# How come a current sheet of $J_s = J_0 \hat{x}$ produces plane wave solution?

Given in the picture. There is a current sheet $J_s = J_0 \hat{x}$. Supposedly Jo is not oscillating. So, how does this thing create a plane waves propagating away from the current sheet? Shouldn't there be an oscillating source to create waves in the medium?

• But the Fourier transform of constant is an impulse at $\omega=0$. Isn't it? Mar 26 '15 at 15:36
The $J$ in the question is not a constant. It is a phasor. It has an inherent $e^{jwt}$ with it. In the book, phasor form is used in these aspects.