On phase matching and power coupling in grating-assisted couplers

Two formulas of phase-matching condition for grating-assisted couplers in the literature are compared. The power exchange between the waveguides is examined by a numerical solution to the coupled-mode equations and a direct simulation by the beam propagation method. It is demonstrated that the phase-matching of the normal modes of the coupler (array modes) maximizes the power coupling. The approximate phase-matching condition for the modes of the individual waveguides (waveguide modes), however, leads to only partial power exchange.>