Asymmetric power coupling in grating-assisted couplers

Asymmetric power coupling in grating-assisted coupler filter is revealed analytically for the first time by coupled-mode theory. An optimum grating period is then proposed and various coupling lengths for maximum power transfer and minimum crosstalk between two waveguides are derived analytically. Comparisons between coupled-mode theory and the vector beam propagation method have been made for possible scenarios of power exchange between the two waveguides. Excellent agreement between them indicates that the coupled-mode theory shown in the paper is able to not only reveal all the physics embedded in the complicated coupling processes, but also predict various possible filtering responses accurately