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The RHS shows the dispersion relations at normal incidence, constructed by assigning a wavevector to each resonance peak. The resonances are denoted by dots, while the horizontal lines are a guide to the eye. As shown in the LHS, the modes for the increasingly singular gratings can be equivalently found by folding the dispersion relation over a gradually narrower Brillouin zone, whose width is dictated by the effective periodicity d of the mother structure in the slab frame. The slab frame periods used are d 1 = 2π, d 2 ≈ 2.6 × 2π and d 3 ≈ 5.3 × 2π.
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