Editing Jones calculus (section)

== Jones matrices ==
Jones calculus is a matrix calculus developed in 1941 by [[Henry Hurwitz Jr.]] and [[R. Clark Jones]] and published in the ''[[Journal of the Optical Society of America]]''.<ref>{{Cite journal |last1= Hurwitz |first1= Henry |last2= Jones |first2= R. Clark |authorlink1=Henry Hurwitz Jr.| date= 1941 |title= A new calculus for the treatment of optical systems, II. Proof of three general equivalence theorems |journal= Journal of the Optical Society of America |volume= 31 |issue= 7 |pages= 493&ndash;499 |doi= 10.1364/JOSA.31.000493 |bibcode= 1941JOSA...31..493H }}</ref><ref>{{Cite journal |last= Jones |first= R. Clark |date= 1941 |title= A new calculus for the treatment of optical systems, I. Description and Discussion of the Calculus |journal= Journal of the Optical Society of America |volume= 31 |issue= 7 |pages= 488&ndash;493 |doi= 10.1364/JOSA.31.000488 |bibcode= 1941JOSA...31..488J }}</ref><ref>{{Cite journal |last= Jones |first= R. Clark |date= 1941 |title= A new calculus for the treatment of optical systems, III. The Sohncke Theory of optical activity |journal= Journal of the Optical Society of America |volume= 31 |issue= 7 |pages= 500&ndash;503 |doi= 10.1364/JOSA.31.000500 |bibcode= 1941JOSA...31..500J }}</ref><ref>{{Cite journal |last= Jones |first= R. Clark |date= 1942 |title= A new calculus for the treatment of optical systems, IV. |journal= Journal of the Optical Society of America |volume= 32 |issue= 8 |pages= 486&ndash;493 |doi= 10.1364/JOSA.32.000486 |bibcode= 1942JOSA...32..486C }}</ref>

The Jones matrices are operators that act on the Jones vectors defined above.  These matrices are implemented by various optical elements such as lenses, beam splitters, mirrors, etc.  Each matrix represents projection onto a one-dimensional complex subspace of the Jones vectors. The following table gives examples of Jones matrices for polarizers:
{| class="wikitable" style="text-align:center"
! Optical element !! Jones matrix
|-
| Linear [[polarizer]] with axis of transmission horizontal<ref name="fowles">{{cite book|author=Fowles, G.|title=Introduction to Modern Optics|url=https://archive.org/details/introductiontomo00fowl_441|url-access=limited|edition=2nd|publisher=Dover|date=1989|page=[https://archive.org/details/introductiontomo00fowl_441/page/n44 35]|isbn=9780486659572 }}</ref> ||
<math>\begin{pmatrix}
1 & 0 \\ 0 & 0
\end{pmatrix}</math>
|-
| Linear polarizer with axis of transmission vertical<ref name="fowles" /> ||
<math>\begin{pmatrix}
0 & 0 \\ 0 & 1
\end{pmatrix}</math>
|-
| Linear polarizer with axis of transmission at ±45° with the horizontal<ref name="fowles" /> ||
<math>\frac{1}{2} \begin{pmatrix}
1 & \pm 1 \\ \pm 1 & 1
\end{pmatrix}</math>
|-
| Linear polarizer with axis of transmission angle <math>\theta</math> from the horizontal<ref name="fowles" /> ||
<math> \begin{pmatrix}
\cos^2(\theta) & \cos(\theta)\sin(\theta) \\ \cos(\theta)\sin(\theta) & \sin^2(\theta)
\end{pmatrix}</math>
|-
| Right circular polarizer<ref name="fowles" /> ||
<math>\frac{1}{2} \begin{pmatrix}
1 & i \\ -i & 1
\end{pmatrix}</math>
|-
| Left circular polarizer<ref name="fowles" /> ||
<math>\frac{1}{2} \begin{pmatrix}
1 & -i \\ i & 1
\end{pmatrix}
</math>
|-
|}