1-dimensional FDTD simulation

The principle of FDTD is to write the Maxwell two vector curl equation into a difference form, and use numerical method to find its solution.

Assuming that the electromagnetic field is in the direction of x-axis, the electric field has only the z-axis method component and the magnetic field has only the y-axis direction. Two curl equations can be written in the following form

The electric field and the magnetic field are written down in the form

Continuous equations written in differential form

Where the constant term factor

wherein the characteristic impedance of the free space is 377 ohms, so that the recursive relationship such as

Available representations when implemented

Thus the differential recurrence equation is obtained as follows

Hy (mm) = hy (mm) + (EZ (mm+1)-EZ (mm))/imp0;

EZ (mm) = EZ (mm) + (hy (mm)-hy (mm-1)) *imp0;

%1D FDTD with Source

SIZE = 200;
EZ = Zeros (1,size);
hy = Zeros (1,size);
imp0=377.0;
MaxTime = 10000;

For qtime = 0:1: MaxTime

for mm = 1:1: SIZE-1
Hy (mm) = hy (mm) + (EZ (mm+1)-EZ (mm))/imp0;
End
Figure (1); T_hy = Plot (hy);
Title (' Magnetic Field ');
for mm = 2:1: SIZE
EZ (mm) = EZ (mm) + (hy (mm)-hy (mm-1)) *imp0;
End
Figure (2); T_ez = Plot (EZ);
Title (' Electric Field ')
EZ (+) = EZ (+) + exp (-(qTime-30.0) * (qTime-30.0)/100.0);

% pause (0.01);
% RefreshData (t_hy);
% RefreshData (T_ez);
% Drawnow;
End

1-dimensional FDTD simulation