Abstract
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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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