Spectral tailoring of silicon grating-assisted contra-directional couplers

Grating-assisted, contra-directional couplers (GA-CDCs), owing to their four-port operations, can offer several important advantages over traditional, single waveguide-based Bragg gratings. However, how to flexibly design the spectral responses of GA-CDCs has been much less studied. We report the spectral tailoring methodology of GA-CDCs to achieve arbitrary, physically realizable, complex spectral responses. Silicon GA-CDCs with various customized responses are demonstrated using the methodology, including sidelobe-suppressed filters, single- and multi-channel flattop filters, sawtooth- and triangle-shaped filters, and three-channel photonic Hilbert transformers.