# Verify definition of circular polarization in Balanis.

1. Jan 15, 2013

### yungman

Attached is a scan of how Balanis define plane wave with circular polarization with Ey having a phase of +∏/2 respect to Ex component of the E field. I don't quite agree with the book. The second attachment is my derivation.

The definition of CW or CCW is with respect to direction of propagation come out of the paper as indicated in my notes ( point towards you!!).

The book claimed for propagation in -ve z direction, if phase is +∏/2 (n=0), the rotation is CW which is Left Hand Rotation. And the book said if the propagation is in +ve z direction, the rotation reverse to CCW.

But as I proofed in my notes: For propagation in -ve z direction, the function is $\cos(\omega{t}+kz+\frac{\pi}{2})$. Which for t=0 and plot the wave along -z, maximum occur at $kz+\frac{\pi}{2}\;=\;0\;\Rightarrow\; z=-\frac{\lambda}{4}$. This is drawn in my notes. I showed the rotation of the E in CCW and is Right Hand Rotation for propagation in -ve z direction.

On the lower part of my notes for propagation in +ve z direction, the result is backed up by "Engineering Electromagnetics" by Ulaby. That it is CW and Left Hand Rotation. Based on all these, I cautiously say Balanis is wrong. Please check my work and tell me whether I am correct or not.

Thanks

Alan

#### Attached Files:

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• ###### CP notes L.png
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Last edited: Jan 15, 2013