Fibre mode expansion for 2-D waveguide calculations

A numerical method is introduced which is devised to calculate the lower-order modes of optical waveguides with two-dimensional transverse index profiles embedded in a homogeneous cladding medium. We propose a method based on a series expansion using guided modes of an optical fibre. To test the method, it is applied to a three-layer optical-fibre and the results are compared with the exact analytical solutions. The error in the calculation of the modal effective indices is found to be less than 10(-6). This method allows the modelling of symmetric 2 x 2 completely fused fibre couplers. Effective indices and polarization corrections are compared with results obtained by the field correction method. The adiabaticity criterion is calculated for these couplers.