  We report the design and characterization of a high performance integrated
arbitrary filter from 1450 nm to 1640 nm. The filter's target spectrum is
chosen to suppress the night-sky OH emission lines, which is critical for
ground-based astronomical telescopes. This type of filter is featured by its
large spectral range, high rejection ratio and narrow notch width.
Traditionally it is only successfully accomplished with fiber Bragg gratings.
The technique we demonstrate here is proven to be very efficient for on-chip
platforms, which can bring many benefits for device footprint, performance and
cost. For the design part, two inverse scattering algorithms are compared, the
frequency domain discrete layer-peeling (f-DLP) and the time domain discrete
layer-peeling (t-DLP). f-DLP is found to be superior for the grating
reconstruction in terms of accuracy and robustness. A method is proposed to
resolve the non-uniformity issue caused by the non-zero layer size in the DLP
algorithm. The designed 55-notch filter is 50-mm-long and implemented on a
compact Si3N4/SiO2 spiral waveguide with a total length of 63 mm.
Experimentally, we demonstrate that the device has a insertion loss as low as
2.5 dB, and that the waveguide propagation loss is as low as 0.10 dB/cm. We are
also able to achieve uniform notch depths and 3-dB widths of about 28 dB and
0.22 nm, respectively.
