Kinematic study of refraction properties of an opal-based photonic crystal

A kinematic analysis of refraction at the boundary between the (1 1 1) surface of a 200 nm close-packed fcc-SiO₂-based opal and vacuum is presented. The dispersion relation and the equi-frequency surface (EFS) of the photonic band structure are calculated using the plane wave expansion method (PWEM) in order to obtain, in a specific case of polarization, the frequency-dependent relation between the incident and propagation angles. From these refraction properties, one can deduce that the system inhibits the transmission of waves, with frequencies in the visible range, in a wide range of incident angles.