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# How can ellipticity angle be negative?

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#### Alan0354

##### Full Member level 4
In plane wave elliptical polarization, the book said if the Ellipticity angle is possitive, it is a Left Hand Circular polarization(LHC). If Ellipticity angle is negative, it is Right Hand Circular polarization(RHC).

My question is how can Ellipticity angle be negative?

https://en.wikipedia.org/wiki/Polarization_%28waves%29

Can anyone show a picture of negative Ellipticity angle?

Thanks

I am wondering which book you are mentioning?! ellipticity is a ratio of two lengths that leads to some value between 0 and 1. the measure doesn't tell anything about handedness...and we don't have negative length, hence no negative ellipticity.

I am wondering which book you are mentioning?! ellipticity is a ratio of two lengths that leads to some value between 0 and 1. the measure doesn't tell anything about handedness...and we don't have negative length, hence no negative ellipticity.

This is from "Engineering Electromagnetics" by Ulaby.

Attached is the page described where χ is the ellipticity angle. That's the reason I don't understand why it can be negative.

#### Attachments

• Ulaby L.png
479.7 KB · Views: 106

in the first paragraph of section 7-3-4, last line, says shape and handedness comes from ratio and phase different. So, if it is saying that ratio is used for handedness, it is violating an early statement...I disagree with the book. you might want to read another book that gives you correct insight. anyway, u seem smarter than the author for figuring this out!

Alan0354

### Alan0354

Points: 2
in the first paragraph of section 7-3-4, last line, says shape and handedness comes from ratio and phase different. So, if it is saying that ratio is used for handedness, it is violating an early statement...I disagree with the book. you might want to read another book that gives you correct insight. anyway, u seem smarter than the author for figuring this out!

Thanks for looking at this. Yes, it does not make sense. I have 4 other EM books and none claimed anything like this. But the problem is no body else really get into the detail of how to characterize the elliptical polarization. Ulaby's book is an excellent book out of 8 other EM books I have. I am surprised that it made this mistake. I studied and worked through the formulas of over 95% of the book and never once found a mistake, this is the first one and it's big!!!

The only info is from The antenna theory by Balanis that make sense. That you can determine whether it's a RHC or LHC by looking at the phase of Ex and Ey component. Where if the phase constant $\Delta\phi =\phi_{y}-\phi_{x}$ is positive, it is LHC. And if $\Delta\phi$ is negative, it's a RHC.....exactly like how to determine the polarization of a circular polarization. If you know some other article that explains elliptical polarization better, please give me the link.

Many thanks

Alan

I just double checked Kraus' EM book. It supported everything Ulaby's book. All the formulas in the attached scan have been verified. So they must be correct.

I just double checked Kraus' EM book. It supported everything Ulaby's book. All the formulas in the attached scan have been verified. So they must be correct.

No, both are wrong! the polarization is a simple topic and that's strange why authors having problem dealing with that...

for characterization of elliptical polarization, you need two parameters: rotation and ellipticity. To find handedness, some info on the phase difference must be provided. I am not sure if you are familiar with Jones method or not, but it the best method to deal with polarization. And also keep in mind about sign convention because some time RCP is called LCP and vice versa.

I don't know enough to say at this point. Kraus derive the formulas using Poincare Sphere and I am part way verifying the formulas, so far, the ones I verified looks good. Apparently it is related to Jones vector.

But if the formulas are originated by from Poincare sphere which from my understanding is from Jones vector, then I don't know what to even make of it. At this point, all I can say is the Electromagnetics with Application by Kraus and Fleisch is a very famous book that even Balanis referenced to. Please give me some more guidance while I am reading into this.

Thanks

Alan

The same thing is in Balanis. see fig 4-21. Ellipticity angle is an angle and you can think of -pi/2 as 3pi/2!. So the first is RC and second is LC?!

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