Time-dependent adjoint-based optimization of photonic crystals and metamaterials using a stabilized finite element method

In the current research, a time-dependent discrete adjoint algorithm for optimization of electromagnetic problems is developed. The proposed algorithm improves the efficiency for gradient-based optimization. The time-dependent Maxwell equations are discretized using a semi-discrete Petrov-Galerkin method, and time advancement is accomplished with an implicit, second-order backward differentiation formulation (BDF2). Utilizing the developed capability, two gradient-based shape design optimizations are conducted. In the first optimization an optical waveguide is designed with photonic crystals, and in the second an all-dielectric metamaterial is designed. A motivation for optimizing photonic crystals is due to their use as multi-band optical waveguides for telecommunication applications. For this design optimization, to ensure smooth surfaces, Bezier curves are employed to parametrically represent the shape. To reflect the design changes on the mesh, linear elasticity is used to adapt interior mesh points to boundary modifications. The cost function used in this design attempts to shift the band gap of the photonic crystals to desired frequency ranges. Results demonstrate a band gap shift from one single band gap to multiple band gaps is achievable. The motivation for optimizing broadband metamaterials is for their use as dielectric mirrors for applications where high power reflection is required. In this optimization, Hicks-Henne functions are utilized for shape parameterization and linear elasticity used once again for mesh adaptation. The cost function used attempts to widen the bandwidth of the metamaterial over a desired frequency range. Results demonstrate an increase of the full width at half maximum (FWHM) of reflection from 111THz to 303THz

Higher-order Petrov-Galerkin methods for analysis of antennas

A temporally and spatially high-order accurate Petrov-Galerkin finite-element method is applied to the analysis of several antenna configurations. The method obtains numerical solutions of Maxwell\u27s equations in the time domain using implicit time stepping and introduces energy into the domain using a Gaussian pulse to allow frequency-domain parameters to be computed over a range of frequencies with a single time-dependent solution. Verification cases for a monopole antenna and a microstrip patch antenna are used to examine the accuracy of the algorithm. Effects of varying antenna parameters on subsequent performance metrics are discussed based on the results from the simulations. Post-processing procedures are developed to obtain scattering parameters, input impedance and radiation patterns. For verification, the antenna characteristics obtained with the present methodology are compared with the results from two commercial codes. Mesh and time-step refinement studies are also conducted to assess the level of discretization errors in the solutions