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The E-field of a right-circularly polarized electromagnetic wave propagating in the \(z\) direction:$$ \boldsymbol{E} ~=~ E_0 \, \begin{bmatrix} \cos(\omega \, t - k\,z) \\ \sin(\omega \, t - k\,z) \\ 0 \end{bmatrix} $$where \(E_0\) is the amplitude of the E-field. \(\omega\) is the angular frequency, \(t\) time, \(k\) wavenumber and \(z\) spatial coordinate.
The electric field \(\boldsymbol{E}\) has only one \(E_{\text x}\) and \(E_{\text y}\) component for a circularly polarized wave. And the phase shift between \(E_{\text x}\) and \(E_{\text y}\) is \(\pm \pi/2\).