We report on controllable cavity modes through controlling the backscattering by two identical scatterers. Periodic changes of the backscattering coupling between two degenerate cavity modes are observed with the angle between two scatterers and elucidated by a theoretical model using two-mode approximation and numerical simulations. The periodically appearing single-peak cavity modes indicate mode degeneracy at diabolical points. Then interactions between single quantum dots and cavity modes are investigated. Enhanced emission of a quantum dot with a six-fold intensity increase is obtained in a microdisk at a diabolical point. This method to control cavity modes allows large-scale integration, high reproducibility and fexible design of the size, location, quantity and shape for scatterers, which can be applied for integrated photonic structures with scatterer-modified light-matter interaction.
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