  The iso-frequency contours of a photonic crystal are important for predicting
and understanding exotic optical phenomena that are not apparent from
high-symmetry band structure visualizations. Here, we demonstrate a method to
directly visualize the iso-frequency contours of high-quality photonic crystal
slabs that shows 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 iso-frequency contours in our technique.
Furthermore, the iso-frequency contours provide information about the
characteristics of the disorder and therefore serve as a feedback tool to
improve fabrication processes.
