Mechanism and sensitivity of Fano resonance tuning in high-contrast gratings

We develop a theory for Fano resonance tuning in dual-mode high-contrast gratings (HCGs). Compact analytical formulas of tuning sensitivity are derived and verified numerically, and are in good agreement with reported experiments. We show that the resonance tuning in HCGs, containing cooperative contribution from two propagating modes, is fundamentally different from that in single-mode microresonators. Our theory reveals the important role of the higher-order mode, which can possess large modal dispersion, especially in the long-wavelength limit beyond the cutoff of slab waveguides, to enable large tuning sensitivity. Our findings will simplify the design and optimization of active and passive tuning in HCG resonators.