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## Using Axial Ratio AR to predict R or L hand polarization.

I take issue with the "Advanced Engineering Electromagnetics" 2nd edition by Balanis again. In Page 156, it claimed for AR=-ve, it is Right Hand rotation, AR=+ve is Left Hand rotation.

For plane wave propagates in z direction and at z=0:

A)Let Ey lag Ex by $\frac{\pi}{2}$
$$\Rightarrow\;\vec E(0,t)=Re[\hat x (E_R+E_L)e^{j(\omega t)}+\hat y (E_R-E_L) e^{j(\omega t -\frac{\pi}{2})}]\;=\;\hat x ( E_R+E_L) \cos \omega t +\hat y (E_R-E_L) \sin \omega t$$
Where $E_{x0}=E_R+E_L \;\hbox { and }\;E_{y0}=E_R-E_L$.
$$AR=\frac{E_{max}}{E_{min}}\;=\;\frac{+(E_R+E_L)}{+(E_R-E_L)}$$
AR is positive

2)But Ey lag Ex by $\frac{\pi}{2}$ can be represented by:
$$\vec E(0,t)=Re[\hat x (E_R+E_L)e^{j(\omega t+\frac{\pi}{2})}+\hat y (E_R-E_L) e^{j\omega t}]\;=\;-\hat x ( E_R+E_L) \sin \omega t +\hat y (E_R-E_L) \cos\omega t$$
$$AR=\frac{E_{max}}{E_{min}}\;=\;\frac{-(E_R+E_L)}{+(E_R-E_L)}$$
AR is negative.

AR is different even if you use different representation of Ey lagging Ex!!!

Also, even if you stay with one convention, Right and Left change between propagation in +z or -z.

This is too important for the book to have a blanket statement, AR cannot predict the direction of rotation of the polarized wave. Can anyone verify this?

Thanks

Alan

What's the matter with this topics? I have 8 EM books, only Balanis get more into this polarization. The book is inconsistent. This is not that hard a topic but I am stuck for like two weeks because every time I turn around, I cannot verify the book. Then information on this is hard to get on the web. I finally get the rotation right, but this AR thing is something again!!!
I am not even talking about difference in conventions, I know Kraus uses different conventions, you either follow Balanis or Kraus. Balanis is more detail, so I follow Balanis. Then Balanis is not consistent in it's own either!!!
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