Digest (Optical Society of America, 1997) paper WL25.

,21

21. W. Zou, Z. He, A. D. Yablon, and K. Hotate, “Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains,” IEEE Photon. Technol. Lett. 19(18), 1389–1391 (2007). [CrossRef]

], however, this analysis is beyond the scope of this work. Complete details for the remaining three B + G fibers (Fibers 5-7) are not available, but since they each have similar Stokes’s shifts, they probably have very similar dopant compositions [9

9. 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]

]. Additionally, due to their application as photosensitive fiber, it is believed that they each possess similar optical properties and therefore similar proportions of germania and boric oxide as compared with Fibers 1 – 4. The final fiber that is tested is Corning SMF-28TM, containing about 4.0 mol% GeO2 (also EPMA data).

In Fig. 3
Fig. 3 A plot of the measured RIPs of SMF-28TM (dashed line) and Fiber 4 (solid line). Both fibers have a similar central dip. Also shown is a plot of the L01 acoustic mode (Fiber 4) at 1534 nm (slightly wider in the central region) and 1064 nm. Their amplitudes were adjusted for visual clarity with respect to the RIPs.
are provide the refractive index profiles (RIPs) of both SMF-28TM (measured by Interfiber Analysis Inc.) and Fiber 4 (provided by Nufern). Fibers 1 – 3 have similar RIPs to Fiber 4, but with slightly greater index differences due to the differing draw conditions [22

22. A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004). [CrossRef]

]. In particular, the NAs of Fibers 1 – 4 are 0.141, 0.127, 0.112, and 0.107, respectively. Furthermore, because our fibers are acoustically guiding (and acoustically multimode) structures, the Brillouin spectrum will be dominated by light scattering from acoustic modes of the acoustic waveguide [23

23. N. Shibata, K. Okamoto, and Y. Azuma, “Longitudinal acoustic modes and Brillouin-gain spectra for GeO2-doped-core single-mode fibers,” J. Opt. Soc. Am. B 6(6), 1167–1174 (1989). [CrossRef]

]. Since we are focusing on the fundamental L01 acoustic mode in this work, a plot of the fundamental mode (normalized field) is also provided in Fig. 3 (red curves) for both 1064 nm and 1534 nm, with the acoustic mode at 1534 nm being insignificantly wider. It is clear that the fundamental acoustic mode is well-confined to the uniform region of the fiber (about 1 to 4.5 microns in position). More specifically, it is calculated that the L01 acoustic power confinement in this ring region is > 99% in all Fibers 1 – 4 at both wavelengths. That the modes at the two wavelengths have essentially the same spatial distribution within a uniform region of the fiber helps to remove uncertainty in the measurements caused by non-uniform acoustic profiles. In other words, we assume that measurements on the L01 acoustic mode (acoustic velocity, viscosity) will be close to the material values in the uniform portion of the waveguide at both wavelengths. Finally, the similarity of the SMF-28TM RIP to that of Fibers 1 – 4 provides confidence that SMF-28TM can serve as a reasonable control or reference fiber.

Figure 4
Fig. 4 Typical spectrum obtained at 1534 nm and 1064 nm (Fiber 4). Several acoustic modes are observed including peaks due to the measurement apparatus (circulator). The best fit to the fundamental mode is also shown (dashed line) to make the HOAMs more obvious.
provides an example of Brillouin spectra obtained at 1534 nm and 1064 nm (Fiber 4). This data is provided as ‘typical’ of the spectra obtained for the fibers of the present study. In both cases, the contributions due to the circulator, in addition to several higher-order acoustic modes (HOAMs), are observed. The HOAMs are clearly visible in the spectra, but not directly pointed out. The dashed line shown in Fig. 4 represents the best fit to the L01 acoustic mode.

Provided in the inset of each plot is the fitted spectral width (ΔνB) of the L01 acoustic mode and the measured peak frequency (νB). It is worthy of note that the ratio of the peak frequencies is slightly different than the ratios of the wavelengths. In particular, νB1064/νB1534=1.446, while 1534/1064 = 1.442. Most of this difference can be attributed to chromatic dispersion in the glass since the material index of refraction is slightly higher at 1064 nm.

As a point of reference, a segment of SMF-28TM was also tested for comparison. The results are shown in Fig. 5
Fig. 5 Spectra of SMF-28TM obtained at 1534 nm and 1064 nm. Some HOAMs are visible. The best fit to the fundamental mode is also shown (dashed line).
, along with the best fit to the L01 mode. HOAMs are visible at both wavelengths. To compare the spectra, we first point out that the ratio of the square of the Brillouin frequencies is 2.08, while that of the spectral widths is 2.06. Therefore, we can conclude that the lightly Ge-doped silica fiber appears to follow the frequency-squared law.

It is worth pointing out that Fiber 1 shows an abnormal spectral width at 1534 nm. From Table 1, the spectral width at 1534 nm of this fiber appears to be anomalous in that it has broken a trend by being larger than that of the next-higher-temperature fiber. This observation suggests that there may be more effects in the relationship for the spectral width that may not be accounted for in this work. And as a result, the 1900 °C data point in Fig. 6 also appears visually anomalous. We are continuing to investigate the cause of this anomaly.

4. Discussion

4.1 Theory

Table 1 suggests that the B-Ge doped fibers have an anomalous behavior in the wavelength-dependence of the Brillouin spectral width that departs from the usual frequency-squared law. To explain this, we will first investigate the derivation of the Brillouin spectral width. There are some phenomena to explain the internal friction which is equal to the Brillouin spectral width divided by the Stokes’ frequency shift. Anderson and Bommel proposed that structural relaxation may be responsible for the internal friction in fused silica and speculated that the lateral motion of the oxygen atom in the Si-O4 tetrahedron probably results in the internal friction effect [25

25. O. L. Anderson and H. E. Bömmel, “Ultrasonic absorption in fused silica at low temperatures and high frequencies,” J. Am. Ceram. Soc. 38(4), 125–131 (1955). [CrossRef]

]. Next, based on the glassy states associated with certain activation energies, the tunneling model was developed to explain the low-temperature anomalies of amorphous solids, but at the higher temperature the thermally activated relaxation process rather than the tunneling process seems to dominate the anomalous properties in vitreous silica [26

26. D. Tielbürger, R. Merz, R. Ehrenfels, and S. Hunklinger, “Thermally activated relaxation processes in vitreous silica: An investigation by Brillouin scattering at high pressures,” Phys. Rev. B Condens. Matter 45(6), 2750–2760 (1992). [CrossRef] [PubMed]

] and in vitreous germania [27

27. J. Hertling, S. Baeßler, S. Rau, G. Kasper, and S. Hunklinger, “Internal friction and hypersonic velocity in vitreous germania under high pressure,” J. Non-Cryst. Solids 226(1-2), 129–137 (1998). [CrossRef]

]. We follow the theory (thermally activated relaxation process) which can be found in greater detail in [24

24. J. Kieffer, “Mechanical degradation and viscous dissipation in B2O3.,” Phys. Rev. B Condens. Matter 50(1), 17–29 (1994). [CrossRef] [PubMed]

] but is presented here for the convenience of the reader. The wave number q of acoustic phonons defines the elastic wave with respect to the angle θ between the incident and scattered light. Since Brillouin scattering is a backward Stokes’ wave scattering, θ = 180°, giving rise to
q=2nλosin(θ/2)=2nλo=1λa=ωVa.
(1)
In Eq. (1) n is the refractive index of the scattering media, λo is the wavelength of the incident light, λa is the acoustic wavelength, ω is the acoustic frequency (ω from [24

24. J. Kieffer, “Mechanical degradation and viscous dissipation in B2O3.,” Phys. Rev. B Condens. Matter 50(1), 17–29 (1994). [CrossRef] [PubMed]

] is identical to the Stokes’ frequency shift νB of the present analysis), and Va is the acoustic velocity.

τ=τoeEAkT.
(4)

In addition, the frequency-dependent kinematic viscosity ν´(ω) [10

10. J. E. Masnik, J. Kieffer, and J. D. Bass, “Structural relaxations in alkali silicate systems by Brillouin light scattering,” J. Am. Ceram. Soc. 76(12), 3073–3080 (1993). [CrossRef]

] is defined as
ν(ω)=η(ω)ρo.
(5)
From Eqs. (3), (4), and (5) we can get the relationships between the kinematic viscosity, ν´(ω), and the loss modulus, M, giving rise to
ν(ω)=η(ω)ρo=Mρoω=M2ρoτ1+(ωτ)2
(6)
and
ξ=ν(ω)ω=η(ω)ωρo=Mρo=M2ρoωτ1+(ωτ)2=M2ρoωτ0eEAkT1+(ωτoeEAkT)2.
(7)
Continuing, pure B2O3, is found to be best represented by three principal relaxation mechanisms [24

24. J. Kieffer, “Mechanical degradation and viscous dissipation in B2O3.,” Phys. Rev. B Condens. Matter 50(1), 17–29 (1994). [CrossRef] [PubMed]

], including non-planar BO3 distortions, impurity diffusion, and final network disintegration, contributing to the specific loss modulus, M/ρo (viscous dissipation). This transforms Eq. (7) (a single mechanism relationship) into a linear combination of the three individual mechanisms as follows:
ξ=ν(ω)ω=η(ω)ωρo=Mρo=n=13gnM2ρoωτ0,neEA,nkT1+(ωτo,neEA,nkT)2.
(8)
In Eq. (8) gnis the weight factor for the relaxational mechanism n with the definition gnM2=V0,n. Then, Eq. (8) is substituted into Eq. (2) to yield Eq. (9) below, which we will use to explain the apparent anomalous behavior of the spectral width ratio, ΔωB(1064nm)/ΔωB(1534nm),

ΔωB=(2nλo)2η(ω)ρo=(ωVa)2n=13V0,nρoτ0,neEA,nkT1+(ωτo,neEA,nkT)2.
(9)

The fact that the B-Ge doped fibers have a smaller measured spectral width ratio than expected suggests that we need to consider not only the wavelength (Bragg-matched acoustic frequency) but also the viscous relaxation mechanism terms in Eq. (9). It is the ratio of the summation terms (η´(1064nm)/η´(1534nm)) that contributes the factor of less than 1 to the frequency-squared law (ΔωB(1064nm)/ΔωB(1534nm) = (ω1064nm/ω1534nm)2 ≈ (1534nm/1064nm)2 = 2.08) thus reducing the spectral width ratio. This seems to be a plausible explanation for the observed anomalous behavior of the B-Ge doped fibers.

4.2 Analysis

In Fig. 8 the curves show that the modulus not only depends on the temperature but also on the operating wavelength. In the comparison of the solid (1534 nm) and dashed (1064 nm) lines, the low temperature peaks may not immediately show that there are apparent shifts, but we point out that at the middle valley around 900K the loss modulus at 1064nm is very close to that at 1534nm due to the overlap of the tails of the two dominant dissipation mechanisms and broad curves. Then, at higher temperatures, the curves diverge in that the upper end of the loss modulus shifts from 1300K to 1400K (at 1 GPa), that is, the third peak has moved towards higher temperature for the smaller optical wavelength. This further implies that the third dissipation mechanism will strongly dominate at high temperature at all wavelengths, while it is possible that other unknown mechanisms with higher activation energy could also be present. In summary, the main result that is seen in Fig. 8 is that the peaks of the loss modulus curves shift to higher temperatures with decreasing optical wavelength. The loss modulus curves are also observed to be broader at a shorter optical wavelength.

Because the resulting curves shift to higher temperature with decreasing wavelength, we can see that the value of M at 1064nm, for example at a temperatures higher than 1000K in Fig. 8, will be lower than that at 1534nm, while we point out to the reader in Eqs. (2) and (3) the relationships among M, η´(ω), and ΔωB. Therefore, taking each of these together, we may conclude that in addition to a wavenumber-dependence, ΔωB will decrease when Mdecreases due to a decrease in η´(ω). This effect is observed in the whole range of possible as-drawn fiber fictive temperatures (note the draw temperatures of Fibers 1 – 4). This suggests that the observed Brillouin spectral width of fibers derived from boric oxide-containing glasses will be smaller at 1064 nm than expected when compared with measurements at 1534 nm assuming the frequency-squared law.

We would like to point out that the spectral widths shown in Table 1 are consistent with an increasing spectral width (from Fibers 1 to 4 in order) due to an increasing fiber fictive temperature resulting from increasing fiber draw temperature. In particular, by inspecting Fig. 8, the Mvalue increases when the temperature increases (beyond ~900K) and thereby ΔωBwould be expected to increase with increasing fictive temperature. Therefore, we may conclude that Table 1 confirms this trend whereby ΔωB increases from 99MHz to 120MHz at 1064 nm as the draw temperature increases from 1950°C to 2150°C.

Next, we consider the ratios of the measured spectral widths at 1064nm to those at 1534nm for the B2O3 fibers. From the data presented in Table 1 one may conclude that Eq. (2), with an additional term η(ω)/ρo, is most representative of the observed spectral widths. In order to confirm this, Fig. 11
Fig. 11 The ratio of the spectral width at 1064nm to 1534nm for pure B2O3.
provides the ratio of the Brillouin spectral width at 1064 nm to that at 1534 nm as a function of temperature (ratio of the green to blue curves in Fig. 9). We see that the ratio is lower than the ratio of the square of the acoustic frequencies at temperatures lower than around 3000K. This suggests that the additional term contributes a factor (η´(1064nm)/η´(1534nm)) of less than 1 to the frequency-squared law, while it decreases with decreasing temperature. In contrast, when the temperature is larger than around 3000K, this factor reaches unity and therefore the ratio approaches a constant value of about 2.08, corresponding to the ratio of the square of the acoustic frequencies. Thus, beyond this temperature the spectral width ratio follows the frequency-squared law. This suggests that at temperatures much higher than the peak of the viscosity curve the wavelength-dependence of the Brillouin spectral width reduces to the frequency-squared law. Silica (or predominantly silica) fibers, for example, would then be expected to follow the frequency-squared law since the peak of the viscosity curve would always lie well-below (at cryogenic temperatures) any expected fictive temperature of a derived fiber [16

16. A. S. Pine, “Brillouin scattering study of acoustic attenuation in fused quartz,” Phys. Rev. 185(3), 1187–1193 (1969). [CrossRef]

]. This is evident in the SMF-28TM fiber (see data in Table 1), which contains about 4mol% GeO2 in silica.

More specifically along these lines, in contrast to the B + Ge fibers, the lightly Ge-doped silica fiber data shows that the spectral width roughly follows the frequency-squared law. For a simulation of silica glass, we refer to Fig. 12(a)
Fig. 12 (a) The ratio of the spectral width at 1064nm to 1534nm and (b) the spectral width of 1064nm for the pure silica simulation.
, where based on the work found in [16

16. A. S. Pine, “Brillouin scattering study of acoustic attenuation in fused quartz,” Phys. Rev. 185(3), 1187–1193 (1969). [CrossRef]

,29

29. S. Le Floch and P. Cambon, “Study of Brillouin gain spectrum in standard single-mode optical fiber at low temperatures (1.4-370K) and high hydrostatic pressures (1-250 bars),” Opt. Commun. 219(1-6), 395–410 (2003). [CrossRef]

] a rough example of an arbitrary glass with a single-mechanism and a peak viscosity at cryogenic temperatures is provided. (Fig. 12(b) shows the corresponding spectral width dependence on temperature at a wavelength of 1064nm.) It is seen that the curve reaches the ratio value greater than 2.0 at temperatures above 200K. Therefore, for all possible fiber fictive temperatures (T > room or ambient temperature), the silica glass has already reached this constant ratio value.

With respect to the fibers in Table 1, we can see that there does indeed appear to be a dependence of measured spectral width on the fiber draw temperature, and that the ratios of observed spectral widths may in fact be a way to gauge the fictive temperature of a fiber. Along these lines, one may conclude that fibers 5, 6, and 7 are drawn at temperatures close to that of fiber 4 (2150 °C). Another observation is that in our data, the ratio from Fiber 2 to Fiber 4 changes from 1.57 to 1.76 with a change in draw temperature of 200 K. We will initially neglect the anomalous data point observed for Fiber 1. This is consistent with the slope of the curve in Fig. 11 in the region of 1400K to 2400K. Furthermore, since silica follows the frequency-squared law for any anticipated fiber fictive temperature, the addition of it to pure boric oxide is expected to increase the ratio of the spectral widths (to closer to the frequency-squared law) calculated in Fig. 11 for regions less than about 3000K. Thus, since our maximum observed ratio is 1.76, we can state based on Fig. 11 that the fibers’ fictive temperatures probably lie below 1900K. From this observation, it is clear that the fictive temperature is less than the draw temperature, consistent with some glass relaxation during the fiber draw process.

Finally, we point out that this is a coarse analysis, and not a complete one. While the study above assumes bulk B2O3, the present case is in reality complicated by the presence of germania (as well as silica) in the fiber which also influences the spectral width. Therefore, in order to comprehend the B + G fiber characteristics, we need to further understand the various relationships among dopants, temperature, precise oxide concentrations, index of refraction, acoustic modes, and so on. We are working to extend this analysis with a model for several mixed materials. This may prove to be useful in the design of optical fibers with tailored Brillouin properties for a number of different applications.

5. Conclusion

We have presented Brillouin spectral width measurements of B2O3 and GeO2 co-doped silica fibers at two wavelengths, 1064 nm and 1534 nm. Our data indicates that fibers containing boric oxide do not follow the conventional frequency-squared law for the Brillouin spectral width. Instead the measured ratio appears to depart from the ratio of the square of the acoustic frequencies. We have presented an analysis for bulk B2O3 in order to explain this behavior. It was proposed that since the peak of the viscosity versus temperature curve lies within the vicinity (or greater than that) of the anticipated fiber fictive temperature, a usually-neglected dynamic viscosity term reduces this ratio. In contrast, at fiber fictive temperatures much higher than the peak of the viscosity curve, the wavelength-dependence of the Brillouin spectral width reduces to the frequency-squared law.

Acknowledgements

This work was supported in part by the Joint Technology Office (JTO) through their High Energy Laser Multidisciplinary Research Initiative (HEL-MRI) program entitled “Novel Large-Mode-Area (LMA) Fiber Technologies for High Power Fiber Laser Arrays” under ARO subcontract # F014252. The authors are grateful to Nufern of East Granby, CT for the custom fabrication of Fibers 1 – 4, the fiber samples, and for several fruitful discussions with their team. The authors would also like to acknowledge Professor Gary R. Swenson for his full support.

References and links

1.

D. Culverhouse, F. Farahi, C. N. Pannell, and D. A. Jackson, “Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensors,” Electron. Lett. 25(14), 913–915 (1989). [CrossRef]

2.

K. Shimizu, T. Horiguchi, and Y. Koyamada, “Measurement of distributed strain and temperature in a branched optical fiber network by using Brillouin OTDR,” Proc. SPIE 2360, 142–145 (1994). [CrossRef]

3.

D. Pohl, M. Maier, and W. Kaiser, “Transient and steady-state gain in stimulated Brillouin amplifiers,” IEEE J. Quantum Electron. 4(5), 320–321 (1968). [CrossRef]

4.

Z. Zhu, M. D. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS slow light in an optical fiber,” J. Lightwave Technol. 25(1), 201–206 (2007). [CrossRef]

5.

A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: theoretical analysis,” Phys. Rev. A 62(2), 023803 (2000). [CrossRef]

6.

P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” in Conference on Lasers and Electro-Optics/Quantum Electronics and laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CTHZ3.

7.

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

8.

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

9.

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]

10.

J. E. Masnik, J. Kieffer, and J. D. Bass, “Structural relaxations in alkali silicate systems by Brillouin light scattering,” J. Am. Ceram. Soc. 76(12), 3073–3080 (1993). [CrossRef]

11.

J. E. Masnik, J. Kieffer, and J. D. Bass, “The complex mechanical modulus as a structural probe: the case of alkali borate liquids and glasses,” J. Chem. Phys. 103(23), 9907–9917 (1995). [CrossRef]

12.

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

13.

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

14.

C. Krischer, “Optical measurements of ultrasonic attenuation and reflection losses in fused silica,” J. Acoust. Soc. Am. 48(5B), 1086–1092 (1970). [CrossRef]

15.

T. M. Gross and M. Tomozawa, “Fictive temperature of GeO2 glass: its determination by IR method and its effects on density and refractive index,” J. Non-Cryst. Solids 353(52-54), 4762–4766 (2007). [CrossRef]

16.

A. S. Pine, “Brillouin scattering study of acoustic attenuation in fused quartz,” Phys. Rev. 185(3), 1187–1193 (1969). [CrossRef]

17.

R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode fiber characterization,” Electron. Lett. 22, 1101–1113 (1986).

18.

P. D. Dragic, “Brillouin spectroscopy of Nd-Ge co-doped silica fibers,” J. Non-Cryst. Solids 355(7), 403–413 (2009). [CrossRef]

19.

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

20.

C. Headley, J. B. Clayton, W. A. Reed, L. Eskildsen, and P. B. Hansen, “Technique for obtaining a 2.5 dB increase in the stimulated Brillouin scattering threshold of Ge-doped fibers by varying fiber draw tension,” in Optical Fiber Communication Conference, Technical Digest (Optical Society of America, 1997) paper WL25.

21.

W. Zou, Z. He, A. D. Yablon, and K. Hotate, “Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains,” IEEE Photon. Technol. Lett. 19(18), 1389–1391 (2007). [CrossRef]

22.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004). [CrossRef]

23.

N. Shibata, K. Okamoto, and Y. Azuma, “Longitudinal acoustic modes and Brillouin-gain spectra for GeO2-doped-core single-mode fibers,” J. Opt. Soc. Am. B 6(6), 1167–1174 (1989). [CrossRef]

24.

J. Kieffer, “Mechanical degradation and viscous dissipation in B2O3.,” Phys. Rev. B Condens. Matter 50(1), 17–29 (1994). [CrossRef] [PubMed]

25.

O. L. Anderson and H. E. Bömmel, “Ultrasonic absorption in fused silica at low temperatures and high frequencies,” J. Am. Ceram. Soc. 38(4), 125–131 (1955). [CrossRef]

26.

D. Tielbürger, R. Merz, R. Ehrenfels, and S. Hunklinger, “Thermally activated relaxation processes in vitreous silica: An investigation by Brillouin scattering at high pressures,” Phys. Rev. B Condens. Matter 45(6), 2750–2760 (1992). [CrossRef] [PubMed]

27.

J. Hertling, S. Baeßler, S. Rau, G. Kasper, and S. Hunklinger, “Internal friction and hypersonic velocity in vitreous germania under high pressure,” J. Non-Cryst. Solids 226(1-2), 129–137 (1998). [CrossRef]

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.

S. Le Floch and P. Cambon, “Study of Brillouin gain spectrum in standard single-mode optical fiber at low temperatures (1.4-370K) and high hydrostatic pressures (1-250 bars),” Opt. Commun. 219(1-6), 395–410 (2003). [CrossRef]

OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(060.2290) Fiber optics and optical communications : Fiber materials
(160.2290) Materials : Fiber materials
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(190.5890) Nonlinear optics : Scattering, stimulated

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: May 21, 2010
Revised Manuscript: July 12, 2010
Manuscript Accepted: July 14, 2010
Published: August 19, 2010

Citation
Pi-Cheng Law and Peter D. Dragic, "Wavelength dependence of the Brillouin spectral width of boron doped germanosilicate
optical fibers," Opt. Express 18, 18852-18865 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-18-18852


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References

  1. D. Culverhouse, F. Farahi, C. N. Pannell, and D. A. Jackson, “Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensors,” Electron. Lett. 25(14), 913–915 (1989). [CrossRef]
  2. K. Shimizu, T. Horiguchi, and Y. Koyamada, “Measurement of distributed strain and temperature in a branched optical fiber network by using Brillouin OTDR,” Proc. SPIE 2360, 142–145 (1994). [CrossRef]
  3. D. Pohl, M. Maier, and W. Kaiser, “Transient and steady-state gain in stimulated Brillouin amplifiers,” IEEE J. Quantum Electron. 4(5), 320–321 (1968). [CrossRef]
  4. Z. Zhu, M. D. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS slow light in an optical fiber,” J. Lightwave Technol. 25(1), 201–206 (2007). [CrossRef]
  5. A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: theoretical analysis,” Phys. Rev. A 62(2), 023803 (2000). [CrossRef]
  6. P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” in Conference on Lasers and Electro-Optics/Quantum Electronics and laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CTHZ3.
  7. M.-J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” in Optical Fiber Communication Conference and National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2006), paper OTuA4.
  8. P. D. Dragic, “Novel dual-Brillouin-frequency optical fiber for distributed temperature sensing,” Proc. SPIE 7197, 719710 (2009). [CrossRef]
  9. 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]
  10. J. E. Masnik, J. Kieffer, and J. D. Bass, “Structural relaxations in alkali silicate systems by Brillouin light scattering,” J. Am. Ceram. Soc. 76(12), 3073–3080 (1993). [CrossRef]
  11. J. E. Masnik, J. Kieffer, and J. D. Bass, “The complex mechanical modulus as a structural probe: the case of alkali borate liquids and glasses,” J. Chem. Phys. 103(23), 9907–9917 (1995). [CrossRef]
  12. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972). [CrossRef] [PubMed]
  13. G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, 1995).
  14. C. Krischer, “Optical measurements of ultrasonic attenuation and reflection losses in fused silica,” J. Acoust. Soc. Am. 48(5B), 1086–1092 (1970). [CrossRef]
  15. T. M. Gross and M. Tomozawa, “Fictive temperature of GeO2 glass: its determination by IR method and its effects on density and refractive index,” J. Non-Cryst. Solids 353(52-54), 4762–4766 (2007). [CrossRef]
  16. A. S. Pine, “Brillouin scattering study of acoustic attenuation in fused quartz,” Phys. Rev. 185(3), 1187–1193 (1969). [CrossRef]
  17. R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode fiber characterization,” Electron. Lett. 22, 1101–1113 (1986).
  18. P. D. Dragic, “Brillouin spectroscopy of Nd-Ge co-doped silica fibers,” J. Non-Cryst. Solids 355(7), 403–413 (2009). [CrossRef]
  19. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990). [CrossRef] [PubMed]
  20. C. Headley, J. B. Clayton, W. A. Reed, L. Eskildsen, and P. B. Hansen, “Technique for obtaining a 2.5 dB increase in the stimulated Brillouin scattering threshold of Ge-doped fibers by varying fiber draw tension,” in Optical Fiber Communication Conference, Technical Digest (Optical Society of America, 1997) paper WL25.
  21. W. Zou, Z. He, A. D. Yablon, and K. Hotate, “Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains,” IEEE Photon. Technol. Lett. 19(18), 1389–1391 (2007). [CrossRef]
  22. A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004). [CrossRef]
  23. N. Shibata, K. Okamoto, and Y. Azuma, “Longitudinal acoustic modes and Brillouin-gain spectra for GeO2-doped-core single-mode fibers,” J. Opt. Soc. Am. B 6(6), 1167–1174 (1989). [CrossRef]
  24. J. Kieffer, “Mechanical degradation and viscous dissipation in B2O3.,” Phys. Rev. B Condens. Matter 50(1), 17–29 (1994). [CrossRef] [PubMed]
  25. O. L. Anderson and H. E. Bömmel, “Ultrasonic absorption in fused silica at low temperatures and high frequencies,” J. Am. Ceram. Soc. 38(4), 125–131 (1955). [CrossRef]
  26. D. Tielbürger, R. Merz, R. Ehrenfels, and S. Hunklinger, “Thermally activated relaxation processes in vitreous silica: An investigation by Brillouin scattering at high pressures,” Phys. Rev. B Condens. Matter 45(6), 2750–2760 (1992). [CrossRef] [PubMed]
  27. J. Hertling, S. Baeßler, S. Rau, G. Kasper, and S. Hunklinger, “Internal friction and hypersonic velocity in vitreous germania under high pressure,” J. Non-Cryst. Solids 226(1-2), 129–137 (1998). [CrossRef]
  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. S. Le Floch and P. Cambon, “Study of Brillouin gain spectrum in standard single-mode optical fiber at low temperatures (1.4-370K) and high hydrostatic pressures (1-250 bars),” Opt. Commun. 219(1-6), 395–410 (2003). [CrossRef]

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