Abstract
We study the dispersion relations and field maps of the propagating modes in one dimensional models of photonic crystal fibers. This simple model allows the derivation of rigorous electromagnetic theory, and provides insight for the properties observed in actual waveguides. The theory is developed through a particularly efficient impedance formulation of the problem. The dispersion 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.
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