Fig. 1. (a) Electronic and (b) photonic implementations of SISD and SIMD operations. (a1) An SISD electronic arithmetic unit that performs multiplication and addition. (a2) SIMD design with multiple, pipelined inputs for dot-product calculation. (b) Individual single-mode coherent mixers as multiplier units without parallelism, equivalent to SISD architecture in digital electronics.

Fig. 2. Photonic implementation of vector dot-product core based on mode-division multiplexing. (a) Implementation based on the traditional MDM infrastructure in optical communications, using two MUXs and one MMI. (b) An end-to-end photonic dot-product core that integrates the functionalities of two MUXs and one MMI. The inset shows the photonic structure from inverse design.

Fig. 3. Characterization of the fabricated dot-product core. (a) Microscope image of the fabricated dot-product core under test. (b) Experimentally observed intensity profiles on the two output couplers when the inputs a1 and a2 were individually excited. (c) Structure of the ideal inversely designed dot-product core and simulated electrical field profiles within the core. (d) SEM image of the fabricated dot-product core and simulated electrical field profiles within the core based on the SEM image. The side views show the electrical field profiles at the location marked by the orange dashed line.

Fig. 4. Characterization of (a1), (b1) designed and (a2), (b2) fabricated dot-product core. (a) Crosstalk matrix MX of the core. (b) Insertion loss and crosstalk (in dB) as a function of wavelength.

Fig. 5. General-purpose computing examples as dot-products on the photonic core. (a) Dot-product calculation of a sequence of 16 two-element vectors. (b) Complex number multiplications encoded as two equivalent dot-products in time-division multiplexing. (c1), (c2) Multiplication results between 16 complex numbers. Blue circles indicate ground truth results, green circles indicate simulated results from the ideal inversely designed core in (b), and red circles indicate experimental results calculated on the fabricated dot-product core.

Fig. 6. Optical flow calculation between two adjacent frames of a spinning wheel animation. (a) Two frames from the spinning wheel animation with 100 ms interval (10 frames per second). (b) Optical flow vector of eight edge pixels. Red arrows indicate the ground truth of the flow vectors, and orange arrows indicate experimental results calculated on the photonic dot-product core. (c) Comparison of the calculated angular speed on the dot-product core with ground truth.

Fig. 7. Transfer matrix of the fabricated dot-product core St and the corresponding compensation matrices Cfull and Cemp. Only the magnitudes of the matrix elements are shown.

Fig. 8. Comparison of the different compensation methods. (a) TDM dot-product output sequence before and after compensation using the full transfer matrix St and the empirical method with/without phase modulation. (b) Comparison between the NMSE of the raw and compensated dot products.

Fig. 9. Comparison of the dot products before and after calibration in experiments.

Fig. 10. Design and FDTD simulations of the photonic crystal output coupler supporting the observation of multimode intensity profiles from the top.