# Talk:Jones calculus

WikiProject Mathematics (Rated Start-class, Low-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 Start Class
 Low Importance
Field: Mathematical physics
WikiProject Physics (Rated Start-class, Mid-importance)
This article is within the scope of WikiProject Physics, a collaborative effort to improve the coverage of Physics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Start  This article has been rated as Start-Class on the project's quality scale.
Mid  This article has been rated as Mid-importance on the project's importance scale.

## Untitled

Do we know who Mr. Jones who invented this was? I ask because I suspect it was Isaac Newton's contemporary Sir William Jones and we might as well link to that if so. -- Paul Drye

I'm not sure. --Georg Muntingh

I very much doubt it. Try this:

Jones, R. C., New Calculus for the Treatment of Optical Systems I. Description and Discussion of the Calculus, Journal of the Optical Society of America, 31, 488-493 (1941)

I think we should expand this section to include elliptical jones vectors and how to get their magnitudes.

The polarizer with azimuth 0:

$P(0) = \begin{pmatrix} 1 & 0 \\ 0 & 0 \\ \end{pmatrix}$

The rotation by $\varphi$:

$R(\varphi) = \begin{pmatrix} \cos\varphi & -\sin\varphi \\ \sin\varphi & \cos\varphi \\ \end{pmatrix}$

The polarizer with azimuth $\varphi$:

$P(\varphi) = R(\varphi) P(0) R(-\varphi) = \begin{pmatrix} \cos^2\varphi & \cos\varphi\sin\varphi \\ \sin\varphi\cos\varphi & \sin^2\varphi \\ \end{pmatrix}$

--HarpyHumming 22:01, 28 Feb 2004 (UTC)

## conflicting definitions for right- and left-hand circular

In a couple of places (e.g. "The Depolarisation of Electromagnetic Waves", Beckmann 1968) I've seen a conflicting definition of Jones vectors for right- and left-hand polarisations, where right circular is (1, i) - not the (1, -i) that is quoted here. In this Wiki article, I assume the wave propagates along +z, so E has components in x and y directions. Beckmann assumes the wave propagates along +x, so the corresponding E vectors are y and z (if we stick with a right-handed coordinate system!), thus a right circular wave screws clockwise if viewed in the direction of propagation. A right circular wave, by his definition, has Ey = 1 and Ez = +i, which correspond to Ex = 1 and Ey = +i in this article, hence my confusion. Any ideas?

Rob Granger. —The preceding unsigned comment was added by 213.123.216.147 (talk) 10:39, 11 April 2007 (UTC).

There has been a lot of flipping of signs and changing of phase factors in this article. Someone should really go through, with reference to a text, and ensure that the entire article is using a single sign convention.--Srleffler (talk) 03:58, 8 December 2007 (UTC)
The confusion is caused by a split in the literature regarding the sign convention. Some authors (Jackson, Goodman) use the decreasing phase sign convention (phase = kz - wt - initial_phase). Other authors (Jenkins & White, Gaskill) use the increasing phase sign convention (phase = wt - kz + initial_phase). Even the phrases "increasing phase" and "decreasing phase" assume that you are referring to the phase with respect to time rather than space. The upshot is that if you switch the sign convention, the Jones Vector becomes the complex conjugate and the Jones Matrices for components also change. Asparkswiki (talk) 02:05, 1 February 2009 (UTC)
Another inconsistency lies in the table equating the Jones vectors and corresponding Ket notation for right and left circularly polarised light. The Jones vectors are consistent with the Jones matrices listed later in the page (and I suspect are using the phase = kz - wt convention), but the Ket notation seems to be using the opposite convention. The result being that the Jones vector for R polarised light actually corresponds to the listed Ket notation for L polarised light and vice versa. -- LixinChin (talk) —Preceding unsigned comment added by 130.95.35.54 (talk) 05:54, 19 April 2011 (UTC)
The inconsistency on this is detrimental to the usefulness of the equations as provided. I don't think LixinChin is fully correct, in that the Jones vectors and matrices do not match. For example, simply apply the provided RCP Jones matrix for an RCP polarizer to the definition of an RCP input vector. I suggest using the notation of RCP = [1 i] and leaving the rest unchanged, or vice versa. The page itself should at least be consistent, even if the literature is not. Mattmisk (talk) 19:37, 30 January 2014 (UTC)

## Jones matrix for mirror

Unless I am mistaken, the Jones matrix for a mirror1 is:

$\begin{pmatrix} 1 & 0 \\ 0 & -1 \\ \end{pmatrix}$

Should we add it to the list? Gellule (talk) 22:27, 12 January 2010 (UTC)

## Inconsistency in phase

In Jones vectors section, it is written

Note that all Jones vectors and matrices on this page assumes that the phase of the light wave is $\phi = kz - \omega t$, which is used by Hecht. Collett uses the opposite definition ($\phi = \omega t - kz$).

Then,

1. Quarter-wave plate with fast axis vertical must be $\begin{pmatrix} 1 & 0 \\ 0 & -i \end{pmatrix}$, while Quarter-wave plate with fast axis horizontal must be $\begin{pmatrix} 1 & 0 \\ 0 & i \end{pmatrix}$, i.e., they must be opposite. (previously, this point was correct. This was changed by the Revision as of 13:39, 31 March 2010. What is written on the note of this revision is “inverted signs for quarter wave plates, see source (Collett)”. It is clear that the description is inconsistent.)
2. In Jones vector section (just before the table), $+i$ must represent a retarded (delayed) signal (-90 degree phase shift), while $-i$ must represent a time advanced signal (+90 degree phase shift). (the present description in Jones vector is opposite to that in Phase retarders section.)

I believe these (maybe no more) should be fixed.WiOp (talk) 09:12, 2 November 2010 (UTC) Slightly changed.WiOp (talk) 04:08, 4 November 2010 (UTC)

I am a graduate student in optics (at the best optical sciences university in the world) and it is appalling that this is still in the main article. Pick a phase convention and stick with it consistently throughout the article! — Preceding unsigned comment added by 68.228.251.197 (talk) 03:25, 8 January 2013 (UTC)

## photon spins

Add a sentence stating that Jones vectors are not about single photons. Its not the same as describing a photon spin in Pauli vectors. — Preceding unsigned comment added by 188.105.17.135 (talk) 21:38, 28 October 2012 (UTC)

Are you sure they don't describe single photons? -- cheers, Michael C. Price talk 23:35, 28 December 2012 (UTC)

I'm sure they do not. You have to properly normalize photon states and deal with collapse, which classical Jones vectors can avoid. --Israel Vaughn — Preceding unsigned comment added by 68.228.251.197 (talk) 03:36, 8 January 2013 (UTC)

Collapse and normalisation are red herrings in a classical description. Single photons can be polarised, and I see no reason why they can't be described by Jones' vectors.-- cheers, Michael C. Price talk 17:13, 26 July 2013 (UTC)

Cite error: There are <ref> tags on this page, but the references will not show without a {{reflist}} template (see the help page).

 HPTS - Area Progetti - Edu-Soft - JavaEdu - N.Saperi - Ass.Scuola.. - TS BCTV - TS VideoRes - TSODP - TRTWE TSE-Wiki - Blog Lavoro - InterAzioni- NormaScuola - Editoriali - Job Search - DownFree !
 TerritorioScuola. Some rights reserved. Informazioni d'uso ☞