Photonic crystal waveguides: A one-dimensional model theory

We study the dispersion relations and field maps of the propagating modes i n one dimensional models of photonic crystal fibers. This simple model allo ws the derivation of rigorous electromagnetic theory, and provides insight for the properties observed in actual waveguides. The theory is developed t hrough a particularly efficient impedance formulation of the problem. The d ispersion relations of propagating modes are presented and discussed. Field maps of certain modes are also illustrated, and allow an understanding of the low loss behavior of holy fibers.