A rigorous approach for the analysis of diffraction from quasicrystalline gratings is presented. Previous methods for determining the diffraction properties of quasicrystalline gratings have relied on periodic supercell approximations. Our method exploits the cut-and-project method, which constructs quasicrystals as irrational slices of higher-dimensional periodic structures onto the physical space. The periodicity in the higher-dimensional space allows for the application of Floquet's theorem. The solutions can then be obtained by solving Maxwell's equations in the higher-dimensional space and projecting the results to the lower dimensional physical space. As an example, the method is applied to a one-dimensional aperiodic grating based on a Fibonacci quasicrystal (QC) where the results that were generated are shown to be in near-perfect agreement with those obtained using the supercell approximations. (Graph Presented).
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Atomic and Molecular Physics, and Optics
- Electrical and Electronic Engineering