Optical Frequency Selective Surface Design Using a GPU Accelerated Finite Element Boundary Integral Method

Open Access
Ashbach, Jason Andrew
Graduate Program:
Electrical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
March 02, 2016
Committee Members:
  • Douglas Henry Werner, Dissertation Advisor
  • George Kesidis, Committee Member
  • Timothy Joseph Kane, Committee Member
  • Lyle Norman Long, Committee Member
  • Computational Electromagnetics
  • Finite Element Method
  • General Purpose Computing
  • Frequency Selective Surfaces
Periodic metallodielectric frequency selective surface (FSS) designs have historically seen widespread use in the microwave and radio frequency spectra. By scaling the dimensions of an FSS unit cell for use in a nano-fabrication process, these concepts have recently been adapted for use in optical applications as well. While early optical designs have been limited to well-understood geometries or optimized pixelated screens, nano-fabrication, lithographic and interconnect technology has progressed to a point where it is possible to fabricate metallic screens of arbitrary geometries featuring curvilinear or even three-dimensional characteristics that are only tens of nanometers wide. In order to design an FSS featuring such characteristics, it is important to have a robust numerical solver that features triangular elements in purely two-dimensional geometries and prismatic or tetrahedral elements in three-dimensional geometries. In this dissertation, a periodic finite element method code has been developed which features prismatic elements whose top and bottom boundaries are truncated by numerical integration of the boundary integral as opposed to an approximate representation found in a perfectly matched layer. However, since no exact solution exists for the calculation of triangular elements in a boundary integral, this process can be time consuming. To address this, these calculations were optimized for parallelization such that they may be done on a graphics processor, which provides a large increase in computational speed. Additionally, a simple geometrical representation using a Bézier surface is presented which provides generality with few variables. With a fast numerical solver coupled with a low-variable geometric representation, a heuristic optimization algorithm has been used to develop several optical designs such as an absorber, a circular polarization filter, a transparent conductive surface and an enhanced, optical modulator.