  We present and investigate theoretically photonic integrated filters based on
2 Sagnac coupled loop reflectors (SLRs) that are arranged in a self-coupled
optical waveguide. We recently presented photonic integrated filters based on
coupled and cascaded SLRs. In this paper, we advance this field by
investigating a unique approach of employing coupled SLRs formed by
self-coupled waveguides. This allows 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 advantageous for applications such as
optical interleavers that require a symmetric flat-top filter shape. Optical
de-interleavers and interleavers are key components for optical signal
multiplexing and demultiplexing for 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 for many applications.
