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Coupled non-identical microdisks: avoided crossing of energy levels and unidirectional far-field emission

We investigate two coupled microdisks with non-identical radii focusing on the parametric evolution of energy levels and the unidirectional far-field emission. We show that the evolution of energy levels is characterized by the avoided crossing intrinsically associated with the exceptional point or the non-Hermitian degeneracy. These spectral properties explain highly asymmetric near-field intensity pattern of the resonance mode. The observed unidirectional far-field emission is shown to be understood by considering the forbidden inter-disk coupling in the ray picture induced by the frustrated total internal reflection near the closest point between two disks when the inter-disk distance is small enough.