Coupled-mode formulation for novel waveguide geometries

We present a consistent vector formulation of the improved coupled-mode theory (ICMT) based on a new and most general perturbative expansion of the electric field in the complete waveguide of array over known eigenstates of the individual channels in the subspace spanned by the vector fields. It is shown that the effectively scalar TE and TM coupled-mode equations directly follow from full vector coupled-mode theory (VCMT). Errors in the mode splitting of the ICMT and the VCMT approaches, in the case of simple 1D symmetric double-waveguide model widely used for testing different CM theories, are compared.