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We show that by using a perturbed photonic Dirac-cone, one can realizeultra-narrow and finite Q-factor peak in the wavevector space, with both thepeak value and the width separately tunable. We also discuss a lower bound inthe minimal viable width given a peak Q-value while maintaining sufficient Qdifferentiation among modes. The strong angular and frequency Q-selection findsapplications in optical devices where strong angle- and frequency-selection isneeded.

Controllable finite ultra-narrow quality-factor peak in a perturbed Dirac-cone band structure of a photonic crystal slab