How can the spectral representation of a plane EM wave be found?

[Madara]

Hi,

Let E(r,t) = E(r)exp(-ikz)exp(iwt)
be a plane wave in time domain, propagating along Z direction.

I wonder how to find the spectral representation of it (i.e. E(r,w))??

I know, for a finite intensity field (i.e. |E(r,t)|^2 < infinity), we can give the spectral representation of the signal by,

E(r,w) = Fourier Transform of [E(r,t)].

But when I do the intergration in Fourier Transform between the + infinity and - infinity, I can't get a solution for above.

Can anyone help me with this?

Thanks
Madara

 

[Meir Achuz]

The spectrum is a Dirac delta function in omega $$\delta(\omega-\omega_0)$$
if E(t)~$$e^-i\omega_0 t$$.

 

[Madara]

Thanks Clem.