Stimulated brillouin scattering in double-clad thulium-doped fiber amplifier
doi: 10.37188/CO.EN-2023-0011
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摘要:
理论分析了波长为2 µm的掺铥光纤放大器中受激布里渊散射（SBS）对 输出性能的影响，研究了双包层掺铥光纤在793 nm的泵浦波长和1.9~2.1 µm的 工作波段的光模分布、有效折射率、有效模场面积和归一化频率，数值计算了在1.9~2.1µm的 工作波段双包层掺铥光纤中的布里渊频移和布里渊增益谱等SBS特性。利用增益光纤中的受激布里渊散射理论模型，研究了受激布里渊散射对掺铥光纤放大器 输出性能的影响。在DTDF-10/130双包层掺铥光纤中，使用功率为100 W、波长为793 nm的连续光作为泵浦，可对波长为2 μm、功率为0.01 W的连续信号光进行放大。当泵浦光功率填充因子为0.01、0.02和0.03时，信号光的最大输出功率分别为25.27 W、31.08 W和34.06 W。对应的最佳双包层光纤长度为2.66 m、2.02 m和1.75 m，由受激布里渊散射产生的斯托克斯光功率分别为1.68 W、1.39 W和1.14 W。结果表明，在掺铥光纤放大器中使用泵浦光功率填充因子大的双包层光纤可以降低光纤长度，从而减小受激布里渊散射对信号 输出功率的影响。本文的数值模型可以对光纤放大器的光纤长度进行优化，对提高实验效率、降低实验成本具有重要价值。
Abstract:In this paper, the effect of Stimulated Brillouin Scattering(SBS) on the laser output performance in a 2 µm thulium-doped fiber amplifier was analyzed theoretically. The optical mode distribution, the effective refractive index, the effective mode field area, and the normalized frequency of the double-clad thulium-doped fiber at 793 nm pump wavelength and 1.9−2.1 µm laser waveband were studied. The stimulated Brillouin scattering characteristics, including the Brillouin frequency shift and the Brillouin gain spectrum, in the double-clad thulium-doped fiber were numerically simulated in the laser waveband of 1.9−2.1 µm. The influence of stimulated Brillouin scattering on the laser output performance of thulium-doped fiber amplifiers was investigated using the theoretical model of stimulated Brillouin scattering in gain fibers. In the DTDF-10/130 double-clad thulium-doped fiber, a continuous wave with power of 100 W and wavelength of 793 nm is used as a pump to amplify a continuous signal wave with wavelength of 2 µm and power of 0.01 W. The maximum output powers of the signal wave are 25.27 W, 31.08 W and 34.06 W when the pump power filling factors are 0.01, 0.02 and 0.03, respectively. The corresponding optimal double-clad fiber lengths are 2.66 m, 2.02 m and 1.75 m. Additionally, the Stokes optical powers generated by the stimulated Brillouin scattering are 1.68 W, 1.39 W and 1.14 W, respectively. The results show that the double-clad fiber with large pump power filling factor in the thulium-doped fiber amplifier can effectively reduce the fiber length, thus to minimize the influence of stimulated Brillouin scattering on the output power of the signal laser. The numerical model can optimize the fiber length of the fiber amplifier, which is of great significance to improve experimental efficiency and reduce experimental costs.
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Key words:
- stimulated brillouin scattering /
- double-clad /
- thulium-doped fiber /
- amplifier
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Figure 1. Structure and refractive index distribution of DTDF-10/130 double-clad thulium-doped fiber
Figure 2. Structure and refractive index distribution of DTDF-25/400 double-clad thulium-doped fiber
Figure 3. Schematic diagrams of the (a) two-dimensional and (b) three-dimensional optical field distributions of the LP01 mode of the DTDF-10/130 double-clad thulium-doped fiber at 2 μm wavelength, respectively
Figure 4. Optical field distribution of DTDF-25/400 double-clad thulium-doped fiber at 2 µm wavelength. (a)−(c) Schematic diagrams of the two-dimensional optical field distributions for LP01, LP11 (o) and LP11 (e); (d)−(f) schematic diagrams of three-dimensional optical field distributions for LP01, LP11 (o) and LP11 (e)
Figure 5. Schematic diagram of the normalized frequency with signal wave wavelength for DTDF-10/130 and DTDF-25/400 double-clad thulium-doped fibers
Figure 6. Effective refractive index and effective mode field area of different optical wave modes in two fibers in the 1.9~2.1 µm band. (a) LP01 mode in DTDF-10/130 double-clad thulium-doped fiber; (b) LP01 and LP11 modes in DTDF-25/400 double-clad thulium-doped fiber
Figure 7. Variation of power filling factor with wavelength in double-clad thulium-doped fibers DTDF-10/130 and DTDF-25/400
Figure 8. Optical wave modes of 793 nm pump wave in different fibers. (a)-(d) DTDF-10/130; (e)-(h) DTDF-25/400 double-clad thulium-doped fiber
Figure 9. Optical modes corresponding to small power filling factor in the inner cladding at a wavelength of 793 nm for the pump wave
Figure 10. Schematic diagram of intra- and inter-mode Brillouin scattering of different optical wave modes in two fibers operating at 1.9~2.1 µm laser wavelengths
Figure 11. LP01-LP01 intra-mode Brillouin gain coefficient in DTDF-10/130 double-clad thulium-doped fiber, LP01-LP01 intra-mode, LP11-LP11 intra-mode and LP01-LP11 inter-mode Brillouin gain coefficients in DTDF-25/400 double-clad thulium-doped fiber at the 1.9~2.1 µm laser waveband
Figure 12. Brillouin gain spectra at laser wavelength of 2 µm. (a) Brillouin scattering within LP01-LP01 mode in DTDF-10/130 double-clad thulium-doped fiber; (b) Brillouin scattering within LP01-LP01 mode, LP11-LP11 mode and LP01-LP11 inter-mode in DTDF-25/400 double-clad thulium-doped fiber
Figure 13. Distribution of pump wave power, signal wave power and Stokes wave power along the fiber
Figure 14. Residual pumping optical powers varying with fiber length at different pump optical power filling factors
Figure 15. Variation of laser output power and Stokes optical power with fiber length when pump power filling factors are (a) 0.01, (b) 0.02, and (c) 0.03, respectively
Table 1. Geometry and optical properties of double-clad thulium-doped fibers
Properties Unit DTDF-10/130 DTDF-25/400 Core diameter µm 10.0 ± 1.0 25.0 ± 2.5 Diameter of inner cladding µm 130.0 ± 3.0 400.0 ± 15.0 Concentricity error of core/internal cladding µm ≤ 2.0 ≤ 4.0 Diameter of coating layer µm 215.0 ± 10.0 550.0 ± 20 Operating wavelength nm 1900 ~ 2100 1900 ~ 2100 Core numerical aperture —— 0.150 ± 0.010 0.090 ± 0.010 Numerical aperture of inner cladding —— ≥ 0.460 ≥ 0.460 
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Table 2. Simulation parameters of thulium-doped fiber amplifier
Parameter Symbol Value Unit Fiber core diameter a 10.0 µm Inner cladding diameter b 130.0 µm Tm3+ doping concentration N0 5.5×1025 m−3 Pump wavelength λp 793 nm Signal wave wavelength λs 2 µm Pump wave absorption cross section σa(λp) 8.5×10−25 m2 Pump wave emission cross section σe(λp) 8.9×10−25 m2 Signal wave absorption cross section σa(λs) 0.1×10−25 m2 Signal wave emission cross section σe(λs) 6.2×10−25 m2 Stimulated Brillouin scattering gain gB 2.803×10−11 m/W Brillouin noise ISBS 3.350×10−7 W Pumped optical fiber loss αp 1.2×10−2 m−1 Signal optical fiber loss αs 2.3×10−3 m−1 Pump optical power filling factor Γp Influenced by the shape of the inner cladding - Signal optical power filling factor Γs 0.817 -
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