OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 18 — Aug. 31, 2009
  • pp: 16225–16237
« Show journal navigation

SBS threshold measurements and acoustic beam propagation modeling in guiding and anti-guiding single mode optical fibers

Marc D. Mermelstein  »View Author Affiliations


Optics Express, Vol. 17, Issue 18, pp. 16225-16237 (2009)
http://dx.doi.org/10.1364/OE.17.016225


View Full Text Article

Acrobat PDF (353 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A 4.3 dB stimulated Brillouin scattering (SBS) threshold suppression is measured in a passive Al-doped acoustically anti-guiding single mode optical fiber relative to that of a Ge-doped acoustically guiding single mode optical fiber. Stimulated scattering is generated by the electrostrictive acoustic wave generated in the fiber core. This acoustic excitation has a decay length Ld related to the sound absorption decay length Labs and the acoustic waveguide decay length Lwg by: Ld−1= Labs−1+ Lwg−1. The acoustic waveguide decay length Lwg is associated with the diffraction, refraction and reflection of the acoustic wave in the elastically inhomogeneous optical fiber cores. The SBS gain is proportional to the net acoustic decay length Ld and the relative SBS suppression is proportional to the ratio of the net decay lengths of the Al and Ge doped cores (LAl/ LGe). An acoustic beam propagation model is used to calculate the evolution of the complex acoustic excitations in the optical cores and determine the acoustic wave decay lengths Lwg. Model predictions for the relative SBS suppression for the two fibers are in good agreement with experimental values obtained from Stokes power and optical heterodyne linewidth measurements.

© 2009 OSA

1. Introduction

The report is structured in the following manner: Section 2 is the experimental section that presents the measurements of SBS gain coefficients. The SBS gain coefficient ratio, and therefore the SBS threshold suppression, is measured in three ways. In the first case, it is extracted from very low (<0.01) SBS reflectivity measurements with a high resolution optical spectrum analyzer (OSA). In the second case, it is measured from the backscattered Stokes power with a power meter (PM) at 1% and 10% SBS reflectivities and in the third case it is extracted from optical heterodyne linewidth measurements of the Stokes light with an electrical spectrum analyzer (ESA). Section 3 discusses the SBS process in the two fibers and models the relative SBS gain with an acoustic adaptation of the BPM used for optical waveguides. The BPM is used to calculate a value for the waveguide decay length Lwg of the Al-doped fiber and estimate the SBS suppression relative to that of the Ge-doped fiber. The model prediction of −4.7 dB SBS suppression is in good agreement with the measured suppression levels. These experimental and theoretical results present a good basis for the further design of SBS suppressing optical fibers. Section 4 contains a summary of the results presented in this report.

2. Experiment

The experimental arrangement is shown in Fig. 1
Fig. 1 Experimental arrangement for measurement of the SBS threshold and spectra in the FsUT (SF-single frequency, CW-continuous wave, LO-local oscillator).
. The seed laser source is a distributed feedback fiber laser that provides approximately 15 mW of single frequency (linewidth ~25 kHz) light at 1083 nm to a double clad Yb-doped fiber amplifier. The amplifier output is controlled by adjusting the power of the 915 nm pump light. The amplified radiation passes through an isolator and a 1% fused coupler to the fibers-under-test (FsUT). The tap monitors both the backscattered and injected light. Two 500 m spools of SMF are investigated. The first fiber has a Ge doped core and is acoustically guiding, i.e. the optical core has an acoustic index N=V0/Vc greater than that of the optical cladding where V0 is the sound speed in the cladding. Further details and measurement results concerning the two optical fibers are presented below in Table 1

Table 1. Fiber parameters and measurement results.

table-icon
View This Table
| View All Tables
at the end of this section. The fused coupler monitors the injected Brillouin pump light and the backscattered Stokes light. The Stokes power is investigated with the OSA and the PM, and the optical heterodyne linewidth measurements are made with the ESA. The FsUT are terminated with an angle cleave to minimize Fresnel reflections for the PM and OSA measurements and are terminated with a flat cleave to provide an optical local oscillator for the heterodyne measurements.

Figure 3
Fig. 3 Plot of SBS reflectivities as a function of pump power for the guiding and anti-guiding SMFs along with fitting parameters to Eq. (2).
is a plot of the SBS reflectivity in dB as a function of the Brillouin pump power for the guiding and anti-guiding optical fibers. The Stokes powers are extracted from the OSA spectra shown in Figs. 2a and 2b. The solid line is a least-squares fit of Eq. (2) for the SBS reflectivity RSBS to the Brillouin pump powers. The two fitting parameters, ηβS and CB are shown in the figure.The relative SBS gain coefficients, and therefore the SBS suppression, is given by:
gB[Al]gB[Ge]=CB[Al]CB[Ge]Aeff[Al]Aeff[Ge].
(5)
Substitution of the extracted values for CB and Aeff from Table 1 yields an SBS gain suppression of −4.0 dB.

Figure 4
Fig. 4 Backscattered optical power PS as a function of the Brillouin pump power PP for the two fibers. The slanted dotted lines correspond to 1% and 10% SBS reflectivities. The curved dashed lines show numerical solutions to the coupled rate equations with ηβS and CB taken from Fig. 3.
shows a plot of the backscattered Stokes power, obtained from the PM measurements, as a function of the Brillouin pump power at higher SBS reflectivities. The dotted lines correspond to backscatter reflectivities of 1% and 10%. These reflectivities are used to define the SBS threshold powers Pth. For example, 1% reflectivities are achieved in the Ge and Al doped fibers at Brillouin pump powers of 60 mW and 140 mW, respectively.The SBS threshold powers are given by [17

17. M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency and modeling in 1714 μm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24), 15952–15963 (2007). [CrossRef] [PubMed]

]:
Pth=κAeffgBLeff
(6)
where
κ=ln[RSBSηβSCBPth].
(7)
κ is a number that is dependent upon several experimental and fiber parameters and is generally taken to be equal to 21 for 100% reflectivity [19

19. 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]

]. A complete description of the power evolution in the optical fiber, including pump depletion, can be described by the coupled rate equations [15

15. G. P. Agrawal, Non-Linear Optics, (Academic Press, San Diego, 1995).

,17

17. M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency and modeling in 1714 μm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24), 15952–15963 (2007). [CrossRef] [PubMed]

] for the Stokes power PS and the Brillouin pump power PP. A numerical solution of these coupled differential equation yields the relation between κ and the SBS reflectivity RSBS and is shown in Fig. 5
Fig. 5 Plot of κ versus RSBS for the guiding and anti-guiding SMFs.
for the both the Ge doped and Al doped fibers.The numerical values for the captured spontaneous Brillouin scattering coefficient ηβS and the SBS gain efficiency CB are taken from Fig. 3. It is found that the values for κ are nearly the same for the two fibers and approach 21 for RSBS=1. The SBS gain suppression, as determined by Eqs. (6) and (7), is given by:
gB[Al]gB[Ge]=Pth[Ge]Pth[Al]Leff[Ge]Leff[Al]κ[Al]κ[Ge]Aeff[Al]Aeff[Ge].
(8)
Substitution of the values for Pth, Leff and Aeff from Table 1 yields an SBS gain suppression of −4.3 and −4.4 dB for 1% and 10% SBS reflectivities, respectively. The curved dashed lines appearing in Fig. 3 are a numerical computation of the Stokes powers obtained from the coupled rate equations [17

17. M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency and modeling in 1714 μm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24), 15952–15963 (2007). [CrossRef] [PubMed]

] for the Stokes power PS and the Brillouin pump power PP that includes pump depletion. The agreement of the numerical results is excellent for the Ge-doped guiding fiber while there is some discrepancy noted for the Al-doped anti-guiding fiber. Good agreement between the measured result and the numerical calculation can be obtained for a gain efficiency of 0.18 (m-W)−1, so these results show a 10% discrepancy.

The intensity of spontaneous Brillouin back-scattered light may be estimated from the Rayleigh ratio R [20

20. I. L. Fabelinskii, Molecular Scattering of Light,”(Plenum Press, 1968).

,21

21. H. Z. Cummins, and P. Schoen, Linear scattering from thermal fluctuations, in Laser Handbook (North Holland, Amsterdam 1971).

] (or differential cross-section per unit length) for optical and acoustic plane waves:
R=π2kBTn8p1222Eλ4
(9)
where kB is the Boltzman constant, T is the temperature in degrees Kelvin and E is the Young’s modulus. The Rayleigh ratio has unit of m−1 and includes both the Stokes and anti-Stokes light scattering. The fiber collection solid angle is Ω=πNA2 where the fiber numerical aperture is: NA=λ/(πAeff)1/2 [22

22. E.-G. Neumann, Single Mode Fibers, (Springer Verlag, New York, 1985).

] for a Gaussian optical mode. Hence, the back-scattered Stokes power captured by the fiber per unit length is given by: ηβS=RΩ/2. This relation yields values for ηβS of 5.6x10−9 m−1 and 6.7x10−9 m−1 for the Ge and Al-doped fibers, respectively. The order of magnitude agreement with the measured values presented in Fig. 3 is reasonable given that the calculated values pertain to plane waves and do not include the transverse optical and acoustic mode structure.

3. SBS mechanism, acoustic beam propagation modeling and data analysis

There are three physical mechanisms that will govern the evolution of the acoustic disturbance. First, the acoustic wave will spread due to diffraction with an angle θ~0.66Λm/a (Airy disk) where ‘a’ is the core radius. For Λm~0.4 μm and a~3 μm we find that θ~0.1 radians so that the launched acoustic wave is collimated along the fiber axis. Secondly, the acoustic frequency of the sound wave is equal to that of the Brillouin shift (15-16 GHz) and exhibits a decay length of ~25 μm due to viscous damping [24

24. R. W. Boyd, Non-linear Optics, (Academic Press, New York, 2003).

]. And third, the inhomogeneous elastic medium in the fiber core and nearby cladding, due to the differing dopants and dopant concentrations, causes the acoustic wave to refract as it propagates along the fiber. A complete description of the dynamic acoustic disturbance generated in the optical fiber by the volumetric source term Eq. (14) is given by the inhomogeneous acoustic wave equation for an unbounded inhomogeous elastic medium [25

25. G. Barton, Elements of Green’s Functions and Propagation, (Oxford University Press, New York, 1989).

]. Rather than solve this wave equation, the approach taken here is to launch an acoustic wave with a transverse density fluctuation profile f(r)2 into an inhomogeneous elastic medium characterized by N(r) and calculate the evolution of the complex density fluctuation profile as it propagates along the fiber axis with a beam propagation code [26

26. J. Yamauchi, Y. Akimoto, M. Nibe, and H. Nakano, “Wide-angle propagating beam analysis for circularly symmetric waveguides: comparison between FD-BPM and FD-BPM,” IEEE Photon. Technol. Lett. 8(2), 236–238 (1996). [CrossRef]

]. Here we take advantage of the fact that the optical waves and the acoustic waves can both be described by a scalar wave equation. The acoustic index profiles for the Ge and Al doped fibers are shown in Fig. 8
Fig. 8 Plot of the acoustic index N as a function of radial position in the fiber. The inset shows the optical intensity distribution in the fiber which is also the distribution of the electrostrictive density fluctuation source.
. The empirical relations used are:
N[Ge]=1.00+5.235Δn[Ge]N[Al]=1.003.512Δn[Al]
(15)
where Δn is the core-cladding optical index difference. Equation (15) is taken from Ref [27

27. Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and Designing Brillouin gain spectra in single mode fibers,” J. Lightwave Technol. 22(2), 631–639 (2004). [CrossRef]

]. for the Ge doped fiber. The dependence of Vc upon Δn for the Al doped fiber was obtained by measuring the Brillouin shift frequencies νΒ=2nVc/λ in three Al doped fibers with differing Al concentrations and measured index profiles. An acoustic index N=1 corresponds to a cladding sound speed of 5944 m/s [27

27. Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and Designing Brillouin gain spectra in single mode fibers,” J. Lightwave Technol. 22(2), 631–639 (2004). [CrossRef]

]. The inset shows the intensity distributions of the fiber modes. Note that the intensity distributions extend into regions of the fiber core that experience significant gradients in the acoustic index.

Figure 9
Fig. 9 Plot of acoustic amplitude magnitude as a function of radius for an elastically homogeneous fiber, the acoustic guiding fiber and acoustic anti-guiding fiber at differing propagation distances. Blue shaded region highlights acoustic energy refracted from fiber core in the anti-guiding case. The window size for the BPM code is 50 μm in the radial direction and 62.5 μm in the longitudinal direction with a radial resolution of 0.2 μm and a longitudinal resolution of 0.25 μm.
shows the evolution of the complex density fluctuation amplitude along the fiber length for three cases: (i) an elastically homogeneous fiber, (ii) the guiding Ge doped core fiber and (iii) the anti-guiding Al doped fiber at longitudinal distances of 0, 10, 20 and of 30 μm. The first case for an elastically homogeneous material shows some small spreading the acoustic waveform due to diffraction. In the acoustic guiding fiber, the acoustic amplitude remains within the fiber core exhibiting some refraction and reflection at the core-cladding interface. However, the energy again remains within the fiber core. In the anti- guiding case, the acoustic wave migrates out of the core region into the nearby cladding at propagation distances comparable to and less than the acoustic decay length. The amount of energy that leaves the core is significant since is scales with the radius squared.

Figure 10
Fig. 10 Plot of the radial phase of the acoustic waves for the homogeneous elastic medium, acoustic guiding fiber and acoustic anti-guiding fiber at a propagation distance of 20 μm.
shows the radial phase of the complex acoustic disturbance over a radius of 5 μm after propagating 20 μm along the fiber axis. In the elastically homogeneous case, some curvature of the phase front of ~2 radians is evident, indicating the beam spreading due to diffraction. The Ge doped fiber shows less spreading of ~1 radian due to the acoustic guiding properties of this fiber. Here beam spreading due to diffraction is compensated by the acoustic waveguide. However, the Al doped fiber shows a large phase curvature of ~10 radians representative of the strong acoustic anti-guiding properties of this fiber.

The electrostrictively generated acoustic wave Δρe will be absorbed as it propagates along the fiber length. The acoustic amplitude will decay Δρe ~exp(-z/2Labs) and the acoustic intensity will decay as |Δρe|2~exp(-z/Labs). The decay of the acoustic amplitude from its initial value is generalized in an ad hoc fashion by calculating the cross-sectional correlation function or normalized overlap integral of the complex density fluctuations at location z compared with those appearing at z=0:
γ(z)=Δρe(r,z)*Δρe(r,0)|Δρ(r,0)|2
(16)
where γ(z) is the complex transverse correlation function or overlap integral. In this manner, the effect of the inhomogeneous elastic medium on the electrostrictively generated acoustic wave for the guiding and anti-guiding fibers may be characterized in a quantitative manner.

Figure 11
Fig. 11 Plots of the magnitude squared of the transverse acoustic amplitude correlation function as a function of propagation distance z for various cases discussed in the text.
shows plots of | γ(z)|2 as a function of propagation distance z for several situations. The solid black line shows the decay for viscous damping with a phonon linewidth of 75 MHz. This phonon linewidth is consistent with the low gain bandwidth extracted from the heterodyne measurements for the guiding Ge-doped fiber. The e−1 point corresponds to a decay length of 25.1 μm. The dotted lines show |γ(z)|2 for elastically homogeneous bulk media with the same dopant concentrations as the guiding and anti-guiding optical fibers.These lines show the effects of diffraction and exhibit e−1 levels at ~50 μm. This length scale is significantly greater than that of the viscous damping; therefore, acoustic diffraction is not expected to play a large role in determining the acoustic decay length. The solid blue line is |γ(z)|2 for the acoustic guiding structure. It exhibits some fluctuations due to the structure of the acoustic guiding refractive index N. However, it remains highly correlated over the range of the calculation and is therefore interpreted to have a correlation length that significantly exceeds that due to the viscous damping. Therefore the decay length of the acoustic guiding fiber is taken to be determined by the viscous damping. The red line shows |γ(z)|2 for the acoustic anti-guiding fiber. It shows a more rapid and pronounced decay due to the acoustic waveguide effects and the dispersal of the acoustic energy away from the central core region. The total decay length Ld therefore has contributions from the viscous damping and waveguide effects and may be written as [28

28. P. D. Dragic, “SBS-suppressed single mode Yb-doped fiber amplifiers,” Proc. OFC-NFOEC,2009, JThA10.

]:
1Ld=1Labs+1Lwg.
(17)
Taking Lwg>>Labs=25.1 μm for the Ge doped fiber and Lwg=14.9 μm for the Al doped fiber, we find that Ld=25.1 μm for the acoustic guiding fiber and that Ld=9.35 μm for the acoustic anti-guiding fiber. The SBS suppression is determined by the ratio of the gain coefficients gB given by Eq. (1) with the spectral widths Δν expressed by the BPM-determined decay lengths Ld:
gB[Al]gB[Ge]=νB[Ge]2νB[Al]2Ld[Al]Ld[Ge].
(18)
This yields an SBS suppression of the Al doped fiber relative to that of the Ge doped fiber of −4.7 dB in agreement with the threshold measurements obtained from the Stokes power and heterodyne linewidth measurements. A summary of the SBS threshold determinations is shown in Table 2

Table 2. SBS suppressions

table-icon
View This Table
| View All Tables
. Other physical parameters used in these calculations are shown in Table 3.

Table 3. Parameters

table-icon
View This Table
| View All Tables

4. Conclusion

The relative SBS gain coefficients of a Ge doped step index acoustic guiding SBS an Al doped acoustic anti-guiding fiber have been measured. Stokes power and linewidth measurements demonstrate a relative SBS suppression level of ~ 4.0-4.8 dB. The SBS suppression mechanism is modeled with an acoustic adaptation of the BPM for optical waveguides. SBS suppression in the anti-guiding fiber is attributed to the decorelation of the electrostrictively generated acoustic intensity by the inhomogeous elastic medium. This decorelation is quantified by an acoustic waveguide decay length Lwg which provides an additional decay mechanism to the viscous damping decay length Labs. Agreement between the BPM model and the experimental results indicate that the BPM may be useful in the design of other SBS suppressing optical fibers.

The author thanks Man Yan for providing the Al doped fibers and helpful discussions with David DiGiovanni and Ben Ward. Andrew Yablon is thanked for many in-depth discussions and his assistance with the BPM code.

References

1.

D. Cotter, “Stimulated Brillouin scattering in monomode optical fibers,” J. Opt. Commun. 4, 10–19 (1983). [CrossRef]

2.

D. A. Fishman and J. A. Nagel, “Degradations due to stimulated Brillouin scattering in multigigabit intensity-modulated fiber-optic systems,” J. Lightwave Technol. 11(11), 1721–1728 (1993). [CrossRef]

3.

G. Kulcsar, Y. Jaouen, G. Canat, E. Olmedo, and G. Debarge, “Multi-Stokes stimulated Brillouin scattering generated in pulsed high-power double cladding Er-Yb codoped fiber amplifiers,” IEEE Photon. Technol. Lett. 15(6), 801–803 (2003). [CrossRef]

4.

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master oscillator power amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007). [CrossRef]

5.

Y. Feng, L. Taylor, and D. Bonaccini Calia, “Multiwatts narrow linewidth fiber Raman amplifiers,” Opt. Express 16(15), 10927–10932 (2008). [CrossRef] [PubMed]

6.

K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol. 14(1), 50–57 (1996). [CrossRef]

7.

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1(5), 107–108 (1989). [CrossRef]

8.

J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, “Increase of the SBS threshold in short highly nonlinear fiber by applying a temperature distribution,” J. Lightwave Technol. 19(11), 1691–1697 (2001). [CrossRef]

9.

M. D. Mermelstein, A. D. Yablon and C. Headley, “Suppression of Stimulated Brillouin Scattering in Er-Yb Fiber Amplifiers Utilizing Temperature-Segmentation,” Optical Amplifiers and Their Applications, paper TuD3 (2005).

10.

P. D. Dragic, “Acoustical-optical fibers for control of stimulated Brillouin scattering,” in 2006 Digest of the LEOS Summer Topical Meeting, 3–4 (2006).

11.

M. J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, and L. A. Zenteno., “Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express 15(13), 8290–8299 (2007). [CrossRef] [PubMed]

12.

M. D. Mermelstein, M. J. Andrejco, J. Fini, A. Yablon, C. Headley, D. G. DiGiovanni, and A. H. McCurdy, “11.2 dB SBS gain suppression in large mode area Yb-doped optical fiber,” Proc. SPIE 6873, U63–U69 (2008).

13.

S. Yoo, J. K. Sahu, and J. Nilsson, “Optimized acoustic refractive index profiles for suppression of stimulated Brillouin scattering in large core fibers,” in Optical Fiber Communication Conference (Optical Society of America, Washington, DC, 2008).

14.

B. G. Ward and J. B. Spring, “Brillouin gain in optical fibers with inhomogeneous acoustic velocity,” Proc. SPIE 7195, 71951H (2009). [CrossRef]

15.

G. P. Agrawal, Non-Linear Optics, (Academic Press, San Diego, 1995).

16.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation, (Springer Verlag, New York, 1985).

17.

M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency and modeling in 1714 μm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24), 15952–15963 (2007). [CrossRef] [PubMed]

18.

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994). [CrossRef]

19.

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]

20.

I. L. Fabelinskii, Molecular Scattering of Light,”(Plenum Press, 1968).

21.

H. Z. Cummins, and P. Schoen, Linear scattering from thermal fluctuations, in Laser Handbook (North Holland, Amsterdam 1971).

22.

E.-G. Neumann, Single Mode Fibers, (Springer Verlag, New York, 1985).

23.

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

24.

R. W. Boyd, Non-linear Optics, (Academic Press, New York, 2003).

25.

G. Barton, Elements of Green’s Functions and Propagation, (Oxford University Press, New York, 1989).

26.

J. Yamauchi, Y. Akimoto, M. Nibe, and H. Nakano, “Wide-angle propagating beam analysis for circularly symmetric waveguides: comparison between FD-BPM and FD-BPM,” IEEE Photon. Technol. Lett. 8(2), 236–238 (1996). [CrossRef]

27.

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and Designing Brillouin gain spectra in single mode fibers,” J. Lightwave Technol. 22(2), 631–639 (2004). [CrossRef]

28.

P. D. Dragic, “SBS-suppressed single mode Yb-doped fiber amplifiers,” Proc. OFC-NFOEC,2009, JThA10.

OCIS Codes
(190.4370) Nonlinear optics : Nonlinear optics, fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: July 6, 2009
Revised Manuscript: July 27, 2009
Manuscript Accepted: July 27, 2009
Published: August 27, 2009

Citation
Marc D. Mermelstein, "SBS threshold measurements and acoustic beam propagation modeling in guiding and anti-guiding single mode optical fibers," Opt. Express 17, 16225-16237 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-18-16225


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. Cotter, “Stimulated Brillouin scattering in monomode optical fibers,” J. Opt. Commun. 4, 10–19 (1983). [CrossRef]
  2. D. A. Fishman and J. A. Nagel, “Degradations due to stimulated Brillouin scattering in multigigabit intensity-modulated fiber-optic systems,” J. Lightwave Technol. 11(11), 1721–1728 (1993). [CrossRef]
  3. G. Kulcsar, Y. Jaouen, G. Canat, E. Olmedo, and G. Debarge, “Multi-Stokes stimulated Brillouin scattering generated in pulsed high-power double cladding Er-Yb codoped fiber amplifiers,” IEEE Photon. Technol. Lett. 15(6), 801–803 (2003). [CrossRef]
  4. Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master oscillator power amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007). [CrossRef]
  5. Y. Feng, L. Taylor, and D. Bonaccini Calia, “Multiwatts narrow linewidth fiber Raman amplifiers,” Opt. Express 16(15), 10927–10932 (2008). [CrossRef] [PubMed]
  6. K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol. 14(1), 50–57 (1996). [CrossRef]
  7. T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1(5), 107–108 (1989). [CrossRef]
  8. J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, “Increase of the SBS threshold in short highly nonlinear fiber by applying a temperature distribution,” J. Lightwave Technol. 19(11), 1691–1697 (2001). [CrossRef]
  9. M. D. Mermelstein, A. D. Yablon and C. Headley, “Suppression of Stimulated Brillouin Scattering in Er-Yb Fiber Amplifiers Utilizing Temperature-Segmentation,” Optical Amplifiers and Their Applications, paper TuD3 (2005).
  10. P. D. Dragic, “Acoustical-optical fibers for control of stimulated Brillouin scattering,” in 2006 Digest of the LEOS Summer Topical Meeting, 3–4 (2006).
  11. M. J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, and L. A. Zenteno., “Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express 15(13), 8290–8299 (2007). [CrossRef] [PubMed]
  12. M. D. Mermelstein, M. J. Andrejco, J. Fini, A. Yablon, C. Headley, D. G. DiGiovanni, and A. H. McCurdy, “11.2 dB SBS gain suppression in large mode area Yb-doped optical fiber,” Proc. SPIE 6873, U63–U69 (2008).
  13. S. Yoo, J. K. Sahu, and J. Nilsson, “Optimized acoustic refractive index profiles for suppression of stimulated Brillouin scattering in large core fibers,” in Optical Fiber Communication Conference (Optical Society of America, Washington, DC, 2008).
  14. B. G. Ward and J. B. Spring, “Brillouin gain in optical fibers with inhomogeneous acoustic velocity,” Proc. SPIE 7195, 71951H (2009). [CrossRef]
  15. G. P. Agrawal, Non-Linear Optics, (Academic Press, San Diego, 1995).
  16. B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation, (Springer Verlag, New York, 1985).
  17. M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency and modeling in 1714 μm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24), 15952–15963 (2007). [CrossRef] [PubMed]
  18. M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994). [CrossRef]
  19. 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]
  20. I. L. Fabelinskii, Molecular Scattering of Light,”(Plenum Press, 1968).
  21. H. Z. Cummins, and P. Schoen, Linear scattering from thermal fluctuations, in Laser Handbook (North Holland, Amsterdam 1971).
  22. E.-G. Neumann, Single Mode Fibers, (Springer Verlag, New York, 1985).
  23. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990). [CrossRef] [PubMed]
  24. R. W. Boyd, Non-linear Optics, (Academic Press, New York, 2003).
  25. G. Barton, Elements of Green’s Functions and Propagation, (Oxford University Press, New York, 1989).
  26. J. Yamauchi, Y. Akimoto, M. Nibe, and H. Nakano, “Wide-angle propagating beam analysis for circularly symmetric waveguides: comparison between FD-BPM and FD-BPM,” IEEE Photon. Technol. Lett. 8(2), 236–238 (1996). [CrossRef]
  27. Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and Designing Brillouin gain spectra in single mode fibers,” J. Lightwave Technol. 22(2), 631–639 (2004). [CrossRef]
  28. P. D. Dragic, “SBS-suppressed single mode Yb-doped fiber amplifiers,” Proc. OFC-NFOEC,2009, JThA10.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited