<p>We propose and theoretically investigate integrated
photonic filters based on two coupled Sagnac loop reflectors (SLRs) formed by a
self-coupled optical waveguide. Recently we investigated integrated photonic
filters based on cascaded SLRs and coupled SLRs. Here, we advance this field by presenting a unique approach
of using coupled SLRs formed by a self-coupled
optical waveguide. This enables us to achieve high performance filter
functions including Fano-like resonances and
wavelength interleaving with a simpler design and a higher fabrication tolerance by tailoring coherent mode interference in the device. Our design
takes into account the device fabrication issues as well as the requirements
for practical applications. As a guide for practical device fabrication, an analysis of the impact of
the structural parameters and fabrication tolerance on each filter function is also provided. The Fano-like resonances show a low insertion
loss (IL) of 1.1 dB, a high
extinction ratio of 30.2 dB, and a high slope rate (SR) of 747.64 dB/nm. The combination of low IL and high SR promises this device
for Fano resonance applications. Our device also can achieve wavelength
de-interleaving function with high fabrication
tolerance which is attractive for optical interleavers that need a flat-top
symmetric filter shape. Optical interleavers and de-interleavers are
core elements for signal multiplexing and demultiplexing in wavelength division
multiplexing optical communication systems. Versatile
spectral responses with a simple design, compact device footprint, and high fabrication tolerance make this
approach highly promising for flexible response
shaping in a wide variety of applications.</p>