  Silicon microring resonators (MRRs) have shown strong potential in acting as
the nonlinear nodes of photonic reservoir computing (RC) schemes. By using
nonlinearities within a silicon MRR, such as the ones caused by free-carrier
dispersion (FCD) and thermo-optic (TO) effects, it is possible to map the input
data of the RC to a higher dimensional space. Furthermore, by adding an
external waveguide between the through and add ports of the MRR, it is possible
to implement a time-delay RC (TDRC) with enhanced memory. The input from the
through port is fed back into the add port of the ring with the delay applied
by the external waveguide effectively adding memory. In a TDRC, the nodes are
multiplexed in time, and their respective time evolutions are detected at the
drop port. The performance of MRR-based TDRC is highly dependent on the amount
of nonlinearity in the MRR. The nonlinear effects, in turn, are dependent on
the physical properties of the MRR as they determine the lifetime of the
effects. Another factor to take into account is the stability of the MRR
response, as strong time-domain discontinuities at the drop port are known to
emerge from FCD nonlinearities due to self-pulsing (high nonlinear behaviour).
However, quantifying the right amount of nonlinearity that RC needs for a
certain task in order to achieve optimum performance is challenging. Therefore,
further analysis is required to fully understand the nonlinear dynamics of this
TDRC setup. Here, we quantify the nonlinear and linear memory capacity of the
previously described microring-based TDRC scheme, as a function of the time
constants of the generated carriers and the thermal of the TO effects. We
analyze the properties of the TDRC dynamics that generate the parameter space,
in terms of input signal power and frequency detuning range, over which
conventional RC tasks can be satisfactorily performed by the TDRC scheme.
