Since FDTD requires that the entire computational domain be meshed, and the mesh spatial discretization must be sufficiently fine to resolve both the smallest electromagnetic wavelength and the smallest geometrical feature in the model, very large computational domains can be developed, which results in very long CPU times and huge memory usage. For normal dielectric material, numerical dispersion analysis shows that to get accurate results, the mesh size should be at least 10% of the simulated smallest wavelength in medium; for surface plasma layout where metallic material is usually needed, the mesh size should be even smaller to catch the wave attenuation within the skin depth.
The strength for non-uniform FDTD is to save the memory usage and consequently to save the CPU time, for high refractive index region, the fine mesh should be sued, while in the low index region, the coarse mesh can be applied. Before we learn the non-uniform mesh simulation in OptiFDTD, we should also discuss several benchmarks for this feature:
• FDTD accuracy refers to the time and space mesh size. Non-uniform mesh FDTD accuracy refers to the largest mesh in the simulation. When numerical dispersion are not in the same level that refers to the mesh size, the largest error that comes from the largest mesh size will be affected and accumulated the whole simulation
• The Courant-Friedrichs-Lewy condition (CFL condition) in FDTD method ask the time step must be less than a certain otherwise the simulation will not be stable. The CFL condition for non-uniform mesh FDTD should refers to the smallest mesh size. From this point of viewer the time iteration number does not saved.
• Non-uniform mesh sometimes introduces errors of the geometry representation that is due to a staircase approximation of curved structure surface.
• Boundary condition in each direction for non-uniform mesh will also affect the simulation accuracy.
• When input wave is put in the non-uniform mesh region, it will introduce additional interpolation errors.
The following explains the non-uniform simulation with OptiFDTD. User is supposed already know OptiFDTD design environment and uniform mesh simulations.
Please use OptiFDTD layout designer open sample file named “X64_Sample58_SilverParticle_Non_Uniform_Mesh.FDT”. This is a 100nm diameter silver particle putting in a 0.7 μm *0.7 μm *0.8 μm simulation space. Double click on each object in the layout to check the layout setting.
• Click “3D Layout Model” button under the layout window to observe the layout in 3D mode.
• The silver particle center is put at domain center (x=0 μm , y=0.35 μm , z=0.4 μm ), so the particle edge is from -0.05 μm to +0.05 μm in x-direction, 0.3 μm to 0.4 μm in y-direction, 0.35 μm to 0.45 μm in z-direction.
• The time domain input wave is “Gaussian Modulated Continuous Wave” with center wavelength as 0.5 μm , bandwidth covers from 0.35 μm to 0.65 μm . (Right click on the spectrum graph and select the zoom in tool to enlarge the selected graph area, this can read the bandwidth)
• Transverse input field pattern is a truncate plane wave (rectangular wave).
• An observation area is put after the sphere, it will detect the transmission spectrum.