Now, if we consider a plane wave with \(\mathbf{E}\) field of amplitude \(E_{0}\), pointing in a direction \(45^{circ}\) with respect to the \(x\)-axis and traveling in the \(+z\) direction, the \(\mathbf{E}\) field phasor is

\[\mathbf{E}(\mathbf{r}) = \Bigg(\frac{\hat{x}+\hat{y}}{\sqrt{2}}\Bigg)~E_{0}~\text{e}^{-j~k~z}\]