  Based on the scalar Helmholtz equation and the finite-difference
approximation, we formulate a matrix eigenvalue problem for the calculation of
propagation constants, beta(omega), 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.
