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This can cause discretization errors even if the calculation itself implements the physical laws without any approximations like in full wave solvers. In any electromagnetic simulation there will be some discretization involved, due to the fact that we are solving a continuous system on a computer. The entire cylindrical, GaN and Air, structure is placed on a SiO2 substrate. These configurations were defined in PlanOpSim and MEEP for comparison. The figure below is the top-view of the simulated nano-pillar for a diameter of 200nm. Periodic boundary conditions are applied. The polarization is set to TM, although the result will be the same for TE given the symmetry of the problem. The incident light is set at normal incidence and a wavelength of 460nm. In this example we obtain this behaviour by modifying the radius of the cylinder while keeping all other parameters (most importantly the height) fixed. In many meta-surfaces the goal of the meta-atom design is to find a range of structure parameters who cause different phase delays (from -180 to +180°) while also being highly transmissive. The pillars are 460nm high and separated with a pitch of 330nm in a square periodic arrangement. The figure below shows a meta-lens consisting of such dielectric nano-rods.Ī metalens using nano-rod structures to achieve wavefront control.įor this benchmark we use a GaN pillar on a SiO2 substrate. Common choices are SiN, GaN or TiO2 for the visible spectrum and Si and GaAs for the infra-red spectrum. In addition, the material should be transparent for the spectrum of interest. The pillars are made of a high refractive index material. Many meta-surface use sub-wavelength cylinders as the basic building block for the metasurface (). Nevertheless, the solutions found by both methods should be the same. RCWA first transforms the equations to the frequency domain (both time-frequency and spatial frequency). In FDTD the Maxwell equations are discretized directly in both time and space. However both solve the Maxwell equations via a different mathematical and numerical approach.
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Since exact solutions are not known for the sub-wavelength structures that make up a meta-atom, a validation is performed by comparing the results of different methods.įDTD and RCWA both model the same underlying physical laws. Some of the most common methods are FEM, FDTD and RCWA.Ī common question with any simulation method is whether the calculation produces physically accurate results. Their design is thus done by numerical method, known as full-wave solvers. The design of these structures requires a full solution of Maxwell’s equations in three dimensions.įor such sub-wavelength calculations there are (in general) no exact solutions. Meta-surfaces rely on sub-wavelength structures to manipulate light in different ways such as phase delay, polarization conversion, specific dispersion. Benchmark Comparison for the transmission and phase delay of a cylindrical nano-rod.Convergence checks to determine which settings give reliable results.A comparison is made to the widely known finite difference time domain (FDTD) method. In that spirit this article investigates the accuracy of the Rigorous Coupled Wave analysis (RCWA) methods implemented in the PlanOpSim software. It is a common saying that all models are wrong but some models are useful.