A comparison between different methods to calculate grating assisted asymmetrical couplers

In this paper we present the basic formulation of the eigenmode expansion method, coupled mode theory and show, in case of resonance, the equivalence of the guided eigenmode matching and propagation method (GEMP) with simple coupled mode theory on the basis of coupler eigenmodes in the limit of weak coupling. It will be shown, that the key parameters alpha rot of GEMP and the coupling coefficient kappa of coupled mode theory (CMT) are correlated and that for practical applications a combination of both methods are advantageous. Some results on codirectional grating assisted couplers and the recently published sampled grating structure, which is the basis of an electro-optically tunable filter, will be discussed