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# Help: fdtd in Sullivan's book

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#### joywwj

##### Newbie level 2
I am a newer to fdtd. I am reading Sullivan's book. In the FDTD_2.2.c program, they caculate the Fourier transform of the input pulse.

/* Fourier transform of the input pulse*/ ---> why have to caculate the Fourier transform of the input pulse.

if (T<100) ---->why T have to be smller than 100
for (m=0;m<=2;m++)
{ real_in[m]=real_in[m]+cos(arg[m]*T)*ex[10] --->why have to time ex[10]
imag_in[m]=imag_in[m]-sin(arg[m]*T)*ex[10]
}

thanks a lot

Hi joywwj
As you know FDTD equations are in time domain but some of our interesting parameters are in frequency domain such as reflections coefficients and other S parameters so we have to use Fourier transform of the input pulse and the other parameters for FT convergence

I've been wondering about this, too. I think it's got to do with the fact that he's just collecting data points for that incident field - the Ex(10) is actually a location 10 cells into the simulation space. The T<100 has to do with the propagation of that wave from one side of the simulation space to the other - he wants to stop after 100 iterations of the field calculation, which I think would be about where the signal would hit that dielectric medium if you look at Fig. 1.5.

If somebody has a good explanation of how this works with the Fourier transform, that would be awesome!

I don't have the book available right now but I think skysearcher is right.

1) T<=100 probably means that by that time the pulse has weakened to a negligible amount.
2) EX[10] is just the location (if I remember correctly chapter 2 is for 1d-simulations then
this should mean the 10th or 11th cell from the boundary
3) The reason for using the FT is that you want to know the spectral content (= the strength of
each frequency) of the pulse.

If you do this at some other point (e.g. after an interface between two materials) you can compute
the transmission and reflection coefficients for several frequencies in a single simulation

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