Exit pupil expander with non-hexagonal 2D grating

Recently, an increasing interest in utilizing 2D gratings on the waveguide for exit pupil expander (EPE) designs has been observed. However, to the best of author's knowledge, most of these designs use only hexagonally arranged lattice for the 2D grating and do not investigate how varying lattice vector angle can help the optimization. In this paper, we will first discuss the consideration of non-orthogonal lattice vectors in Rigorous Coupled Wave Analysis (RCWA), provided by Ansys Lumerical RCWA. We will explain how a hexagonal 2D grating can be simulated with a set of orthogonal lattice vectors and why the same trick does not work for non-hexagonal 2D grating with arbitrary lattice vector angle. We will explain what it means when the grating is non-hexagonal in k-space and real space, and the consequent benefits. Based on the concept, initial simulation results, using dynamic link between Ansys Lumerical RCWA and Ansys Zemax OpticStudio, will be demonstrated. The simulation with different lattice vector angle are performed for understanding the system behavior. Finally, we set up an optimization workflow in Ansys optiSlang, considering lattice vector angles as one of variables. The optimization results will be discussed.