Theory of short-wavelength dispersion and modal properties of photonic crystal fibers

We consider photonic crystal fibers made from arbitrary base materials and derive a unified semi-analytical theory for the dispersion and modal properties which applies to the short-wavelength regime. In particular we calculate the dispersion and the effective index and comparing to fully-vectorial plane wave simulations we find excellent agreement. We also calculate asymptotic results for the mode-field diameter and the V-parameter and from the latter we predict that the fibers are endlessly single mode for a normalized air-hole diameter smaller than 0.42, independently of the base material