Fig. 4: Phase conditions for BICs.

a, b Magnitude and phase for the BIC condition. They are automatically satisfied for lossless/reciprocal networks containing at least two modes. c Conditions for half round-trip propagation phases of the two different modes. They are only satisfied at discrete points due to dispersion. BICs occur at the intersection of the two curves, which are guaranteed for discrete sets of pillar heights and effective wavelengths