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The E-field of a linearly polarized electromagnetic wave propagating in the \(z\) direction is:$$ \boldsymbol{E} ~=~ \boldsymbol{E}_0 \, \cos(\omega \, t - k\,z) $$where \(\boldsymbol{E}_0 = (E_{0 \text x}, E_{0 \text y}, 0)\) is the amplitude. \(\omega\) is the angular frequency, \(t\) time, \(k\) wavenumber and \(z\) spatial coordinate as a propagation direction.
The electric field \(\boldsymbol{E}\) oscillates in a plane (here \(x\)-\(y\)-plane) for a linearly polarized wave and the components of the E-field have no phase shift.