Accelerating simulations in inverse photonic design through factorization caching

Abstract

As the demand for scalable and complex on-chip nanophotonic devices with multi-wavelength and multi-mode optical functionalities increases, fast and efficient design algorithms have become an essential tool in silicon photonics. Although inverse design coupled with adjoint optimization has emerged as a powerful method to design such devices by requiring only two simulations in each iteration of the optimization process, these simulations still make up the vast majority of the necessary computations, and render the design of complex devices with large footprints computationally infeasible. Here, we present a substantial speed-up in the finite-difference frequency-domain (FDFD) simulations by introducing a factorization caching approach, and significantly reduce the computational requirements for device optimization. Specifically, we cache the symbolic and numerical factorizations of system matrices corresponding to discretized Maxwell’s equations, and re-use them throughout the entire optimization. Using this method, we reduce the majority of the computational operations in the FDFD simulations and drastically improve the simulation speeds. To demonstrate the resulting computational advantage compared to conventional FDFD methods, we show simulation speedups reaching as high as 8.5-fold in the design of broadband wavelength and mode multiplexers. These results present significant enhancements in the computational efficiency of inverse photonic design, and can greatly accelerate the use of machine-optimized devices in future photonic systems.