Fano-Like Resonance from Disorder Correlation in Vacancy-Doped Photonic Crystals

By preparing colloidal crystals with random missing scatterers, crystals are created where disorder is embodied as vacancies in an otherwise perfect lattice. In this special system, there is a critical defect concentration where light propagation undergoes a transition from an all but perfect reflector (for the spectral range defined by the Bragg condition), to a metamaterial exhibiting an enhanced transmission phenomenon. It is shown that this behavior can be phenomenologically described in terms of Fano-like resonances. The results show that the Fano's parameter q experiences a sign change signaling the transition from a perfect crystal exhibiting a reflectance Bragg peak, through a state where background scattering is maximum and Bragg reflectance reaches a minimum to a point where the system reenters a low scattering state recovering ordinary Bragg diffraction. A simple dipolar model considering the correlation between scatterers and vacancies is proposed and the reported evolution of the Fano-like scattering is explained in terms of the emerging covariance between the optical paths and polarizabilities and the effect of field enhancement in photonic crystal (PhC) defects.