A multiple-scale analysis of grating-assisted couplers

Optical directional couplers with longitudinal periodic perturbations or gratings are analyzed by a multiple-scale solution to the coupled-mode equations. The use of two length scales in the analysis becomes the key to obtaining globally valid analytic solutions, which are shown to be in excellent agreement with the exact numerical solutions. Because of the nonorthogonality of the coupled modes in the structure, two different coupling lengths, a maximum power transfer length and a zero crosstalk length, are predicted for the power exchange. The spectral properties of the coupler are also studied through a generalized multiple scale method.>