Effective index method for an optical waveguide with an arbitrary refractive index distribution

A new effective index method (EIM) is introduced to reduce a two-dimensional refractive index structure to a one-dimensional one accurately. The present EIM can be implemented for arbitrarily shaped waveguides. An explicit formula is obtained for the effective refractive index profile determined by the model filed and the cross-sectional refractive index of the original structure. In order to show how the present method is carried out, a silicon-on-insulator (SOI) rib waveguide is used in a numerical example. The effective model field distribution and the effective index profile are calculated with the present EIM. The bending loss of a SOI bent waveguide is also calculated with the present and conventional EIMs respectively. The numerical results show that the present method is much more accurate than the conventional EIM.