Question

What is the meaning of a Fourier Transform in an electric field $E(\omega,t)$?

Answer 1

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There is this electric field in one dimension:

E(ω,t)=E0cos(ωt)

It is reaching the surface of a semiconductor. The number of photons reaching the surface per unit of area is given by

NA=|E~(ω)|2cℏω

Where E~(ω) is:

E~(ω′)=12π∫∞−∞E(ω,t)eiω′tdt

So, when I make the Fourier Transform, are ω and ω′ the same?