Zou Chang-Ling, Shu Fang-Jie, Sun Fang-Wen, Gong Zhao-Jun, Han Zheng-Fu, Guo Guang-Can
Key Lab of Quantum Information, University of Science and Technology of China, Hefei 230026, PR China.
Opt Express. 2013 Apr 22;21(8):9982-95. doi: 10.1364/OE.21.009982.
Theoretical study of free space coupling to high-Q whispering gallery modes (WGMs) are presented in circular and deformed microcavities. Both analytical solutions and asymptotic formulas are derived for a circular cavity. The coupling efficiencies at different coupling regimes for cylindrical incoming wave are discussed, and the maximum efficiency is estimated for the practical Gaussian beam excitation. In the case of a deformed cavity, the coupling efficiency can be higher than the circular cavity if the excitation beam can match the intrinsic emission which can be tuned by adjusting the degree of deformation. Employing an abstract model of slightly deformed cavity, we find that the asymmetric and peak like line shapes instead of the Lorentz-shape dip are universal in transmission spectra due to multi-wave interference, and the coupling efficiency cannot be estimated from the absolute depth of the dip. Our results provide guidelines for free space coupling in experiments, suggesting that the high-Q asymmetric resonator cavities (ARCs) can be efficiently excited through free space which will stimulate further experiments and applications of WGMs based on free space coupling.
本文介绍了在圆形和变形微腔中自由空间与高Q回音壁模式（WGM）耦合的理论研究。推导了圆形腔的解析解和渐近公式。讨论了圆柱入射波在不同耦合区域的耦合效率，并估计了实际高斯光束激发下的最大效率。在变形腔的情况下，如果激发光束能够与通过调整变形程度可调节的本征发射相匹配，则耦合效率可能高于圆形腔。通过采用微变形腔的抽象模型，我们发现由于多波干涉，透射光谱中普遍存在不对称且类似峰的线形，而不是洛伦兹形凹陷，并且不能从凹陷的绝对深度来估计耦合效率。我们的结果为实验中的自由空间耦合提供了指导，表明高Q非对称谐振腔（ARC）可以通过自由空间有效地激发，这将推动基于自由空间耦合的WGM的进一步实验和应用。
