Inverse design of broadband highly reflective metasurfaces using neural networks

Eric S. Harper, Eleanor J. Coyle, Jonathan P. Vernon, and Matthew S. Mills

Phys. Rev. B 101, 195104 – Published 4 May 2020

Abstract

Metamaterials exhibit optical properties not observed in traditional materials. Such behavior emerges from the interaction of light with precisely engineered subwavelength features built from different constituent materials. Recent research into the design and fabrication of metamaterial-based devices has established a foundation for the next generation of functional materials. Of particular interest is the all-dielectric metasurface, a two-dimensional metamaterial exploiting shape-dependent resonant features while avoiding losses through the use of dielectric building blocks. However, even this simple metamaterial class has a nearly infinite number of possible configurations; researchers now require new methods to efficiently explore these types of design spaces. In this work, we employ rigorous coupled wave analysis to calculate reflection and transmission spectra associated with a class of open-cylinder all-dielectric metasurface. By altering the geometric parameters of open-cylinder metasurfaces, we generate a sparse training data set and construct artificial neural networks capable of relating metasurface geometries to reflection and transmission spectra. Here, we successfully demonstrate that pseudo autodecoder neural networks can suggest device geometries based on a requested optical performance—inverting the design process for this metasurface class. As an example, we query for and discover a particular open-cylinder metasurface displaying a reflection band $R \geq 99 %$ centered at $λ_{0} = 1550 nm$ that is much broader $Δ λ = 450 nm$ than anything reported for optical metasurfaces. We then analyze the modal interplay in the open-cylinder metasurface to better understand the underlying physics driving the broadband behavior. Ultimately, we conclude that neural networks are ideally suited for generally approaching these types of complex inverse design problems.

Received 9 January 2020
Revised 21 February 2020
Accepted 25 February 2020

DOI:https://doi.org/10.1103/PhysRevB.101.195104

Physics Subject Headings (PhySH)

Machine learning Metamaterials

Artificial neural networks

Rigorous coupled-wave analysis

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Eric S. Harper ¹, Eleanor J. Coyle ^1,2, Jonathan P. Vernon ¹, and Matthew S. Mills ^1,*

¹Materials and Manufacturing Directorate, Air Force Research Laboratory, 2179 12th St., Wright-Patterson Air Force Base, Ohio 45433, USA
²Azimuth Corporation, 4027 Colonel Glenn Hwy #230, Beavercreek, Ohio 45431, USA

^*matthew.mills.25@us.af.mil

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Vol. 101, Iss. 19 — 15 May 2020

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Images

Figure 1
Top and angled views of a unit cell for an open-cylinder metasurface design defined with Floquet boundary conditions in the transverse directions, $x$ and $y$ , with finite layers in the $z$ direction. This example design has an outer radius $r_{o} = 211$ nm, inner radius $r_{i} = 89$ nm, height $h = 942$ nm, and lattice spacing $L = 964$ nm.
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Figure 2
(a) SPN architecture. The SPN is trained to rapidly predict the expected reflection and transmission spectra. (b) A comparison of the RCWA-generated spectra (green) and the SPN-predicted spectra (black) for reflection (solid) and transmission (dotted) shows general trend agreement. (c) DPN architecture. The DPN may be trained independently with the raw RCWA simulation data (IDPN) or as part of a pseudo autodecoder (PDPN). (d) Open-cylinder metasurface predicted by the DPN based on input spectral data.
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Figure 3
(a) Loss value comparison for single replicas of the simulator network (blue), the IDPN (red), and the PDPN (purple). All three networks successfully converge, with the PDPN outperforming the IDPN. (b) Performance comparison of the IDPN (red) and PDPN (purple) on validation data sets averaged across ten replicas. The input and output validation data more closely correlate in the PDPN than in the IDPN (error bars are determined by $err = σ_{R^{2}} / \sqrt{10}$ ). (c) and (d) Lattice regression performance plot for single DPN replicas of (c) the IDPN and (d) the PDPN, demonstrating superior performance of the PDPN.
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Figure 4
Inverse design pipeline for open-cylinder metasurfaces with targeted performance. (a) User-input targeted broadband reflection and transmission spectra centered around $λ_{0} = 1550$ nm. (b) Inverse ANN architecture formed by “flipping and stitching” together the already-trained PDPN and SPN. (c) SPN output indicating the predicted performance of the open-cylinder metasurface designed by the PDPN, showing good agreement with the core features of the target spectra. Together, the PDPN and SPN predict both the metasurface design and resulting reflection and transmission spectrum based on the desired input spectra. High-resolution RCWA verification of (d) the square lattice open-cylinder metasurface and (e) the hexagonal lattice.
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Figure 5
Comparison of (a), (c), and (e) solid cylinders with geometry $r = 221 nm, h = 502 nm, L = 679 nm$ and (b), (d), and (f) open cylinders with geometry $r_{o} = 247 nm, r_{i} = 106 nm, h = 804 nm, L = 870 nm$ . (a) and (b) The real component of the first 15 eigenmodes $Re \{λ_{i}\}$ for three different wavelengths in the reflection spectra for solid and open cylinders. $Re \{λ_{i}\}$ is plotted on a log scale to show the significant difference in values between the first few eigenmodes and the rest of the eigenmodes. Insets show the top view of the unit cell. (c) and (d) Comparison of reflection spectra and number of contributing eigenmodes for both geometries, showing $2 \leq N_{modes} \leq 10$ active modes across the range of interest $(λ \approx [1.3 μ m, 2.0 μ m])$ . The reflection spectra are marked with circles corresponding to the wavelengths considered in (a) and (b). (e) and (f) The first ten $E_{y}$ mode profiles with the active modes highlighted in the corresponding color.
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