Higher-dimensional application of rigorous coupled-wave analysis to quasicrystalline gratings

A novel approach for analysis of the scattering response of aperiodic quasicrystalline gratings is proposed. The method exploits the fact that mathematically quasicrystals can be obtained as irrational projections of higher-dimensional periodic structures onto the physical space. The periodicity in the super-space allows for application of plane wave expansion methods such as Rigorous Coupled-Wave Analysis (RCWA) and projecting the solutions onto the physical space. Analytically, this technique is far superior to the current principal method of analysis for quasicrystals which approximates them as periodic supercells. As an example, the method is applied to a Fibonacci dielectric grating and there is perfect agreement with the results obtained using the super-cell approach.