Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Polarization rotation: Jones Matrix that maps Horizontal to right circular

+ 4 like - 0 dislike
780 views

I am looking at the Poincaré sphere and I am trying to compute a Jones matrix for a particular rotation. Specifically, I would like it to perform the following maps:

$O :|H \rangle \rightarrow |R \rangle$

$O :|V \rangle \rightarrow |L \rangle$

$O :|L \rangle \rightarrow |H \rangle$

$O :|R \rangle \rightarrow |V \rangle$

where $|R \rangle$, $|L \rangle$ are right circular and left circular light. Is this possible? I should mention that I would also accept the same equations with L,R replaced by linearly polarized light $|D \rangle$, $|A \rangle$. If it is possible, what would be common plates that could do it?

This post imported from StackExchange Physics at 2017-10-08 21:12 (UTC), posted by SE-user Ben Sprott
asked Feb 22, 2012 in Theoretical Physics by Ben Sprott (30 points) [ no revision ]

1 Answer

+ 4 like - 0 dislike

@wsc answer is interesting but misses a key point. Jones vector are defined upto a global phase, which gives us enough degree of freedom to solve your problem. Since your operation corresponds to a $\frac\pi2$-rotation around the $Y$ axis in the Poincaré sphere, it is physically doable.

Algebraically, after the first to equations, the matrix is determined to be $$\frac1{\sqrt2}\begin{bmatrix}1&e^{i\phi} \\ -i&i e^{i\phi}\end{bmatrix}.$$ The third condition imposes $\phi=-\frac\pi2$, which gives the final matrix $$M=\frac1{\sqrt2}\begin{bmatrix}1&-i \\ -i&1\end{bmatrix}.$$ $M$ is fully determined and consistent with the fourth condition.

Edited to add: A little linear agebra will show you that this matrix corresponds to a quarter wave plate rotated with a $\frac\pi4$ angle relatively to the vertical direction. Of course, it is easy to give physical intuition after I deduced it from the algebra:

  • a quarter wave plate is needed to transform a circular polarization into a linear polarization and vice-versa;
  • Applying twice the transformation swaps $|H\rangle$ and $|V\rangle$. This is what a half-wave plate at a $\frac\pi4$-angle does. And a half-wave plate is nothing more that 2 stacked quarter-wave plates (at least in theory). This gives the $\frac\pi4$-angle needed for our quarter-wave plate. QED without algebra.
This post imported from StackExchange Physics at 2017-10-08 21:12 (UTC), posted by SE-user Frédéric Grosshans
answered Feb 22, 2012 by Frédéric Grosshans (250 points) [ no revision ]
Haha, oops. Forgot about that.

This post imported from StackExchange Physics at 2017-10-08 21:12 (UTC), posted by SE-user wsc

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOver$\varnothing$low
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...