  Ring resonators provide a means of filtering specific wavelengths from a
waveguide, and optionally dropping the filtered wavelengths into a second
waveguide. Both of these features are potentially useful for astronomical
instruments.
  In this paper we focus on their use as notch filters to remove the signal
from atmospheric OH emission lines from astronomical spectra, however we also
briefly discuss their use as frequency combs for wavelength calibration and as
drop filters for Doppler planet searches.
  We derive the design requirements for ring resonators for OH suppression from
theory and finite difference time domain simulations. We find that rings with
small radii (<10 microns) are required to provide an adequate free spectral
range, leading to high index contrast materials such as Si and Si$_{3}$N$_{4}$.
Critically coupled rings with high self-coupling coefficients should provide
the necessary Q factors, suppression depth, and throughput for efficient OH
suppression.
  We report on our progress in fabricating both Si and Si$_{3}$N$_{4}$ rings
for OH suppression, and give results from preliminary laboratory tests. Our
early devices show good control over the free spectral range and wavelength
separation of multi-ring devices. The self-coupling coefficients are high
(>0.9), but further optimisation is required to achieve higher Q and deeper
notches, with current devices having $Q \approx 4000$ and $\approx 10$ dB
suppression. The overall prospects for the use of ring resonators in
astronomical instruments is promising, provided efficient fibre-chip coupling
can be achieved.
