FDTD 101: Numerical dispersion in FDTD
Lecture 8: Numerical dispersion in FDTD
A key source of error in FDTD simulations lies in the spatial and temporal discretization. The behavior of the wave propagating in such a discrete numerical lattice can deviate from that of the physical wave. This phenomenon is known as numerical dispersion. In this lecture, we derive and visualize the effect of numerical dispersion, as well as provide a rule of thumb to suppress the error.
- Derive and compare the dispersion relations of a numerical wave and a physical wave in 1D. Their difference grows with frequency and grid step size.
- Taking light transmission through a silicon slab as an example, show that the deviation of the simulated frequency position of transmission peaks can be fully captured by numerical dispersion.
- Derive and visualize numerical dispersion in 2D. Show that in higher dimension, numerical wave has anisotropic phase velocity. This is illustrated by simulating the radiation from a dipole, whose wavefront on a plane deviates from the circular shape at high frequency or with coarse spatial resolution.