Second-harmonic generation for enhancing the performance of diffractive neural networks

Abstract

Diffractive neural networks (DNNs) are an emerging approach for the realization of photonic artificial intelligence, especially due to their suitability for machine-vision applications and high-dimensional photonic information processing at lower power consumption. However, incorporating optical nonlinear activation functions to make DNNs a feasible alternative to their electronic counterpart remains a challenge. Here, we investigate the inclusion of second-harmonic generation (SHG), as one of the simplest and most efficient types of optical nonlinearities, in DNNs. We numerically investigate the impact of SHG on the performance of classification tasks in an all-optical nonlinear DNNs. Specifically, we investigate and discuss the essential requirements for an effective arrangement of the SHG layer in single and multilayer DNNs. We find that the performance, in terms of classification accuracy and class contrast, is affected strongly by the positioning of the SHG layer. Finally, we discuss and outline the constraints for including SHG in an experimental realization. Taking these constraints into account, we estimate the power-related efficiency of the nonlinear DNN system. Overall, our results provide a path towards implementing nonlinear DNNs using the SHG process.

Figures (13)

• Figure 1: (A) The nonlinear DNN consists of an amplitude encoded input, followed by a 2f-Setup, a single or a series of phase modulation masks, a $\chi^{(2)}$-crystal and a second 2f-Setup. Light around the phase modulation layers is blocked, such that only lower spatial frequency components are transmitted. The DNN is trained to focus light into specific regions at the output plane, corresponding to different classes as illustrated by the output detector array. Below the setup, we plot the corresponding amplitude at the input plane (B), after the first 2f-setup, delivering a Fourier transform (C), after an exemplary phase modulation layer (D), the amplitude before (E) and after (F) the $\chi^{(2)}$-crystal, and the resulting intensity at the detection plane (G).
• Figure 2: SHG layer positioned at different positions in a single-layer DNN. The figure displays the different DNN configurations (A), the intensity at the detection plane for a sample input digit (B) and the corresponding accuracy and class contrast for the MNIST digit dataset after training (C).
• Figure 3: Accuracy and class contrast for a single-layer DNN. We compare the performance of the DNN without SHG and SHG at position 3 across the MNIST digit, fashion MNIST, and EMNIST handwritten letters datasets.
• Figure 4: Schematic of the four-layer DNN with the SHG layer located at different positions (A), and its performance in terms of accuracy and class contrast at the detection plane (B)
• Figure 5: Schematic showing the envisioned use of a $\chi^{(2)}$ bulk crystal in our proposed nonlinear DNN. At the left, we have the final layer of the linear DNN. In practice, placing the nonlinear crystal right after or after some propagation distance after the final phase modulation layer can be realized by imaging the fundamental harmonic (FH) output from the final linear layer directly, or after some propagation distance $z$ onto the input facet of the nonlinear crystal. This also allows for controlling the overall size of the FH beam, and consequently the transverse minimum feature size $\Delta x$, at the input facet of the $chi^{(2)}$ crystal.