| Summary: | 博士 === 國立交通大學 === 電子物理系所 === 104 === It is commonly presumed that the resonant spectrum and resonant mode in experimental wave systems can be straightforwardly described by the theoretical eigenvalue and eigenmode solved by the homogeneous Helmholtz equation in the same bounded domain. However, the coupling between the excitation source and the cavity in experimental resonator inevitably deviate the resonant behaviors from the intrinsic properties of ideal eigen-system. In this thesis, several quantum and classical systems including quantum billiards, microcavity lasers, acoustic vibrating plates, and RLC circuit networks with mutual coupling to a scattering potential or an excitation source are explored. In the weak-coupling regime, it is confirmed that the experimental resonant spectra of the microcavity laser can still be utilized to manifest the characteristics of theoretical eigenvalue spectra of the ideally bound system. On the other hand, for the vibrating plates and RLC circuit networks in which the resonators are strongly coupled with the excitation source, the resonant spectra and resonant modes are found to be dramatically different from the eigenvalues and eigenmodes of the source-free cavity. According to these experimental findings, we further develop a theoretical model for analyzing resonators subject to the coupling from excitation source. The resonant modes derived from the theoretical model are verified to successfully describe the experimental observations from weak to strong coupling regime.
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