[论文解读] Theoretical and experimental study of stimulated and cascaded Raman scattering in ultra-high-Q optical microcavities

Tobias J. Kippenberg, S. M. Spillane+2 more|ArXiv.org|Nov 4, 2004

Photonic and Optical Devices被引用 5

一句话总结

本文对超高品质因数（ultra-high-Q）熔融石英微腔中的受激和级联拉曼散射进行了理论与实验研究，采用光纤探针耦合技术实现了创纪录的低阈值拉曼激光。研究展示了在芯片级微环腔中实现单模拉曼振荡，其阈值低于62 μW，得益于模式体积减小和高Q因子，其光谱纯度和效率优于球形微腔。

ABSTRACT

Stimulated Raman scattering (SRS) in ultra-high-Q surface-tension-induced spherical and chip-based toroid microcavities is considered both theoretically and experimentally. These microcavities are fabricated from silica, exhibit small mode volume (typically 1000 $μm^{3}$) and possess whispering-gallery type modes with long photon storage times (in the range of 100 ns), significantly reducing the threshold for stimulated nonlinear optical phenomena. Oscillation threshold levels of less than 100 $μ$% -Watts of launched fiber pump power, in microcavities with quality factors of 100 million are observed. Using a steady state analysis of the coupled-mode equations for the pump and Raman whispering-gallery modes, the threshold, efficiencies and cascading properties of SRS in UHQ devices are derived. The results are experimentally confirmed in the telecommunication band (1550nm) using tapered optical fibers as highly efficient waveguide coupling elements for both pumping and signal extraction. The device performance dependence on coupling, quality factor and modal volume are measured and found to be in good agreement with theory. This includes analysis of the threshold and efficiency for cascaded Raman scattering. The side-by-side study of nonlinear oscillation in both spherical microcavities and toroid microcavities on-a-chip also allows for comparison of their properties. In addition to the benefits of a wafer-scale geometry, including integration with optical, electrical or mechanical functionality, microtoroids on-a-chip exhibit single mode Raman oscillation over a wide range of pump powers.

研究动机与目标

• 研究超高品质因数光学微腔中的受激和级联拉曼散射，以实现低阈值非线性光学。
• 比较芯片级微环腔与球形微腔在拉曼阈值、模式控制和效率方面的性能表现。
• 通过1550 nm通信波段的光纤探针耦合，实验验证拉曼激光的理论模型。
• 量化品质因数、模式体积和耦合强度对拉曼振荡阈值和效率的影响。
• 在宽泵浦功率范围内实现微环腔中的单模拉曼激光，推动实际应用。

提出的方法

• 利用耦合模方程对超高品质因数谐振腔中泵浦与拉曼导行模的受激拉曼散射进行理论建模。
• 通过稳态分析推导受激拉曼散射的阈值条件、转换效率和级联行为。
• 采用有限元法数值模拟，计算微环腔有效模式体积随次级直径的变化关系。
• 实验上采用光纤探针耦合器，实现微球和微环腔中拉曼信号的高效激发与提取。
• 测量不同Q因子、耦合强度和模体积下的阈值泵浦功率、输出功率及光谱特性。
• 在相同条件下比较微环腔与微球腔的拉曼振荡性能，评估其在光谱和功率效率方面的优势。

实验结果

研究问题

• RQ1 在超高品质因数微腔中，受激拉曼散射的理论阈值是多少？品质因数、模式体积和耦合强度如何影响该阈值？
• RQ2 这些微腔中的级联拉曼散射行为如何？随着拉曼阶数增加，阈值和效率的标度规律是什么？
• RQ3 在拉曼激光阈值、光谱纯度和单模工作方面，芯片级微环腔与球形微腔相比有何优势？
• RQ4 光纤探针耦合在实现这些系统中超低阈值拉曼激光中起到什么作用？
• RQ5 通过几何设计能将微环腔的模式体积降低到何种程度？这种减小对拉曼阈值有何影响？

主要发现

• 在光纤探针耦合的微环腔中，实验测得拉曼激光阈值为62 μW，相比自由空间泵浦的微液滴，实现了近三个数量级的降低。
• 由于更强的横向限制和更小的模式体积，微环腔在宽泵浦功率范围内表现出单模拉曼振荡，优于球形微腔。
• 第N阶级联拉曼振荡的阈值随阶数N呈立方关系增长，而效率则与N的平方成反比。
• 偶数阶斯托克斯场的生成功率与泵浦功率呈线性关系，而奇数阶斯托克斯场则表现出平方根依赖关系。
• 数值模拟表明，当次级直径减小至10 μm以下的强横向限制区域时，微环腔的有效模式体积显著减小，出现急剧下降。
• 基于耦合模方程的阈值和效率理论预测，在不同Q因子和耦合强度下均得到实验验证。