  We consider photonic crystal fibres (PCFs) made from arbitrary base materials
and introduce a short-wavelength approximation which allows for a mapping of
the Maxwell's equations onto a dimensionless eigenvalue equations which has the
form of the Schrodinger equation in quantum mechanics. The mapping allows for
an entire analytical solution of the dispersion problem which is in qualitative
agreement with plane-wave simulations of the Maxwell's equations for large-mode
area PCFs. We offer a new angle on the foundation of the endlessly single-mode
property and show that PCFs are endlessly single mode for a normalized air-hole
diameter smaller than ~0.42, independently of the base material. Finally, we
show how the group-velocity dispersion relates simply to the geometry of the
photonic crystal cladding.
