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Optical activity in reflection

When I was a PhD student I remember  I often wondered  why circular dichroism (CD) was measured only in transmission.  At that time I was already familiar with ellipsometry measurements (in reflection) that are typically used to determine the dielectric function of materials and I did not understand why optical activity, arguably also a optical property of material, seemed to manifest transmission but not in reflection.

It took me some more time to realize that all was a mater of scale. I learned that optical activity can (in some occasions) have some effect on the specular reflection of light onto a surface but, this effect, was too subtle to be “seen”. The literature about this topic was very scarce, and this question was only properly analyzed in several helpful papers published by Mark P. Silverman in the 80s and 90s.

Last year I had the intuition that I would be able to sense optical activity in reflection if I chosed the adequate material and had the right instrument (I had it!). I discovered that this suitable material should have a large optical activity (this is not too surprising!) but also have a very anisotropic gyration (i. e. with its values changing a lot with the orientation). This is why I started measurements on a AgGaS2 crystal. All these steps eventually ended in this recently published paper: O. Arteaga, “Spectroscopic sensing of reflection optical activity in achiral AgGaS2,” Opt. Lett. 40, 4277-4280 (2015).

Fig. 5.

This measurement is more than an anecdotal verification of an idea because it proved to be also practical. It allowed the study of optical activity in spectral regions that cannot be studied in transmission.

A note on optical activity and extrinsic chirality

“Optical activity produces a differential absorption or refraction according to the handedness of circular polarized light, but the inverse is not necessarily true: a differential absorption of refraction of circular polarized light does not imply optical activity”

This simple statement has been sometimes overseen and there exist some confusion among researchers studying optical activity in several fields of science, from chemistry to material science.

Last year I  wrote a short comment addressing this topic and with the focus on metamaterials and nanostructures.  It was under consideration in Nature Photonics for a long time, but finally they decided that  this topic was already clear and had been discussed elsewhere. Just in case I make it now available as a preprint at:

Abstract: It has been assumed that optical activity can be measured by illuminating alternatively a material with left- and right- handed circular polarized light and analyzing the differential response. This simple and intuitive approach is in general incorrect, and has led to misleading idea that extrinsic chirality involves optical activity.

Evolving Mueller matrix microscopy

For over a year and a half I have been working on Mueller matrix microscopy.  Now I can say that I have no doubts that, when it is properly implemented, Mueller matrix microscopy is nothing but the perfect upgrade for polarization microscopy. I know polarization microscopy is not the most trendy technique in these days, but polarization microscopes are so widespread that even if only a tiny fraction of core polarization microscopy users become aware of what Mueller matrix microscopy can offer, the usage and the applications for Mueller matrix microscopy will grow exponentially.


Detail of the scale of a Morpho butterfly captured with a Mueller microscope.

With this objective in mind we have been working in the last few months on a compact, table-top prototype of a Mueller matrix microscope. The skeleton and the optics of the instruments are based on commercial polarization microscope, but it has been heavily modified to work as a fully-automatized Mueller matrix microscope. The aim was to keep all the advantages of polarization microscopy, with a very compact instrument in which it is very easy to manipulate the sample and find a focus but, at the same time, all the power of Mueller matrix analysis is just available after a “click”. The working principle of this Mueller microscope was described in Oriol Arteaga, et al. “Mueller matrix microscope with a dual continuous rotating compensator setup and digital demodulation,” Appl. Opt. 53, 2236-2245 (2014).


Photo of our benchtop Mueller matrix miscroscope. It is based on classic ZEISS Jenaval microscope that has been modified.

The project is being carried with the technical collaboration of  A.COLOMA Microscopios y Aparatos Ópticos and we work together to offer complete solutions for Mueller matrix microscopy. At this early stage, you can contact me ( or Francesc Gomez (  in case you are interested on getting a Mueller matrix microscope or if you would like to make a custom modification on your  polarization microscope.

 UPDATE! Click on the following image the pdf version of a presetation about MM microscopy that I did some time ago.


Happy New International Year of Light

It is time to welcome 2015. This New Year should be specially interesting for us since it is the International Year of Light and Light-based TechnologiesThe International Year of Light is a global initiative adopted by the United Nations to raise awareness of how optical technologies promote sustainable development and provide solutions to worldwide challenges in energy, education, agriculture, communications and health.


From this tiny spot I hope I can contribute with a grain of sand to these goals by showing how a property of light that we can not perceive, polarization, becomes our tool to investigate many properties of the world that surround us.

After a long time without updates, I have just renewed the design of the website. My New Year’s resolution should be to update this website much more often.

Summary of last activities

  • 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.


  • 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.


Analytic interpretation of Mueller matrices based on a continuous medium description

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 “”. 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


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’). **

**. 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.

Setember update

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.