Fast 3D Nanophotonic Inverse Design Using Volume Integral Equations

Designing nanophotonic devices with minimal human intervention has gained substantial attention due to the complexity and precision required in modern optical technologies. While inverse design techniques typically rely on conventional electromagnetic solvers as forward models within optimization routines, the substantial electrical size and subwavelength characteristics of nanophotonic structures necessitate significantly accelerated simulation methods. In this work, we introduce a forward modeling approach based on the volume integral equation (VIE) formulation as an efficient alternative to traditional finite-difference (FD)-based methods. We derive the adjoining method tailored specifically for the VIE framework to efficiently compute optimization gradients and present a novel unidirectional mode excitation strategy compatible with VIE solvers. Comparative benchmarks demonstrate that our VIE-based approach provides multiple orders of magnitude improvement in computational efficiency over conventional FD methods in both time and frequency domains. To validate the practical utility of our approach, we successfully designed three representative nanophotonic components: a 3 dB power splitter, a dual-wavelength Bragg grating, and a selective mode reflector. Our results underscore the significant runtime advantages offered by the VIE-based framework, highlighting its promising role in accelerating inverse design workflows for next-generation nanophotonic devices.