Marcel Urban

A particle mechanism for the index of refraction

We propose to go away from the electromagnetic wave description of light and to explain through a purely corpuscular and neutral approach, the phenomenon of the slowing down of light in a transparent medium. The quantum predictions and ours are compared against experimental refractive indices. In our framework the optical Kerr phenomenon finds a very natural interpretation and its numerical values are obtained easily.

Introduction

Leon Foucault showed experimentally [1] that light slows down in water with respect to vacuum. More generally visible light velocity is reduced in transparent media. In a homogeneous material this is described by a single constant: the index of refraction n, which is the ratio of the velocity of light in vacuum to its velocity in the medium. Molecules have energy states quantized and in a gas these states are very well separated as opposed to solids where they can merge and form continuous bands. A photon propagating through a gas is absorbed by a molecule only if its energy corresponds to an allowed difference of energies in this molecule. For instance if the first excited state is 10 eV above the ground state, visible photons of a few eV should do nothing to these molecules. Why then do we have an index of refraction for a continuum of photon energies? Or put differently, how come a photon whose energy does not fit an atomic line can be influenced by the medium? We begin to recall the wave approach to the origin of the index of refraction. Then we propose another mechanism for the slowing down of the photons. The idea is to push the particle model of light as far as possible without using wave's properties. We describe our model of the interaction between a photon and a molecule in matter and we undertake a comparison between the two approaches. In this corpuscular framework, we predict that there will be a dispersion of the arrival times for mono energetic photons traversing a sheet of matter. This could have been already seen in 1987. Another benefit of the corpuscular approach is that we understand the optical Kerr phenomenon easily and that we derive its magnitude in gases and in condensed matter.

The usual explanation for the index of refraction

To the best of our knowledge there is only one explanation for the origin of the index of refraction and a clear description is made in [START_REF] Feynman | The Feynman Lectures on Physics[END_REF] and in [START_REF] Van De Hulst | Light Scattering by Small Particles[END_REF]. The first step considers an electromagnetic monochromatic plane wave falling on a sphere of dielectric whose diameter is very much smaller than the wave length λ . The electric field of the incident wave induces a vibrating electric dipole in the sphere which emits a spherical wave of the same frequency as the one of the incoming wave. This is the incoherent Rayleigh scattering on a single scattering centre. The downstream amplitude of the incident plane wave is slightly reduced but there is no change in its velocity. The second step considers a continuous slab of dielectric having a small depth and a large extension perpendicular to the axis of propagation of the plane wave. The slab of dielectric is decomposed into small volumes, as compared to , where the incident plane wave induces electric dipoles. These elementary vibrating dipoles emit secondary spherical waves according to the Rayleigh incoherent cross section. The reason to consider a very thin slab of matter is that the sum of these secondary waves on one particular elementary dipole is negligible compared to the incident light amplitude. The driving of the elementary dipoles is then proportional only to the amplitude of the incident light. All these secondary waves add up coherently downstream to the incoming light. The coherent integration of these secondary waves is phase shifted by 2 / π with respect to the incident wave. Since the thickness of the slab is small, the amplitude iA of this integration has a smaller modulus than the amplitude of the incident plane wave taken as 1. The sum, downstream, of the incident light and of the secondary waves takes the form 1+iA which is approximated as e iA . Thus instead of being 1 the incident wave is transformed into e iA which displays a phase shift interpreted as a delay in time due to a smaller speed in the slab of dielectric. This at last gives the index of refraction. The strength of the induced electric dipoles is given by their amount of polarisation under the influence of the incident electric field. This approach was envisaged for a continuous distribution of matter, and when the atomic nature of matter was established it became possible to have a microscopic model for the incoherent polarisation. At the same time we have the difficulty to go from a discrete to a continuum. The continuum is necessary in order to use the framework of the coherent integration producing the phase shift and thus explaining the index of refraction. The small dielectric sphere of the incoherent Rayleigh scattering is replaced by the molecule. The electric field of the incident wave sets the electrons in the molecule into a dipolar periodic motion and these electrons are supposed to reemit light spherically and at the same frequency as the one of the incoming wave. Any approach to the prediction of the index of refraction is based upon the calculation of the average electric polarisation of the molecule, produced by the incident electric field of the plane wave. Then, as soon as possible, go to the macroscopic polarisation. Once in the continuum theory framework the dielectric constant ε is obtained as a function of frequency and finally the index of refraction is predicted through the Maxwell formula:

. We will call this line of thought the Maxwellquantum framework. The semi classical and quantum predictions of the index of refraction can be found in textbooks [START_REF] Lorentz | The Theory of Electrons[END_REF]. The semi classical formula for the index of refraction of a photon of energy admits that the electrons in the molecule, behave like oscillators with discrete energies

γ E i W ∑ - = - i i i e E W N c r n 2 2 2 2 ) ( 4 1 γ π h elec i i N N = ∑ (3.1)
N elec is the number of valence electrons per unit volume and r e = 2.83 10 -15 m, is the classical radius of the electron.

∑ - = - i i i elec e E E f c N r n 2 2 2 2 ) ( 4 1 γ π h 1 = ∑ i i f (3.2)
If the ground state energy of the atom is W 0 then:

0 W W E i i - =
.

The hydrogen atom has E 1 = W 1 -W 0 = 10.2 eV. Therefore the Maxwell-quantum formula differs mainly in the characteristic energies E i which are smaller than the W i of the semi classical formula. In a condensed medium, Lorentz and Lorenz try to take into account the difference between the incident and the local electric field and suggest the following formula:

∑ - = + - i i i elec e E E f c N r n n 2 2 2 2 2 ) ( 3 4 2 1 γ π h (3.3)
So we understand that the mediums where we have a chance to predict correctly the index of refraction are the gases. However a surprise awaits us. All textbooks concerning the index of refraction theory spend a fair amount of pages and mathematics to first derive the semi classical formula (3.1) then the Maxwell-quantum formula (3.2) and yet no comparison with real data is made! They are in fact copying each other about this subject. A. Sommerfeld is an exception because he does compare, quickly, the classical formula with the experimental data on gaseous hydrogen [START_REF] Koch | [END_REF] and he recognises that 'the theory is still very crude…' Because of this copying we may as well go to one of the first textbook like H. A. Lorentz. Arriving more than half way through the book he states: "We could now enter upon a comparison of our dispersion formula with the measurements of the indices of refraction, but I shall omit this, because we must not attach too much importance to the particular form which we have found for the equations".

How bizarre! We will not know how well the final formula for the dispersion of light reproduces the measurements. This attitude is culminating in two review articles [START_REF] Breit | Quantum theory of dispersion[END_REF]. These are 120 pages about the different theoretical approaches which derive, with the help of quantum mechanics, the expression of the index of refraction. It is astonishing but there is not a single comparison between the theories and the indices of refraction data. We know of two attempts about helium gas [7]. The authors tried an unnatural extension of the formula (3.2) where the ionisation of the atom enters the sum as a continuum and dominates that sum.

Vinti supposes that the probability for the atom to be virtually ionised by a visible photon is 2.6 times larger than the probability to be excited. With Wheeler this ratio goes up to 3. Indeed, all measurements of refraction indices are summarized through old empirical formulas:

, around 1840, The physical origin for the reduced speed is thus very mathematical indeed, limited to dilute medium (but not too much), to plane waves established since the beginning of time and to molecules standing still. From this review we have to conclude that we lack of a proper interpretation of the slowing down of light in transparent mediums.

Our corpuscular approach

We propose a particle model for the index of refraction. It is based on a stop and go process. The photon has energy and is propagating through molecules in their ground state.

γ E Like in the Maxwell-quantum framework the molecules are described with quantum mechanics and they offer an infinite number of discrete excited energy states W i above their ground state W 0 .

The photon, on the contrary, is very different from what it is in the Maxwell-quantum framework. We describe it as a particle with energy and a direction of propagation. It has no spatial extension or, at least, it is smaller than the atomic dimensions. There is no frequency, no wavelength and no electric field associated with our photon.

Propagation through a gas

The photon borrows an energy

γ E E E i i - = Δ
in order to be absorbed by the molecule and to stop inside for a time:

i i E t Δ = Δ
h . After its stop, it gives back the energy i E Δ and it resumes its trip with the speed c, the vacuum velocity. We will thereafter summarize these possibilities into a single average > Δ < E to be borrowed and a corresponding average stop time <t stop >.

The stop time is given roughly by

A eV A eV t c stop & & 200 10 2000 = >= <
. It is therefore about 100 times as long as the time light takes to cross a few angstroms.

Let the mean free path between collisions be: Λ . The total average time to cross a distance Λ , is <t stop >+ , and the average speed V is

c / Λ 1 ) ( - Λ + > < Λ c t stop .
Finally, the refractivity is

Λ > < = - stop t c n 1 (4.1)
The photon has to propagate along a straight line and therefore the photon atom interaction is not an elastic process, otherwise the photon could be reemitted in other directions than the incident one. The process does not conserve energy anyway and it is reasonable to put back everything the way it was but for time. When the photon starts again it gets back the energy and the momentum that it had before the stop. The molecule stays still. Concerning the cross section for the photon to be absorbed momentarily by a molecule, we try the following:

. R is the radius of the molecule and

⊥ = ≈ ασ απ σ 2 R
α the fine structure constant characteristic of the low efficacy of light interactions. ⊥ σ is the geometric cross section of the molecule seen from the photon. The average volume that a molecule occupies is obtained from the mass density of the solid or the liquid, the mass of a mole and the Avogadro number.

The mean free path for a photon is then:

( ) 1 - ⊥ = Λ mol N ασ
. N mol is the number of molecules per unit volume. Finally our prediction for the refractivity is:

n -1 [ ] corpuscular = ασ ⊥ N mol hc f i E i -E γ i ∑ (4.2)
We simplify this formula by defining an average molecular excitation energy E AV such that

∑ - ≈ - i AV i i E E E E f γ γ 1
Then we get:

n -1 [ ] corpuscular ≈ N mol ασ ⊥ hc E AV -E γ (4.3)

Propagation through a condensed medium

The formula for the index of refraction in a condensed medium is going to be simplified with respect to what we have in a gas. In a crystal we have the molecules packed and touching each other. The numerical density of these molecules can be expressed in terms of the spacing between them. If we have three axes Ox, Oy and Oz and the corresponding spacings: . If the photon is propagating along Ox we have:

N mol = δ x δ y δ z ( -1
)

z y δ δ σ = ⊥ => x mol N δ α ασ = ⊥ γ γ δ α ασ E E c E E c N n AV x AV mol x - = - = - ⊥ h h 1 (4.4)
This shows that having a cross section in our index formula leads to sensitivity to the spacing in the direction of propagation. When the molecule is very asymmetrical and fixed in position like in a crystal, there will be a varying index with the direction of the light in the crystal. In the Maxwellquantum formula this does not happen because the number of valence electrons in a molecule does not depend upon the direction of propagation. This could be an important aspect of the physics behind the phenomenon of birefringence.

Questions to the Maxwell-quantum model

We list now five questions which are in fact criticisms to the Maxwell-quantum framework and which motivated the development of our corpuscular approach.

1-What happens to light going through a gas with, for instance, less than one molecule per 3 λ ?

This question concerns the limits in the use of the Maxwell theory of electromagnetism in macroscopic media. In our corpuscular approach the photon being a neutral object has no electric field and thus there is no problem since we do not use Maxwell theory of light.

2-What do we do for condensed mediums? This is linked to the local field not being the incident field. The light is considered to be a wave and has therefore a spatial extent. This question is coming about because of this extended aspect of light. In our approach there is no problem of local fields versus incident fields since we do not have fields.

3-If instead of an everlasting plane wave we envisage a more realistic burst of light it seems clear that a large part of the secondary waves will not have time to catch up with the incident light and will not therefore change the incident burst. Does the velocity appear to change as we move downstream? Again this is linked to the extended aspect of light in the classical theory and it disappears in our local photon theory.

4-If instead of steady we consider moving molecules like in the Fizeau experiment with running

water, then the molecules will reemit Doppler shifted waves with a frequency which will depend upon the angle of emission. Therefore the summation with the incident plane wave will be composed of different frequencies. Then the resulting apparent phase shift depends upon time! Is it reasonable to have an index of refraction which depends upon time? This is a mix between the extended aspect and the summing of the secondary wavelets to the main incident wave. We do not have the extended problem and our photons do not scatter, they keep going straight. Further it is well known that the Lorentz transformation applied to the photons in water gives back the results of Fizeau.

5-Is it reasonable to imagine that the atomic electrons reemit light of the same frequency as the incoming wave when we know that atoms in a gas emit lines and not a continuum? This is a very serious concern for the Maxwell-quantum framework. The way we see it in our approach is that since a photon does not possess an electric field it does not set the atomic electrons into a periodic motion. In its way through matter, a photon is either absorbed momentarily by the molecule or it ignores the molecule. In any case the molecules do not emit photons on top of the propagating one.

Comparisons between the Maxwell-quantum and the corpuscular expressions.

We will compare the two formulas (3.2) and (4.3) in gases. As we did for our corpuscular model we will approximate (3.2) by an average excitation energy E AV .

n -1 [ ] Maxwell ≈ N elec 2π r e (hc) 2 E AV 2 -E γ 2 (6.1) n -1 [ ] corpuscular ≈ N mol ασ ⊥ hc E AV -E γ (6.2)
The number density N elec of dispersion electrons is not the number of electrons in a molecule (14 for N 2 ) times the number density of molecules N mol . It is in fact the number of valence electrons: n valence times N mol . n valence is the number of electrons missing to get to 8, a complete shell. For instance in N 2 this is n valence = 2x3 = 6. Since we have:

valence n mol N elec N = n -1 [ ] Maxwell ≈ N mol n valence 2π r e (hc) 2 E AV 2 -E γ 2 (6.
3)

The two formulas (6.2) and (6.3) differ both in the constants and in the energy dependences.

Close to an atomic line

We can imagine that if we get close to an atomic line, E 0 , the data will show which form is right. In alkali vapours it is possible to get close to a line with visible light. For instance, within a few percent of the yellow doublet of Na, the data [8] are best fit with

n -1 [ ] data ∝ λ 0 λ -λ 0 m 6 0 10 589 . 0 - = λ , 0 0 2 E c h π λ = , γ π λ E c h 2 = n -1 [ ] data ∝ λ 0 E γ 2π hc -λ 0 E γ n -1 [ ] data ∝ -1 + 2π hc 2π hc -λ 0 E γ = -1 + E 0 E 0 -E γ
In [8] E γ is within a few percent of E 0 ,. We can therefore drop (-1) and we get

n -1 [ ] data ∝ E 0 E 0 -E γ
This is exactly our corpuscular formula.

The Maxwell-quantum formula does well also since

n -1 [ ] Maxwell ∝ 1 E 0 2 -E γ 2 ≈ 1 E 0 -E γ 1 2E 0
Thus the two formulas show the same energy behaviour close to an atomic line.

Far from an atomic line

Let us compare the constants when

E γ << E AV n -1 [ ] corpuscular ≈ N mol ασ ⊥ hc E AV -E γ n -1 [ ] Maxwell ≈ N mol n valence 2π e 2 m e c 2 hc E AV hc E AV -E γ
We treat the molecules exactly in the same way as in the Maxwell-quantum approach therefore E AV should be the same. If we want the refractivity to be the same we have to have:

γ γ π ασ E E c E c c m e r n N E E c N AV AV e e valence mol AV mol - ≈ - ⊥ h h h 2 2 2 AV e valence E c c m c n h h 2 2π σ ≈ ⊥ valence n
is a few units, and E AV is between 10 and 20 eV. These numbers imply that the radius of the molecule is a few Angstrom, which is correct. This shows that the two formulas are not orders of magnitude away from each other. However, in the next paragraph we show that, in order to reproduce the data, the Maxwell-quantum E AV has to be larger than the E AV of the corpuscular approach. Further, in the condensed phase, the Maxwell-quantum E AV is much larger than the typical excitation energies of the medium.

Comparisons to experimental data far from resonances

One problem with the light wave or Maxwell-quantum framework is the fact that there is no unique way to define the speed of a wave packet. At least five velocities can be defined for a wave packet: phase, group, front, signal and energy velocities [START_REF] Brillouin | Wave Propagation and Group Velocity[END_REF]. It has been shown experimentally [START_REF] Steinberg | [END_REF] that a single photon with energy far from atomic resonances, travels at the group velocity. In our corpuscular approach there is a statistical distribution of the number of stops but there is a single, definite, average velocity and it is, obviously, the photon velocity. Therefore our corpuscular formula (4.3) is to be compared with the group index data. The theoretical Maxwell-quantum index (3.1, 3.2 and 3.3) is obtained through the phase shift of the incident plane wave thus it corresponds to the phase index: n p . We determine the group index: n g , both for the Maxwell-quantum formula and for the experimental data, through the following relationship: We will consider the experimental data about Air and fused silica group indices.

Air

For many purposes like astronomy, GPS communications and light detection and ranging (LIDAR), the knowledge of the refractive index of air is very important. The number of measurements is large and this is the reason why we choose air as an example. The group index data are taken from [11] with the following conditions: dry air, 15°C, 450ppm CO 2 , 1013 hPa => N mol = 2.55 10 25 molecules/m 3 . In our corpuscular model we need to estimate the geometric cross section ⊥ σ of the air molecules. N 2 => 6 10 23 molecules weigh 28g and the liquid has a density of 808.6 kg/m 3 . A single molecule occupies a volume: 28/(6 10 23 8.09 10 5 ) = 57.7 10 -30 m 3 The transverse area is thus estimated as 4 / π (V N2 ) 2/3 = 11.7 10 -20 m 2 . O 2 => 6 10 23 molecules weigh 32g and the liquid has a density of 1141 kg/m 3 . A single molecule occupies a volume: 32/(6 10 23 11.41 10 5 ) = 46.7 10 -30 m 3 The transverse area is thus estimated as In th e M a x w e l l -q u a n t u m m o d e l we need the number density of the valence electrons. For N 2 , n valence = 2x3 and for O 2 , n valence = 2x2. For Air this will average to 0.8*6+0.2*4 = 5.6 valence electrons per air molecule. Then under our Air conditions we get: N elec = 14.28 10 25 valence electrons/m 3 . As for the corpuscular formula we try a one term approach with an average energy. The phase refractivity is then approximately

n P -1 [ ] Maxwell = 98.5 10 -3 E AV 2 -E γ 2
The energies E AV and E γ are in eV.

Then we make use of (7.1) to get the group index of the Maxwell-quantum approach. The figure 1, shows the Maxwell-quantum prediction with E AV = 16.7 eV. It is clear that it needs to be reduced. When E AV = 19 eV, the group index values are fine but the Maxwell-quantum curve is then too flat. We conclude that the two predictions for Air are not very different except that the Maxwellquantum formula demands the average excitation energy to be larger than in the corpuscular formula.

Fused silica

The data for synthetic fused silica, SiO 2 , were found in [12]. The weigh of 6 10 23 molecules is 60.1 g and the density at 25°C is 2200 kg/m 3 . Thus a molecule occupies a volume: 60.1/(6 10 23 22 10 5 ) = 45.4 10 -30 m 3 . In other words, there are 2.2 10 28 molecules per m 3 .

The spacing is:

, and the corpuscular prediction is δ SiO2 = 45.4 10 -30 ( )

1/ 3 m = 3.57 10 -10 m n gSiO2 -1 ⎡ ⎣ ⎤ ⎦ corpuscular = α δ SiO2 hc E AV -E γ = 4.08 eV E AV -E γ
In the Maxwell-quantum framework we use the Lorenz-Lorentz formula (3.3).

The number of valence electrons for SiO 2 is 4+2x2 = 8

The number density is: 2.2 10 28 *8 = 17.6 10 28 valence electrons/m 3 .

A E E E E n n AV AV P P = - = - = + - - - 2
n p -1 ⎡ ⎣ ⎤ ⎦ LL = 1 + 2A 1 -A -1
Lorentz explains in his book that formula (3.3) is not always working fine and that the old Laplace formula (3.2) is to be considered too because experimental data sometimes stand in between. So we will also draw the refractivity obtained with Laplace formula:

n p -1 ⎡ ⎣ ⎤ ⎦ Laplace = 1 + 3A -1
Then we calculate n g from n p with formula (7.1).

Figure 2. The fused silica group refractivity: n g -1, as a function of the photon energy in eV.

The figure 2, shows the data together with our simplified formula with E AV = 10.6 eV. The UV absorption band in SiO 2 begins at 0.15 m μ (8.2 eV) so an average excitation energy of about 10 eV is reasonable. Similarly to what we did with the Air data we show the Maxwell-quantum prediction with the same average excitation energy of 10.6 eV.

Clearly, in order to get a reasonable value for the silica refractivity, the Maxwell-quantum predictions need higher average excitation energy than for Air data. We have to plug a value of 17.3 eV for the average excitation energy in the Lorenz-Lorentz formula and 14.8 eV in the Laplace one. We understand now why Vinti and Wheeler had to weigh heavily the ionization energies in order to lower sufficiently the index of refraction of helium. We conclude by saying that the situation is bad for the Maxwell-quantum predictions in a condensed medium while it looks good for our corpuscular approach.

Distribution of the traversal times of a photon through a crystal

In our corpuscular model, the time, for a photon, to cross a given thickness of transparent matter is not a constant. The time dispersion is given by the statistical fluctuations of the number of photonmolecule encounters which lead to a stop.

In the Maxwell-quantum model the inverse of the bandwidth gives the coherence time which, multiplied by c, is considered as the length of the photon. The detection of a photon will occur along that length. This leads to a distribution of traversal times although it is independent of the matter being traversed. Independently of the model choosen, the dispersion of the index of refraction, roughly proportionnal to the dispersion in photon energies, does produce a scatter of the traversal times.

It turns out that we may already have a hint about these phenomenons in the results of a remarkable experiment [13]. A KDP crystal pumped with a 351nm laser was producing, through the parametric down-conversion effect, a signal and an idler photon. They were selected to have the same energy

( eV E E nm 8 . 1 700 0 ≈ = ⇒ = γ λ
) and sent on each side of a beam splitter. The time coincidences between the two outputs of the beam splitter were then registered as a function of the difference in path length. The boson character of the photons implies that when they arrive at the same time at the beam splitter and with the same energy, they leave the beam splitter in the same state. This means that they both end up in the same detector and the coincidence rate drops to zero. The width of the coincidence dip is interpreted as the time dispersion between the two photons in the pair. We examine now the possible origins for that time dispersion.

effect of the bandwidth

Interference filters of about 7nm were inserted both in the signal and in the idler path. As

f f Δ = = Δ 700 7 λ λ
we conclude that:

Hz f f 12 10 4 100 = = Δ
. This, if light is a wave, implies a time dispersion such that:

fs f t FWHM traversal 250 1 ) 1 , ( = Δ > γ
The experimental set up had also two pinholes that could have further restricted the energy dispersion of the photons and that explain why the FWHM could be larger. The time difference between the signal and the idler photon will be given by the folding of the two distributions. This leads to adding the variances and thus:

fs f t FWHM traversal 350 2 ) 2 , ( = Δ > γ 8.

effect of the dispersion

When the energy of the photon is such that:

ε ε γ + < < - 0 0 E E E
, the energy dispersion will change the traversal times as:

γ ε γ ε γ γ dE E dn c L E V L dE d t FWHM traversal ) ( 2 ) ( 2 ) ( = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =
The energy bandwidth is given by: 700 [13] The observed FWHM is 56fs but it has to be doubled because when the beam splitter moves so as to reduce one path length it increases at the same time, the other path. Further if the beam splitter is attacked with a 45° incident angle there is a further multiplicative factor 1/cos(45°). The real time FWHM turns out to be 56*2*1.414 = 158 fs. The effect of the bandwidth is predicted to be larger than 350 fs. The effect of the dispersion is less than 30 fs. The only effect which corresponds to the measurements is our statistical stop time prediction. We conclude that light does not seem to be a wave and that it may very well be that our prediction of the statistical distribution of traversal times has been already seen in 1987!

7 = Δ = Δ λ λ γ γ E E , eV E 018 . 0 < Δ

Understanding the optical Kerr effect

An intense beam of light produces, in a medium, an increase of its refractive index [15], [16], [17], [18], [19], [20]. This phenomenon has been observed in solids, liquids and gases and is known by the names of AC Kerr, optical Kerr or self focusing effect. This is usually expressed empirically with the formula:

. n

I n n n 2 0 + =
0 is the usual index of refraction at low light intensity I. The constant n 2 is comprised between 10 -20 m 2 /W for dense media and 10 -23 m 2 /W for gases.

The physics of the Kerr effect in our corpuscular approach

A photon crossing a molecule has a probability α to stop. If the photon stops and if we have, at the same time, α / 1 photons on top of the first, we will have on average two photons stopping in the molecule. The stop time for a photon is proportional to

E Δ / 1
where E Δ is the energy borrowed to get from to . These two photons need only borrow

γ E 1 E 2 2 1 γ E E - each.
When , this is roughly half the value for a single photon. Therefore they will stop for a time twice as long and since the refractivity: (n γ E E >> 1 0 -1), is proportional to the stop time, we expect a doubling of the refractivity. Thus when the density of photons is α / 1 in a molecular volume, the refractivity is roughly multiplied by a factor two. Let us consider visible photons of energy 1 eV propagating through water, and estimate the energy flux necessary to get such a density. A water molecule occupies approximately, a volume of 30 10 -30 m 3 . 3-the refractivity: n -1, is proportional to the number density of incoming photons and is also roughly proportional to the density of the medium. We understand therefore why n 2 is about 1000 times smaller for gases than for condensed mediums.

αρ

, will be absorbed together with a companion and this corresponds to a stop time of

γ γ E E E E t AV AV 2 2 2 / ) 2 ( 2 - = - = Δ h h
The stop time affects two photons.

] ) 2 ( 2 / / 1 2 2 1 1 2 2 1 2 1 t t N t N I E t E I N t E I N N t Δ - Δ + Δ = Δ + Δ - >= Δ < γ γ γ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ - - + - Λ >= Δ < γ γ γ αρ E E E E V E E L t AV AV molecule photon AV 2 2 3 1 h
The total time spent crossing the distance L is:

> Δ < + t c L / .
The average speed is thus

> Δ < + >= < t c L L V / and the index n, is c/<V>: ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ - - + - Λ = > Δ < = - γ γ γ αρ E E E E V E E c L t c n AV AV molecule photon AV 2 2 3 1 1 1 h γ ρ E I c n photon 0 =
We recognise our expression for the usual refractivity (see §4): This is in agreement with the experimental measurements [15], [16], [17], [18], which are between 0.5 and 5 10 -20 m 2 /W In Air:

, n It is a bit smaller than the experimental findings [19], [20], which scatter, with large errors, between 4 10 -23 and 12 10 -23 m 2 /W. We can understand that the effective area of the laser beam is not an easy quantity to measure. Finally the optical Kerr effect is not, in our point of view, connected to a non linearity of the interaction light-medium.

Conclusions

We have shown that the Maxwell-quantum framework does not satisfactorily explain the very basic phenomenon of the slowing down of light in a transparent medium. We showed that a corpuscular approach explains naturally this fact and that it leads to easy and satisfactory predictions of the refractive indices. In our approach there is no need to associate some frequency or wave length to the photon. We do not need either an electric field of the photon and this is fortunate because the photon being a neutral elementary object cannot be at the origin of an electric field. Indeed the only variables we need, in this approach, to describe the photon, are its energy, its direction of propagation and its dimension way smaller than the atomic sizes. Another difference with the usual electro-magnetic wave or Maxwell-quantum approach is the importance of the cross section of molecules to visible photons. The geometric cross section of a very asymmetrical molecule depends upon its orientation with respect to the direction of propagation of the photon. This allows our index to depend upon that direction of propagation. This is not possible in the Maxwell-quantum framework which is sensitive to the volume density of electrons independent of the direction of travel. In our model the measured speed of the photon which traverses a transparent material is a statistical process and we predict a Gaussian distribution of the crossing times. We believe that this prediction was present in the results of an experiment on photons from parametric down conversion. At last our corpuscular description leads to new viewpoints and for instance we understand and predict the magnitudes of the optical Kerr effect both in gases and in condensed matter.

ε = 2 n 3 .

 23 What is found in the literature?

.

  13.6 eV and W 1 = -3.5 eV. When the polarisation of the molecule is calculated with the quantum mechanics, we get what we call the Maxwell-quantum formula

  . Most of the time, two terms are enough to reproduce the data. Strangely enough the theoretical formulas (3.1), (3.2) or (3.3) are never used.

Figure 1 .

 1 Figure 1. (n g -1)*10 3 for Air, as a function of the photon energy in eV.

  photons = = = -

9. 2

 2 photons ρ

2 tΔ

 2 This leads to an average stop time which is given by:

[

  We can now calculate n 2 for different materials and compare with the experimental data. In water:

  This is linear with the thickness of the crystal and with the energy bandwidth of the photons.

																																	and	ε	<	0	.	009	eV
	Experimentally [14]:	n	KDP	(	E	γ		≈	2 eV	)	=	. 1	5	and	dn	KDP	( dE E γ γ	≈	2 eV	)	=	1	.	3	10	-	2	(	eV	)	1 -
																	t FWHM traversal (	)	86	10	12	L	ε
																				t FWHM traversal (	)	<	730	L	fs
	The length of the KDP crystal in this experiment is 8cm and the pair production is a rare
	process, thus the average thickness is <L> = 4cm. We end up with
																						t FWHM traversal (	)	<	30	fs
	8.3 effect of the statistics of the number of stops
	In our corpuscular model, the average number of stops follows a Poisson law.
	We will assume that	δ	KDP	≈		3	.	6	10	-	10	m		and	E AV 12 ≈	eV
	The average number of stops is:
															N	stop	=		Λ	L KDP	=	α	δ	L KDP	=	210	7	L
	And the average stop-time:
																<	t	stop	>=	E	AV	-h	E	γ	≈	18 60 -10	s
	FWHM	(	t	traversal	1 , γ	)	=	2	.	35	<	t	stop	>		N	stop	=	2	.	35	60	10	-	15	4	.	5	L	=	630	L	fs
	This is proportional to the square root of the thickness.
	Again with an average <L> = 4cm we have t FWHM traversal (	1 , γ	)	≈	120	fs
	We have to fold the two Gaussian distributions since we have two photons and this is
												t FWHM traversal (	,	2 γ	)	≈	2	120	fs	=	170	fs
	8.4 Comparison with the experimental result

γ -=

λ

Acknowledgements

I wish to thank my colleagues: Barrand G, Haïssinski J and Zomer F, for numerous and helpful discussions.


Yehya Nasser

Jean-Christophe Prévotet

Maryline Hélard

Maryline Hélard Power

Power Modeling for Fast & Early Power Estimation of FPGA-based Communications Systems

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


Maxime Berthou
email: maxime.berthou@gmail.com

Besar Asllani

Pierre Brosselard

Philippe Godignon

Cryogenic to High Temperature Exploration of 4H-SiC W-SBD

come

Introduction

W-SBD and JBS have shown high temperature capability and reliability for spacial applications [START_REF] Godignon | Industrial Electronics[END_REF] superior to Ni or Ti-SBD. Their higher barrier provides lower leakage current with similar commutation capability [2] compared to Ni barrier diodes. Thanks to its chemical properties and temperature stability, Tungsten barrier shows exceptional uniformity on 4H-SiC. Recent works have proven the role of defects [3] in the creation of microscopic areas of lower barrier height. These areas will later create leakage current paths or deteriorate the reliability of the device. Some of these defects are inevitable on 4H-SiC commercial wafers but they don't seem to have such impact on W-SBD as on Ni-SBD at room temperature.

Tested Devices

On an entire 1.2kV commercial wafers, the fabrication of 4 mm2 devices at CNM commonly yield more than 80% of good diodes. At room temperature, these diodes present a barrier height of 1.25 eV, ideality factor under 1.05 and leakage current under 10uA at 1kV. Two devices (A and B) were selected after cautious screening of double barriers and reverse capability for the measurement. They were made in different batches with similar fabrication technologies [2] except that the device A termination is made of two aluminium implantations to create the JTE and field stopper (see figure 1), and device B's uses one implantation to create the JTE. Device A and B drift thickness and doping are of 12 µm 5x10 15 cm-3 and 6 µm 10 16 cm-3 respectively. The difference of drift thickness will not change the barrier characteristics but its lower doping can have an impact.

Cryogenic measurement setup

Considering that BPD, TSD, etc. are in the density of more than 1000cm-2 on wafers of commercial quality, we theorized that the parallel barrier they cause is too close to the dominant barrier created by W/SiC interface and it is not perceptible in the IV curves at room temperature. In order to electrically characterize the Schottky barrier in a wide range of temperatures, we employed a cryogenic chamber under vacuum and cooled by liquid nitrogen presented in figure 2. This setup allows measuring the device from 81 to 500K with temperature precision of 1K. The electrical characteristics were captured with an Agilent B1505 equipped with high voltage, capacitance and current precision modules and connected to the device in the cryogenic chamber with coaxial cables. This tool allowed us to measure the forward current and leakage current with great precision down to 100pA, which is very important for barrier

Measurement results

Considering the theory [4,5], if the Schottky contact is composed of areas of different barrier heights with different ratios, they will be more distinguishable at lower temperature. Our cryogenic I-V measurements of the W-SBD devices, shown in fig. 1, did not evidence the presence of multiple barriers at low temperature. This characterizes high degree of barrier homogeneity. We then based our analysis on this device with barrier of high quality. Until now, the W-SiC barrier analysis was performed at room or higher temperature. On various articles, difference between measurements and theory on SiC-SBD have often been attributed to Tung's model [4,5]. Such study has never been performed on W-SBD at low temperature and using samples of such quality allows us to explore it.

Forward IV characteristics

For devices A and B, IV characteristics were measured from 81 to 500 K every 20 K as shown in figure 3 and4. We can see that no double barrier is perceivable down to 81 K, which shows its purity and presents an ideal case for barrier analysis from I-V curves. As the I-V curve evolves a lot with temperature, it is difficult to choose the voltage or current criteria to extract the different physical parameters such as barrier height (ΦB), ideality factor (η) and Richardson coefficient (A*).

Two methods were used and compared on the two devices; the first one consists in choosing several voltages around which to perform the regression and extract η and ΦB in order to sweep through the whole range of temperatures as shown in figure 5. The second one consists in choosing a current range, as shown by the greyed area in figure 3 and4, in which to perform the regression in order to measure η and ΦB for each temperature. The figure 5 shows the results obtained with the second method. We can see that the second method provides more uniform results and is more appropriate for this analysis. At temperatures under 250K, the barrier height decreases and the ideality factor increases, this effect is linked to the partial ionization effect which decreases the effective drift doping concentration and thus In the equation 2, partial ionization is neglected and taking it into account yields the equation 3; as the temperature decreases and N D + /N C decreases, the intersection with y axe should decrease, which is the phenomenon observed in figure 6 and reflected in the extracted Richardson coefficient in figure 7. This shows that the partial ionization phenomena must be taken into account for the analysis of the Schottky barrier at low temperature. More detailed studies of the theory behind this effect are currently performed to explain it scientifically.

Reverse IV characteristics

As the partial ionization may have strong impact on reverse characteristics, we measured it up to 1.2kV for device A (see figure 8) and 400V for device B (see figure 9) from 81 to 480 K. Both measurements have shown unusual effects at low temperatures. When temperature decreases below 260 K, we can observe an increase of the leakage current under 800V. As the barrier height decreases, the leakage current increases and this phenomena becomes dominant under 260 K. At higher voltage bias, we can note that the leakage current behaviour changes, as it is constant under 260K. This second phenomenon might be explained by the influence of depletion area on the partial ionization or termination issues due to interficial traps over the JTE. The partial ionization can explain the barrier degradation at low temperature shown in figure 5, which shows stronger effect on the barier height of Device A compared to Device B. If this hypothesis is valid, it may explain the leakage current behavior at low temperature. This phenomenon is less visible on device B as shown in (3)

(1) figure 9. The partial ionization can still explain the difference; as the impurity concentration is one order of magnitude higher, the partial ionization cannot lower the effective doping concentration as low as in device A and the barrier quality suffers less from it. Concerning the interficial traps over the termination, we know that their density increases at lower temperature and the leakage channel may be enhanced we the temperature decreases as shown in figure 8 and9.

Capacitive Measurements have been performed on device B to extract the effective drift layer concentration at different temperatures from 300 to 81 K as presented in figure 10. Taking the incomplete ionization equation from [6] and expressing it in function of the carrier concentration instead of the quazi-fermi level, we obtain the equation 3. In the depleted area, free carrier concentration tends toward 0 thus N D + increases toward N D,0 . Classical formula used here (see equation 4) to calculate of the doping concentration, does not take the partial ionization into account, which produces an increasing drift doping profile with voltage bias instead of a constant one.

Nonetheless, in figure 10, we can see the temperature influence on the measured effective drift doping as the doping stays constant from 300 down 260 K, then decreases and stabilizes at 140 K. This stabilization is questioning, further theoretical studies and more measurements are required to confirm and explain this phenomenon. However, these temperatures correspond well with the reverse leakage current temperature thresholds observed on both devices in figures 8 and 9.

Conclusion

Characterisations of W-SBD at cryogenic temperatures allowed us to study its barrier physics and fundamental parameters on an extended temperature range. High voltage measurements have evidenced the presence of a second current leakage mechanism and two hypothesis have been stated to explain it. Further measurements and analysis are required to validate one of the theories. Extracted doping concentration from capacitance measurement has also shown strong dependency with temperature and incomplete ionization can also explain such behaviour. All measurement tend to show that incomplete ionization has a strong impact of the different characteristics of the SiC device and taking it more into account may help better modelize the Schottky devices.

Fig. 2 -Fig. 1 -

 21 Fig. 2 -pictures of the measurement tool B1505 and cryogenic chamber employed for the study

Fig. 4 -Fig. 5 -Fig. 3 -

 453 Fig. 4 -Direct characteristics of device B on wide temperature range from cryogenic to high temperature conditions

Fig. 8 -

 8 Fig. 8 -Reverse characteristics of device A up to 1200V from 475 K down to 81 K

Acknowledgements

This study was funded by PEA-DGA MADASIC project.


Karypis Al Zoltan

Keywords:

High Performance Computing on distributed memory architectures.

To get an efficient code, one must:

1 balance the workloads of each processor 2 overlap or minimize communications 3 take care of memory accesses 4 exploit full processor characteristics We focus on the 1st and 2nd items. Direct application: multi-physics numerical simulations using 2D or 3D meshes.

Hypergraph model

Mesh

Dual Hypergraph H = (V, E) Our approach: Multi-level multi-criteria algorithm Refinement algorithm: Fiduccia-Mattheyses Key points:

cell c i vertex v i ∈ V
Move vertices according to their gain ("moves").

Avoid opposite moves: lock on the moved vertices.

When no more moves are possible: restore the best partition found.

If improvement: start a new "pass". Otherwise, end of the algorithm.

Algorithm 2 Fiduccia-Mattheyses algorithm

  weight vector of a cell weight vector of a vertex c i and its neighboring cells N i hyperedge e = N i ∪ c i ∈ E communicate c i means y communications weight y on the hyperedge corresponding to cell c i partitioning (mesh of 3500 cells) Multi-criteria partitioning (mesh of 3500 cells) Multi-criteria partitioning (mesh of 22800 cells)

  10/2016 | PAGE 5/18 Initial partitioning algorithm Problem: partition a set of vectors of numbers The vertices' weights alone are considered, not the hyperedges. Some algorithms exist in mono-criterion (number partitioning), but in our knowledge not in multi-criteria. Algorithm 1 Initial partitioning algorithm Require: V set of vertices, Π partition 1: b max ← max criterion c Imbal c (Π) until No more vertex move can decrease b max | 12/10/2016 | PAGE 6

  Restore the best partition reached in the pass 8: until No improvement on the best partition quality | 12/10/2016 | PAGE 8/18Refinement algorithm: Fiduccia-Mattheyses

Summary of the algorithm

2 By default, Scotch launches 2 independent runs and returns the best partition found.


Loïc Vial
email: loic.vial@imag.fr

Benjamin Lecouteux
email: benjamin.lecouteux@imag.fr

Didier Schwab
email: didier.schwab@imag.fr

UFSAC: Unification of Sense Annotated Corpora and Tools

Keywords: word sense disambiguation, sense annotated corpora, unified resource, tools

In word sense disambiguation, sense annotated corpora are often essential for evaluating a system and also valuable in order to reach a good efficiency. Always created for a specific purpose, there are today almost fifteen sense annotated English corpora, in various formats and using different versions of WordNet. The main hypothesis of this work is that it should be possible to build a disambiguation system by using any of these corpora during the training phase or during the testing phase regardless of their original purpose. In this article, we present UFSAC: a format of corpus that can be used for either training or testing a disambiguation system, and the process we followed for constructing this format. We give to the community the whole set of sense annotated English corpora that we know, in this unified format, when the copyright allows it, with sense keys converted to the last version of WordNet. We also provide the source code for building these corpora from their original data, and a complete Java API for manipulating corpora in this format.

Introduction

Whether they are used for the evaluation or for the learning process of a Word Sense Disambiguation (WSD) system, the importance of sense annotated corpora in Natural Language Processing (NLP) is considerable. On one hand, the evaluation in vivo, i.e. the evaluation of a WSD system as part of a larger task, has never been really exploited. On the other hand, the evaluation in vitro, which uses directly sense annotated corpora by comparing the output of a system to manual annotations, is predominant. Moreover, WSD systems exploiting examples from sense annotated corpora are generally far better than those which do not [START_REF] Navigli | Semeval-2007 task 07: Coarse-grained english all-words task[END_REF][START_REF] Moro | Semeval-2015 task 13: Multilingual all-words sense disambiguation and entity linking[END_REF]. At the time of its creation, WordNet [START_REF] Miller | Wordnet: A lexical database[END_REF] was undoubtedly the only lexical database freely available for English. Since the beginning of the 2000s, it has become the de facto standard for WSD in this language. Indeed, most of sense annotated corpora are either directly annotated with WordNet sense keys or they are annotated with a sense inventory linked to the senses of WordNet, such as BabelNet [START_REF] Navigli | Babelnet: Building a very large multilingual semantic network[END_REF]. However, it is not trivial to use these corpora, because most of them differ in their format and on the version of Word-Net they use. As a consequence, very few works in the literature of WSD are trained or evaluated on more than two annotated corpora. Also, WSD systems are systematically evaluated on corpora that have been initially created for the purpose of evaluation, and never on corpora that have been created for another purpose, such as training or for sense distribution estimation, whereas there is no scientific reason for that. This paper presents a work of unification of all existing English corpora annotated with any version of WordNet to our knowledge, in a unique format, easy to understand, and easy to work with in practice. We put on the same level the corpora originally created for the evaluation and those for the learning, so to facilitate the creation of robust WSD systems which could for example be evaluated in a way where all corpora except one are used for the learning, and the remaining one is used for the evaluation, then switch the corpora and do this for every existing corpus. The language resource that we provide contains all English sense annotated corpora in UFSAC (Unified Format for Sense Annotated Corpora), the format that we propose, with sense annotations converted to the last version of WordNet (3.0), along with Java code to easily read, write and modify any corpus in this format, and scripts for converting a corpus from its original format to UFSAC. Our work differs from the recent work of [START_REF] Raganato | Word sense disambiguation: A unified evaluation framework and empirical comparison[END_REF] in several points. Their work is more about the evaluation of WSD systems, so they split their corpora set in a training and an evaluation set. We also propose five additional corpora in our resource among the most difficult to parse. And finally we provide a complete API for manipulating corpora in UFSAC, and conversion scripts allowing the full reconstruction of the corpora from the original data. In our resource, we provide a script for converting a corpus from our format to theirs, so existing WSD systems that rely on their format can be trained or evaluated on any of the corpus that we produced. We also provide a script for converting their format to ours in order to facilitate any collaborative work in the community.

Sense Annotated Corpora: rare and costly resources

Generally speaking, a corpus is a collection of documents which can be used as samples of text for a particular language [START_REF] Habert | DE L'ECRIT AU NUMERIQUE. Constituer, normaliser et exploiter les corpus électroniques[END_REF]. A corpus may contain several millions of words, which can be lemmatized and annotated with information concerning their part of speech for example. Among these corpora, we can find the British National Corpus [START_REF] Burnard | The British National Corpus[END_REF] (100 million words) and the American National Corpus [START_REF] Ide | The american national corpus: A standardized resource of american english[END_REF]) (20 million words). The texts come from several sources such as newspapers, books, encyclopedias or from the Web. A sense annotated corpus is a corpus in which some or all words are annotated with an identifier of sense that comes from a specific lexical database. For example, in the cor-pus of the 7th task of the SemEval 2007 semantic evaluation campaign [START_REF] Navigli | Semeval-2007 task 07: Coarse-grained english all-words task[END_REF], all words are annotated with sense identifiers from WordNet 2.1, whereas in the English corpus of the 13th task of SemEval 2015 [START_REF] Moro | Semeval-2015 task 13: Multilingual all-words sense disambiguation and entity linking[END_REF], all words are annotated with sense identifiers from WordNet 3.0, BabelNet 2.5 and Wikipedia pages. There are at least three reasons to create a sense annotated corpus:

• Estimate the distribution of senses in the language. It is for this purpose that the SemCor [START_REF] Miller | A semantic concordance[END_REF] was annotated. And consequently, the senses in Word-Net are, since version 1.7, sorted by this distribution of senses estimated on the SemCor.

• Build a Word Sense Disambiguation system which learns from examples contained in the annotated corpus. For instance, the OMSTI [START_REF] Taghipour | One million sensetagged instances for word sense disambiguation and induction[END_REF] was created for this purpose.

• Evaluate a WSD system by comparing its output to the annotations in the corpus, as it is the case for instance with corpora created as part of the evaluation campaigns SensEval-SemEval.

After their distribution, there is no scientific reason not to use indistinctly these corpora either for building a WSD system, for estimating the distribution of senses or for evaluating a WSD system. Indeed, the SemCor is used since a long time for the learning of WSD systems [START_REF] Chan | Nus-pt: exploiting parallel texts for word sense disambiguation in the english all-words tasks[END_REF][START_REF] Navigli | Semeval-2007 task 07: Coarse-grained english all-words task[END_REF] or more recently for the evaluation of different methods [START_REF] Yuan | Semi-supervised word sense disambiguation with neural models[END_REF]. This last usage is still very rare, since it is one of the first experiment that we found in the literature, along with [START_REF] Màrquez | Experiment a : Several all-words wsd systems for english[END_REF]. However, the format of the resources differs greatly depending on their original purpose. For the SemCor, a single file groups all the information, whereas in the case of the evaluation corpora, there are two files: one that contains the unannotated corpus, and the other that contains the sense annotations. In some corpora, like in the DSO and the OM-STI, there is one file for every lemma in the dictionary, and each file contains thousands of example sentences, where this lemma is the only word that is sense annotated. Few data are manually sense annotated. The Global Word-Net Association made a list of 26 corpora annotated with WordNet1 . These corpora concern 17 languages, but only three of them reach 100,000 annotations. English, with more than 2 million words sense annotated ranks first, before Dutch with nearly 300,000 annotations and Bulgarian with 100,000 annotations. Thus, it is unsurprising that most of researches in WSD focus on English.

A single format for sense annotated corpora

The main purpose of this work is to help the construction and the evaluation of WSD systems, by giving to the community the set of all existing English sense annotated corpora to our knowledge, in the same format, using the same sense inventory, and tools to easily parse them, manipulate

Provided resource

Our work consists in gathering all English corpora sense annotated with WordNet, and convert all of them to a unified format that is able to contain all the informations present in the original format. We created format conversion scripts for this purpose, as well as scripts for cleaning the corpora, and converting the sense annotation to the last version of WordNet (3.0). The resulting corpora are parts of the resource when the copyright allows it, along with the format conversion scripts, the cleaning scripts, and the sense conversion scripts. For the corpora that we cannot distribute because of the licence, anyone that possess them can still run our scripts to turn the original resource into our format. Finally, an API is provided for parsing, creating and manipulating corpora in our format.

Sense annotated corpora

Our resource contains the following corpora:

• The SemCor [START_REF] Miller | A semantic concordance[END_REF], a subset of the Brown Corpus [START_REF] Francis | A standard corpus of present-day edited american english, for use with digital computers (brown)[END_REF]. Original annotations are done with WordNet 1.6.

• The DSO (Defence Science Organisation) [START_REF] Ng | Integrating multiple knowledge sources to disambiguate word sense: an exemplar-based approach[END_REF], a non-free corpus, that is focused on 121 nouns and 70 verbs among the most frequently used and the most ambiguous words in English and have been annotated in various contexts with WordNet 1.5.

• The WordNet Gloss Tag, a corpus which consists of all definitions of WordNet 3 with every words sense annotated since version 3.0.

• The OMSTI (One Million Sense-Tagged Instances) [START_REF] Taghipour | One million sensetagged instances for word sense disambiguation and induction[END_REF], a huge corpus of approximately one million words sense annotated with Word-Net 3.0.

• The MASC (Manually Annotated Sub-Corpus [START_REF] Ide | Masc: the manually annotated sub-corpus of american english[END_REF], we used the version given in the article of [START_REF] Yuan | Semi-supervised word sense disambiguation with neural models[END_REF], annotated with the NOAD (New Oxford American Dictionary), but with corresponding WordNet 3.0 sense keys.

• The Ontonotes 5.0 [START_REF] Hovy | Ontonotes: The 90 In Proceedings of the Human Language Technology Conference of the NAACL, Companion Volume: Short Papers[END_REF], annotated with WordNet 3.0.

• The corpora of the English WSD evaluation campaigns SemEval-SensEval, and in particular the corpora of SensEval 2 (using WordNet 1.7), SensEval 3 (WordNet 1. Table 1 summarizes statistics concerning these corpora.

After the conversion of all these corpora into our format, we executed a cleaning step which consisted of trimming words, removing invisible characters, removing inconsistent annotations (i.e. when the part of speech annotation and the sense annotation differ), and finally, merging identical sentences which have annotations on different words. This last step is very important as it actually adds information to some corpora, especially the DSO and the OM-STI: because these corpora are constructed such that they contain lists of sentences with only one word that is sense annotated, surrounded by words not annotated, some sentences are present in different places across the corpus, but with different words that are sense annotated.

The merging phase identifies identical sentences with annotations on different words, and creates a single sentence containing all annotations. Thus, this steps adds a crucial information for some WSD systems. For instance, a similarity-based WSD system can now "learn" that two word senses are often located in the same sentence. Finally, sense annotations have been converted, when necessary, from their original WordNet sense key to the last version of WordNet (3.0) thanks to conversion tables from [START_REF] Daudé | Mapping wordnets using structural information[END_REF]. However, because some senses have been dropped from the old versions of WordNet, some sense annotations have not been converted. In any case, the original sense annotations are always kept alongside the converted sense annotation.

UFSAC File format

Our approach for the unification of the different annotated corpora begins with a file format that is descriptive, easily understandable and readable by a human, and at the same time, efficient for a program to parse and create. Finally, it should be able to contain all the information contained in the original resources. These informations are represented with the following concepts:

-A Lexical Entity (LE) is something that contains a set of annotations.

-A Corpus is a LE which contains a set of documents.

-A Document is a LE hich contains a set of paragraphs.

-A Paragraph is a LE which contains a set of sentences.

-A Sentence is a LE which contains a set of words.

-A Word is a LE which has a special mandatory annotation "surface form", which is the value of the word.

In order to represent these concepts, UFSAC is based on a simple XML syntax with some conventions: lexical entities are represented by XML nodes (corpus, document, paragraph, sentence and word), and annotations are node attributes.

The annotations also follow a certain convention, we used the following to annotate words:

-The identifier (id) of a lexical entity, particularly useful for corpora originally created for the evaluation (e.g. "d001.s002.t003").

-The surface form (surface form) of a word.

-The lemma (lemma) of a word.

-The part of speech (pos) of a word.

-The sense of a word, in a specific lexical database, for example WordNet 3.0 (wn30 key), WordNet 1.7.1 (wn171 key)... The information of the sense is the one which is the most useful in our case, and it is specific to each lexical database, instead of having a unique "sense" annotation as we can find in most other formats. That way we allow multiples sense annotations from different lexical databases at the same time. For example, the DSO is originally annotated with senses from WordNet 1.5, and the conversion to Word-Net 3.0 is sometimes impossible for some senses which were deleted between the two versions. This convention allows us to keep the original annotations, yet to have the annotations from the last version of WordNet, or any other lexical database (for instance BabelNet) at the same time. The following is an example of the resulting UFSAC XML: <corpus> <document id="d001" > <paragraph> <sentence > <word surface_form="A" pos="DT" /> <word surface_form="precise" wn30_key="precise%3:00:00::" /> <word surface_form="example" lemma="example" /> <word surface_form="." /> </sentence> </paragraph> </document> </corpus> Our format thus allows to integrate the whole corpus in a single file, and it is easily readable, especially comparing to most original formats (c.f. the end of section 2.).

API and tools

An easy-to-use Java API is also provided to read, write and modify efficiently corpora in our format. It allows two styles of programming: you can either load a full corpus in memory, perform all your calculations and save it entirely in a file; or you can sequentially scan, edit or print a corpus

Streaming API

For some corpora particularly huge, like the OMSTI, we also provide a sub-package streaming, which allows to read, write or modify a corpus sequentially, without being fully loaded into memory. This is similar to the Java SAX library (Simple API for XML), events are fired when reading a word, sentence, paragraph, etc., and the user can choose to respond to this event or not.

In practice, we provide a set of classes which cover most use cases.

The class StreamingCorpusReader allows to respond to the events readBeginCorpus, readBeginDocument, readWord, etc.. This can be useful for printing every word that is sense annotated for example. The class StreamingCorpusModifier allows to modify a corpus in-place. This is specially useful for preprocessing, for instance convert every word to lowercase. The class StreamingCorpusWriter is used for creating a new corpus, with its methods writeBeginSentence, writeWord and so on.

Scripts

Finally, we provide a set of examples and useful scripts which use our format and our API, they will be more described in the final version of this article. Important scripts are the conversion scripts, which allow to turn every corpus from its original format, to our XML format. This is specially valuable for non-free corpus like the DSO, that we cannot share directly in our format, but that people can still buy in their original format, and convert to our format. Other useful scripts are pre-processing scripts, for example we provide a script which uses an external POS tagger and lemmatizer to annotate all words in a corpus. To conclude, we offer also scripts that can compute the frequency of senses of each words in a set of corpora, scripts that evaluate a WSD system, and so on.

Conclusion

In this paper we advocate for a more uniform way of distributing sense annotated corpora, through a unique and uncomplicated file format. This unification can facilitate both the creation and the evaluation of word sense disambiguation systems. Indeed, sense annotated corpora are historically separated between those created for the purpose of training, and those created for the purpose of evaluation. In addition, the formats of these corpora are often very different from each other: different file hierarchy, different syntax, and different sense inventory are used. The unification of all sense annotated corpora could hence allow to quickly expand a system which is trained on some resources to new data without the effort of writing another parser. Also, a system could easily include to its training phase some corpora that were originally created for evaluation, and/or evaluate its performance on parts of corpora originally created for training. This would easily allow a much better coverage and a more fine-grained analysis of the WSD systems performance. In our language resource, we gathered all existing English sense annotated corpora that we know, and we converted them in a simple and consistent XML file format that we named UFSAC. We also converted their sense annotations to the last version of WordNet (3.0). The corpora are only available when the licence authorizes it, but we also provide scripts that can easily convert a corpus from its original format to the one we propose. Thus, anyone who possess the corpora that we cannot distribute can still benefit from this work. In addition, we provide a complete Java API for reading, writing and modifying corpora in our unified format, along with example codes and tools for many applications such as pre-processing, sense distribution estimation, etc..

  7.1), SemEval 2007 (WordNet 2.1), Se-mEval 2013 (WordNet 3.0) and SemEval 2015 (Word-Net 3.0).

Table 1 :

 1 Statistics related to our set of annotated corpora, after the conversion and cleaning phase. from a file, in a streaming manner. The latter is particularly useful when working with huge files which do not fit into memory. Finally, we offer a set of scripts that perform the conversion of a corpus from its original format to our one, and some pre-processing and analyses scripts.

	Corpus	Sentences	Total	Words Annotated	Annotated parts of speech Nouns Verbs Adj.	Adv.
	SemCor	37176	778587	229517	87581	89037	33751	19148
	DSO	178119	5317184	176915	105925	70990	0	0
	WordNet GlossTag	117659	1634691	496776	232319	62211	84233	19445
	MASC	34217	596333	114950	49263	40325	25016	0
	OMSTI	820557	35843024	920794	476944 253644 190206	0
	Ontonotes	21938	435340	52263	9220	43042	0	0
	SemEval 2007 task 07	245	5637		2261	1108	591	356	206
	SemEval 2007 task 17	120	3395		455	159	296	0	0
	SemEval 2013 task 12	306	8142		1644	1644	0	0	0
	SemEval 2015 task 13	138	2638		1053	554	251	166	82
	Senseval 2	238	5589		2301	1061	541	422	277
	Senseval 3 task 1	300	5511		1957	886	723	336	12
	4.3.1. Core API
	The core API is a package containing the base classes
	for manipulating corpora. For simplicity, the class names
	match exactly what is described in section 4.2..
	The class Annotation describes an annotation on a lex-
	ical entity. Concretely, it is a pair of Strings (name/value)
	and a pointer to the annotated lexical entity.
	The class LexicalEntity describes something that has
	zero or more annotations, with public methods for access-
	ing/modifying them.
	The class Word inherits from LexicalEntity, has a special
	mandatory annotation surface form, which is the value
	of the word, and a parent sentence.
	The class Sentence inherits from LexicalEntity, contains
	a list of words and a parent paragraph.
	The class Paragraph inherits from LexicalEntity, con-
	tains a list of sentences and a parent document.
	The class Document inherits from LexicalEntity, contains
	a list of paragraphs and a parent corpus.
	Finally, the class Corpus inherits from LexicalEntity and
	contains a list of documents.
	These few classes, coupled with two functions
	Corpus.saveToXML and Corpus.loadFromXML
	allow to create, save, load and modify any corpus easily.

http://globalwordnet.org/wordnet-annotated-corpora/ them, and convert corpora from their original format to our one. Indeed, a large quantity of sense annotated data is vital for the construction of WSD systems. In evaluation campaigns, this often makes the difference. For example, looking at the data from the SemEval

campaign[START_REF] Navigli | Semeval-2007 task 07: Coarse-grained english all-words task[END_REF], which most of the recent systems were evaluated on, we observe that systems that did not use sense annotated data obtain a precision score up to 78-79% 2[START_REF] Schwab | Désambiguïsation lexicale de textes : efficacité qualitative et temporelle d'un algorithme à colonies de fourmis[END_REF] [START_REF] Chen | A unified model for word sense representation and disambiguation[END_REF] whereas those which use a lot of annotated data reach a score up to 82%[START_REF] Chan | Nus-pt: exploiting parallel texts for word sense disambiguation in the english all-words tasks[END_REF])[START_REF] Navigli | A quick tour of word sense disambiguation, induction and related approaches[END_REF] [START_REF] Vial | Extension lexicale de définitions grâce à des corpus annotés en sens[END_REF] and even 84%[START_REF] Yuan | Semi-supervised word sense disambiguation with neural models[END_REF]. Therefore, having all existing corpora in a unique format and using the same sense inventory offers several advantages: it allows to easily expand the quantity of data available for improving WSD systems, it allows to better estimate the distribution of senses in English, and finally, this format can help creating more robust WSD systems. Indeed, we still find a lot of works that focus on a single evaluation task[START_REF] Vial | Extension lexicale de définitions grâce à des corpus annotés en sens[END_REF][START_REF] Chen | A unified model for word sense representation and disambiguation[END_REF], and in these cases, the analysis of the results concerning the robustness of the methods is limited. The unification of the format of sense annotated corpora could improve the evaluation process by facilitating a cross validation process for instance, where the system is evaluated sequentially on every corpus, with all others used for the training.

This means that the system has chosen the same sense than the human annotators in 78 to 79% of cases