Establishing metasurface robustness through deep learning

1. Pre-reading

Freeform nanophotonic metasurfaces hold the promise of remarkable size and weight reduction for optical systems. However, their design is often complicated by real-world fabrication considerations which constrain and challenge the design process. Moreover, global optimization of structures which are robust to a range of fabrication defects has remained intractable until now due to the computational expense required by meticulous full-wave modeling. Recently, researchers in the area of Topology Optimization have found methods for imbuing designs with some increased robustness. Although these methods are local, they have significantly moved the state-of-the-art forward in robust freeform metasurface design.

New work from Prof. Werner’s group at The Pennsylvania State University builds on these and other techniques, expanding the scope of the design process to use global optimization methods, and introducing deep learning to make exhaustive robustness analysis tractable for the first time. Deep neural networks act as a surrogate model for dosing/etching related lithographic defects, which then allows a global multiobjective optimizer to characterize the optimal tradeoff curve between nominal performance and robustness. As a demonstration of the power of the technique, the researchers apply this new method to freeform near-IR supercell design. The method is exhaustive—probing defect variations with a high degree of granularity to discover truly robust structures. Moreover, by augmenting the optimization process with deep learning, the method exhibits a significant speedup over conventional full-wave-only optimization.

2. Background

Robust metasurface designs are very attractive from a manufacturing standpoint, paving the way toward the realization of high-performance wafer-scale optical metasurfaces. From the design standpoint, the goal is to find structures which are tolerant to typical fabrication errors, a task which can be extremely challenging. Using E-beam lithography, structures can typically be fabricated with sufficiently high accuracy (as low as 2-4 nm). However, increased precision requires increasingly expensive, finely-tuned, and small-scale fabrication processes which all work together to make inherently robust designs very desirable.

Robustness optimization techniques using Topology Optimization demonstrated over the past decade have taken the first steps toward truly robust metasurface designs, but there are limitations to their exhaustiveness. In addition to being local methods, there are practical computational challenges which any robustness optimization must overcome—namely the explosion of variations which must be evaluated for each design tested. Any path forward for truly exhaustive robustness optimization must find some way to overcome this tractability problem.

3. Innovative research

This recent work by Prof. Werner’s group overcomes the computational challenges inherent to exhaustive robustness optimization by leveraging the power of deep learning. A pair of deep neural networks were trained to a high degree of accuracy against tens of thousands of different supercells, each with different defects. Forming a chain, the first network receives a mask representing the structure and then predicts E-fields internal to the structure. The second network then takes these E-fields and predicts final diffraction coefficients for the system.

Figure 1: Topologies for the pair of deep neural networks used in the study.

The deep learning models are used as part of a multiobjective optimization procedure which allows for the characterization of an optimal tradeoff between metasurface performance and robustness. Robustness is measured exhaustively, each design being subjected to a range of erosion and dilation defects (± 20 nm), with the worst among the set deciding the cost. Furthermore, due to the sensitivity of the supercell designs, a very high resolution was required to simulate the structures.

Figure 2: Comparison of three devices designed using the multiobjective deep learning augmented method. Subpanel C shows how a robust design will achieve a better performance across the range of edge deviations tested.

The product of this optimization procedure is a Pareto front, the green curve in Fig. 2, which shows an optimal tradeoff between supercell nominal performance and guaranteed performance. The power of this method is clear—a robust design achieves an increase of 35% absolute performance gain over a design optimized only for nominal performance for a loss of <5% in nominal performance as shown in Fig. 2E. Combined with multiobjective optimization, these deep learning models also provide a substantial performance boost of more than 10x amortized across several optimizations.

4. Applications and perspectives    

This deep learning-augmented multiobjective optimization method provides a cutting-edge approach for metasurface designers to actively optimize for robustness. The results demonstrate the kind of significant boost in guaranteed performance made possible by this method, as well as a substantial speedup enabled by the deep learning models. While the example demonstrated in the paper is specific to supercell optimization in the near-IR, the method can be generalized to other frequency regimes, as well as many more nanophotonic design problems and fabrication processes.

These research results are published online with the title “Establishing exhaustive metasurface robustness against fabrication uncertainties through deep learning” in Nanophotonics.

The authors of this article are Ronald P. Jenkins, Sawyer D. Campbell, and Douglas H. Werner. Ronald P. Jenkins is the corresponding author of this work. Prof. Douglas H. Werner’s research group, the Computational Electromagnetics and Antennas Research Lab (CEARL) is part of the Department of Electrical Engineering at The Pennsylvania State University, University Park, Pennsylvania, USA.