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.

翻译：硅微环谐振器（MRR）在作为光子储备池计算（RC）方案的非线性节点方面展现出巨大潜力。通过利用硅微环谐振器内部的非线性效应，例如由自由载流子色散（FCD）和热光（TO）效应引起的非线性，可以将RC的输入数据映射到更高维空间。此外，通过在微环的直通端口与添加端口之间引入外部波导，可以实现具有增强记忆能力的时延储备池计算（TDRC）。来自直通端口的输入被反馈到微环的添加端口，外部波导引入的延迟有效地增加了记忆能力。在TDRC中，节点在时间上复用，其各自的时间演化在下载端口被检测。基于微环的TDRC性能高度依赖于微环中的非线性程度。非线性效应反过来又取决于微环的物理特性，因为这些特性决定了效应的寿命。另一个需要考虑的因素是微环响应的稳定性，因为已知FCD非线性会由于自脉动（高度非线性行为）在下载端口产生强烈的时域不连续性。然而，量化RC为特定任务达到最佳性能所需的非线性程度是具有挑战性的。因此，需要进一步分析以充分理解该TDRC设置的非线性动力学。在此，我们量化了前述基于微环的TDRC方案的非线性和线性记忆容量，并将其作为所产生载流子的时间常数和热光效应热时间常数的函数。我们分析了TDRC动力学的特性，这些特性生成了参数空间（就输入信号功率和频率失谐范围而言），在该参数空间内，TDRC方案可以令人满意地执行常规RC任务。