Analytic properties of photonic crystal superprism parameters.

We study the analytic properties of the photonic crystal superprism resolution parameters p , q , and r introduced previously by Baba and Matsumoto [Appl. Phys. Lett. 81, 2325 (2002)], which characterize the potential dispersive power of a superprism. We find closed form expressions for these quantities that greatly simplify their accurate evaluation and reveal significant insights about their behavior. The expressions imply general properties of the parameters which are true for all bands and all photonic crystals. In particular, we demonstrate that all photonic crystals exhibit infinite resolution as measured by the parameter r along particular contours in any photonic band.