In this paper, we analyze a chain-linked triple-cavity photonic molecule (TCPM) with controllable coupling strengths between the cavities on their spectral properties and field (energy) distributions by solving eigenvalues and eigenvectors of the Hamiltonian matrix based on coupled mode theory. Phase transition is extended from double-cavity photonic molecules (DCPMs) to TCPMs, and evolutions of the supermode frequencies and linewidths are analyzed, which have synchronous relations with the degree of coherence between adjacent optical microcavities and energy distributions in the three cavities, respectively. We develop a superposition picture for the three supermodes of the TCPM, as interferences between supermodes of sub-DCPMs. In particular, we demonstrate the abnormal properties of the central supermode in TCPMs, such as dark state in middle cavity and phase shift when energy flowing between side cavities, which are promising in information processing and remote control of energy. General properties of TCPMs are summarized and limitation on linewidths are given. Finally, we make an interesting analog to intracavity electromagnetically induced transparency in multi-level atomic systems using the flexible TCPM platform under appropriate conditions.
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