Model of light collimation by photonic crystal surface modes

We propose a quantitative model explaining the mechanism of light collimation by leaky surface modes that propagate on a corrugated surface around the output of a photonic crystal waveguide. The dispersion relation of these modes is determined for a number of surface terminations. Analytical results obtained on the basis of the model are compared to those of rigorous numerical simulations. Maximum collimation is shown to occur at frequency values corresponding to excitation of surface modes whose wave number retains a nonzero real part.