Fig. 1. Conceptual diagram of the self-calibrating microring synapse with dual-wavelength synchronization. Monitoring wavelengths are added to monitor and calibrate the synaptic weights, and a thermally insensitive mapping between the synaptic weights and monitoring wavelengths can be established to provide accurate initial reference points for the parameter update procedure.

Fig. 2. Detailed design of the integrated microring synapse. (a) The schematic structure of the 4×4 MRR array. Different colors correspond to different wavelength channels. (b) The micrograph of the microring synapse cascading four MRRs and the zoomed-in micrograph of an individual MRR. (c) The overall and detailed photos of the packaged layout. The integrated photonic core is wire bonded with a tailored printed circuit board (PCB) and mounted on a thermo-electric cooler (TEC). The optical input and output (I/O) are through the fiber V groove on the top left. (d) The measured output spectral response of the MRR synapse at the THRU and DROP ports.

Fig. 3. Comparison of the calibrated weights and theoretical weights of the individual MRR of the microring synapse.

Fig. 4. The calibration with dual-wavelength synchronization improves the precision of weighting in the two-MRR synapses. (a) The measurement of the weighting precision before the self-calibration. (b) The measurement of the weighting precision after the self-calibration. The weighting precision is evaluated at equally spaced weights on the heatmap. Each sub-square in the heatmap represents the weighting error of a measured weight, and its shade represents the magnitude of the error. (c) and (d) are the weighting error for the evaluation in (a) and (b), respectively, calculated as Δw=w−wset, where w is the measured weight and wset is the set weight. The dashed and solid circles correspond to different bit precisions to provide an intuitive distribution of weight precision.

Fig. 5. Robust performance of the self-calibrating microring synapse against environmental temperature fluctuations. The tested weights consist of positive, zero, and negative weights, including weight of (a) 0.3, (b) 0, (c) −0.2, and (d) −0.5.

Fig. 6. Simulation results of Newton’s iterative method for matrix inversion tasks with bit precision of 4 bits, 5 bits, 6 bits, 7 bits, and 8 bits.

Fig. 7. Matrix inversion based on Newton’s iteration for two different initial matrices. (a) The implementation of an individual Newton’s iteration expressed by Eq. (3). (b) The theoretical and experimental results for the initial matrix A1. (c) The error distribution of the inverse of A1. (d) The theoretical and experimental results for the initial matrix A2. (e) The error distribution of the inverse of A2.