| Summary: | A coupled structure, consisting of two perpendicular cavities coupled with a waveguide, has been proposed and researched numerically and theoretically. It is found that the lateral displacement <italic>S</italic> plays a key role in transmission spectrum. Whether the first- or the second-order mode can exist in the horizontal cavity has been well explained. Owing to the interaction among two discrete and a continuous states, four Fano resonance can be achieved to set appropriate <italic>S</italic>. When the coupled structure is filled with liquid crystal (LC), the refractive index can be regulated dynamically by external voltage. The coupled structure can be act as a filter which filters arbitrary wavelength within the scope of certain wavelength. At the same time, in a certain wavelength range, an optical switch can be achieved with different voltage at any wavelength. This structure has the advantages of simple, easy fabrication and tunability, which has potential applications in integrated optical devices.
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