# Matrix description of optical devices

#### naima

Gold Member
I read that Jones matrices can descibe optical devices with polarized light. They are 2 by 2 matrices.A basis can be Linear polarization along x or along y for a photon moving along z. I can use when there is a device with one input channel.
Consider now a Mach Zehnder Interferometer (MZI). there is a beam splitter with 2 input channels.
I saw papers which use Jones like matrices but where the input polarizations H and V were replaced by Port1 and port2 and the output giving the detectors.
A MZI needs 4 input parameters LH, LV, BH, BV (L B for left bottom)
I did not see descriptions of MZI using 4*4 matrices.
I found Mueller 4*4 matrices but they speak of something else.

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#### UltrafastPED

Gold Member
Here is a paper which uses both Jones and and Mueller matrix techniques in the description of a Mach-Zender interferometer: http://arxiv.org/pdf/1211.3194.pdf

And "Matrix operators for complex interferometer analysis":
http://arxiv.org/ftp/arxiv/papers/1012/1012.0063.pdf

BTW, while the Jones matrix technique works with 2 port devices, in linear optics (which is implicitly assumed) you can simply run a second input through the same system to see the effects of multiple inputs; see section 1 of the second paper.

For auditors unfamiliar with Jones & Mueller, a brief introduction:
http://www.ece.rice.edu/~daniel/262/pdf/lecture17.pdf

#### naima

Gold Member
I read Dahlgren's paper. This what i am looking for.
How did you find his method? in a course or in a book or on the web?
We have Eout = H E0
What is the value of H for a general beam splitter?
I was first interested in the subject when i read http://arxiv.org/abs/quant-ph/0408011

#### UltrafastPED

Gold Member
I read Dahlgren's paper. This what i am looking for.
How did you find his method? in a course or in a book or on the web?
I first studied the Jones & Mueller matrix methods as an undergraduate, so I am familiar with them, though in my work I've seldom used them.

Once you are familiar with a topic it is easy to find good references - it only takes a moment to sort through a stack of reference works in the library to find the work that meets your needs, or to read abstracts which contain the key words that are relevant.

It is the same with Google: first understand the technical question, then select the relevant terms: "Jones Mueller matrix Mach Zender two port" and launch the search. Finally read the abstracts until a good paper is found.

Just like getting started on any research project!

#### naima

Gold Member
Could you look at fig 1 in http://arxiv.org/abs/quant-ph/0408011
When there is only one input channel, a beam splitter has two output ports.
There are " beam splitters" P1 and P2 which merge two inport channels toward one port.
Are they rotated BS or other devices?

#### UltrafastPED

Gold Member
From the caption for figure 1: "All beamsplitters are polarizing beamsplitters with the same polarization basis and transmit photons in the |H> state, while reﬂecting photons in the |V> state"

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