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Giant Resonance and Anomalous Quality Factor Scaling in Degenerate Band Edge Coupled Resonator Optical Waveguides

We propose a novel scheme for enhancing the quality factor (Q factor) of coupled resonators optical waveguides (CROWs) side coupled to a straight waveguide when operating near a degenerate band edge (DBE). The DBE is an exceptional point of degeneracy occurring without the need of loss or gain when four Bloch eigenwaves coalesce, providing a resonance condition with field enhancement and other unique properties associated with such frozen mode. We derive an analytic expression that describes the flatness of the dispersion diagram at the DBE and show how this is related to engineering the quality factor. We report an anomalous scaling law of the quality factor for a cavity made of the DBE-CROW with the fifth power of the number of rings when operating at the resonance frequency closest to the DBE frequency, even in the presence of losses and structural perturbations. Remarkably, the Q factor of the proposed DBE-CROW can be engineered to exceed that of a single ring resonator having a diameter equal to the total DBE-CROW length; hence, the DBE leads to an overall huge area reduction. We also demonstrate the robustness of the DBE-CROW's Q factor scaling near the DBE against perturbations and disorders that could arise from tolerances in fabrication. The findings reported in this paper are critical for enhancing field's amplitudes to giant levels and the Q factor of ring resonators, and are very beneficial for various applications including four-wave mixing, Q switching, lasers, and highly sensitive sensors.