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本文推导了单模光纤中的声波亥姆霍兹方程, 利用分离变量法求解并获得正规声波导导模的特征方程, 定义了声模的归一化频率, 结合贝塞尔函数的宗量近似分析了声波模式的特征值范围、截止频率和远离截止, 探讨了声模的色散和布里渊增益谱的多峰成因. 研究结果表明单模光纤中纵向声波基模L 01模无截止, 主要被限制在纤芯中, 与光基模耦合形成布里渊增益谱的主峰; 高阶声模都存在低频截止, 在包层分布比基模多, 与LP 01模耦合形成布里渊增益谱的次峰. 只有纵向L 0n声模对后向布里渊增益谱有贡献, 纤芯掺锗浓度增大能使布里渊增益谱发生红移, 声模数量增多, L 01模的增益峰值逐渐变大而高阶模的贡献减小. 泵浦波长为1.55 μm, 纤芯掺锗浓度3.65%、纤芯半径4.2 μm的单模光纤存在4个L 0n和16个L mn( m> 0)声模, 声模L 01, L 03, L 04与光模LP 01声光耦合产生布里渊增益谱的1个主峰和2个弱峰; 纤芯掺锗浓度15%, 纤芯半径1.3 μm的单模光纤存在3个L 0n模和7个L mn( m> 0)模, L 01, L 02, L 03模与LP 01模声光耦合使得布里渊增益谱呈现3个主峰. 这些结论可以完全解释相应的实验现象, 也为光纤SBS声波导研究及应用提供理论参考.In this work, the acoustic Helmholtz equation is derived, and its analytical solution and the characteristic equation of the uniform guide mode in single mode fibers are obtained by the method of separation of variables. The normalized frequency of the acoustic mode is defined. By combining the argument approximation of the Bessel function are analyzed the eigenvalue range of the acoustic mode, the cut-off frequency, far from the cut-off state of the acoustic mode induced by backward stimulated Brillouin scattering, the dispersion and the multi-peak Brillouin gain spectrum. The research results indicate that the longitudinal acoustic fundamental mode L 01cannot be cut-off and is mainly confined in the fiber core, which is coupled with the optical fundamental mode LP 01to form the main peak of the Brillouin gain spectrum. The other higher-order acoustic modes all have low cut-off frequencies and are distributed more in the fiber cladding than mode L 01which couples with the optical fundamental mode LP 01to form the subpeaks of the Brillouin gain spectrum. The transverse normalized phase constant and effective refractive index of the acoustic mode increase with normalized frequency increasing. Only longitudinal acoustic modes L 0ncontribute to backward Brillouin gain spectrum in single mode fiber. When the GeO 2concentration is less than 4% and core radius is 4.5 μm, the single mode characteristics of the fiber remain unchanged, but the maximum number of acoustic L 0nmodes is 4. With the increase of GeO 2concentration in the fiber core, the Brillouin gain spectrum is red-shifted and the number of acoustic modes increases, the Brillouin gain peak value of L 01mode gradually increases, and the contributions of higher-order modes decrease. The single-mode fiber with a core’s germanium doped concentration of 3.65% and core radius of 4.3 μm has 4 L 0nmodes and 16 L mn( m>0) modes at a wavelength of 1.55 μm, with one main peak and two subpeaks in the Brillouin gain spectrum appearing due to the acousto-optic coupling of the acoustic L 01, L 03, and L 04modes with the optical LP 01mode. The single-mode fiber with a core’s germanium doped concentration of 15% and core radius of 1.3 μm has 3 L 0nmodes and 7 L mn( m>0) modes, with the Brillouin gain spectrum having 3 main peaks due to the acousto-optic coupling of the L 01, L 02, and L 03modes with the LP 01mode. These conclusions are well consistent with the reported experimental phenomena and provide theoretical references for studying and utilizing the SBS acoustic waveguide in optical fibers.
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Fiber type m n 1 2 3 4 Fiber 1 0 10.9244 10.9694 11.0488 11.1576 1 10.9407 11.0032 11.0985 — 2 10.9620 11.0418 11.1576 — 3 10.9880 11.0848 11.2052 — 4 11.0185 11.1318 — — 5 11.0532 11.1812 — — 6 11.0921 — — — 7 11.1349 — — — 8 11.1814 — — — Fiber 2 0 10.0902 10.4721 11.0857 — 1 10.2306 10.7466 — — 2 10.4117 11.0438 — — 3 10.6287 — — — 4 10.8779 — — — 5 11.1511 — — — 
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Fiber type Aeff/μm2 Aao/μm2 I BFS/GHz Relative error/% Reference This paper Fiber 1 76.32 78.87 0.9668 10.9170[22] 10.9244 0.0678 15612.35 0.0049 10.9630[22] 10.9694 0.0584 14173.60 0.0054 11.0430[22] 11.0488 0.0525 11249.48 0.0068 11.1540[22] 11.1576 0.0323 Fiber 2 21.02 26.06 0.8068 10.0000[23] 10.0902 0.8087 482.47 0.0436 10.5000[23] 10.4721 0.2657 328.89 0.0639 11.1100[23] 11.0857 0.2187 下载:
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