Fig. 1. Proposed optical crossbar array. The matrix and vector are generated by MRRs and MZIs, respectively. Multiple wavelengths are injected into four input ports simultaneously. The MRRs are tuned to align with different wavelengths, and the associated matrix element is represented by the transmittance of optical power at the drop port. (a) By injecting a forward signal x, which represents the output signal from the previous layer in an ANN, the crossbar array performs the multiplication between W and x. (b) By injecting a backward signal σ, which represents the error signal backpropagated from the next layer in an ANN, the crossbar array performs the multiplication between W⊤ (the transpose of W) and σ.

Fig. 2. Microscope images of a 4×4 MRR crossbar array fabricated on an SOI platform. (a) The entire circuit consists of MZIs, MRRs, and TE-pass filters. The consumed chip area is 3.7  mm×2.4  mm. (b) Enlarged view of one MZI. Only one input port and one output port are used. The other two ports are terminated with inverse waveguide tapers. (c) Enlarged view of one MRR. The radii of all MRRs are 20 μm.

Fig. 3. Experimental setup. Four CW lights at different wavelengths are generated by a four-channel tunable laser and combined into a single optical fiber by inversely using two stages of 1×2 optical splitters. The MEMS optical switch directs the combined light to the ports for either the forward or backward signal. The chip is wire-bonded for external electrical control and packaged with a fiber array for stable fiber coupling.

Fig. 4. Characterizations of MZIs and MRRs. (a) Characterization result of the MZI at the In 1 port as a function of heater power. The MZI exhibits a high extinction ratio of 51 dB. (b) Transmission spectra measured at the Out 1–4 ports when sweeping the wavelength of light injected into the In 1 port. No electric power is applied to the phase shifters for MRRs. The resonant wavelengths of the four MRRs slightly differ due to fabrication non-uniformity. (c) Illustration of characterizing the difference between the forward and backward paths of each MRR. (d) Optical power measured at the output ports for forward and backward signals of one MRR. The two directions exhibit almost the same characteristics.

Fig. 5. Experimental implementations of various matrices for forward and backward signals. Each matrix element is measured by setting one MZI into the maximum-transmittance state and the others into the minimum-transmittance state. The matrices measured from the forward and backward directions are transposed to each other. Error signals in these matrices are suppressed to the level of approximately −15  dB.

Fig. 6. Inference tasks using the optical crossbar array. (a) Three-layered neural network for classifying iris flowers. The sigmoid function is used as the nonlinear activation function. (b) Inference results after the neural network is trained on a computer using the stochastic gradient descent algorithm. Classification accuracies of 97.8% and 93.3% are obtained using the computer and this circuit, respectively.

Fig. 7. Training of the neural network using simulated on-chip backpropagation. (a) Look-up table for one MRR characterized in the forward direction that maps the settings of the MZI and the MRR to the measured output power. (b) Changes in cost functions in four independent trainings, all of which converged successfully after 100 epochs. (c) Inference results after training using the simulated on-chip backpropagation. Classification accuracies of 91.1% are obtained using both the computer and this circuit.

Fig. 8. Simulation of handwritten digit recognition using a 9×9 MRR crossbar array. (a) CNN for handwritten digit recognition. A 9×9 MRR crossbar array is used to perform the convolution operations. (b) Changes in classification accuracies during training. The accuracy reaches 93.4% after 10 epochs. (c) Confusion matrix after 10 epochs of training.

Fig. 9. Characterization results of all MZIs.

Fig. 10. Characterization results of all MRRs. No electric power is applied to the heaters of MRRs.

Fig. 11. Measured differences between the forward and backward paths of all MRRs.