# Question on characterization of elliptical polarization of EM wave.

1. Jan 29, 2013

### yungman

I am using "Advanced Engineering Electromagnetics" 2nd edition by Balanis AND "Antenna Theory" 3rd edition also by Balanis. I found an inconsistency in how to characterize RHC (CW) and LHC ( CCW) elliptical polarization.

1) In Advanced EE Page 159, for
$$\vec E(0,t)=Re[\hat x (E_R+E_L)e^{j\omega t}+\hat y (E_R-E_L)e^{j(\omega t+\Delta \phi)}]$$
$$\hbox { Where}\;\Delta\phi=\phi_x-\phi_y≠\frac{n\pi}{2}\;\hbox {where }\;n=0,2,4,6.....$$
If $\Delta \phi ≥ 0$, then, it is CW if $E_R>E_L$, CCW if $E_R<E_L$
If $\Delta \phi ≤ 0$, then, it is CCW if $E_R>E_L$, CW if $E_R<E_L$

2) In Antenna Theory Page 74,
$$\Delta\phi=\phi_y-\phi_x≠^+_-\frac{n\pi}{2}\;\hbox {where }\;n=0,1,2,3.....$$
If $\Delta \phi ≥ 0$, then, it is CW.
If $\Delta \phi ≤ 0$, then, it is CCW.

To avoid confusion, just use one example where $\Delta\phi=\frac {\pi}{4}$, you can see using Advanced EE, there are two condition that can give you CW or CCW. But in Antenna, there is only one condition which is CW.

How do you explain the inconsistency? Yes, there are confusion as the definition of $\Delta\phi$ is opposite between the two. But if you look pass the difference, you can still see the inconsistency. Am I missing something?

Thanks

Alan

2. Jan 31, 2013

### yungman

Anyone has comment? You don't have to know the answer, just comment on this. This is another inconsistent from Balanis. It is from two books that he wrote.

3. Jan 31, 2013

### M Quack

Circular polarization of electromagnetic waves is a mess. There are two different conventions (at least), one predominantly used in visible light optics and the other one predominantly used in radio and long-wavelength electromagnetics.

Basically, you can look at the wave at a fixed time and see how the electric field vector spirals around the direction of propagation, or you can look at a fixed location and see how it spirals as function of time.