  We theoretically investigate integrated photonic resonators formed by two
mutually coupled Sagnac loop reflectors (MC-SLRs). Mode interference in the
MC-SLR resonators is tailored to achieve versatile filter shapes with high
performance, which enable flexible spectral engineering for diverse
applications. By adjusting the reflectivity of the Sagnac loop reflectors
(SLRs) as well as the coupling strength between different SLRs, we achieve
optical analogues of Fano resonance with ultrahigh spectral slope rates,
wavelength interleaving / non-blocking switching functions with significantly
enhanced filtering flatness, and compact bandpass filters with improved
roll-off. In our designs the requirements for practical applications are
considered, together with detailed analyses of the impact of structural
parameters and fabrication tolerances. These results highlight the strong
potential of MC-SLR resonators as advanced multi-functional integrated photonic
filters for flexible spectral engineering in optical communications systems.
