New high-order microring filter architectures based on the coupling between counterpropagating modes in the microring resonators are proposed and analyzed. The dual-mode nature of the resonators is exploited to maximize the spectral response order, thereby enabling novel reflection filters to be realized with a superior performance than conventional single-mode microring filters in terms of flat passband and steep skirt rolloff. Filter topologies for two general classes of devices, the serial and parallel reflection filters, will be presented along with general techniques for synthesizing their spectral responses. It is shown that a serial reflection filter consisting of N microring resonators can realize a filter response order of up to 2(N - 1), while the parallel reflection type can be used to realize "superflat" filters, which exhibit a much flatter bandpass response than conventional maximally flat filters having the same number of cavities.
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