Guidance in Kagome-like photonic crystal fibres I: analysis of an ideal fibre structure

Propagation of light in a square-lattice hollow-core photonic crystal fibre is analysed as a model of guidance in a class of photonic crystal fibres that exhibit broad-band guidance without photonic bandgaps. A scalar governing equation is used and analytic solutions based on transfer matrices are developed for the full set of modes. It is found that an exponentially localised fundamental mode exists for a wide range of frequencies. These analytic solutions of an idealised structure will form the basis for analysis of guidance in a realistic structure in a following paper.