Inverse Design of Plasmonic Nanoparticle Metamaterials

Abstract

Self-assembly of strongly coupled plasmonic nanoparticles is a scalable and promising route for producing optical metamaterials with emergent photonic properties, with applications in nanopho- tonic devices to function as energy harvesters, waveguides, optical filters, and photo- and thermo- catalysts. The optical response of these materials can be tuned through nanoparticle size, shape, arrangement, and chemical composition, resulting in a vast design space that is too time-consuming and expensive to navigate using “forward” strategies. To this end, we formulate optical metama- terial design as an inverse problem, where we specify target optical behavior and use numerical optimization to autonomously discover nanoparticle metamaterials possessing the desired features. Our design framework uses a gradient-based iterative optimization approach to rapidly navigate through candidate materials self-assembled from tens of thousands of nanoparticles, specifying the position, size, dielectric properties, and other physical features of each nanoparticle. In particular, we demonstrate inverse-designed nanoparticle metamaterials with tunable extinction spectra of complex lineshape for quasi-2D stratified metasurfaces and 3D metamaterials. The optimizer converges to highly heterogeneous structural motifs with resonance frequencies distributed across the target spectrum. We also describe a general approach for finding the derivative of any optical figure of merit and use it to inverse design electric near-field intensity with spatial profiles matching targeted patterns. In doing so, we show that the optimizer can simultaneously control mesoscale structure and local microstructure. Metamaterial designs optimized at a single angle of incidence have uncontrolled responses at other incidence angles, which limits their use in applications requiring angle-dependent behavior. In the second part of the thesis, we extend our inverse strategy to simultaneously control both the incident frequency and incident angle response of plasmonic metamaterials. We inverse design quasi-2D stratified metasurfaces with tunable extinction spectra that are nearly independent of the incidence angle. To connect directly to measurable observables, we derive expressions for the derivatives of transmittance and reflectance with respect to nanoparticle position and physicochemical features and demonstrate how these can be incorporated into optimization routines. Lastly, we discuss three promising future research projects that leverage our inverse design methodology as a key component: inverse design of the colloidal interactions and self-assembly protocols to produce optical metamaterials, magnetoplasmonic materials controlled with magnetic-field-directed self-assembly, and ellipsometric characterization of nonuniform thin films. In the final section of the thesis, we present a mechanistic study of the depolymerization of polyethy- lene terephthalate (PET), a polymer that frequently adds to postconsumer plastic waste. One of the ways to recover valuable raw materials from postconsumer plastic waste is by depolymerizing PET into its monomeric constituents, dimethyl terephthalate (DMT), and ethylene glycol (EG) through methanolysis with the help of acid or base catalysts. Tertiary amines are attractive base catalysts for this process because, unlike metal-based catalysts, they avoid generating environmen- tally harmful waste. However, their catalytic mechanism remains unexplored, limiting efforts for plastic upcycling. Using density functional theory (DFT) and transition state analysis, we show that tertiary amine-catalyzed methanolysis of PET can proceed through a stepwise mechanism involving multiple discrete steps, rather than a single concerted step. Comparing our calculations with experimental results, we find that DMT yield correlates with charge polarization in the amine catalyst, suggesting a possible atomic-level descriptor for future catalyst design.