Mueller Matrix Polarimetry

• In the last few months a good part of my research has been about Mueller matrix microscopy.  We have developed a new MM microscope that uses a dual rotating compensator setup and digital demodulation.  The spatial resolution and measurement quality is really good. See related publications here and here.

• This week we have published a paper titled Complete polarimetry on the asymmetric transmission through subwavelength hole arrays. I think it is a quite interesting topic because it mixes polarimetry, which by default is quite cool, with a surprising effect such as extraordinary optical transmission. Also the paper offers some clarification on concepts about 2d chirality, asymmetric transmission.

• During the past week I was in Ecole Polytechnique, working with Razvigor Ossikovski and Enric Garcia Caurel for a scientific collaboration. Hopefully the results will be seen soon.

• At the beginning of May I attended SPIE.DSS conference 2014 in Baltimore (Maryland, USA). I had never been in a conference that huge.   Also I took advantage that Baltimore is close to NYC to visit again my old  laboratory. I was happy to see that my old 4PEM  MM polarimeter is doing fine.

For some reason I cannot fully understand, certain types of serial decompositions of Mueller matrices became quite popular among experimentalists. I am talking about the polar decomposition and the Lu-Chipman decompositions. These matrix decompositions allow to decompose a matrix in a series of a retarder, a diattenuator and, eventually, also a depolarizer. Of course matrix multiplication is not commutative and, therefore, these decompositions are not unique. In general my advise would be to avoid serial decomposition of a Mueller matrix unless you have reasonable suspects that the investigated sample really corresponds to a certain succession of a retarder, diattenuator and a depolarizer. And, as a experimentalist, I can say that this will rarely happen.

In my view, the decompositions of the Mueller matrix based on a continuous medium have a much more general applicability and they should be the best choice for unknown samples. Some years ago we published the analytic equations find the results straightforwardly (Optics letters 35.4 (2010): 559-561 and Optics Letters 35.20 (2010): 3525-3525). However such equations apply to a Mueller-Jones matrix (non-depolarizing Mueller matrix) and I am aware that some people is having difficulties to apply them to general (depolarizing) Mueller matrix. In the papers that procedure was outlined, but anyway I upload here the code for such calculation, to clarify how the results should look like.

I upload a Labview library program that does such interpretation (run the vi “MManalysis.vi”. I also upload the same program but as an application in case there is anybody that cannot use Labview. Once you open it you will find something like this:

Labview Library www.mmpolarimetry.com/MManalysis%20Labview%202012.llb
Application www.mmpolarimetry.com/MManalysis.rar

You only need to write down a Mueller matrix (preferably an experimental one) and the program will give the closest Mueller-Jones and Jones matrices (in the Cloude sense) and the 6 independent parameters that better define your media (CD,CB,LD,LB,LD’ and LB’). **

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**. This analytic interpretation of continuous medium coincides 100% with the Log/differential method of analysis of Mueller matrices for nondepolarizing media, and it is computationally faster and numerically more robust. In the presence of strong depolarization there will be differences among both techniques, but that will be a topic for another day.

I took these two pictures last week in the lab. Too amazing for not sharing.

(click on the image to enlarge)

 These are three Cetonia Aurata beetles showing different cuticle colors. Can you anticipate how their Mueller matrix looks like?

During 2014-2015 I will be working on a European Marie Curie IIF project, titled  Polarimetric characterization of natural and artificial chiral anisotropic media (Nanochirality) at University of Barcelona.

Not many updates lately! I hope this semester I will manage to  keep the website more up-to-date.  I also want to add a section with some  new scientific content in the form of a tutorial, let’s see if I find the time. For the moment today I have updated the publication list in the lazy way, with a link to Google Schoolar. You can check my latest publications there. Any kind of feedback will be very appreciated!

By the way,  we are happy because  the Mueller Matrix XT150 polarimeter I mentioned in the previous post and sold by Hinds Instruments has won one of the 2013 R&D 100 Awards.

The working principle of this instrument is explained in this publication.

 Hinds Intruments  is selling the new 150XT Mueller Polarimeter. This instrument was developed in collaboration with New York University using the 4 Photoelastic Modulator (PEM) technology we pioneered. To my knowledge this is the first commercial full Mueller matrix polarimeter with research-grade specifications ever made available . The key element here is the sensitivity.  The instrument was developed to solve complex optical activity measurements involving chiral molecules molecules and crystals that show the tiniest bias to circular polarization. The result is a highly versatile instrument, capable of studying the transmitted complicate optical response of virtually any sample, even highly depolarizing one. The tiniest strain in a glass,  the optical rotation of a birefringent crystal, the circular dichroism of a oriented molecular aggregate,  the heterogeneous response of a  petrological sample, and many other can be studied with this polarimeter.

You can have more information about this instrument checking their brochure:

http://www.hindsinstruments.com/wp-content/uploads/150XT-Mueller-Polarimeter.pdf

After more than two years in New York University this month I have started to work again in Universitat de Barcelona.  This was possible because some time ago I got a Beatriu de Pinos Fellowship. These are grants to encourage the recruitment of research personnel in the Catalan public sector, be they in universities, research centers or hospital foundations, who have had postdoctoral stays abroad.

Lately I have been quite busy with the move but now I am already resettled. I pretend to keep working in the same reseach areas as before so expect here more stuff about Mueller Matrix polarimetry and others.

Recently I have been working on how Mueller matrices handle reciprocal and nonreciprocal optical effects. Mueller matrices are truly informativative about reciprocity, but one needs to know how the information is “stored”.  A series of two papers are going to be published in Optics Letters about the topic.  For the moment they can be accessed in early view.

Mueller matrix description of homogeneous depolarizing media. I. Number of independent parameters

Mueller matrix description of homogeneous depolarizing media. II. Differential decomposition

First message of 2013!  Happy New Year to any eventual visitor. Some quick updates to start the year:

• I have updated the Publications section using an embedded PDF file. I hope this way it is easier to keep it updated!
• I have recently known that my Phd Thesis [available here] has won the 2nd prize of the  16th Award of the Council of Doctors of the University of Barcelona.
• Hinds Instruments has anounced a first commercial version of the 4-PEM Mueller matrix polarimeter we have developed [see the original publication here]. They have named it the 150XT Mueller Polarimeter

Last year I spent a lot of my time to build the instrument reported in this paper. It is one of  the bests polarimeters/ellipsometers to date, because it measures simultaneously the 16 elements of a Mueller matrix without any moving part.

• Oriol Arteaga, John Freudenthal, Baoliang Wang, and Bart Kahr, “Mueller matrix polarimetry with four photoelastic modulators: theory and calibration,” Appl. Opt. 51, 6805-6817 (2012)

You can get it here.

More exciting instrumental things should be coming soon!