Percolation in photonic crystals revealed by Fano Resonance

The understanding of how the arrangement of defects in photonic crystals impacts its photonic properties is cru-cial for the design of functional materials based thereon. By preparing photonic crystals with random missing scatterers we create crystals where disorder is embodied as vacancies in an otherwise perfect lattice rather than the usual positional or size disorder. We show that the amount of defects not only determines the intensity but also the nature of the light scattering. As the amount of defects varies, light scattering undergoes a transition whereby the usual signatures of photonic gaps (Bragg peak) suffer line-shape changes (Bragg dip) that can be readily described with the Fano resonance q parameter. When the amount of vacancies reaches the percolation threshold, q undergoes a sign change signaling the transition from a crystal to a mosaic of microcrystals through a state where scattering is maximum. Beyond that point the system reenters a state of low scattering that ap-pears in the guise of normal Bragg diffraction.