Phase and polarization: from Fresnel-Arago interference Laws to metasurfaces

I am sharing here the slides of a presentation I did for the course Séminaires en sciences physiques, from Université de Moncton, in Quebec, Canada.

Phase and polarization are the two main actors of this presentation. The ‘phase’ describes the cyclic change of electric and magnetic fields during one period of the wave, while the ‘polarization’ describes the shape and orientation of the path traced by the electric field during one period. This presentation will look back into two historical experiments that made revolutionary steps for understanding the interference of polarized beams of light, but that are often omitted in textbooks of current use. The first experiment is from the early XIXth century and served Fresnel and Arago to define their laws of interference. The second experiment is from mid XXth century when S. Pancharatnam pioneered the unintuitive concept of geometric phase to explain the results of his apparently simple interference experiments in crystals. Finally, we will study the ever-lasting influence of these experiments in modern research, especially in the novel designed metasurfaces for photonics applications.

Henri Poincaré Webinar Series on Optical Polarization and Related Phenomena

I got involved in the committe of this new webinar series that has been promoted by Thomas Germer.

This series of webinars will bring together an international audience interested in exploring topics associated with optical polarization and related phenomena. Monthly webinars will be presented by leaders in the field, and ample time will be provided for live discussion of the topic. Initiated during the COVID-19 pandemic, the series will attempt to replicate as much as possible the dynamics of in-person conferences.

More information is available and you can join there the mailing list.


The scheduled initial speakers are:

•            September 29, 2020 – 1500 UTC – Miguel Alonzo (Institut Fresnel)

•            October 27, 2020 – 1300 UTC – Federico Capasso (Harvard University)

•            November 24, 2020 – 1300 UTC – Frans Snik (Universiteit Leiden)

•            December 29, 2020 – open

•            January 26, 2020 – 1300 UTC – Bart Kahr (New York University)

Henry Poincaré did many things in Polarization Optics but AFAIK he never draw his famous Sphere.

2020 OSA Outstanding Reviewer Recognition

I have mixed feeling about journal reviewing. I generally like it, but it certainly takes a lot of time and it is not always the case that you feel that this time is truly profitable. So I think it is good that at least journals make some sort of recogniztion to reviewers. This year I have received from OSA the Outstanding Reviewer Recognition. The OSA Outstanding Reviewer recognition is given annually to commend the top reviewers for their outstanding peer review efforts over the past year.

The dramatic event in the life of Paul Soleillet

In my research for more bibliographic information about Paul Soleillet I have found some additional information about the “drame familial” (family drama) mentioned by Jean Claude Pecker in his bibliography.

This happened in December 1931 when P. Soleillet was 29 years old.

Jean Claude-Pecker, told me he had the opportunity to meet Soleillet (“homme charmant et discret” according to his words) when Soleillet was working with Daniel Chalonge. However he was unable to send me a picture of him (Jean Claude-Pecker is 96 years old) . My search has been completely unsuccessful and, apparently, there are no traces of him at any of the institutions he worked. He remains as a misterious man.

Completing an experimental nondepolarizing Mueller matrix whose column or row is missing [code provided]

During the last months I have been working with Razvigor Ossikovski in a method to complete an experimental Mueller matrix with a row or column missing into a full Mueller matrix in situations where is no depolarization. Thus this method converts a 12-element partial Mueller matrix into a 16-element Mueller matrix. We are talking about these type of incomplete matrices, which are rather common in many ellipsometers/polarimeters:

The code we propose has many advantages over other approaches we have tested because it is algebraic (no fitting involved), numerically very robust and very fast. The details of the method are given in the following two papers (specially in the first one):

In this post we include a simple Matlab script that applies our method to a single 12-element partial Mueller matrix. Feel free to use this script adapting it to your needs. But please cite it!

The Fresnel Triprism and the circular polarization of light

Last year I talked many times about the Fresnel triprism in this website. Recently our research work about this composite prism was published in Optics Express where we make an analogy with the famous Stern-Gerlach experiment.

Almost at the same time, we have published a more divulgative report about the history of the Fresnel Triprism in a special issue of the journal Photoniques from the French Optical Society I hope it is an interesting reading for you.

A summary of recent activities

As I do not update this site very often, it is worth to make a very quick summary of recent reseach-related activities I have done:

BIOAM Conference

In October I attended the “2nd International Workshop on Biophotonics and Orbital Angular Momentum” (BIOAM-2018). My talk was titled “Separating photons by spin with the method of A. Fresnel“.

Fresnel’s Triprism

My talk in the BIAOM conference was mainly devoted to something I already mentioned in this blog: the Fresnel triprism.  Since I published that post, I got more and more interested in Fresnel’s alternative method to generate circularly polarized light. I should comment two relevant things that boosted my interest:

  • Fresnel’s original memoir from 1822 is very interesting and easy to read (you can find it in Fresnel’s Ouvres Completes). It is mostly a descriptive  work that I am not sure it has been fully appreciated.
  • I was able to find and use a Fresnel’s polyprims! I found it in the Museum of the École Polytechnique, that was recently inaugutared. Even more surprising was to discover that it was not a triprism, as I assumed when I saw it for first time, but an octoprism! (featuring eight quartz prisms of alternating handedness) and more than 150 years old!.

In our preprint, you can find more information  about the experiments we did and other findings related to  Fresnel polyprisms

Trip to China

  • In November I visited the group of Prof. Shiyuan Liu in the Huazhong University of Science and Technology (in  Wuhan, CHINA). They are doing a really impressive work in ellipsometry instrumentation and optical metrology. They have created a spin-off company E-optics that is commertiallizing several of the ellipsometers that they have developed.
  • During the trip to China I also attended to the 3rd China Symposium on Polarimetry an Ellipsometry, held in Shenzhen, China. This was mainly a chinese conference but a few international speakers giving plenary talks. My talk was titled: “Complete Mueller matrix from a partial polarimetry experiment“. This topic of research is part of an on-going collaboration work with Razvigor Ossikovski (École Polytechnique, France).

New paper: Light scattering by coupled oriented dipoles: Decomposition of the scattering matrix

In this paper we study the optical response of two coupled oriented dipoles with the dimer axis perpendicular to the wave vector of light by analyzing how their scattering matrix can be decomposed. The scattering matrix can be written as a linear combination of three terms with a clear physical meaning: one for each particle and another that is responsible for the coupling and that vanishes for noninteracting or distant particles. We show that the interaction term may generate optical activity for certain scattering directions and that this effect manifests itself mostly in the near field. This simple and intuitive theory based on matrix and vector states of oriented dipoles also describes hybridization processes and Fano resonances. The decomposition method can be also formulated in terms of a hybrid basis that allows us to quantitatively determine the individual contribution of the in-phase and out-of-phase coupling modes to the overall intensity. Our method can help to understand the optical response of more complex nanostructures that can be decomposed into dipole terms. The results are illustrated in gold nanoantenna dimers which exhibit a strong dipolar resonance.

The paper is published in Phys. Rev. B an available at

Here you can get a preprint version

Download (PDF, 2.03MB)