  In this work, we describe a procedure for synthesizing racetrack resonators
with large quality factors and apply it to realize a multi-channel
wavelength-selective switch (WSS) on a silicon photonic chip. We first
determine the contribution of each component primitive to propagation loss in a
racetrack resonator and use this data to develop a model for the frequency
response of arbitrary order, coupled-racetrack channel dropping filters. We
design second-order racetrack filters based on this model and cascade multiple
such filters to form a 1x7 WSS. We find good agreement between our model and
device performance with second-order racetrack that have ~1 dB of drop-port
loss, ~2 GHz FWHM linewidth, and low optical crosstalk due to the quick filter
roll-off of ~ 5.3 dB/GHz. Using a control algorithm, we show three-channel
operation of our WSS with a channel spacing of only 10 GHz. Owing to the high
quality factor and quick roll-off of our filter design, adjacent channel
crosstalk is measured to be <-25 dB for channels spaced on a 10 GHz grid. As a
further demonstration, we use five of seven WSS channels to perform a
demultiplexing operation on both an 8 GHz and a 10 GHz grid. These results
suggest that a low-loss WSS with fine channel resolution can be realized in a
scalable manner using the silicon photonics platform.
