How can ellipticity angle be negative.

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?

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

Can anyone show a picture of negative Ellipticity angle?

In case this sounds ridiculous, attached is the scan of the paragraph from the "Engineering Electromagnetics" by Ulaby. I have to scan in two part to fit the size limit. First is Ulaby1 and then Ulaby2.

Thanks
Attached Thumbnails

 Recognitions: Science Advisor I don't see what is the problem with a negative ellipticity angle. The sign of the arcus tangens is not fixed by it's argument, it can be either positive or negative. To decide which one to choose, you have to look at the polarisation of the wave.

 Quote by DrDu I don't see what is the problem with a negative ellipticity angle. The sign of the arcus tangens is not fixed by it's argument, it can be either positive or negative. To decide which one to choose, you have to look at the polarisation of the wave.
The question is how to draw a negative ellipticity angle physically?
$$\chi\;=\;\tan^{-1} \frac {a_{\eta}}{a_{\epsilon}}$$
Both are just length and is never negative.
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