This paper reports the main characteristics of the Stokes spectra for typical pumped and unpumped Erbium-Ytterbium doped fibers. Doped fibers show shorter Brillouin shifts and their spectra are up to 1.6 times broader than undoped fibers. Those spectra are composed of several peaks originating from several longitudinal acoustic modes. The effective Brillouin gain of the secondary modes can be as large as 20% of the main peak gain. They can merge into a more complex structure for the largest cores. Simulations allow to relate these characteristics to the influence of codoping and index profile inhomogeneity. An additional broadening of the Stokes spectrum in pumped fibers is reported and attributed to thermal effects.
©2008 Optical Society of America
In fiber optics, the tight optical mode confinement leads to large intensities resulting in nonlinear effects. For spectroscopy and heterodyne Lidar applications, amplification of narrow linewidth (Δυ<10 MHz) signal is limited by stimulated Brillouin scattering (SBS) especially in the hundreds of nanoseconds pulsed regime (with a gain linewidth ΔυB~30 MHz in silica at 1.5 µm ). The signal light is mainly backscattered into the Stokes wave which is downshifted by ~11 GHz for a 1.5 µm signal. When the threshold is reached a large amount of power can be backscattered limiting the transmitted power. In fiber amplifiers, the stochastic dynamics of SBS induces large optical power fluctuations . The backscattered light is then amplified leading to powerful spiking potentially harmful for passive components such as optical isolators. In a typical commercial amplifier for optical communications with 8 m fiber length, the SBS threshold is reached at only 10 W peak power. Several methods have been demonstrated to increase the SBS threshold. For example, it has then been observed that thermal gradient along fiber amplifiers can lead to a strong increase in the SBS threshold [3,4]. Indeed, the Brillouin main frequency is increased by about 1.3 MHz / °C. Splicing fibers with different SBS shifts can also lead to an increase in the SBS threshold . In order to predict the SBS threshold in doped fibers, the Brillouin gain and linewidth must be known. The SBS power threshold scales as the ratio of the laser linewidth to the Brillouin gain linewidth. Up to now, no information has been published for Erbium-Ytterbium doped (Er-Yb) fibers to the best of our knowledge.
Er-Yb doped fibers are composed of silica doped with rare-earth, phosphorous and alumina. Phosphorous is used to decrease the lifetime of the metastable 4I11/2 level of Erbium in order to improve the overall efficiency. Alumina is used to increase rare-earth solubility. At usual concentrations, alumina, phosphorous and rare-earth increase the refractive index . The acoustic properties of all these dopants are not well-known and Brillouin shift measurement is a way to have access to these information.
In this paper we present what we believe to be the first measurement and modeling of Stokes spectrum in Er-Yb doped fibers. Our model relies on the weak guidance assumption and a few empirical rules. It gives a qualitative agreement with the experimental results. We show how the fiber doping and large diameter lead to the guidance of many acoustic modes. The Stokes spectrum can then be very different from a lorentzian. Its width can be 1.6 times broader than the individual mode linewidth which must be used for threshold prediction.
2. Stokes spectrum measurement
We have measured the Stokes spectrum of commercial Er-Yb fibers (Table 1) using the usual heterodyne detection setup (Fig. 1). All fibers except for fiber B are commercial fibers. Fiber B was prepared at Laboratoire de Physique de la Matière Condensée, CNRS, France and the phosphorous content was intentionally lowered. A DFB laser is used as a signal source at 1552 nm with a full-width at half-maximum (FWHM) of 600 kHz. Half of the input signal is used as a local oscillator for the heterodyne detection. The remaining laser power is amplified with a 1 W Er–Yb optical fiber amplifier and injected into the fiber under test (FUT) through a circulator. The backscattered Stokes signal is collected through the circulator and mixed with the local oscillator. The beating is detected with a 21-GHz photodetector (NewFocus) and displayed on a spectrum analyzer with a resolution bandwidth of 100 kHz. The polarization is adjusted to maximize the heterodyne efficiency using a polarization controller.
Figure 2 shows the results for 3 doped fibers with various diameters and numerical apertures (NA). Several features can be identified. The Brillouin shift in Er-Yb doped fibers is shorter than in SMF 28 (10.86GHz) by several hundreds of MHz. For example, comparing fiber B and C shows that the stronger the NA, the smaller the Brillouin shift.
The spectrum displays several peaks for fiber A with the smallest core diameter or a broad secondary peak which departs from the usual lorentzian shape for fibers with larger core (fibers C, D). The linewidth of the main peak is larger than for SMF 28 (30 MHz): we measured 50 MHz for unpumped fibers and 82 MHz for fiber D when pumped. This value is 3 times larger than the value measured in SMF. The results are summarized in table 1.
In order to analyze these measurements, we have computed the theoretical Stokes spectra. For this calculation, a modeling of the optical and longitudinal acoustic waves guided by the fiber was performed. This model, similar to , is valid in the frame of the acoustic and optical weak guidance approximation. The fiber is approximated by an acoustic waveguide with a radially dependant longitudinal acoustic velocity VL(r). The transverse profile uk(r), pulsation ΩB and wave number q of the acoustic waves obey the equation:
Assuming that the Brillouin frequency shift υB is much smaller than the optical frequency, the phase matching condition with the optical waves leads to the relation q≈2β with β the effective wave number of the optical mode.
The acoustic velocity profile VL(r) is not well-known in Er-Yb fiber as it depends on doping and possible strains between the different core layers. Strain has been neglected in our analysis. This analysis focuses on the influence of dopants on Brillouin spectrum. The core is usually codoped with phosphorous and alumina. A few studies have been conducted on the influence of doping on the acoustic velocities . From these data, quantitative relations can be used for phosphorous codoping (typically 18 % weight) and alumina codoping (typically 1.9 % weight) . We used ΔW(P205)=18 %wt and ΔW(Al203)=1.1%wt for best fit. The difference could come from the rare-earth doping. Rare-earth concentration is usually smaller and has been neglected. The relative variation (in percent) of the refractive index Δn and the acoustic velocity ΔVL can be related to first order to the Phosphorous doping level in weight percents ΔW by Δn=+0.02 ΔW(P205) and ΔVL=-0.31ΔW(P205) . In the same way, we have for the Alumina Δn=+0.038 ΔW(Al203) and ΔVL=+0.42ΔW(Al203) . To first order, these changes add up similarly to . We can then relate the acoustic velocity change ΔVL to the index variation Δn using these relations:
During the collapse of the preform, dopants diffusion and evaporation lead to index inhomogeneity with the presence of a central dip in the profile . Figure 3 illustrates how a velocity profile can thus be computed from an approximated refractive index profile. The exact index profile was not known as those fibers were commercial. We used instead a real profile measured on similar preform. The real and simplified index profile n(r) are displayed on Fig. 3a.
Knowing VL(r) and the sound speed in undoped silica VL,clad=5944 m/s , equation (1) was then solved using a scalar solver similar to the one used for optical mode computation. Several solutions are found corresponding to acoustic modes with pulsation ΩB(k) and amplitude distribution uk(x,y).
Figure 4 displays the fundamental optical mode LP01 and the three lowest order acoustic modes. We can observe that due to the central dip in the refractive index, the optical mode is flattened and the acoustic modes are more strongly confined into the outermost part of the core. The reason is that the acoustic wavelength is half the optical wavelength. Unlike the optical mode, the acoustic field maxima are not localized at the fiber center. The acoustic modes follow the index profile more closely then the optical mode.
In order to compute the Stokes spectrum, we make several simplifications. First, we assume that the only excited optical mode is the fundamental mode LP01. The only excited acoustic modes are then the longitudinal acoustic modes L0m with no azimuthal dependence. Second, we assume that the local Brillouin gain gB is the same in the core and in the cladding. The relative intensity scattered by each acoustic mode is then proportional to the normalized overlap between the acoustic and optical mode profiles. This overlap is thus defined by the equation :
where F01 is the fundamental optical mode LP01 amplitude distribution.
The shift between the acoustic and the optical modes maxima reduces the value of the overlap Iao u compared to uniformly doped core. For instance, the overlap of the fundamental acoustic mode L01 is Iao u=0.75 in fiber A compared to Iao u=0.98 in SMF28 fiber. The effective Brillouin gain of low birefringence fibers is then given by geff B=2/3·gB·Iao 0 where for SMF 28, gB·Iao 0=2.6 10-12 m/W . The correction factor of 2/3 accounts for polarization effects due to random birefringence. Its value in doped fibers it thus reduced in Er-Yb fibers compared to undoped fibers by a factor 0.75. In standard telecom fibers geff B (SMF28)≈1,7 10-12 m/W . In low birefringence Er-Yb fibers, geff B≈0.75 geff B (SMF28)≈1.3 10-12 m/W in good agreement with the value used for SBS modeling in amplifiers .
Each mode contribution adds up in an incoherent way. The spontaneous spectrum is then finally computed by adding lorentzian curves centered at each mode pulsation ΩB(k), with linewidth ΓB and relative intensity Iao u(k)/Iao u(0). The power spectrum is then:
A fit of the spectral shape with (4) leads to a linewidth value ΓB=2π×50 MHz somewhat larger than in pure silica (ΓB=2π×30 MHz). This value is consistent with the presence of dopants as in the case of Ge doped fibers . This linewidth increase can be attributed to the larger sound attenuation by acoustic scattering and glass viscosity. Our model can compute the spectrum of the fibers used in the experiments. Figure 5 shows the comparison between the fiber A spectrum from measurement and from modeling.
Figure 5 shows a qualitative agreement with the presence of 3 distinct peaks. They correspond to the first acoustic longitudinal modes L01, L02 and L03. This behaviour is similar to the spectrum observed in standard Germanium doped telecom fibers.
Fiber C has a 18 µm core. Figure 6 shows the refractive index profile used in the modeling of fiber C with its fundamental optical mode. The NA and core diameter were provided by manufacturer data. The refractive index profile was taken from the measurement on a large core fiber preform. The Stokes spectrum is displayed on Fig.7. The structure differs strongly from the usual Lorentzian spectrum: on the high frequency side of the main peak, a broad bump extending on about 100 MHz is clearly visible.
The modeling shows that this structure is due to several higher order acoustic modes that have merged. The acoustic mode amplitude uk oscillates k times. Their maxima are shifted from the maximum of the optical mode. The dip presence then reduces the L01 mode overlap whereas higher order acoustic modes have their overlaps increased (to about 20 % of the main peak overlap). It can be compared to the modeling of a simple step index fiber with same core diameter and NA but without central. In that case, the fundamental mode frequency is the same (10.16 GHz) but the overlap of the L02 mode is only 2% and the overlap of the higher order modes does not exceed 2 10-3.
The presence of the large secondary peaks is therefore due to the inhomogeneity in the refractive index profile. In the next part we study the influence of temperature on the Brillouin threshold of a highly acoustically multimode Er-Yb fiber.
4. Effect of temperature gradient
Fiber D, with 20 µm core diameter, is too short to generate enough Stokes power without pumping. A tapered fiber bundle (OFS) is therefore inserted to couple the pump light into the outer clad of the fiber whereas the signal was copropagating in the core. Up to 10 W of 975 nm pump power are coupled and Stokes light can be measured (Fig. 8). Fiber D spectrum differs from the usual lorentzian shape as shown on Fig. 8. It widens on the high frequency part when pump power is increased: the linewidth increases from 48 to 82 MHz. At the same time, the Brillouin shift νB increases by up to 63 MHz. These evolutions are induced by a thermal gradient along the doped fiber due to pump absorption [3, 13]. An increase of temperature of 50K is measured using a thermocouple and is consistent with usual values of ΔνB/ΔT~1.3 MHz /K .
If gB eff(υ,T0) is the spectrum of the Brillouin gain at room temperature T0, the gain spectrum of a piece of fiber at temperature T is given by the equation:
In the spontaneous regime, the reflected Stokes power scales linearly with the incident signal power . Let us consider a signal at frequency νs injected at z=0. The Stokes power is then counterpropagating. In the presence of the amplifier gain g(z), the Stokes power evolves according to equation:
where k is the Boltzman constant and T the room temperature.
As a first order approximation, we assume that the gain g(z) and the temperature T(z) decrease linearly along the fiber due to the copropagating pumping configuration. The total experimental gain of the amplifier was 3 dB at full pump power. The temperature decreases from 70°C to 40°C along the fiber. Equation (6) is solved with the boundary condition Pstokes(L)=0. The resulting Stokes spectrum is displayed on Fig. 9. The frequency shift of the maximum peak is +70 MHz both in modeling and measurements. The peak broadens to about 80 MHz. The high frequency wing of the peak can also be explained by the presence of the high order acoustic modes.
The SBS threshold scales inversely with the effective Brillouin gain of the fundamental acoustic mode. In the absence of amplification, the latter scales roughly with the maximum of the Stokes spectrum in the undepleted signal regime . The SBS threshold then scales inversely with the Stokes fluorescence maximum. Figure 10 shows its value as a function of the temperature gradient computed for various values of the acoustic mode linewidth ΓB. It can be seen that this evolution is strongly dependent on the exact value of ΓB. For a 80°C gradient, modeling with ΓB=30 MHz (as for Yb doped fibers) gives a threshold 1.5 times larger than modeling with ΓB=50 MHz (measured for fiber D). As stated in table 1, the acoustic linewidth in Er-Yb doped fibers is about 50 MHz. This linewidth must be measured in unpumped regime and taking care of the overlap of higher order modes. It is 1.6 times smaller than the total width measured in the pumped regime This is due to the large amount of heat released when the Er-Yb fiber are pumped.
Er-Yb doped fibers present a broader linewidth and a shorter Brillouin shift than undoped fibers. Modeling shows that the phosphorous codoping increases the acoustic NA. It reduces the Brillouin shift and allows many acoustic modes to be guided. The effect is more significant for larger core fibers which spectrum shape strongly differs from a lorentzian. On the one hand, the overall dopant effect is to increase the number of guided acoustic modes and their individual linewidth to 50 MHz. On the other hand, the double-hump shape of the index profile pulls the optical intensity maximum towards the outer region of the core. It enhances the role played by higher order modes. The fundamental mode effective gain is reduced compared to step index fibers. Higher order acoustic modes can have a gain which is as large as 20 % of the main mode. This is due to the presence of the refractive index dip. For fibers guiding only a few modes (fiber A), the increase of the individual mode linewidth is the main effect. For fibers guiding many modes (such as fibers C and D), both effects contribute to the large measured spectrum width.
Furthermore the stokes spectrum shape is affected by pumping due to heat generation. The Brillouin gain linewidth, useful for threshold prediction, is given by the fundamental acoustic mode linewidth. The measured width can then be up to 1.6 times larger than the fundamental acoustic mode linewidth when pumping with 10 W pump power.
Financial support for this research was partially provided by the SOFIA project from region Ile de France and the FIDELIO European project.
References and links
1. A. Yeniay, J.-M. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. 20, 1425–1432 (2002). [CrossRef]
2. G. Kulcsar, Y. Jaouën, G. Canat, and E. Olmedo, “Multiple-stokes Stimulated Brillouin Scattering generation in pulsed high-power double-cladding Er3+-Yb3+ codoped fiber amplifier,” IEEE Photon. Technol. Lett.15, 801–803 (2003). [CrossRef]
3. V.I. Kovalev and R.G. Harrisson, “Analytic modeling of Brillouin gain in rare-earth doped fiber amplifiers with high-power single-frequency signals,” Proc. SPIE 5709, 142–146 (2005). [CrossRef]
4. Y. Jeong, J. Nilsson, and J.K. Sahu et. al., “Single-frequency, polarized ytterbium-doped fiber MOPA source with 264 W output power,” Conference on Lasers and Electro-Optics, 2004. (CLEO) 2, 1065–1066 (2004).
5. C.A.S. de Oliveira and C.K. Jen, “Fiber Brillouin laser with two cascaded fibers of different Brillouin frequency shifts,” Microwave Conference/Brazil, 1993., SBMO International Vol. 2, 697–702 (1993).
6. G. Vienne, “Fabrication and characterization of Ytterbium:Erbium codoped phosphosilicate fibers for optical amplifiers and lasers,” Ph.D. dissertation (University of Southampton, Southampton, 1996).
7. A. Kobyakov, S. Kumar, and D. Chowdhury et. al., “Design concept for optical fibers with enhanced SBS threshold,” Opt. Express 13, 5338–5346 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-14-5338 [CrossRef] [PubMed]
8. Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” J. Lightwave Technol. 22, 631–639 (2004). [CrossRef]
9. A. B. Ruffin, M. -J. Li, X. Chen, A. Kobyakov, and F. Annunziata, “Brillouin gain analysis for fibers with different refractive indices,” Opt. Lett. 30, 3123–3125 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-23-3123 [CrossRef] [PubMed]
10. M. Nikles, L. Thevenaz, and P.A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15, 1842–1851 (1997). [CrossRef]
11. G. Canat, Y. Jaouën, and J.-C. Mollier, “Performance and limitations of high brightness Er3+-Yb3+ fiber sources,” C.R. Physique 7, 177–186 (2007). [CrossRef]
12. S. Le Floch and P. Cambon, “Theoretical evaluation of the Brillouin threshold and the steady-state Brillouin equations in standard single-mode optical fibers,” J. Opt. Soc. Am. A 20, 1132–1137 (2003) [CrossRef]
13. K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol. 14, 50–57 (1996) [CrossRef]