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

Stimulated Brillouin scattering (SBS) can be the primary power limiting mechanism in many fiber optic applications that require narrow linewidth (<100 MHz) laser light. For example, single mode optical fiber telecommunication data links [1,2], high power rare-earth doped optical fiber amplifiers [3,4] and Raman amplifiers [5] can all be power limited by SBS. SBS is initiated by the spontaneous Brillouin scattering of the forward propagating laser light by density fluctuations associated with the thermally driven acoustic phonons. A fraction of the scattered light is captured by the fiber mode. The counter propagating electric fields exhibit an optical frequency difference equal to that of the acoustic phonon and create a forward propagating pressure wave by means of the electrostrictive effect. This pressure wave modulates the core refractive index and constitutes a traveling Bragg grating that leads to further light scattering, thereby generating stimulated light scattering.

Several approaches have been demonstrated for increasing the SBS threshold in optical fibers. One approach has been to vary the center frequency of the Brillouin gain along the fiber length by varying the dopant concentrations [6], the strain [7] or the temperature [8,9]. Alternatively, varying the acoustic properties of the optical fiber in the transverse direction has demonstrated significant SBS suppression levels [1012]. Ref. 12 introduced an acoustic beam propagation method (BPM) model to design a ramp-like anti-guiding acoustic index profile in a large mode area [LMA] Yb-doped gain fiber that provides ~11 dB of SBS suppression. A recent elaboration of the acoustic BPM [13] and a finite element analysis [14] has shown this ramp structure to be nearly optimal. The purpose of this paper is to measure the SBS suppression in acoustically guiding and anti-guiding single mode fibers [SMFs] and to interpret the measured SBS suppression levels with the acoustic BPM model. The SBS threshold is usually defined in terms of a Brillouin pump power PP that generates a Stokes power PS corresponding to a chosen SBS reflectivity RSBS=PS/PP. The pump power at which the SBS reflectivity reaches the designated reflectivity level is the threshold power Pth. This threshold power is dependent upon various fiber characteristics; material properties, optical modal properties, fiber length and others. The SBS process is seeded by the spontaneous Brillouin scattering, however the growth of the Stokes power is dominated by the SBS gain coefficient gB which appears in the exponential function. Therefore, the relative SBS suppression of the anti-guiding Al-doped fiber relative to that of the guiding Ge-doped fiber is investigated by measuring the relative strengths of the gain coefficients gB and normalizing for the other fiber properties. In this manner, a meaningful comparison between the intrinsic SBS thresholds of two fibers can be made.

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 relative SBS suppression of the Al-doped anti-guiding single mode fiber (SMF) to that of the Ge-doped guiding SMF is quantified by the ratio of the SBS gain coefficients: gB[Al]/gB[Ge] [15] where

gB=2πn7p122cλ2ρVcΔν.
In Eq. (1), n is core refractive index, p12 is the Pockel’s coefficient, c is the speed of light in vacuum, Vc is the sound speed in the core and ρ is the material density. The spectral with Δν, full-width at half-maximum (FWHM), is related to the lifetime τ of the electrostrictively generated acoustic disturbance by τ=1/πΔν and is also related to the acoustic decay length by Ld=Vc/πΔν. Here we distinguish between bulk electrostrictive acoustic waves that grow the SBS and the acoustic phonons, driven by thermodynamic fluctuations, which generate the spontaneous Brillouin scattering that seeds the SBS process.

The experimental arrangement is shown in Fig. 1 . 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 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.

 

Fig. 1 Experimental arrangement for measurement of the SBS threshold and spectra in the FsUT (SF-single frequency, CW-continuous wave, LO-local oscillator).

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Tables Icon

Table 1. Fiber parameters and measurement results.

OSA spectra are shown for the Al and Ge-doped fibers are shown in Fig. 2(a) and Fig. 2(b), respectively. At low powers, the Brillouin triplet is evident showing the elastic Rayleigh scattering peak and the two inelastic Stokes and anti-Stokes peak at the shift wavelength of ~60 pm which corresponds to a frequency shift of ~15 GHz. As the Brillouin pump power is increased the Stokes component to the spectrum increases with the onset of stimulated Brillouin scattering. The SBS reflectivity at very low reflectivities (RSBS<<1) is given by [16,17]:

RSBS=ηβSLeff[exp(CBPPLeff)1CBPPLeff]
where η is the fiber capture fraction, βS is the spontaneous Brillouin scattering coefficient per unit length, CBPgB/Aeff is the SBS gain efficiency, ηP is the polarization efficiency factor [18], Leff is the effective interaction length [15],
Leff=1eαLα
and Aeff is the optical effective area [15]:
Aeff=E(r)22E(r)4.
In Eqs. (3) and (4), α is the optical absorption in m−1, E(r) is the optical fiber modal electric field distribution, r is the radial coordinate and <…> is a cross-sectional spatial average. The optical fibers are low-birefringent single mode fibers and are wound on identical 6 inch diameter spools. The polarization efficiency factors ηP is estimated to be 2/3 [18] and is assumed to be the same for the two fibers. Therefore, they do not appear in the relative gain coefficient measurements.

 

Fig. 2 High resolution (10 pm) OSA spectra of the Stokes growth in (a) an acoustically guiding Ge doped core SMF and (b) an acoustically anti-guiding Al doped core SMF.

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Figure 3 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].
Substitution of the extracted values for CB and Aeff from Table 1 yields an SBS gain suppression of −4.0 dB.

 

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).

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Figure 4 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]:

Pth=κAeffgBLeff
where
κ=ln[RSBSηβSCBPth].
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]. A complete description of the power evolution in the optical fiber, including pump depletion, can be described by the coupled rate equations [15,17] 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 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].
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] 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.

 

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.

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Fig. 5 Plot of κ versus RSBS for the guiding and anti-guiding SMFs.

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The intensity of spontaneous Brillouin back-scattered light may be estimated from the Rayleigh ratio R [20,21] (or differential cross-section per unit length) for optical and acoustic plane waves:

R=π2kBTn8p1222Eλ4
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] 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.

Figure 6 shows the heterodyne spectra obtained with the ESA of the FsUT. The Ge and Al doped fibers exhibit Brillouin shift frequencies of 15.525 and 16.329 GHz and SBS gain bandwidths ΔνG (FWHM) of 16 and 54 MHz at 56 and 90 mW of Brillouin pump power, respectively. Note the measurable broadening of the SBS gain in the acoustically anti-guiding fiber. The SBS gain bandwidth ΔνG is related to the spectral width Δν of the acoustic disturbance by [23]:

Δν=ΔνGGln(2)
where the Brillouin gain G=CB PP Leff is estimated to be 11.1 for the Ge-doped fiber and 8.1 for Al-doped fiber. The low-gain bandwidths Δν may be calculated from Eq. (10) and the measured SBS gains G and SBS gain bandwidths ΔνG. They are found to be 64 and 185 MHz for the Ge and Al-doped fibers, respectively.The SBS suppression may be calculated from the heterodyne measurements and the relation:
gB[Al]gB[Ge]=νB[Ge]Δν[Ge]νB[Al]Δν[Al]
where the Brillouin shift frequency νΒ is proportional to the core sound speed Vc. This analysis yields a suppression level of −4.8 dB in good agreement with the suppression levels determined by the OSA and PM measurements

 

Fig. 6 Heterodyne rf power spectra of the SBS Stokes power for the two FsUT.

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

Stimulated Brillouin scattering has been described in monographs by Fabelinskii [20] and Boyd [24]. A representation of the SBS process in a single mode fiber is presented in Fig. 7 . Light guided in the forward direction with an electric field E1, optical frequency ω1 and propagation constant β1 is scattered by acoustic phonons exhibiting an acoustic frequency Ωm and wavevector Qm where the index ‘m’ labels the relevant acoustic eigenmode or phonon. For SBS in a SMF we are primarily interested in acoustic phonons traveling along the fiber axis in the direction of the forward propagating light and spontaneous Brillouin scattering events that generate Stokes light propagating in the backward direction with electric field E2, optical frequency ω2 and propagation constant β2. The optical propagation constants and optical frequencies are related by: β1,21,2neff/c where neff is the effective index of the optical mode. Conservation of energy and momentum require that the phonon acoustic frequency is equal to the difference in optical frequencies, i.e. Ωm1−ω2 and that the acoustic wavevector is Qm1+ β2=4πn/λ where the effective index neff is approximately equal to the core index n. The total electric field may be written as:

E(r,z;t)=A1f(r)cos(ω1tβ1z)+A2f(r)cos(ω2t+β2z)
where A1,2 are the amplitudes of the two counter-propagating waves and f(r) is the modal electric field distribution. The counter-propagating fields generate a traveling intensity pattern that produces the electrostrictively-induced density fluctuation given by:
Δρe=ρCγEEt8π
where C is the compressibility, γ is the electrostrictive constant and <…>t is a time average that is long compared to the optical period and short compared to the acoustic period. The electrostrictive density fluctuations are found to be:
Δρe(r,z;t)=Af(r)2cos(ΩmtQmz)
where A=ρCγA1A2/8π. These density fluctuations constitute a traveling wave or grating exhibiting an acoustic frequency Ωm, an acoustic wavelength Λm=2π/ Qm and a transverse distribution given by the optical intensity distribution f(r)2. The density fluctuations Δρe represent a volumetric acoustic source which, in a distributed manner, launches an acoustic disturbance into the transversely inhomogeneous elastic medium of the optical fiber core and surrounding cladding. It is assumed that optical and elastic properties of the optical fiber are homogeneous in the longitudinal direction.

 

Fig. 7 Schematic of the SBS process in the optical fiber.

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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]. 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]. 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]. 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 . The empirical relations used are:

N[Ge]=1.00+5.235Δn[Ge]N[Al]=1.003.512Δn[Al]
where Δn is the core-cladding optical index difference. Equation (15) is taken from Ref [27]. 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]. 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.

 

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.

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Figure 9 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.

 

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.

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Figure 10 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.

 

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.

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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
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 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]:

1Ld=1Labs+1Lwg.
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].
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 . Other physical parameters used in these calculations are shown in Table 3.

 

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.

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Tables Icon

Table 2. SBS suppressions

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.

References

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  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.

2009

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

2008

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).

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

2007

2004

2003

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]

2001

1996

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]

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]

1994

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]

1993

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]

1990

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

1989

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]

1983

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

1972

Akimoto, Y.

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]

Andrejco, M. J.

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).

Andrekson, P. A.

Bonaccini Calia, D.

Boot, A. J.

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]

Boyd, R. W.

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

Canat, G.

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]

Chen, X.

Chujo, W.

Cotter, D.

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

Crowley, A. M.

Debarge, G.

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]

Demeritt, J. A.

DiGiovanni, D. G.

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).

Dross, F.

Feng, Y.

Fini, J.

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).

Fini, J. M.

Fishman, D. A.

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]

Ghalmi, S.

Gray, S.

Hansryd, J.

Headley, C.

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).

Hickey, L. M. B.

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]

Horiguchi, T.

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]

Horley, R.

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]

Jaouen, Y.

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]

Jeong, Y.

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]

Knudsen, S. N.

Koyamada, Y.

Kulcsar, G.

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]

Kurashima, T.

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]

Li, M. J.

Liu, A.

McCurdy, A. H.

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).

Mermelstein, M. D.

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).

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]

Nagel, J. A.

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]

Nakamura, S.

Nakano, H.

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]

Narum, P.

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

Nibe, M.

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]

Nilsson, J.

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]

Ohashi, M.

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]

Olmedo, E.

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]

Payne, D. N.

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]

Ramachandran, S.

Ruffin, A. B.

Rzaewski, K.

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

Sahu, J. K.

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]

Sato, S.

Shiraki, K.

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]

Smith, R. G.

Sotobayashi, H.

Spring, J. B.

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

Tateda, M.

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]

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]

Taylor, L.

Turner, P. W.

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]

van Deventer, M. O.

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]

Walton, D. T.

Wang, J.

Ward, B. G.

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

Westlund, M.

Yablon, A.

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).

Yamauchi, J.

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]

Zenteno., L. A.

Appl. Opt.

IEEE J. Sel. Top. Quantum Electron.

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]

IEEE Photon. Technol. Lett.

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]

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]

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]

J. Lightwave Technol.

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]

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]

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]

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]

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]

J. Opt. Commun.

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

Opt. Express

Phys. Rev. A

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

Proc. SPIE

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).

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

Other

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

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

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

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).

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

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

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).

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

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

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

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

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Figures (11)

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).

Fig. 2
Fig. 2

High resolution (10 pm) OSA spectra of the Stokes growth in (a) an acoustically guiding Ge doped core SMF and (b) an acoustically anti-guiding Al doped core SMF.

Fig. 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).

Fig. 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.

Fig. 5
Fig. 5

Plot of κ versus RSBS for the guiding and anti-guiding SMFs.

Fig. 6
Fig. 6

Heterodyne rf power spectra of the SBS Stokes power for the two FsUT.

Fig. 7
Fig. 7

Schematic of the SBS process in the optical fiber.

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.

Fig. 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.

Fig. 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.

Fig. 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.

Tables (3)

Tables Icon

Table 1 Fiber parameters and measurement results.

Tables Icon

Table 2 SBS suppressions

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

gB=2πn7p122cλ2ρVcΔν.
RSBS=ηβSLeff[exp(CBPPLeff)1CBPPLeff]
Leff=1eαLα
Aeff=E(r)22E(r)4.
gB[Al]gB[Ge]=CB[Al]CB[Ge]Aeff[Al]Aeff[Ge].
Pth=κAeffgBLeff
κ=ln[RSBSηβSCBPth].
gB[Al]gB[Ge]=Pth[Ge]Pth[Al]Leff[Ge]Leff[Al]κ[Al]κ[Ge]Aeff[Al]Aeff[Ge].
R=π2kBTn8p1222Eλ4
Δν=ΔνGGln(2)
gB[Al]gB[Ge]=νB[Ge]Δν[Ge]νB[Al]Δν[Al]
E(r,z;t)=A1f(r)cos(ω1tβ1z)+A2f(r)cos(ω2t+β2z)
Δρe=ρCγEEt8π
Δρe(r,z;t)=Af(r)2cos(ΩmtQmz)
N[Ge]=1.00+5.235Δn[Ge]N[Al]=1.003.512Δn[Al]
γ(z)=Δρe(r,z)*Δρe(r,0)|Δρ(r,0)|2
1Ld=1Labs+1Lwg.
gB[Al]gB[Ge]=νB[Ge]2νB[Al]2Ld[Al]Ld[Ge].

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