# Simple question about Jones vector

In Wikipedia, left hand circular polarized light is $$\frac{1}{\sqrt{2}}\left(\begin{array}{c} 1\\ i \end{array}\right)$$. However, $$\frac{1}{\sqrt{2}}\left(\begin{array}{c} 1\\ i \end{array}\right)e^{-i \omega t}$$ gives $$\frac{1}{\sqrt{2}}\left(\begin{array}{c} \cos\omega t\\ \sin\omega t \end{array}\right)$$ as the real part, which is the "right hand circular polarized light in x-y plane". I believe I must have misunderstood something, can anyone help me out? Thanks!

(I guess Jones vector's handedness is defined from the receiver, but shouldn't it be defined from the source so that it is consistent with helicity?)

• There are two conventions in use. en.wikipedia.org/wiki/… – Farcher Mar 24 '17 at 10:31
• @Farcher Well, I know there are two conventions, but is it true that Jones vector uses the second convention(from the receiver)? – Jieyu You Mar 25 '17 at 21:45

## 2 Answers

Apparently the Jones Vector displayed on the Wikipedia page is defined using the receiver convention. Here is a SPIE photonics source which uses the opposite convention.

It looks to me like there is probably not a standard. What follows are my strong opinions about which standard one should follow. When dealing with any convention you should be very clear in your own notes or in any public notes what convention you are using and how you are defining the conventions.

Frankly the receiver convention sounds ridiculous to me. If I am going to point the z-axis in a particular direction with respect to a beam of light it is definitely going to be the propagation direction.. Personally I would define the receiver convention as: Work out whether you think the light is right or left hand circular polarized and then say the opposite. But of course this is all a matter of opinion/convention..

The expression you wrote is for left handed circular polarized light.

In physics, positive angle are given in the anti-clockwise direction, so given your expression, when the time increases, the electric field is moving from x to y so toward the left in the receiver convention, so everything is correct.