All-optical doubly resonant cavities for energy-efficient ReLU function in nanophotonic deep learning

This paper presents a novel approach to implementing all-optical Rectified Linear Unit (ReLU) activation functions using compact doubly-resonant cavities with dimensions of approximately 10[Formula: see text]m. The proposed design leverages [Formula: see text] nonlinear processes within carefully engineered photonic structures that simultaneously resonate at both fundamental and second-harmonic frequencies. By exploiting the phase-sensitive nature of second-harmonic generation, we demonstrate an optical analog to the ReLU function, achieving femtojoule-level activation energy-comparable to state-of-the-art approaches-while reducing device footprint by two orders of magnitude compared to previous implementations. The theoretical framework is developed using coupled-mode theory and validated through rigorous finite-difference time-domain simulations. Beyond ReLU, we show that the same physical structure can implement alternative activation functions such as ELU and GELU through simple adjustments to input conditions. Neural network simulations demonstrate that the proposed optical activation functions achieve classification accuracy within 0.4% of ideal electronic implementations while offering significant advantages in energy efficiency and processing speed. This work represents a significant advancement toward realizing energy-efficient, high-density optical neural networks for next-generation artificial intelligence hardware.