Fast Inverse Design of 3D Nanophotonic Devices Using Boundary Integral Methods

Abstract

Recent developments in the computational automated design of electromagnetic devices, otherwise known as inverse design, have significantly enhanced the design process for nanophotonic systems. Inverse design can both reduce design time considerably and lead to high-performance, nonintuitive structures that would otherwise have been impossible to develop manually. Despite the successes enjoyed by structure optimization techniques, most approaches leverage electromagnetic solvers that require significant computational resources and suffer from slow convergence and numerical dispersion. Recently, a fast simulation and boundary-based inverse design approach based on boundary integral equations was demonstrated for two-dimensional nanophotonic problems. In this work, we introduce a new full-wave three-dimensional simulation and boundary-based optimization framework for nanophotonic devices also based on boundary integral methods, which achieves high accuracy even at coarse mesh discretizations while only requiring modest computational resources. The approach has been further accelerated by leveraging GPU computing, a sparse block-diagonal preconditioning strategy, and a matrix-free implementation of the discrete adjoint method. As a demonstration, we optimize three different devices: a 1:2 1550 nm power splitter and two nonadiabatic mode-preserving waveguide tapers. To the best of our knowledge, the tapers, which span 40 wavelengths in the silicon material, are the largest silicon photonic waveguiding devices to have been optimized using full-wave 3D solution of Maxwell's equations.

Windowed Green Function MoM for Second-Kind Surface Integral Equation Formulations of Layered Media Electromagnetic Scattering Problems

“…The increasing σ n values for n ≥ 4 demonstrate the super-algebraic convergence of the WGF-MoM achieved for sufficiently small mesh sizes (when the windowing error is dominant). Figure 3 displays the errors (27) in the total field E tot for various mesh and window sizes. The target point set Θ used to compute the errors encompasses 2,332 points lying on the surface of the cylinder containing the dipole sources (see inset in Fig.…”

“…Finally, we mention that the LGF code [40] took ∼8.2 min to carry out the 23320 LGF evaluations needed to produce the reference field E ref , while our (non-accelerated) FORTRAN implementation of the WGF-MoM took just ∼5.8 min to produce E tot with a relative error (27) smaller than 5%. The calculations were performed on the same machine using one thread in both cases.…”

“…This work presents a fully 3D EM layered-media windowed Green function (WGF) method. The WGF method, which was originally developed for scalar layered media problems [24]- [26] and later extended to waveguides in the frequency and time domains [27]- [30], completely bypasses the use of Sommerfeld integrals or other problem-specific Green functions. This is here achieved by first deriving an indirect Müller SIE [31], [32] given in terms of free-space Green functions and featuring only weakly-singular kernels, which is posed on the entire unbounded penetrable interface (see Secs.…”

An Integrated Optical Circuit Architecture for Inverse-Designed Silicon Photonic Components

“…These include the computational techniques of inverse design that are assisted by deep neural networks [ 11 ], deep learning [ 12 , 13 ], physics-informed machine learning [ 14 ], black box algorithms [ 15 ], integral equation methods [ 16 ], and linkage tree genetic algorithms [ 17 ]. Additional computational methods include photonic emulation [ 18 ], the deep adjoint approach [ 19 ], phase-injected topology optimization [ 20 ], and boundary integral methods [ 21 ].…”

Compact simply-connected SOI spot size converters for TE and TM polarizations

“…In recent years, there has been significant progress in the field of computationally driven photonics inverse design methods [28,29]. These methods have facilitated the development of ultra-compact SSCs [6,[30][31][32]. The majority of these SSCs have been designed using topology optimization or binary search techniques, which involve incorporating holes and cracks into the structure.…”