Fast multi-channel inverse design through augmented partial factorization

TL;DR

This paper introduces a novel method combining the adjoint method and augmented partial factorization to enable single-simulation inverse design of complex multi-channel nanophotonic systems, significantly speeding up the process.

Contribution

It generalizes the adjoint and augmented partial factorization methods to perform inverse design of multi-channel systems in a single simulation, reducing computational cost.

Findings

Achieves over-two-orders-of-magnitude speedup in inverse design.

Reduces memory usage compared to traditional methods.

Successfully designs a multi-angle metasurface beam splitter.

Abstract

Computer-automated design and discovery have led to high-performance nanophotonic devices with diverse functionalities. However, massively multi-channel systems such as metasurfaces controlling many incident angles and photonic-circuit components coupling many waveguide modes still present a challenge. Conventional methods require $M_{\rm in}$ forward simulations and $M_{\rm in}$ adjoint simulations -- $2M_{\rm in}$ simulations in total -- to compute the objective function and its gradient for a design involving the response to $M_{\rm in}$ input channels. By generalizing the adjoint method and the recently proposed augmented partial factorization method, here we show how to obtain both the objective function and its gradient for a massively multi-channel system in a single simulation, achieving over-two-orders-of-magnitude speedup and reduced memory usage. We use this method to inverse design a metasurface beam splitter that separates the incident light to the target diffraction orders for all incident angles of interest, a key component of the dot projector for 3D sensing. This formalism enables efficient inverse design for a wide range of multi-channel optical systems.