Abstract

A numerical investigation is presented of Brillouin gain in SBS-suppressing optical fibers with non-uniform acoustic velocity profiles. The equation determining the acoustic displacement in response to the electrostriction caused by the pump and Stokes waves reduces to the non-homogeneous Helmholtz equation for fibers with a uniform acoustic velocity profile. In this special case the acoustic displacement and subsequently the Brillouin gain are calculated using a Green's function. These results are then used to validate a finite-element solution of the same equation. This finite element method is then used to analyze a standard large mode area fiber as well as fibers incorporating four different acoustic velocity profiles with 5% variation in the acoustic velocity across the core. The profiles which suppress the peak Brillouin gain most effectively exhibit a maximum acoustic gradient near the midpoint between the center and boundary of the fiber core. These profiles produce 11 dB of suppression relative to standard large mode area fibers.

© 2009 OSA

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V. I. Kovalev and R. G. Harrison, “Threshold for stimulated Brillouin scattering in optical fiber,” Opt. Express 15(26), 17,625–17,630 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-26-17625 .
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[CrossRef]

M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency measurements and modeling in a 1714 mm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24), 15,952–15,963 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15952 .
[CrossRef]

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. 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]

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8290 .
[CrossRef] [PubMed]

2006

V. I. Kovalev and R. G. Harrison, “Suppression of stimulated Brillouin scattering in high-power single-frequency fiber amplifiers,” Opt. Lett. 31(2), 161–163 (2006), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-2-161 .
[CrossRef] [PubMed]

M. Hildebrandt, M. Frede, P. Kwee, B. Willke, and D. Kracht, “Single-frequency master-oscillator photonic crystal fiber amplifier with 148 W output power,” Opt. Express 25, 11,071–11,076 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11071 .

W. Zou, Z. He, and K. Hotate, “Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers,” IEEE Photon. Technol. Lett. 18(23), 2487–2489 (2006).
[CrossRef]

2005

2002

2000

1999

E. Peral and A. Yariv, “Degradation of Modulation and Noise Characteristics of Semiconductor Lasers After Propagation in Optical Fiber Due to a Phase Shift Induced by Stimulated Brillouin Scattering,” IEEE J. Quantum Electron. 35(8), 1185–1195 (1999).
[CrossRef]

1966

C. Tang, “Saturation and Spectral Characteristics of the Stokes Emission in the Stimulated Brillouin Process,” J. Appl. Phys. 37(8), 2945–2956 (1966), http://link.aip.org/link/?JAPIAU/37/2945/1 .
[CrossRef]

1956

P. C. Hammer, O. J. Marlowe, and A. H. Stroud, “Numerical Integration over Simplexes and Cones,” Math. Tables Other Aids Comput. 10(55), 130–137 (1956).
[CrossRef]

Alegria, C.

Alvarez-Chavez, J. A.

Bickham, S. R.

Chen, X.

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8290 .
[CrossRef] [PubMed]

S. Gray, A. Liu, D. T. Walton, J. Wang, M.-J. Li, X. Chen, A. B. R. J. A. De Meritt, and L. A. Zenteno, “502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier,” Opt. Express 15(25), 17,044–17,050 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-25-17044 .
[CrossRef]

Cheung, E. C.

Chowdhury, D. Q.

Chryssou, C. E.

Codemard, C. A.

Crowley, A. M.

De Meritt, A. B. R. J. A.

S. Gray, A. Liu, D. T. Walton, J. Wang, M.-J. Li, X. Chen, A. B. R. J. A. De Meritt, and L. A. Zenteno, “502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier,” Opt. Express 15(25), 17,044–17,050 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-25-17044 .
[CrossRef]

Demeritt, J. A.

Dupriez, P.

Fini, J. M.

M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency measurements and modeling in a 1714 mm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24), 15,952–15,963 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15952 .
[CrossRef]

Frede, M.

M. Hildebrandt, M. Frede, P. Kwee, B. Willke, and D. Kracht, “Single-frequency master-oscillator photonic crystal fiber amplifier with 148 W output power,” Opt. Express 25, 11,071–11,076 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11071 .

Ghalmi, S.

M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency measurements and modeling in a 1714 mm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24), 15,952–15,963 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15952 .
[CrossRef]

Goldberg, L.

Goodno, G. D.

Gray, S.

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8290 .
[CrossRef] [PubMed]

S. Gray, A. Liu, D. T. Walton, J. Wang, M.-J. Li, X. Chen, A. B. R. J. A. De Meritt, and L. A. Zenteno, “502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier,” Opt. Express 15(25), 17,044–17,050 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-25-17044 .
[CrossRef]

Hammer, P. C.

P. C. Hammer, O. J. Marlowe, and A. H. Stroud, “Numerical Integration over Simplexes and Cones,” Math. Tables Other Aids Comput. 10(55), 130–137 (1956).
[CrossRef]

Harrison, R. G.

He, Z.

Hickey, L.

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. 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]

Hickey, L. M. B.

Hildebrandt, M.

M. Hildebrandt, M. Frede, P. Kwee, B. Willke, and D. Kracht, “Single-frequency master-oscillator photonic crystal fiber amplifier with 148 W output power,” Opt. Express 25, 11,071–11,076 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11071 .

Ho, J. G.

Horley, R.

Hotate, K.

Jeong, Y.

Kliner, D. A. V.

Kobyakov, A.

Koplow, J. P.

Kovalev, V. I.

Kracht, D.

M. Hildebrandt, M. Frede, P. Kwee, B. Willke, and D. Kracht, “Single-frequency master-oscillator photonic crystal fiber amplifier with 148 W output power,” Opt. Express 25, 11,071–11,076 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11071 .

Kumar, S.

Kwee, P.

M. Hildebrandt, M. Frede, P. Kwee, B. Willke, and D. Kracht, “Single-frequency master-oscillator photonic crystal fiber amplifier with 148 W output power,” Opt. Express 25, 11,071–11,076 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11071 .

Li, M.-J.

S. Gray, A. Liu, D. T. Walton, J. Wang, M.-J. Li, X. Chen, A. B. R. J. A. De Meritt, and L. A. Zenteno, “502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier,” Opt. Express 15(25), 17,044–17,050 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-25-17044 .
[CrossRef]

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8290 .
[CrossRef] [PubMed]

Liu, A.

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8290 .
[CrossRef] [PubMed]

S. Gray, A. Liu, D. T. Walton, J. Wang, M.-J. Li, X. Chen, A. B. R. J. A. De Meritt, and L. A. Zenteno, “502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier,” Opt. Express 15(25), 17,044–17,050 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-25-17044 .
[CrossRef]

Marlowe, O. J.

P. C. Hammer, O. J. Marlowe, and A. H. Stroud, “Numerical Integration over Simplexes and Cones,” Math. Tables Other Aids Comput. 10(55), 130–137 (1956).
[CrossRef]

McCurdy, A. H.

Mermelstein, M. D.

M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency measurements and modeling in a 1714 mm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24), 15,952–15,963 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15952 .
[CrossRef]

Mio, N.

Mishra, R.

Moriwaki, S.

Nilsson, J.

Ozeki, T.

Payne, D.

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. 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]

Payne, D. N.

Peral, E.

E. Peral and A. Yariv, “Degradation of Modulation and Noise Characteristics of Semiconductor Lasers After Propagation in Optical Fiber Due to a Phase Shift Induced by Stimulated Brillouin Scattering,” IEEE J. Quantum Electron. 35(8), 1185–1195 (1999).
[CrossRef]

Ramachandran, S.

M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency measurements and modeling in a 1714 mm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24), 15,952–15,963 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15952 .
[CrossRef]

Rice, R. R.

Rothenberg, J.

Ruffin, A. B.

Sahu, J.

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. 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]

Sahu, J. K.

Sauer, M.

Soh, D. B. S.

Stroud, A. H.

P. C. Hammer, O. J. Marlowe, and A. H. Stroud, “Numerical Integration over Simplexes and Cones,” Math. Tables Other Aids Comput. 10(55), 130–137 (1956).
[CrossRef]

Takeno, K.

Tang, C.

C. Tang, “Saturation and Spectral Characteristics of the Stokes Emission in the Stimulated Brillouin Process,” J. Appl. Phys. 37(8), 2945–2956 (1966), http://link.aip.org/link/?JAPIAU/37/2945/1 .
[CrossRef]

Thielen, P.

Turner, P.

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. 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]

Turner, P. W.

Walton, D. T.

S. Gray, A. Liu, D. T. Walton, J. Wang, M.-J. Li, X. Chen, A. B. R. J. A. De Meritt, and L. A. Zenteno, “502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier,” Opt. Express 15(25), 17,044–17,050 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-25-17044 .
[CrossRef]

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8290 .
[CrossRef] [PubMed]

Wang, J.

S. Gray, A. Liu, D. T. Walton, J. Wang, M.-J. Li, X. Chen, A. B. R. J. A. De Meritt, and L. A. Zenteno, “502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier,” Opt. Express 15(25), 17,044–17,050 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-25-17044 .
[CrossRef]

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8290 .
[CrossRef] [PubMed]

Wanzcyk, L.

Ward, B. G.

B. G. Ward, “Finite Element Analysis of Photonic Crystal Rods with Inhomogeneous Anisotropic Refractive Index Tensor,” IEEE J. Quantum Electron. 44(2), 150–156 (2008).
[CrossRef]

B. G. Ward, “Bend performance-enhanced photonic crystal fibers with anisotropic numerical aperture,” Opt. Express 16(12), 8532–8548 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-853 .
[CrossRef] [PubMed]

Weber, M.

Wickham, M.

Willke, B.

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Supplementary Material (1)

» Media 1: MOV (197 KB)     

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Figures (8)

Fig. 1
Fig. 1

Central portion of the finite element mesh used for the electromagnetic and acoustic calculations.

Fig. 2
Fig. 2

Comparison between the Brillouin gain spectrum for a large mode area fiber with a uniform acoustic profile calculated using Eq. (24) and Eq. (37).

Fig. 3
Fig. 3

Acoustic index profile and Brillouin gain spectrum for a conventional large mode area fiber.

Fig. 4
Fig. 4

Acoustic index profile and Brillouin gain spectrum for a fiber incorporating and acoustic guiding layer.

Fig. 5
Fig. 5

Acoustic index profile and Brillouin gain spectrum for a fiber with a linearly-ramped acoustic profile.

Fig. 6
Fig. 6

Acoustic index profile and Brillouin gain spectrum for an improved fiber designed to produce a flat-top Brillouin gain spectrum. The region of high acoustic index is near the core boundary.

Fig. 7
Fig. 7

Acoustic index profile and Brillouin gain spectrum for an improved fiber designed to produce a flat-top Brillouin gain spectrum. The region of high acoustic index is near the core center.

Fig. 8
Fig. 8

(Media 1) A single-frame excerpt from an animation showing how the Brillouin gain and acoustic displacement within the fiber core vary with Brillouin frequency shift for the improved fiber with the greatest acoustic velocity at the center of the core.

Equations (45)

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2E(x,y,z,t)n(x,y)2c22t2E(x,y,z,t)=μ02t2PNL(x,y,z,t)
PNL(x,y,z,t)=γ[uz(x,y,z,t)]E(x,y,z,t)
E(x,y,z,t)=12{ap(z)f(x,y)exp[i(kpzωpt)]+as(z)f(x,y)exp[i(ksz+ωst)]+c .c .}
uz(x,y,z,t)=12{φ(x,y)exp[i(βzΩt)]+c .c.}
as(z,t)z=14ap(γε0)(2πλ)2f|φ|ff|f
[Vt2t2+(Vl2+ηρt)2z22t2]u(x,y,z,t)=12γρE(x,y,z,t)2
Vl2=E(1ν)ρ(1+ν)(12ν)
Vt2=E2ρ(1+ν)
nac=Vl,t,bulkVl,t(x,y)
[Vt2t2+Ω2β2(Vl2+iηρΩ)]φ(x,y)=i2πnγλρapas(z)f(x,y)2
[t2+Ω2Vt2β2Vl2Vt2iΓΩVt2]φ(x,y)=i2πnγλρVt2apas(z)f(x,y)2.
[t2κ2(x,y)]φ(x,y)=Φ(x,y)
κ2(x,y)1Vt2(β2Vl2Ω2iΓΩ)
Φ(x,y)i2πnγλρVt2apas(z)f(x,y)2
Lφ=Φ
φ(x,y)=G(x,y,x,y)Φ(x,y)dxdy(GΦ)
Ps,p=12cnε0f|f|as,p|2
dPs(z)dz=gBAeffPsPp
gBAeff=(1ρc)(γε0)2(2πλ)3f|(Gg)|ff|f2,
g(x,y)f(x,y)2Vt(x,y)2
Aeff=f|f2f|f2|f
gB,peak=2π2n7p122cλ2ρVlΓ.
G(r,r)=12πK0(κ|rr|)
f(r)2=8πd2exp[8r2d2]
φ(r)12π8πd2002πK0(κr2+r2+2rrcosθ)exp[8r2d2]rdrdθ
gBAeff=(1ρVt2c)(γε0)2(2πλ)3(8πd2)2×0002πK0(κr2+r2+2rrcosθ)exp[8(r2+r2)d2]rrdrdrdθ
S(φ)={12[tφ(r)]212κ(r)2φ(r)2Φ(r)φ(r)}d2r
{x,y,φ}=k=16Ak(L1,L2){xk,yk,φk}
A1=L1(2L11)A2=L2(2L21)A3=(1L1L2)(12L12L2)A4=4L1L2A5=4L2(1L1L2)A6=4L1(1L1L2)
xφ=k=16xAk(L1,L2)φk
yφ=k=16yAk(L1,L2)φk
[xAkyAk]=J1[L1AkL2Ak]
J=[xL1xL2yL1yL2].
φ˜i=Nij(L1,L2)φj
xφ˜i=Nx,ij(L1,L2)φj
yφ˜i=Ny,ij(L1,L2)φj
S(φ)=12φTKφRφ.
K=k=17Wk[NxkTJkNxkNykTJkNykNkTJkMNk]
R=k=17Wk[ΦkTNkTJkNk].
Kφ=R
φ=K1R.
gBAeff=(1ρc)(γε0)2(2πλ)3ETV(K1R)×E(ETVE)2
V=k=17Wk[NkTJkNk]
[φ(r)ψ(r)]d2r=φTVψ.
νB=2neVl,bulknacλ

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