Fig. 1. Concept of the micrometer-scale DNN at the visible wavelength and the comparison of cubical neurons and cylindrical neurons. (A) The DNN for image classification is based on light propagation according to Huygens’ principle and the Rayleigh–Sommerfeld diffraction theory. (B) Cylindrical diffraction neurons with different heights; (C) cubical diffraction neurons with different heights; (D) phase modulation as a function of heights for cubical neurons (squares) and cylindrical neurons (dots) simulated by FDTD, where the red dashed line represents the results of the OPD formula; (E) cubical neurons maintain a higher amplitude modulation efficiency than cylindrical neurons.

Fig. 2. Analysis of the influence of the detector area sizes on the classification accuracy of the DNN. (A) Classification accuracy of the single-layer two-classifier DNN as a function of detector area size; (B) numerically calculated phase distribution for the single-layer two-classifier DNN with the detector area size of 6 neurons × 6 neurons; (C) classification accuracy of the two-layer 10-classifier DNN as a function of detector area size; (D) numerically calculated phase distribution for the two-layer 10-classifier DNN with the detector area size of 6 neurons × 6 neurons.

Fig. 3. Single-layer two-classifier DNN for digit classification. (A) CAD model of the single-layer two-classifier DNN for digit classification; (B) left is the numerical phase distribution map of the single-layer two-classifier DNN, and right is the SEM image of the fabricated height map transformed from the phase distribution map (scale bar is 20 µm). (C) Experimental classification results of the single-layer two-classifier DNN and normalized energy distribution compared with numerical results.

Fig. 4. Design and fabrication results of the two-layer 10-classifier DNN. (A) CAD model of the two-layer 10-classifier DNN; (B) numerical phase distribution map of the neurons on layer 1 and layer 2; (C) perspective SEM image of the fabricated two-layer 10-classifier DNN with a tilting angle of 25° (scale bar is 20 µm); (D) SEM images of the fabricated height maps of the neurons on layer 1 and layer 2 transformed from the phase distribution map in (B).

Fig. 5. Experimental classification and simulated results of the two-layer 10-classifier DNN. Output images of handwritten digits ranging from 0 to 9 (the square is the detector area) and the histograms of normalized energy distribution, where orange represents the normalized experimental energy distribution and green represents the normalized numerical energy distribution.

Fig. 6. Home-built 3D TPN system.

Fig. 7. Design and results of characterization experiment. (A) Schematic of characterization system. (B) Experimentally obtained confusion matrix for classification results.