  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.
