Symmetry Reduction in FEM Optics Modeling of Single and Periodic Nanostructures

Abstract

Numerical optics modeling is an invaluable tool in the design of nanostructures for nanophotonics applications where diffraction effects often lead to complex dependency between the nanostructure geometry and its optical properties and response. In order to analyze, design, and optimize such nanostructures, computationally efficient numerical optics modeling methods are required. One way to improve the numerical performance is to exploit symmetries found in many optics problems. By identifying equivalencies and restrictions arising from symmetry, it can be possible to simplify the problem at hand, which is the essence of symmetry reduction. However, applying symmetry reduction in optics modeling problems is not trivial. To the best of our knowledge, symmetry reduction has so-far been applied in finite element method (FEM) optics models only in those specific cases where an incident plane wave shares symmetries with the nanostructure geometry. In this work, we show how to extend the symmetry reduction of FEM optics models to the case of nonsymmetric plane-wave incidence, demonstrate such reduction with numerical examples of incident plane wave absorption in a single nanowire and a periodic nanowire array, and discuss the achieved gains in computational efficiency.