Momentum-Assisted Adjoint Method for Highly Efficient Inverse Design of Large-Scale Digital Nanophotonic Devices

Gradient-descent-based digitized adjoint method offers a way to realize the high-efficiency inverse design of digital nanophotonic devices with diverse functions. However, the vanishing gradient problem encountered in the design of high-dimension devices may lead to significant inefficiencies, making it difficult to integrate novel functions on a single chip. Here, we propose a highly efficient digitized adjoint method for large-scale inverse design, called adaptive gradient-descent with momentum. It uses the first- and second-order momentum, instead of the gradient, to update the device pattern during adjoint optimization. To demonstrate the efficiency of the proposed method, we design a coarse wavelength division multiplexer and a three-mode power divider with design dimensions of 800 and 1360, respectively, which are approximately 2-4 times that of conventional digital nanophotonic devices. The simulation results show that, compared with the conventional gradient descent method, the momentum-assisted adjoint method has about 4-6 times higher efficiency and obtains better optimization performance, which provides a powerful tool for the inverse design of novel digital nanophotonic devices.