What is meaning of $FFT(\vec{E}(x,y ))$

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What is the meaning and how one takes fourier transformation of vector that has spatial distrubution.

Let say electric field (with transfer x, y distibution) with direction

$$FFT(\vec{E}(x,y ))$$

In matlab fft2(E(x,y)) would be fine for scalar. But how one would take FFT if it is a vector.

My question comes from fft beam propagation equation shown bellow. It is for homework and I do not have time, just $\vec{E}(x,y )$ . I do not understand how FFT is taken of a vector.

(e, p are 1x3 vectors and kz is z directed wave number 1x3 vector. The sum is over two polararizations.)

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