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.