Synthesis of direct-coupled-resonators bandpass filters for WDM systems

A simple technique for the exact synthesis of selective bandpass filters for wavelength division multiplexing (WDM) systems is presented. The filters consist of direct-coupled ring resonators or cascaded Bragg gratings. The proposed technique permits the calculation of the physical dimensions of the optical structures given the desired frequency response of the filter in terms of bandwidth, free spectral range, out-of-band rejection, and frequency characteristic. The technique, explained in detail for Butterworth and Chebyshev frequency responses, is exact, uses closed-form formulae, and is physically well based. The resulting devices are very compact, have a high out-of-band attenuation, and are suitable for high-density integrated optics. Several filters for applications such as channel add-drop, channel selection, demultiplexing, multichannel filtering, and interleavers are designed, analyzed, and discussed in the paper.