Another inconsistency from Balanis

I take issue with the "Advanced Engineering Electromagnetics" 2nd edition by Balanis again. In Page 155 to 157, the book is trying to explain that an ellipse is really a super position of a RHC and a LHC circle with amplitude of RHC as [itex]E_R[/itex] and LHC as [itex]E_L[/itex]

The book use the example for wave travel in +z direction:
[tex]\phi_x=\frac{\pi}{2}\;\hbox { and}\;\phi_y=0 \;\hbox { to show Ex wave is leading Ey.}[/tex]
[tex]E_{x0}=E_R+E_L\;\hbox{ and } E_{y0}=E_R-E_L[/tex] AND
[tex]\vec E(0,t)=Re[\hat x (E_R+E_L)e^{j(\omega t+\frac{\pi}{2})}+\hat y (E_R-E_L) e^{j\omega t}]\;=\;Re[(E_R(\hat x j+\hat y)\;+\;E_L(\hat x j -\hat y))e^{j\omega t}]\;=\;
-\hat x ( E_R+E_L) \sin \omega t +\hat y (E_R-E_L) \cos\omega t[/tex]

This equation is independent to whether the wave is propagating in +ve or -ve z direction ( directional independent). The problem is [itex](\hat x j+\hat y)[/itex] is RHC ONLY if travel in +z direction. It is LHC if travel in -z direction. So the whole notion of [itex]E_R\;,\;E_L[/itex] have absolutely no meaning!!! I have not seen so many inconsistency in one book!!! Balanis is a very well regarded author, I cannot imagine he can make so many mistakes.....Within 20 pages, Please advice.

Thanks

Alan