photonic crystal design

Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design

  • Robert M. Freund
  • Han Men
  • Ngoc-Cuong Nguyen
  • Jaime Peraire
  • Joel Saa-Seoane
    • Categories Basic Sciences Applications, Optimization of Systems modeled by PDEs, Robust Optimization Tags , , ,

    It is often the case that the computed optimal solution of an optimization problem cannot be implemented directly, irrespective of data accuracy, due to either (i) technological limitations (such as physical tolerances of machines or processes), (ii) the deliberate simplification of a model to keep it tractable (by ignoring certain types of constraints that pose … Read more

    Band Gap Optimization of Two-Dimensional Photonic Crystals Using Semidefinite Programming and Subspace Methods

  • Robert M. Freund
  • Han Men
  • Ngoc-Cuong Nguyen
  • Pablo A. Parrilo
  • Jaime Peraire
    • Categories Optimization of Systems modeled by PDEs, Semi-definite Programming Tags , ,

    In this paper, we consider the optimal design of photonic crystal band structures for two-dimensional square lattices. The mathematical formulation of the band gap optimization problem leads to an infinite-dimensional Hermitian eigenvalue optimization problem parametrized by the dielectric material and the wave vector. To make the problem tractable, the original eigenvalue problem is discretized using … Read more