Theory of free space coupling to high-Q whispering gallery modes
首发时间:2014-03-10
Abstract:A theoretical study of free space coupling to high-Q whispering gallery modesboth in circular and deformed microcavities are presented. In the case of acircular cavity, both analytical solutions and asymptotic formulas arederived. The coupling efficiencies at different coupling regimes for cylinderincoming wave are discussed, and the maximum efficiency is estimated for thepractical Gaussian beam excitation. In the case of a deformed cavity, thecoupling efficiency can be higher if the excitation beam can match theintrinsic emission well and the radiation loss can be tuned by adjusting thedegree of deformation. Employing an abstract model of slightly deformedcavity, we found that the asymmetric and peak like line shapes instead of theLorentz-shape dip are universal in transmission spectra due to multi-modeinterference, and the coupling efficiency can not be estimated from theabsolute depth of the dip. Our results provide guidelines for free spacecoupling in experiments, suggesting that the high-Q ARCs can be efficientlyexcited through free space which will stimulate further experiments andapplications of WGMs based on free space coupling.
keywords: Free space coupling, Whispering-Gallery mode, Deformed micro-cavity, Cylinder wave, Gaussian beam
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自由空间耦合高Q回音壁模式的理论
摘要:A theoretical study of free space coupling to high-Q whispering gallery modesboth in circular and deformed microcavities are presented. In the case of acircular cavity, both analytical solutions and asymptotic formulas arederived. The coupling efficiencies at different coupling regimes for cylinderincoming wave are discussed, and the maximum efficiency is estimated for thepractical Gaussian beam excitation. In the case of a deformed cavity, thecoupling efficiency can be higher if the excitation beam can match theintrinsic emission well and the radiation loss can be tuned by adjusting thedegree of deformation. Employing an abstract model of slightly deformedcavity, we found that the asymmetric and peak like line shapes instead of theLorentz-shape dip are universal in transmission spectra due to multi-modeinterference, and the coupling efficiency can not be estimated from theabsolute depth of the dip. Our results provide guidelines for free spacecoupling in experiments, suggesting that the high-Q ARCs can be efficientlyexcited through free space which will stimulate further experiments andapplications of WGMs based on free space coupling.
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