A “poor man’s approach” to modelling of micro-structured optical fibres

Based on the scalar Helmholtz equation and the finite-difference approximation, we formulate a matrix eigenvalue problem for the calculation of propagation constants, β(ω), in micro-structured optical fibres. The method is applied to index-guiding fibres as well as air-core photonic bandgap fibres, and in both cases qualitatively correct results are found. The strength of this approach lies in its very simple numerical implementation and its ability to find eigenmodes at a specific eigenvalue, which is of great interest, when modelling defect modes in photonic bandgap fibres. Submitted to: J. Opt. A: Pure Appl. Opt.