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

In summary, the conversation discusses finding the spectral representation of a plane wave in the time domain. The individual is wondering how to find the spectral representation and mentions the use of Fourier Transform for a finite intensity field. However, they are having trouble finding a solution for it. They seek assistance in this matter.
  • #1
Madara
7
0
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
 
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  • #2
The spectrum is a Dirac delta function in omega [tex]\delta(\omega-\omega_0)[/tex]
if E(t)~[tex]e^-i\omega_0 t[/tex].
 
  • #3
Thanks Clem.
 

What is the spectrum of a plane electromagnetic wave?

The spectrum of a plane electromagnetic wave refers to the range of frequencies of the wave's oscillations. This spectrum includes all possible frequencies, from very low (radio waves) to very high (gamma rays) frequencies.

What is the relationship between frequency and wavelength in a plane electromagnetic wave?

The frequency and wavelength of a plane electromagnetic wave are inversely proportional. This means that as the frequency increases, the wavelength decreases, and vice versa.

What is the speed of a plane electromagnetic wave?

The speed of a plane electromagnetic wave is constant and equal to the speed of light, which is approximately 3 x 10^8 meters per second in a vacuum.

How is the spectrum of a plane electromagnetic wave related to its energy?

The energy of a plane electromagnetic wave is directly proportional to its frequency. This means that higher frequency waves have more energy than lower frequency waves.

What is the difference between the spectrum of a plane electromagnetic wave and a continuous spectrum?

A plane electromagnetic wave has a continuous spectrum, meaning it includes all frequencies. However, a continuous spectrum can also refer to a spectrum without any gaps or interruptions, while the spectrum of a plane electromagnetic wave is continuous but not necessarily uninterrupted.

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