微球空腔光致发光谱中Purcell效应、受激发射和漏模的相互作用
Interplay of Purcell effect, stimulated emission, and leaky modes in the photoluminescence spectra of microsphere cavities
摘要：
提出了一个描述微球腔体发射光谱的理论模型，并用光致发光（PL）光谱实验验证了该模型对ZnO微球中各级回音壁模（WGM）发射光谱的详细线形的预测.揭示了与各阶WGM相关的自发和受激发射谱中Purcell效应、品质因数和漏模的相互作用。该理论的关键成功是基于MS的全格林函数在复频率空间中的所有可能的共振模式方面的扩展，其允许将来自泄漏模式、受激发射过程和Purcell效应的贡献并入。结果表明，根据Mie理论计算的自发发射光谱（无Purcell效应）主要由漏模贡献，而自发辐射和Purcell效应增强的受激发射是实验观察到的WGM共振峰的主要来源.发现受激发射峰被其各自的模式品质因数Q双重增强：一个因子来自Purcell效应，另一个因子来自由速率方程导出的光子数。在综合所有这些效应之后，该理论可以提供ZnO MS PL谱中观察到的TE和TM模（包括高阶模）的精细特征的定量描述。令人惊讶的是，发现对于直径大于5 $μm$的ZnO MS，PL发射光谱由高阶模主导。这些发射机制的相互作用的定量理解应被证明是有用的优化基于微谐振器的发光器件的性能。
英文摘要：
A theoretical model for describing the emission spectra of microsphere cavities is presented, and its prediction of detailed lineshapes of emission spectra associated with whispering gallery modes (WGMs) of various orders in ZnO microspheres (MSs) are verified experimentally by photoluminescence (PL) spectroscopy. The interplay of Purcell effect, quality factor, and leaky modes in spontaneous and stimulated emission spectra related to WGMs of all orders is revealed. The key success of the theory is based on the expansion of the full Green function of the MS in terms of all possible resonance modes in complex frequency space, which allows incorporation of contributions from leaky modes, stimulated emission processes, and Purcell effect. We show that the spontaneous emission spectrum calculated according to Mie theory (without Purcell effect) is dominated by the contribution of leaky modes, while the spontaneous and stimulated emission enhanced by Purcell effect are responsible for the main WGM resonance peaks observed experimentally. It is found that the stimulated emission peaks are doubly enhanced by their respective mode quality factor Q: one factor from the Purcell effect and the other factor from the photon number derived from the rate equation. After combining all these effects the theory can provide a quantitative description of fine features of both TE and TM modes (including higher-order modes) observed in the PL spectra of ZnO MSs. Surprisingly, it is found that for ZnO MS with diameter larger than 5 $μm$, the PL emission spectrum is dominated by higher-order modes. The quantitative understanding of the interplay of these emission mechanisms should prove useful for optimizing the performance of light-emitting devices based on micro resonators.
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