Direct imaging of isofrequency contours in photonic structures

The isofrequency contours of a photonic crystal are important for predicting and understanding exotic optical phenomena that are not apparent from high-symmetry band structure visualizations. We demonstrate a method to directly visualize the isofrequency contours of high-quality photonic crystal slabs that show quantitatively good agreement with numerical results throughout the visible spectrum. Our technique relies on resonance-enhanced photon scattering from generic fabrication disorder and surface roughness, so it can be applied to general photonic and plasmonic crystals or even quasi-crystals. We also present an analytical model of the scattering process, which explains the observation of isofrequency contours in our technique. Furthermore, the isofrequency contours provide information about the characteristics of the disorder and therefore serve as a feedback tool to improve fabrication processes.