Simulation Methods for Plasmonic Structures

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In the recent years there has been a growing interest in studying electromagnetic wave propagation at the nanoscale. The interaction of light with metallic nanostructures produces a collective excitation of conduction electrons at the metal surface, also known as surface plasmons. These plasmonic resonances enable an unprecedented control of light by confining the electromagnetic field to regions well beyond the diffraction limit, thereby leading to nearfield enhancements of the incident wave of several orders of magnitude. These remarkable properties have motivated the application of plasmonic devices in sensing, nano-resolution imaging, energy harvesting, nanoscale electronics and cancer treatment. Despite state-of-the-art nanofabrication techniques are used to realize plasmonic devices, their performance is severely impacted by fabrication uncertainties arising from extreme manufacturing constraints. Mathematical modeling and numerical simulation are therefore essential to accurately predict the response of the physical system, and must be incorporated in the design process. Nonetheless, plasmonic simulations present notable challenges. From the physical perspective, the realistic behavior of conduction electrons in metallic nanostructures is not captured by Maxwell’s equations, thus requiring additional modeling. From the simulation perspective, the disparity in length scales stemming from the extreme field localization exceeds the capabilities of most numerical simulation schemes. In addition, relevant data such as optical constants or geometry specifications are typically subject to measurement and manufacturing errors, hence simulations need to accommodate uncertainty in the data. In this thesis we present a collection of numerical methods to efficiently simulate electromagnetic wave propagation through metallic nanostructures. Firstly, we develop the hybridizable discontinuous Galerkin (HDG) method for Maxwell’s equations augmented with the hydrodynamic model for metals, which accounts for the nonlocal interactions between electrons that become predominant at nanometric regimes. Secondly, we develop a reduced order modeling (ROM) framework for Maxwell’s equations with the HDG method, enabling the incorporation of material and geometric uncertainties in the simulations. The result is a family of surrogate models that produces accurate yet inexpensive simulations of plasmonic devices. Finally, we apply these approaches to the study of periodic annular nanogaps, and present parametric analyses, verification with experimental data and design of novel structures.