# Question on characterization of elliptical polarization of EM wave.

• yungman
In summary, Alan is using "Advanced Engineering Electromagnetics" 2nd edition by Balanis AND "Antenna Theory" 3rd edition also by Balanis. He found an inconsistency in how to characterize RHC (CW) and LHC ( CCW) elliptical polarization.
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

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.

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.

Whenever you publish something on circular/elliptical waves make sure to completely specify which convention you use.

Yes, from my research, the two main EM book on radio wave that even get into this are Kraus and Balanis. They are using different convention. BUT all the inconsistency are from the SAME author...Balanis. I know you have to follow one convention...better yet...one author, but all my question is from the same author! That's why it's so frustrating to study this. I have been stuck for like two weeks on this. As you can see, I intentionally bring up all three of my post at the same time to show the questions I have quoting the pages in the books.

I would first like to acknowledge the confusion and inconsistency in the characterization of elliptical polarization of EM waves in the two sources mentioned. It is important to note that inconsistencies like these can arise in scientific literature due to different authors, different approaches, and different conventions being used. In this case, it seems that the two sources are using different conventions for defining the phase difference, \Delta\phi, between the x and y components of the electric field.

In Advanced Engineering Electromagnetics, the phase difference is defined as \Delta\phi=\phi_x-\phi_y, while in Antenna Theory it is defined as \Delta\phi=\phi_y-\phi_x. This results in a difference of sign in the phase difference, which can lead to different interpretations of the polarization.

In the example given, where \Delta\phi=\frac{\pi}{4}, the two sources give different results. In Advanced EE, if \Delta\phi ≥ 0, then the polarization is CW if E_R>E_L and CCW if E_R<E_L. However, in Antenna Theory, if \Delta\phi ≥ 0, then the polarization is always CW, regardless of the relative magnitudes of E_R and E_L.

To address this inconsistency, it is important to clearly define and follow a standard convention for defining the phase difference in the literature. This will help to avoid confusion and ensure consistency in future studies. In addition, it is important to carefully read and understand the conventions used in each source and consider the context in which they are being used.

In conclusion, while the inconsistency in the characterization of elliptical polarization in the two sources may cause confusion, it is important to recognize that this is a common issue in scientific literature. By carefully considering the conventions used and working towards a standard definition, we can ensure more consistent and reliable results in our research.

## 1. What is elliptical polarization of an electromagnetic wave?

Elliptical polarization of an electromagnetic (EM) wave is a type of polarization in which the electric field vector traces out an ellipse as the wave propagates. This is in contrast to linear polarization, in which the electric field vector oscillates in a straight line, and circular polarization, in which the electric field vector traces out a circle.

## 2. How is elliptical polarization characterized?

Elliptical polarization is characterized by the shape and orientation of the ellipse traced out by the electric field vector. This can be described using parameters such as the major and minor axes of the ellipse, the angle of rotation of the ellipse, and the sense of rotation (clockwise or counterclockwise).

## 3. What causes elliptical polarization of EM waves?

Elliptical polarization of EM waves can be caused by a combination of linearly and/or circularly polarized waves with different frequencies and amplitudes. The resulting superposition of these waves creates an elliptical polarization pattern.

## 4. What are the applications of elliptical polarization?

Elliptical polarization has several applications in various fields such as telecommunications, remote sensing, and astronomy. It is used in antenna design, satellite communications, and radar systems. In astronomy, it can provide information about the magnetic field of celestial objects.

## 5. How is elliptical polarization detected and measured?

Elliptical polarization can be detected and measured using polarimeters, which are instruments that measure the state of polarization of light. These devices use various techniques such as rotating waveplates, quarter-wave plates, and polarizing prisms to analyze the polarization state of EM waves.

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