  We demonstrate advanced integrated photonic filters in silicon-on-insulator
(SOI) nanowires implemented by cascaded Sagnac loop reflector (CSLR)
resonators. We investigate mode splitting in these standing-wave (SW)
resonators and demonstrate its use for engineering the spectral profile of
on-chip photonic filters. By changing the reflectivity of the Sagnac loop
reflectors (SLRs) and the phase shifts along the connecting waveguides, we
tailor mode splitting in the CSLR resonators to achieve a wide range of filter
shapes for diverse applications including enhanced light trapping, flat-top
filtering, Q factor enhancement, and signal reshaping. We present the
theoretical designs and compare the CSLR resonators with three, four, and eight
SLRs fabricated in SOI. We achieve versatile filter shapes in the measured
transmission spectra via diverse mode splitting that agree well with theory.
This work confirms the effectiveness of using CSLR resonators as integrated
multi-functional SW filters for flexible spectral engineering.
