Analysis of Electromagnetic Wave Using Explicit FDTD in TM Mode with Extrapolation

Abstract

In this paper, Explicit finite difference time domain (FDTD) method is used for electromagnetic wave analysis. Explicit method has computational simplicity in linear medium with superior stability by the CFL condition. The method is unstable with nonlinear mediums when materials have $\varepsilon_{r} > 1$. Here, a conventional Explicit FDTD method is used along with Interpolation and Extrapolation techniques for the EM wave analysis in TMz mode. Deriving the higher-order approximations from a lower-order approximation is called as Extrapolation. This technique is used to eliminate the second-order error ${\rm O}(h^{2} )$ terms from first-order central difference approximation. The propagating wave Ez in TM mode is the summation of two triangular waves of Hx, Hy fields, which in turn form a 5-point wave stencil. The wave propagates through the grid using a cell-centred technique. The propagation speed of the wave depends on necessary parameters such as numerical dispersion of grid, time-step ($\Delta t$), x and y spatial step ($\Delta x$) and ($\Delta y$).