Photonic crystal fibres: mapping Maxwell's equations onto a Schrödinger equation eigenvalue problem

We consider photonic crystal fibres (PCFs) made from arbitrary base materialsand introduce a short-wavelength approximation which allows for a mapping ofthe Maxwell's equations onto a dimensionless eigenvalue equations which has theform of the Schrodinger equation in quantum mechanics. The mapping allows foran entire analytical solution of the dispersion problem which is in qualitativeagreement with plane-wave simulations of the Maxwell's equations for large-modearea PCFs. We offer a new angle on the foundation of the endlessly single-modeproperty and show that PCFs are endlessly single mode for a normalized air-holediameter smaller than ~0.42, independently of the base material. Finally, weshow how the group-velocity dispersion relates simply to the geometry of thephotonic crystal cladding.Comment: 16 pages including 6 figure