  Microring resonators (MRRs) are a key photonic component in integrated
devices, due to their small size, low insertion losses, and passive operation.
While the MRRs have been established for optical filtering in
wavelength-multiplexed systems, the nonlinear properties that they can exhibit
give rise to new perspectives on their use. For instance, they have been
recently considered for introducing optical nonlinearity in photonic reservoir
computing systems. In this work, we present a detailed numerical investigation
of a silicon MRR operation, in the presence of external optical feedback, in a
time delay reservoir computing scheme. We demonstrate the versatility of this
compact, passive device, by exploiting different operating regimes and solving
computing tasks with diverse memory requirements. We show that when large
memory is required, as it occurs in the Narma 10 task, the MRR nonlinearity
does not play a significant role when the photodetection nonlinearity is
involved, while the contribution of the external feedback is significant. On
the contrary, for computing tasks such as the Mackey-Glass and the Santa Fe
chaotic timeseries prediction, the MRR and the photodetection nonlinearities
contribute both to efficient computation. The presence of optical feedback
improves the prediction of the Mackey-Glass timeseries while it plays a minor
role in the Santa Fe timeseries case.
