Section II describes the reduction of Maxwells equations from 3D to 1D and its subsequent FDTD implementation using Yees algorithm. In the case of free-space where = 0 and = 0, equation (5) takes on the familiar form: 2 1 2 2 2 =0 z 2 c t where c =10 0 This paper addresses all of the above in a step by step process and has the following outline:Ĭombining the partial space derivatives of (3) with the partial time derivative of (4) or vice versa produces the 1D scalar wave equation: 2 2 2 = 0, z 2 t (5) A working FDTD code must propagate waves properly, handle various boundaries, and calculate useful modelling results. Most of the equations in this report can be found in other texts, however, we have listed them here for the reason of continuity. Due to the large amount of book-keeping required in any full 3D-FDTD code, it is common to reduce the dimensionality down to 1D for pedagogical purposes. It is relatively straight forward to produce animations using MATLAB this is often critical to the understanding of a working FDTD algorithm. We choose MATLAB as our coding language because of its comprehensive library of graphics routines.

There are also various books available which contain basic codes gives many good examples in C.

A comprehensive coverage, including a historical recount of the FDTD development can be found in. HE nite difference time domain (FDTD) method has been used extensively in the modelling of electromagnetic wave scattering from complex none-canonical objects.

The goal of this project is to exercise the basic parts of a FDTD code in the simplest system. Source implementation and the effects of various boundaries such as PEC, PMC, Mur on the incident/scattered/total elds are subsequently investigated. The elds Ex and Hy are simulated along the line X = Y = 0, i.e. x = y = 0 equations (1) and (2) reduce down to the 1D case: Ex Hy = z t Hy Ex = z t (3) (4)Ībstract This report presents a simple 1D implementation of the Yee FDTD algorithm using the MATLAB programming language. Reduction of Maxwells equations to 1D The 3D source free (J = 0) Maxwells curl equations of a homogeneous medium are: E E yz zy = Hx t dH E = Ex Ez = Hy (1) z x t Ey dt Ex = Hz x y t H Hy Ex z y z = t dE (2) Hx Hz = Ey H = z x t Hy dt Hx Ez x y = t For a z -directed, x-polarized TEM wave (Hz = Ez = 0), incident upon a modeled geometry with no variations in the x and y direction, i.e. ECEN-6006 NUMERICAL METHODS IN PHOTONICS PROJECT-1, SEPTEMBER 2004ġD-FDTD using MATLABHung Loui, Student Member, IEEEII.

3d fdtd matlab