Design of grating-assisted waveguide couplers with weighted coupling

The design of grating-assisted, channel waveguide codirectional couplers is demonstrated using the Gel´fand-Levitan-Marchenko inverse scattering method. Weighted coupling coefficients are computed from rational expression for the desired wavelength response. Approximate formulas that relate the waveguide and grating geometries to the computed coupling coefficients are derived. The technique is illustrated by designing a directional coupler with a third-order Butterworth filter characteristic and a 130 Å full-width-half-maximum bandwidth