Characterize EM wave propagate in +z and -z

For RHC EM wave travel in +z direction, the unit vector is [itex]\hat {E}=\frac{\hat {x}+\hat{y}j}{\sqrt{2}}[/itex] ignoring the ωt-kz.

What if the RHC EM wave travels in -z direction? The unit vector should be [itex]\hat {E}=\frac{\hat {x}-\hat{y}j}{\sqrt{2}}[/itex] ignoring the ωt+kz.

Am I correct?