_DSC0046.jpg

 

Optical properties of transition metal dichalcogenide monolayers: a new class of 2D semiconductors

 (See the article written in french for the journal of the "Société française de physique" here )

 

 

Since the discovery of graphene in 2004, many layered materials have been thinned down to a monolayer and proven to be stable in ambient conditions. Among these, monolayers of the MX2 family, where M is a transition metal atom (typically Mo, or W) and where X is a chalcogen atom  (S, Se, Te), have been shown to be direct band-gap semiconductors with emission in the visible-near infrared range. This makes them promising candidates for ultrathin electronic and opto-electronic devices. In addition, due to the particular bandstructure and broken inversion symmetry in these atomically thin crystals, the optical selection rules are chiral and electron-hole pairs can be selectively created in one of the two non-equivallent K valleys of the Brillouin zone. This could allow to store and process information via the valley index of carriers in these ideal 2D systems.

 

               Photoluminescence of TMD monolayers deposited onto SiO2 at cryogenic temperatures

 

As shown in the above Figure, the optical properties of these materials are dominated by excitons: bound electron-hole pairs with strong binding energy due to quantum confinement and weak screening of the Coulomb interaction. For all the members of the TMDC family, the photoluminescence spectrum at low temperatures exhibits well resolved neutral excitons (X) and charged excitons (T) peaks. However, for MoS2, which is particularly interesting due to it's abundance in nature (molybdenite), the spectrum which is usually reported in the litterature consistes of a single, very broad peak (50 meV linewidth) at around 1.9 eV that has been attributed before to the neutral exciton. This is in stark contrast with the spectrum shown  in the above figure, which suggests that the spectrum of monolayer MoS2 is actually similar to the ones observed for the other members of TMDC family, with well defined X and T peaks. Where does this discrepancy comes from?. As will be discussed below, it comes from laser induced-doping and degradation of the optical quality of MoS2 monolayers due to interactions with the SiO2 substrate.

 

What is the optical spectrum of monolayer molybdenum disulfide (MoS2) ?

 

- Laser induced changes in optical properties of monolayer molybdenum dichalcogenides

While studying the optical properties of monolayer MoS2 and MoSe2 deposited onto SiO2 substrates, me and my colleagues at LPCNO (Toulouse) have discovered that laser exposure changes the photoluminescence spectrum of monolayers in a non-reversible way. This happens at power densities that so far have been considered to be non-destructive (fractions of µW with a laser spot size of about 1 µm). We have shown that after several minutes of laser exposure, the trion (charged exciton) emission increases while the neutral exciton emission decreases, suggesting a laser induced doping of the monolayers. This is shown in the top pannels of the following figure; the spectra as a function of excitation power reveals an increase of the trion emission in both MoS2 and MoSe2 monolayers. When going back to the lowest power excitation, the PL shape has significantly changed (bottom pannels).

     

 

Interestingly, in MoS2 monolayers the neutral exciton emission can be totally quenched when exposed to a laser of enough power. When this happens, the photoluminescence spectrum of MoS2 at low temperature consists of a broad peak at 1.9 eV followed by a small low energy emission (see blue curve below). This is the most common PL spectrum of MoS2 found in the litterature. This broad peak has been attributed before to the neutral exciton emission. In reality, it lies at a much lower energy than that of the exciton, which is found to be around 1.96 eV previous to high laser exposure. The figure below shows the PL spectrum of a MoS2 monolayer before (red curve) and after (blue curve) being exposed to a pulsed laser with an average power of several tens of µW. Note that both spectra have been obtained for the same monolayer under identical conditions, revealing that the optical properties of this monolayer has been changed in a non reversible way.

 

 

The exact microscopical mechanism by which laser exposure changes the optical properties of TMD monolayers still needs to be clarified, but it seems clear that the SiO2 substrate plays a key role. Indeed, by inserting a buffer layer of hexagonal boron nitride (h-BN) between the silicon substrate and the monolayer, the effects of laser exposure are dramatically reduced. The most immediate consequence of these findings is that in order to study the intrinsic properties of excitons in MoS2 (and other members of the TMD family), very low excitation power densities should be employed if the monolayers are directly in contact with SiO2. In many cases, experiments are performed with pulsed lasers, in which case the peak power densities can be easily larger than the ones required to change the optical response of these materials.

 

See the full article here (published in 2D Materials)

 

 

 

- Valley coherence and valley polarization in MoS2 monolayers

It has been shown recently that treating MoS2 monolayers with an organic superacid (TFSI) can increase the photoluminescence quantum yield up to nearly 100% at room temperature (see here). We have employed this technique and performed photoluminescence spectroscopy at T= 4 K on MoS2. We show that this treatment reduces the localized emission induced by defects on the monolayer, and together with the use of very low excitation power, we were able to obtain very well defined neutral exciton (X) and trion (T) peaks at 1.96 eV and 1.93 eV, respectively. Since the majority of published MoS2 spectra consist of a single broad peak at 1.9 eV, we have performed polarization resolved photoluminescence in order to confirm the correct identification of both peaks.

When excited with circularly polarized light, only one of the two non-equivallent K valleys of the Brillouin zone will be occupied, and at steady state both excitonic complexes exhibit partially circularly polarized emission (see figure below). The very sharp peak at 1.88 eV correspond to a Raman peak (the laser energy is 2.1 eV in these experiments). Note that the low energy emission, possibly related to localized excitons, is unpolarized.

 

 

When excited with linearly polarized light, which is a mixture of right and left circularly polarized photons, a coherent superposition of excitons is created in both valleys (valley coherence). As a consequence, the neutral exciton emission is linearly polarized in the same axis of that of the incident laser (see figure below). As expected, the trion complex presents no linear polarization.

 

See the full article here (published in Applied Physics Letters)

 

 

- Approaching the homogeneous linewdith in MoS2 based Van der Waals heterostructures

Recently, we have shown that encapsulating TMDC monolayers with few-layer hexagonal boron nitride (h-BN) allows to access the intrinsic, high optical quality of these 2D crystals. Indeed, we observe an excitonic linewidth as low as 2 meV at low temperatures (see figure below), which is more than one order of magnitude narrower than the typically broad peak that has been attributed to the neutral exciton in the past. In addition, no signature of charged excitons is visible in the photoluminescence spectra. This spectacular improvement can be due to several reasons:  the capping layers act as a barrier to charge transfer from the SiO2 substrate to the monolayers, and it also avoids any transfer of the substrate's roughness to the MoS2.

 

 

As shown in the figure above, excitation with a circularly-polarized laser 25 meV above the exciton resonance  results in a high degree of circular polarization at steady state (35%), whereas using a linearly polarized laser results in robust valley coherence as evidenced from  the high degree of linear polarization of the exciton peak (55%).

Applying a perpendicular magnetic-field results in a Valley Zeeman effect and a rotation of the linear polarization of the luminescence, which is a key result in what concerns the possibility of manipulating a coherent superposition of valley states in these promising 2D systems.

 

See the full article here (published in Physical Review X)

 

 

 

 

PhD thesis: Spin-dependent electron transport in semiconductors.

 

I did my PhD in the Electrons-Photons-Surfaces group at the Condensed matter physics laboratory of the Ecole polyechnique,

under the supervision of Daniel Paget and Alistair Rowe. 

My thesis work was funded by the Gaspard Monge international grant.

 

To get the manuscript of my PhD thesis, click here.

 

 

 

I am an assistant professor at the physics department of Ecole polytechnique, where I teach/have teached the following courses:

 

Ingénieur polytechnicien program

- 1st year

2017- PHY301 Formation préparatoire (quantum and wave mechanics), petites classes.

- 2nd year

2017-2018 responsible of the option PHY47XA "Plasma physics and elementary particles",

2017- Teaching of the modal "Laser-generated plasmas"

2017- Team leader of France in the International physicist's tournament (2nd place in 2018).

- 3rd year

2017 PHY582 "Current trends in materials science", 1 invited lecture (3h)

 

Bachelor program

- 1st year

2018- PHY104 Physics II: Electromagnetism and Light (TD)

2017- PHY106 Beginner's lab II (2nd semester)

- 2nd year

2018- PHY203 Advanced lab I (3rd semester)

 

 

01- El campo eléctrico, ley de Coulomb  PDF

02- Ley de Gauss PDF

03- Potencial electrostatico PDF

04- Electrostatica de conductores, ecuacion de Poisson PDF

05- El campo en medios dieléctricos PDF

06- Electrocinética PDF

07- El campo magnético, ley de Biot-Savart PDF

08- Ley de Ampère, ley de Gauss magnética PDF

09- Magnetismo en la materia PDF

10- Ley de induccion de Maxwell-Faraday PDF

11- Ecuaciones de Maxwell, ondas electromagnéticas

 

 

Spin-dependent electron transport in semiconductors.

 

I did my PhD in the Electrons-Photons-Surfaces group at the Condensed matter physics laboratory of Ecole polytechnique, under the supervision of Daniel Paget and Alistair Rowe.  

My thesis work was funded by the Gaspard Monge international grant.

 

To get the manuscript of my PhD thesis, click here.

 

 About spintronics

Current technologies are based on electronics for transmitting, processing and receiving information. It is the movement of electrons inside semi-conductors (like Silicon) that is used as a way of representing and transferring digital information. The transistor, invented in 1948, is the fundamental component of processors, having two states of operation (representing a "1" or a "0" ) according to the resistance that opposes to the movement of electrons across a channel. Nowadays, the miniaturization of electronic components have achieved a density of some millions of transistors over a squared millimeter! This has allowed to improve the speed and performance of electronical  devices for the last 60 years. However, the miniaturization of transistors is reaching some fundamental limits, for example because of the problem of evacuating the heat dissipated by currents on such a small surfaces.

The electron not only has a charge, but also another fundamental property called spin, which is a quantized physical quantity that can only have two values when a measurement is performed: 'up' or 'down'. It is therefore an excellent candidate to represent digital information!. Spintronics is an emergent technology whose objective is to use the spin of the electrons (and not only their charge)  to create new devices, with lower power consumption than our current transistors. 

 

Different physical processes are important to understand in order to conceive a spintronic device. First of all, we should be capable of aligning the electron's spin either in the "up" or "down" direction (we call this process "spin orientation") to represent information. In a non-magnetic semiconductor at equilibrium, the number of electrons with spin "up" and "down" are equal, we say that they are unpolarized. On the other hand, if all of the electrons have the same spin, then we say that they are 100 % polarized. After this spin orientation, we need to transport this information from one point to the other within the semi-conductor. For this, we need to consider the fact that the transport of charge and spin may differ strongly. Indeed, different spin transport phenomena have been demonstrated in the last 15 years, such as the spin-Coulomb drag and the Spin Hall Effect. The goal of my thesis was to better understand spin transport in semi-conductors by taking into account the Pauli principle.

 

 Spin transport and the Pauli principle

During my PhD, I studied diffusive transport of polarized electrons in Gallium Arsenide (GaAs). When a conduction electron moves inside the crystal, its momentum changes randomly because of the different scattering mechanisms that can affect its movement. The longer the characteristic time of scattering is, further the electron can diffuse and therefore separate from its initial position during its lifetime in the conduction band. In our experiments, electrons are excited in the conduction band and spin-polarized by the absorption of a circularly polarized laser beam, which is tightly focused in a surface of approximately 1/4th of a squared micron. Electrons diffuse over all directions during their lifetime in the conduction band, moving away from the excitation spot. When electrons leave the conduction band, they emit light whose circular polarization degree is proportional to the electronic spin polarization at the time of emission. I studied this luminescence coming from the spin polarized electrons. Thanks to a special microscope, it is possible to build an image of the spatial electron distribution, and at the same time, of their spin polarization as a function of space.

Typically, electrons loses their spin polarization as a function of time during their movement in the semi-conductor, because of different processes that can relax their spin orientation within and during scattering events. The figure below shows images of the spatially resolved spin-polarization for different excitation powers in p-doped GaAs at 15 K.  As the excitation power increases, the concentration of electrons in the conduction band also increases.

 

 

 

At weak excitation power (from 72 nanowatts to 0.45 milliwatts), the electron polarization is maximum at the position where they are originally excited by the laser spot, and then it exhibits a monotonic decrease as a function of the distance traveled by the electrons. Eventually, the information contained in the electron polarization is completely lost after some tens of microns.

However, we have shown that electron polarization can actually increase during diffusion, as long as the excitation power is high enough. This is a consequence of a fundamental quantum law, known as the Pauli exclusion principle, which says that it is impossible for two electrons to occupy the same quantum state (which is characterized by its wave function and its spin orientation). For a scattering mechanism to be effective, the final state should be available, which is generally true at low electron density. On the other hand, if the density of electrons with a given spin (for example, "up") is of the same order of magnitude than the density of accessible states  (approximately 1017 cm-3 in GaAs), then the final state during a scattering event will be probably occupied by an electron of the same spin, in which case this event is forbidden by quantum mechanics and won't happen. These spin "up" electrons will travel further than the spin "down" electrons, which are less in number. This explains the figures obtained at 1.89 and 2.55 milliwatts, in which we see a progressive increase of the spin polarization from the centre up to a distance of 2 microns. Eventually, the concentration of electrons at higher distances becomes again smaller than the concentration of available states, the spin polarization will start to decrease again as it  should.

Even though the Pauli principle has been known for almost a century, and its consequences have been observed in very different systems (chemical bonds, atomic gases, neutron stars), its effects on spin polarized transport in solids have never been explicitly observed until now. The experimental observation of this Pauli blockade is important because it should modify all of the other observed phenomena on spin polarized transport (such as the spin hall effect) at high electron density. The next step would be to explore lower dimensional systems (quantum wells or nano-wires), in which this effects should be stronger because of the quantum confinement of electrons.

 

 

More information:

Effect of Pauli Blockade on Spin-Dependent Diffusion in a Degenerate Electron Gas

Phys. Rev. Lett. 111, 246601 - Published 9 December 2013

F. Cadiz, D. Paget, and A.C.H. Rowe

 

On the press: 

Researchers in the Condensed Matter Physics Laboratory (École polytechnique / CNRS) have revealed a new spin filter effect in semiconductors 

Press release, published December, 2013 

 

Oral presentations:

Spin-dependent transport as a consequence of Pauli blockade in a degenerate electron gas. 

F. Cadiz, SPIE Optics & photonics, San Diego convention center, 17th-22nd August, 2014

 

Spin/Charge coupled transport in GaAs in the Pauli blockade regime.

A.C.H. Rowe, Condensed matter in paris, 24th-29th August, 2014

 

 

Here is a video of drift and diffusion of photoelectrons in a Hall bar resolved by microluminescence imaging.

 

 

 

 

Joseph-Louis LAGRANGE 

(1736-1813)

Professor of mathematics and mechanics

1794-1799

Lagrangian mechanics

Celestial mechanics

 

Jean-Baptiste BIOT

 (1774-1862)

Promotion X1794

Biot-Savart law

Light polarization

Optical activity, polarimetry

 

Louis POINSOT

(1777-1859)

Promotion X1974

Assistant professor of analysis

and mechanics, 1809-1812

Admission examiner

Inventor of geometrical mechanics

 

Etienne-Louis MALUS

 (1775-1812)

Promotion X1794

 Malus's law

 Light polarization by reflection

 

Jean-Baptiste Joseph FOURIER

 (1768-1830)

Professor of mechanics

1795-1797

Fourier seriesFourier transform

Heat equation

 

Pierre-Simon LAPLACE

(1749-1827)

Mathematics examination

1796-1798

Laplace's equation

Laplace transform

 

 Louis-Joseph GAY LUSSAC

 (1778-1850)

Promotion X1797

Professor of chemistry

1810-1840

 Gay Lussac's law

Properties of gases

Chemistry

 

Siméon Denis POISSON 

(1781-1840)

Promotion X1798

Professor of mathematics 1806-1815

Mathematics examination 1815-1840

Foundations of Electricity and Magnetism

Poisson's equation 

Theory of elasticity

Poisson's ratio

 

Adrien-Marie LEGENDRE 

(1752-1833)

Mathematics examination 1799-1815

           

Legendre polynomials

Legendre transformation

 

Pierre Louis DULONG 

(1785-1838)

Promotion X1801

Professor of chemistry 1820-1829

Specific heat capacity

Dulong-Petit law

Expansion and refractive index of gases

 

Claude Louis Marie Henri NAVIER 

(1785-1836)

Promotion X1802

Professor of mathematics and mechanics

1831-1836

Fluid mechanics

Navier-Stokes equations

 

François ARAGO 

(1786-1853)

Promotion X1803

Professor of mathematics

1810-1830

Wave theory of light

Arago spot

First observation of

eddy currents

Fresnel-Arago experiment

 

Augustin Jean FRESNEL

 (1788-1827)

Promotion X1804

Foundations of wave optics

Fresnel equations

Huygens-Fresnel principle

Fresnel lens

Fresnel-Arago experiment

 

Augustin-Louis CAUCHY 

(1789-1857)

Promotion X1805

Professor of mechanics 1816-1830

Founder of complex analysis

Cauchy's integral theorem

Mechanics

Cauchy stress tensor

 

Antoine-César BECQUEREL

(1788-1878)

Promotion X1806

 

Photovoltaic effect

Diamagnetism

 

 

Jean Victor PONCELET

(1788-1867)

Promotion X1807

Commanding general of Ecole Polytechnique, 1848-1850

Poncelet-Steiner theorem

Poncelet's porism

 

 

Alexis Thérèse PETIT 

(1791-1820)

Promotion X1807

Professor of physics 1814-1820

Specific heat capacity

Dulong-Petit law

 

Gaspard-Gustave CORIOLIS 

(1792-1843)

Promotion X1808

Tutor 1816

Director of studies 1838-1843

Movement on rotating frames 

Coriolis effect

 

André-Marie AMPERE 

(1775-1836)

Professor of mathematics and mechanics

1809-1828

Founder of Electrodynamics

Ampere's law

Ampere's force law

 

Nicolas Léonard Sadi CARNOT 

(1796-1832)

Promotion X1812

 Founder of thermodynamics

Carnot heat engine

Carnot cycle

Second law of thermodynamics

 

Jacques BABINET 

(1794-1872) 

Promotion X1812

Diffraction optics

Babinet's principle

Babinet-Soleil compensator

 

Gabriel LAME 

(1795-1870)

Promotion X1814

Professor of physics 1832-1843

Mathematical theory of elasticity

Lamé parameters

Partial differential equations

Lamé function

 

 

Jean Léonard Marie POISEUILLE

 (1797-1869)

Promotion X1815

Fluid mechanics

Poiseuille law

 

Benoît Paul Emile CLAPEYRON 

(1799-1864)

Promotion X1815

Founder of thermodynamics

Clausius-Clapeyron relation

 

Henry DARCY

 (1803-1858)

Promotion X1821

Hidraulics

Darcy's law

Darcy-Weisbach equation

 

Joseph LIOUVILLE 

(1809-1882)

Promotion X1825

Professor of mathematics and mechanics

1839-1850

Hamiltonian mechanics

Liouville's theorem

Differential equations

Sturm-Liouville theory

Complex analysis

Liouville's theorem

 

Auguste BRAVAIS 

(1811-1863)

Promotion X1829

Professor of Physics 1845-1856

Founder of crystallography

Bravais lattices

Bravais law

 

 

Pierre Alphonse LAURENT

(1813-1854)

Promotion X1830

 

Laurent series

 

Henri Victor REGNAULT

 (1810-1878)

Promotion X1830

Inventor of PVC

 

Urbain LE VERRIER

 (1811-1877)

Promotion X1831

Professor of geodesics, astronomy and machines                               

1837-1851

Celestial mechanics

Mathematical prediction of the existence of Neptune

Discovery of Neptune

 

Jean-Augustin BARRAL

 (1811-1877)

Promotion X1838

Discovery of Nicotine

 

Jacques Charles François STURM

 (1803-1855)

Professor of mathematics and mechanics

1840-1855

Sturm's theorem

Sturm-Liouville theory

 

Charles HERMITE

 (1822-1901)

Promotion X1842

Professor of mathematics 1869-1876

Number theory, algebra, 

orthogonal polynomials

Hermite polynomials

Hermitian operators

 

 

François Jacques Dominique MASSIEU

 (1832-1896)

Promotion X1851

 

Thermodynamic potentials

Characteristic functions

 

Jules JAMIN

 (1818-1886)

Professor of physics 1852-1880

 

Jamin interferometer

 

 

Edmund Nicolas LAGUERRE

 (1834-1886)

Promotion X1853

Tutor

Geometry and complex analysis 

Laguerre polynomials

Laguerre's method

 

Marie Ennemond Camille JORDAN

 (1838-1922)

Promotion X1855

Professor of mathematical analysis 1876

Group Theory

Jordan curve theorem

Jordan matrix

Jordan-Holder theorem

 

Marie Alfred CORNU 

(1841-1902)

Promotion X1860 

Professor of physics 1867-1902

Optics and spectroscopy

Cornu spirals

Cornu depolarizer

 

Emile VERDET

(1824-1866)

 

Professor of physics 1862-1865

Faraday effect

Verdet's constant

 

Henri Louis LE CHATELIER

(1850-1936)

Promotion X1869

Chemistry

Le Châtelier's principle

 

Pierre-Henri HUGONIOT 

(1851-1887)

Promotion X1872

Assistant professor 1884

Fluid mechanics

Shock waves

Rankine-Hugoniot conditions

 

Antoine Henri BECQUEREL 

(1852-1908)

Promotion X1872

Professor of physics 1885-1908

Discovery of radioactivity 

Physics nobel prize 1903

 

Henri POINCARE 

(1854-1912)

Promotion X1873

Professor of mathematical analysis 1883-1897

Theory of special relativity

E= mc^2 

Poincaré conjeture

Poincaré group

 

Paul VIEILLE

(1854-1934)

Promotion X1873

Professor and examiner, 1882-1913

Smokeless powder

Detonation

 

Léon Charles THEVENIN 

(1857-1926)

Promotion X1876

Electrical circuits 

Thévenin's theorem

 

Alfred PEROT 

(1863-1925)

Promotion X1882

Professor of physics 1908-1925

Optics

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History

 

Georges FRIEDEL

 (1865-1933)

Promotion X1885

Crystallography

Friedel's law

Friedel's salt

Liquid crystals

 

Maurice Paul Auguste Charles FABRY 

(1867-1945)

Promotion X1886

Professor of physics (1927-1935)

Optics

Fabry-Pérot interferometer

History

 

Alfred-Marie LIENARD 

(1869-1958)

Promotion X1887

Electrodynamics

Liénard-Wiechert potential

Liénard-Chipart criterion

 

Emile JOUGUET

(1871-1943)

Promotion X1889

Professor of Mechanics, 1927-1941

Thermodynamics and hydrodynamics

Shock waves

Chapman- Jouguet condition

 

 

 

André-Louis CHOLESKY

 (1875-1918)

Promotion X1895

Cholesky decomposition

 

Paul Pierre LEVY 

(1886-1971)

Promotion X1904

Professor of mathematical analysis 1920-1959

Probability theory

Martingale

Lévy process

 

 

Louis LEPRINCE-RINGUET 

(1901-2000)

Promotion X1920

Professor of physics 1936-1969

Nuclear physics

Leprince-Ringuet laboratory

 

Albert MESSIAH

 (1921-2013)

Promotion X1940

Quantum mechanics

 

Jacques FRIEDEL

 (1921-2014)

Promotion X1942

Materials science

 

André LAGARRIGUE

 (1924-1975)

Promotion X1944

Gargamelle experiment (CERN)

Discovery of neutral currents

 Weak interaction

 

Benoît MANDELBROT

(1924-2010)

Promotion X1944

Fractals

Mandelbrot set

 

 

Maurice BERNARD

(1928)

Promotion X1948

Assistant professor 1956-1973

Professor of physics 1973-1980

Directeur de l'enseignement et de la recherche 1983-1990

Bernard-Duraffourg conditions

Semi-conductor lasers

 

 

Laurent SCHWARTZ 

(1915-2002)

Professor of mathematical analysis 1959-1980

Theory of distributions 

Fields medal

 

Ionel SOLOMON

(1929-2015)

Promotion X1949

Professor of physics 1965-1978

Nuclear magnetic resonance

Solomon equations

 

Georges DURAFFOURG

(1933-2016)

Promotion X1952

Laser conditions in semiconductors (Bernard-Duraffourg conditions)

 

 

Marcel FROISSART

(1934-2015)

Promotion X1953

Froissart bound

 

Serge HAROCHE

Professor of physics

1973-1984

Physics nobel prize 2012

Quantum decoherence

 

Gerard MOUROU

Director of LOA 2005-2009

Professor and member of Haut collège de Polytechnique

Physics Nobel prize 2018

 

Alain ASPECT

Professor of physics

1984-

Violation of Bell's inequality

Quantum optics

 

Emmanuel ROSENCHER

(1952-2013)

Promotion X1972

Professor of physics (1992-2013)

Opto-electronics

 

 

See a complete list of famous polytechniciens here.