Comb transmission filters defined by phase-shifted superstructure Bragg gratings

We present a design method and numerical results describing the construction of distributed feedback grating filters that support discrete combs of transmission resonances. These filter designs define open superstructure grating resonators with transmission channels that can be placed at predetermined frequencies, such as those defined by the wavelength division multiplexing grid or by a secondary frequency comb source. Focusing on a specific example with 40 GHz channel spacing, we optimize an active structure that defines three low-threshold lasing modes. How our design approach relates to filter synthesis techniques based on cascaded grating resonators is also discussed.