M O Borovyi
email: mborovyi1@gmail.com

Yu P Gololobov

Dr K Isaieva

Dr M Isaiev

Prof M O Borovyi

Prof P Yu

Gololobov

The effect of X-ray irradiation on conductivity of C and 2C polytypes TlInS2 ferroelectrics

Keywords: electrical conductivity, ferroelectrics, commensurate, incommensurate phases

The influence of X-ray irradiation on DC conductivity of TlInS2 C and 2C polytypes are studied in temperature range of 100 -300 K. The X-ray irradiation (absorbed doses are 0.9 kGy and 2.7 kGy) leads to an increasing conductivity of both C-and 2C-samples in proportion to the absorbed dose; the conductivity decreases on cooling in temperature region of 100 -300 K. An anomaly increase of conductivity is observed in C-polytype samples on cooling in temperature range of the incommensurate phase existence (197 -214 K). The X-ray irradiation causes the "blur" of that anomaly. It is established that the mechanism of hopping conductivity with variable hopping length takes place for both polytypes in temperature range of 125 -175 K and the densities of localized states near the Fermi level ( F N ) are determined. Under irradiation the density F N increases from 3.710 18 eV -1 cm -3 (C) and 6.910 18 eV -1 cm -3 (2C) and exceeds the initial more than three times at D = 2.7 kGy. Using the one-dimensional Kroning-Penney model, the role of incommensurate periodic potential in modification of electron band structure at creation the incommensurate phases in crystals is discussed.

Introduction

 -TlInS2 crystals are the wide-gap semiconductor-ferroelectrics and belong to the class of low-dimensional thallium compounds TlMX2 (M = Ga, In; X = Se, S, Te). At ambient conditions  -TlInS2 crystals are characterized by C2/c space symmetry group of the monoclinic crystal system; unit cell parameters are а = 10.90 Å, b = 10.94 Å, с = 15.18 Å,  = 100.21. [START_REF] Kashida | X-ray study of the incommensurate phase of TlInS2[END_REF] Since TlInS2 crystals are promising materials as detectors of electromagnetic radiation, their dielectric, optical, elastic properties, electric transport has been actively studied in numerous works. [2 -5] It was found a number of anomalies of photoconductivity, permittivity, ultrasonic wave propagation velocity and specific heat of TlInS2 crystals which are due to the existence of phase transitions (PT) in them with the formation of both commensurate and incommensurate modulated structures in temperature range of 170 -240 K (as also in isostructural analog TlGaSe2 but in temperature range 100 -160 K). [START_REF] Panich | Electronic properties and phase transitions in low-dimensional semiconductors[END_REF][START_REF] Panich | Phase transitions and incommensurability in the layered semiconductor TlInS2-an NMR study[END_REF][START_REF] Borovoi | Effect of a periodic temperature variation on the properties of TlGaSe2 crystals[END_REF] However, despite numerous experimental studies, data on the characteristics and mechanisms of PT "paraelectricincommensurate phase (IP)" and "IPcommensurate phase (CP)" in TlInS2 are quite contradictory. For example, according to neutron diffraction data, [START_REF] Vakhrushev | Incommensurate phase transition in TlInS2 crystal[END_REF] modulation satellites in corresponding to IP are observed in temperature range of T = 200 -216 K with a modulation vector ( , ,0.25) q  ( 0.012)  =

. From another side, the X-ray diffraction data in temperature range of T = 194 -214 K indicate the formation of incommensurate waves with the wavevector ( ,0, 0.25)

q   ( 0.04)  =
as the waves of static atomic displacements. [START_REF] Kashida | X-ray study of the incommensurate phase of TlInS2[END_REF][START_REF] Salnik | The incommensurate phase transformation in TlInS2 ferroelectric[END_REF] It was suggested that the incommensurate atomic displacements occur in the a-direction of monoclinic unit cell so the wavelength of incommensurability is the irrational To explain the discrepancy between neutron and X-ray diffraction data, as well as number of other contradictions, it was suggested take into account the existence of a number of polytypes in the  -TlInS2 crystals -C, 2C, 4C and 8C with the unit cell parameter c = c ', 2c', 4c ', 8c' (c' 15  Å), respectively. [START_REF] Alekperov | Dielectric anomalies in monoclinic TlInS2 polytypes[END_REF][START_REF] Alekperov | Polytypes of monoclinic TlInS2[END_REF] In particular, for TlInS2 crystals of 2C polytype the absence of modulation satellites of IP and CP in temperature range of 170 -300 K, which points to absence of incommensurate and commensurate modulation waves, unlike the C polytype, was demonstrated with four circle X-ray diffractometry method. [START_REF] Salnik | The incommensurate phase transformation in TlInS2 ferroelectric[END_REF][START_REF] Borovoi | On the Ferroelectric Phase Transition in Polytypes of β-TlInS2 Crystals[END_REF] Because of these differences of the C and 2C polytypes crystal lattice dynamics, it is crucial compare the transport characteristics of these polytypes, in particular, their electrical conductivity. Since the conductivity of TlInS2 is very sensitive to changes of the defect's concentration level, [START_REF] Mustafaeva | Effect of gamma irradiation on the dielectric properties and electrical conductivity of the TlInS2 single crystal[END_REF][START_REF] El-Nahass | Characteristics of dielectric properties and conduction mechanism of TlInS2:Cu single crystals[END_REF][START_REF] Sheleg | Effect of ionizing radiation on the dielectric characteristics of TlInS2 and TlGaS2 single crystals[END_REF] it is important to study the electrical conductivity of TlInS2 C and 2C polytypes at various doses of X-ray irradiation in temperature range of 100 -300 K. The paper presents the results of such research.

Experimental procedure

The single-crystal samples of TlInS2 C and 2C polytypes grown by the Bridgman-Stockbarger method were used for electrical conductivity measurements. The elemental composition and stoichiometry of the samples were verified by a local elemental analysis technique using energy-dispersive X-ray spectroscopy EDX (the JEOL JEM-2100F TEM). The X-ray diffraction identification of C and 2C polytypes were performed by using a diffractometer DRON-4-07 with a single-crystal goniometer head GP-15. The typical size of rectangular samples was (5x7x0.1) mm; the surfaces (5x7) mm coincided with the cleavage planes (001). Silver probes were applied on both two surfaces (7x0.1) mm using Vacuum spraying method. At that electrodes arrangement the conductivity was measured along a cleavage plane. The samples were placed in the cryostat chamber CS204AEX1-AL; the temperature of samples was controlled using the Lake Shore 331S controller. The range of measurements were performed in the cooling mode (in some cases -in heating mode too) with temperature step 2 K, the rate of temperature change was 1 K / min, the accuracy of maintaining the temperature was 0.1 K.

A DC voltage which was formed by a 12-bit analog-to-digital converter and a buffer amplifier was applied to the sample. The voltage variation on the sample was ( 5) ( 5) U  = --+ V. The current in the sample was converted to voltage using a current-voltage converter, and it was controlled using a 16-bit analog-to-digital converter. The measuring range of current (I) was depended on the resistance of the current-voltage converter (for example, for resistance 30 MΩ the maximum current was about 35 nA), and the minimal current value was determined by the input current of the converter (2 pA in our case). The currentvoltage characteristic of the sample values, but different in polarity; for further analysis the averaged conductivity value was used.

The irradiation of samples was performed by the radiation of the X-ray tube BHV-12 Pd (voltage 30 kV, current 50 mA). The spectrum of X-ray radiation includes the characteristic K and K lines (photons energies were 21.2 keV and 23.8 keV, respectively), L -series lines (2.7-2.9 keV) and bremsstrahlung. The sample was placed parallel to the plane of the X-Ray tube beryllium window at the distance of 7 cm. The radiation was directed perpendicular to the cleavage surface (5x7) mm and was absorbed in a layer of 0.1 mm thick. To achieve a uniform irradiation in volume, the samples were irradiated from two sides. The PTW 23342 soft X-ray ionization chamber has been used to measure the absorbed X-ray dose rate. The dose rate was 1.25 mGy/min when chamber was installed in place of the sample. Each sample was initially irradiated for 12 h (6h for each side) and subsequently for another 24 h (12h for each side) so that the absorbed doses were 0.9 and 2.7 KGy, respectively.

Experimental Results

Figure 1 on cooling in the range of 195 -214 K, in which the IP order parameter linearly increases, [START_REF] Kashida | X-ray study of the incommensurate phase of TlInS2[END_REF] the dependence () T  exhibits temperature behaviour anomalous for semiconductors. In contrast, upon subsequent heating of the samples, cooled to 100 K, in the temperature range of 195 K → 214 К the conductivity was rising monotonically. in which the IP exists in the C-polytype crystals, agrees well with the X-ray diffraction data regarding the absence of modulated structures in the TlInS2 crystals of 2C polytype. [START_REF] Vakhrushev | Incommensurate phase transition in TlInS2 crystal[END_REF][START_REF] Alekperov | Polytypes of monoclinic TlInS2[END_REF] As well as C-polytype, there is an electrical conductivity growing with increasing absorbed dose, and exponential dependences of () T  at T = 255 K -300 K with Ea = 0.51 0.04  eV (unirradiated), Ea = 0.40 0.04  eV (0.9 kGy) and Ea = 0.31 0.04  eV (2.7 kGy) are registries.

In summary, the main experimental results state: i) an anomaly behavior of conductivity in C-polytype samples at cooling in the temperature range of the IP existence (195 -214 K), the Xray irradiation causes the "blur" of that anomaly; ii) the conductivity of 2C-samples at cooling over the temperature range of 100 -300 K is monotonically decreasing; iii) the X-ray irradiation leads to an increasing conductivity of both C-and 2C-samples.

Discussion

The conductivity parameters of the TlInS2 crystals

It was previously found that high defective crystals TlInS2 with layered structure are characterized by a high concentration of localized states ( 10 18 eV -1  cm -3 ) in the bandgap near the Fermi level, and electron hopping conductivity along localized states is realized in them. [START_REF] Mustafaeva | Effect of gamma irradiation on the dielectric properties and electrical conductivity of the TlInS2 single crystal[END_REF][START_REF] Mustafaeva | Investigation of dc hopping conduction in TlGaS2 and TlInS2 single crystals[END_REF] The exponential regions of the dependences () T  for C-samples at 255 -300 K and too exponential regions for 2C-samples at 200 -255 K, 255 -300 K correspond to conductivity with hopping activation energies of 0.1 -0.7 eV. In such systems, upon further cooling one can expect the appearance of hopping conductivity with a variable hopping length. In that case, the temperature dependence of the conductivity takes the form (a is radius of localization in electron wave function

exp( r / a )   - , k is Boltzmann's constant, F N
is the density of states near the Fermi level). [START_REF] Mott | Electron Processes in Non-Crystalline materials[END_REF] In order to clarify the existence of such conductivity the temperature dependence () T  was analyzed in coordinates 0 ln( / )  vs. 14 / T -. Figure 3 and Figure 4 are presented these dependences for radiated and irradiated samples of C-and 2C-polytypes on cooling in temperature range 100 -205 K. The approximating straight lines were constructed by the linear least squares method. As can be seen, for both C and 2C polytypes the linear dependences 0 ln( / )  vs. [START_REF] El-Nahass | Characteristics of dielectric properties and conduction mechanism of TlInS2:Cu single crystals[END_REF] / Tare observed in some temperature intervals, which points to hopping conductivity with a variable hopping length there. Based on the slope of the straight lines, parameter B was determined and values of F N has been estimated. The localization radius of a = 1.4 nm was used. [START_REF] Mustafaeva | Investigation of dc hopping conduction in TlGaS2 and TlInS2 single crystals[END_REF] The values of B and F N , as well as the experimentally measured values of conductivity at 300 K for all types of samples are given in the Table T, K agrees well with result of measured on AС. [START_REF] Borovoi | On the Ferroelectric Phase Transition in Polytypes of β-TlInS2 Crystals[END_REF] After irradiation the concentration F N increases and at D = 2.7 kGy exceeds the initial more than three times. A similar result was obtained for N is accompanied by an increase of the sample's conductivity (see Table 1 This testifies once again to the hopping conduction along localized states near the Fermi level in the TlInS2 crystals.

The generation of defects in the TlInS2 crystals under X-ray irradiation

Let us consider the possible channels of radiation defects generation in TlInS2 crystals by photons with a highest energy of 21 keV (Pd , K  lines are the dominant components in spectrum of X-ray irradiation). The main mechanism of the of X-ray photons interaction with matter is atomic photoeffect if the photons energies below 100 keV [START_REF] Hubbell | Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20 MeV for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest[END_REF] . This is especially true for soft Xrays with energy E(K) = 21 keV. The photoelectrons with kinetic energies ()

ei E E K E =  -are
ejected from atoms as the result of ionization of the atomic electron shells (Ei -ionization potential of i-shell). In the case of the TlInS2 crystals the range of the photoelectrons energies is 5 -21 keV.

At the next step, the photoelectrons undergo inelastic collisions with atoms, followed by secondary ionization of atoms. The energy transferred by a photoelectron to an atom of mass ) it is 14 max E,  eV, while in semiconductors with ionic-covalent bonds the energy of atom's exit from lattice point is not less than 7 -10 eV. [START_REF] Klinger | Defect formation in solids by decay of electronic excitations[END_REF] Therefore, at under-threshold irradiation the impact elastic-shifting mechanism of radiation defects creation in TlInS2 does not work. But in that case the major role in the generation of defects plays the impurity atoms charged. The concentration of defects in unirradiated TlInS2 crystals is high enough ( 1810  cm -1 ), and significant part of them is caused by impurities that are incorporated into the crystal lattice at the stage of crystal growth. [START_REF] Alekperov | γ-Radiation Stimulated Structural Transition of Monoclinic TlInS2 to Hexagonal Phase[END_REF] Then, ionization of atom in the regular position of the crystal lattice (when the charged impurity atom is in certain vicinity of it) is accompanied by the Coulomb interaction of created ion with the impurity atom. As a result, an atom exits to the internode site and forms a vacancy with a fairly high probability. [START_REF] Klinger | Defect formation in solids by decay of electronic excitations[END_REF] As shown, [START_REF] Alekperov | γ-Radiation Stimulated Structural Transition of Monoclinic TlInS2 to Hexagonal Phase[END_REF] it is most probable for TlInS2 crystals the arrangement of impurity atoms in the centre of the InS4 octahedra at replacement of In atoms. Therefore, the ionization of sulphur atoms is accompanied by the appearance of anionic sulphur vacancies. In this case the creation of neutral complexes formed by anionic vacancies, charged impurity atoms and sulphur atoms in interstitials is possible.

Unfortunately, we are not aware of papers in which the classification of defects in TlInS2 crystals have been performed and their quantitative parameters presented. However, above qualitative consideration shows that in TlInS2 crystals at under-threshold irradiation there may be a rather effective impurity-ionization mechanism of intrinsic defect formation.

The one-dimensional model of the static modulation waves effect on the band structure

An interesting experimental result is an increasing of C-samples conductivity on cooling in temperature range of incommensurate phase existence 195 -214 K. It should be noted that an increasing the TlInS2 conductivity on cooling was reported earlier, [START_REF] Mustafaeva | Investigation of dc hopping conduction in TlGaS2 and TlInS2 single crystals[END_REF] however, the effect was observed in temperatures of 240 -270 К, i.e. in the paraelectric rather than incommensurate phase.

The fact the increase of conductivity on cooling C-samples begins at the appearance of IP (214 K) and finishes at the IP -CP PT (197 K) indicates that the presence of incommensurate displacement waves with the wave vector ( ,0,0.25)  q ( 0.04)

 =
effects noticeably on the electrons transport.

That influence can be associated with the appearance in IP an additional potential with the wave vector ( ,0,0.25)

 q , which superimposes on the periodic potential of the crystal lattice. b and the depth equal to 0 U . The presence of the incommensurate phase was simulated with the following potential:

0 2 ( ) 2 ( ) ( ) cos cos 1 x b x b V x U A ac     + +   = + -       , ( 1
)
where c is the wavelength of incommensurate potential,  determines the relation between the amplitudes of rectangular potential and incommensurate one (Figure 5), A is the amplitude of the phase term. This term defines displacements of the perturbated potential respectively to the Kroning-Penney one, and it corresponds to the rate of incommensurability, and in the case of commensurability A is equal to 0.

Thus, the over-all potential can be presented as:

full U U V =+.
In our model we consider the influence of incommensurate potential as a small perturbation 1



, so in the first correction of perturbation theory the energy is:

0

E E V =+ , where ( ) ( ) V x V x  = .
The procedure of evaluation electron energy spectra in Kroning-Penney model is well known. [START_REF] De | Quantum mechanics of electrons in crystal lattices[END_REF][START_REF] Szmulowicz | Kronig-Penney model: a new solution[END_REF] For calculation we used the model parameters In Figure 6 the calculated dispersive curves for non-perturbated and perturbated (A = 0, i.e., commensurate phase, and A ≠ 0incommensurate phase) are presented. As one can see, the addition of commensurate perturbation leads to shift of dispersive curves and to the change of band gaps. Firstly, it should be noted that the presence of the perturbated potential leads to shift of the dispersive curves down. Nevertheless, presence of the perturbation can lead to increase or to decrease of the bandgap. As an example, the presence of commensurate phase decreases the first band gap, while the incommensurate phase with A ≠ 0 increases it. Contrary situation is observed for the second bandgapthe commensurate phase leads to increase of the bandgap value, and the incommensurate phase with considered amplitude decreases it.

Let us further focus on the consideration of the second bandgap, where the general trend of decreasing of bandgap with the amplitude of incommensurability is expected. Figure 7 shows the dependence of the second band gap on the amplitude of the incommensurability for different values of the perturbation magnitude. As one can see, the bandgap decreases with the λ for the case of commensurability (A = 0). For each value of λ, the band gap monotonically decreases with the A until it reaches the value at which the averaging acting of phase term (∆𝜙 = 𝐴 cos(2𝜋(𝑥 + 𝑏)/𝑐) in Eq. ( 1) is in antiphase to the unperturbed potential. The maximum reduction of the bandgap of IP respectively to CP is 1.7 eV for the case of λ = 0.1. Additionally, it should be noted that due to the symmetry of the perturbation, the rate of change of the bandgap with A is small close to A = 0, and it increases with the rise of A and slows down in vicinity of the minimum. Therefore, the effect of the incommensurability starts to be more significant after some threshold value of A. According to the model this threshold value depends on the λ, and for the maximum considered value (λ = 0.1), it may be estimated as A = 0.1.

Figure 7. The dependence of the second band gap on the amplitude of the incommensurability

The amplitude A which determines the value of incommensurate term in the total potential in fact characterizes the order parameter in the IP. Then an increase the order parameter in IP at cooling from 214 K to 197 K correlates with an increase the amplitude A, [START_REF] Kashida | X-ray study of the incommensurate phase of TlInS2[END_REF] and consequently, correlates with a decrease the band gap width in the temperature region of the IP existence. At IP -CP PT (197 K) amplitude A → 0 and the band gap width increases again. Thus, the increase of conductivity on cooling from 214 K to 197 K and its decrease at further cooling can be associated with the changes of the band gap width when IP appears and decays. Аt first glance the electron hopping mechanism of conductivity along localized states near the Fermi level is not directly related with the width band gap.

But the perturbation of energy diagrams and band gap due to the presence of IP phase leads to the modification of the hopping probability between two localized sites, which leads to modification of the involved in Mott equation. Specifically, the modifications of energy distribution results in variation of the energy of separation defining the probability in the case of equal-distance localization sites positions. [START_REF] Apsley | Temperature-and field-dependence of hopping conduction in disordered systems[END_REF] We hope the proposed model will stimulate more complete calculations the effect of incommensurability on the conductivity of TlInS2 crystals.

Conclusions

The

  . According to that model atoms with the same value of Z-coordinate are displaced in the a-b-plane by the same amount, and the Z-component of displacement is characterized by 4 c c = .

  was measured at each temperature in the voltage range U  , on which the linear regions were distinguished in the low-voltage region ( 0.04) ( 0.04) length, S -surface area of sample) at two identical voltage

  Figure 1 shows typical temperature dependences () T  for samples of C-polytype TlInS2 crystals both pristine and irradiated. For the unirradiated C-samples under cooling in temperature range of 255 -290 K an exponential dependence () T  with the activation energy of the charge carriers Ea = 0.65 0.04  eV is observed.

Figure 1 .

 1 Figure 1. The dependence ) (T  for C-samples TlInS2. The activation energies: Ea = 0.65 0.04  eV (pristine), Ea = 0.53 0.04  eV (0.9 kGy), Ea = 0.44 0.04  eV ( 2.7 kGy)

Figure 1

 1 also presents the () T  dependences on cooling for irradiated C-samples under two X-ray absorbed doses. First, there an increasing trend in the conductivity with absorbed dose growing was observed. It should be noted that as the absorbed dose increases, the anomaly on () T  dependence on cooling in the range of 195 -214 K is "blurred", so for the dose D = 2.7 kGy the increase of the conductivity in that temperature range is practically not observed. For irradiated samples, at T = 245 K -300 K on the () T  , there are also exponential regions. As the absorbed doses increases, the activation energy decreases: Ea = 0.53 0.04  eV for D = 0.9 kGy and Ea = 0.44 0.04  eV for D = 2.7 kGy. In Figure 2 the () T  dependences are shown for samples of 2C-polytype TlInS2 crystals. For 2C-samples () T  dependences are substantially different: in the entire temperature range on cooling the conductivity decreases monotonically including the range of 195 -217 К.

Figure 2 .

 2 Figure 2. The dependence ) (T  for 2C-samples TlInS2. The activation energies: a) T = 200 -255 K Ea (1) = 0.51 0.04  eV (pristine), Ea (1) = 0.40 0.04  eV (0.9 kGy); Ea (2) = 0.31 0.04  eV (2.7 kGy); b) T = 255 -300 K Ea (2) = 0.20 0.04  eV (pristine),

Figure 3 .

 3 Figure 3. The dependences

Figure 4 14 /T

 414 Figure 4. The dependences

F

4 (

 4 of the electron.[19] For sulphur atom (the lightest atoms in the crystal TlInS2,

Figure 5 .

 5 Figure 5. The rectangular Kroning-Penney and periodic modulation potentials

Figure 6 .

 6 Figure 6. The dispersive curves for the first and second bands: solid line -non-perturbated, dashed-dotedperturbated solution with A = 0 (CP), dashed -perturbated solution with A = π (IP)

  conductivity of both unirradiated and irradiated TlInS2 crystals of the C and 2C polytypes decreases on cooling in temperature range of 100 -300 K. But for samples of the Cpolytype in the temperature range of the existence of incommensurate phase (197 -214 K) an increase of conductivity is observed, which is absent for samples of the 2C-polytype. The conductivity of samples irradiated by X-rays increases in proportion to the absorbed dose. In the temperature range of ≈ 125 -175 K the mechanism of hopping conductivity with variable hopping length is realized for both polytypes. Based on the Mott equation, the densities of localized states the Fermi level were determined. Using the one-dimensional Kroning-Penney model, it is shown that the addition of an incommensurate periodic potential to the rectangular lattice potential leads to a shift of the dispersion dependences, while the gap of second band decreases with increasing amplitude of the incommensurate potential.

Table 1 .

 1 ). The conductivity parameters of the TlInS2 С and 2С polytypes

	0.26	0.27	0.28	0.29	0.30	0.31


Xin-Yi Chen

Laurent Prévot
email: laurent.prevot@univ-amu.fr

Exploiting weak-supervision for classifying Non-Sentential Utterances in Mandarin Conversations

. Such approaches require relatively large annotated data sets. We explore an approach (Ratner et al., 2017a) that allows the reduce significantly the amount of annotated data needed thanks to strategic use of linguistic knowledge. We explore this method for classifying NSUs in Mandarin conversation corpus. Our evaluation shows that promising results can be obtained with a minimal amount of annotated training data.

Introduction

In dialogue, besides well-formed complete sentences, a sizeable amount of utterances are fragments that could be understood without a problem in their context. Traditional grammar attends mainly to written texts and canonical sentence analysis. The oral language has been often regarded as bad, spontaneous, and wrong, in summary not an appropriate research object, as (Blanche-Benveniste, 1997) regrets it. But as interest in oral communication gets more attention, terms like "fragments", "Nonsententials" in [START_REF] Barton | Nonsentential Constituents and Theories of Phrase Structure[END_REF] or "Non Sentential Utterances" (hereafter NSU) in [START_REF] Fernández | [END_REF] have also attracted more investigation.

The expressions in example 1 below may sound familiar.

(1) What now?

Not you. What's for supper? -Ground Beef Tacos.

Even though they are generally short, such utterances constitute an active part of the conversation. They contribute to the efficiency of the conversation flow. The interpretation of NSU is essential for linguistic theories that attempt to get serious about language as it is produced in its most natural and pervasive setting, and also for applications, like dialogue systems. It can be done in different ways, as discussed in (Ginzburg, 2012, p:229). The analysis result can be implemented in human-machine dialogue systems in various domains such as client service or computer aided language teacher.

The percentage of NSU among other utterances in conversation corpus is non negligible, 11.15 % in [START_REF] Fernández | [END_REF], 9% in [START_REF] Fernández | [END_REF], 10.2 % in [START_REF] Schlangen | The interpretation of nonsentential utterances in dialogue[END_REF]. We think the study of NSUs is useful because of the high frequency mentioned above. What's more, the understanding of NSUs and their classification from their context is not always easy. Even a simple "what" can express various emotions and can have different functions in a context. Apart from the most common function as plain question, it can also express Happiness, Surprise, Sadness, Anger, Disgust or even Fear.

Second, the definition of NSUs can have an impact on the classification of NSU, the inclusion and exclusion of categories can be flexible according to the theories and purpose of classification, the classification criteria could be syntactic leading, semantic leading or a mix of standards. The treatment of some fragments like 'Greetings' and 'Filler' can make a difference in the counts. We will see the detailed discussion in section 2.

The paper is structured as follows. Section 2 presents the related work of utterance classification, including Dialogue Acts and Non-Sentential Utterances. Section 3 introduces the data and methodology. Section 4 provides a qualitative and quantitative description of our corpus and the results of the manual labeling. Section 5 summarizes the labeling functions used in this article. Section 6 talks about the modelling and classification experiment in our work. Section 7 is about the evaluation of the model. Section 8 concludes the article.

Related Work

Non-Sentential Utterances

The NSU taxonomy proposed in [START_REF] Fernández | [END_REF] is supposed to be the first "comprehensive, theoretically grounded classifications of NSU in large-scale corpus". The classification is based on work grounded in British National Corpus (BNC), the classification take into consideration both a relatively complex syntax and the context dynamics. In [START_REF] Fernández | [END_REF], several machine learning experiments were carried out to get an optimal classification result. The features selected for machine learning in this article is limited in a few "meaningful" ones instead of many arbitrary ones. The features selected for NSU classification came from (i) the utterance itself, (ii) its antecedent, and (iii) their relationship. It results in three sets of features in total: NSU features, Antecedent features and Similarity features. The NSU features include four aspects, whether it is proposition or question, presence of wh-word, yes/no word, and different lexical items. The antecedent features are similar to those of NSU features, but it also looks at whether it is a finished utterance. The similarity features is a comparison of the utterance and its antecedent, mainly about the repeated words and POS tags and their proportion. Another machine learning experimentation work for classification of NSU is based on the work of [START_REF] Fernández | [END_REF] with more advanced features in [START_REF] Dragone | Non-sentential utterances in dialogue: Experiments in classification and interpretation[END_REF].

The taxonomy can be adapted for languages besides English, following the work of [START_REF] Fernández | [END_REF], the work of [START_REF] Wong | Investigating nonsentential utterances in a spoken chinese corpus[END_REF] in classifying NSUs in Chinese adds seven subcategories because of the particular behavior of modal verbs in Chinese. The classification we choose is [START_REF] Wong | Classifying Conversations[END_REF], which is based on the work of [START_REF] Fernández | [END_REF] in adding some classes considering particular behaviors in Chinese Mandarin with extended discussion of each category compared with [START_REF] Wong | Investigating nonsentential utterances in a spoken chinese corpus[END_REF].

Utterance Classification

NSU classification is an utterance classification task, of the same kind as the better known Dialogue Act tagging [START_REF] Stolcke | [END_REF]. Dialogue Act (DA) is about the meaning at the illocutionary level defined in [START_REF] Langshaw | How to do things with words[END_REF], which is the intent or effect produced along with the things being said. In [START_REF] Stolcke | [END_REF], it is said that DAs can be considered "as a tag set that classifies utterances according to a combination of pragmatic, semantic, and syntactic criteria." The DA labels demonstrate the hidden information of the utterance for higher-level processing. It can be used in the interpretation and generation and prediction of utterances and their functions in dialogue systems, as stated in [START_REF] Stolcke | [END_REF]. Therefore DA-tagging is a major applicative task for NLP and Human-Machine Interaction.

Lexical and prosodic cues are both useful for the dialogue act classification. It is observed that some words are symbolic of some DAs. For example, in [START_REF] Stolcke | [END_REF], "92.4% of the uh-huh's occur in Backchannels, and 88.4% of the trigrams '(start) do you' occur in Yes-No-Questions." For some shared patterns, the differentiation is by pronunciation.

The methodology in DA classification bears similarity with NSU classification. Nevertheless, DA and NSU have differences in their theoretical frameworks and distinctions in aspects such as label uniqueness. NSU is an utterance that is not realized by a full syntactic sentence but produces an effect just like sentential utterances. All utterances can receive a DA label, but only those fragments with incomplete syntactic structure and full semantic value can be labeled as NSU.

By many aspects such as their size as well as their lack of completeness, NSUs can be confused with disfluencies. Shriberg [START_REF] Shriberg | Disfluencies in switchboard[END_REF] talked about several types of disfluency: filled pause, repetition, substitution, insertion, deletion and speech error. In [START_REF] Tseng | Grammar, Prosody and Speech Disfluencies in Spoken Dialogues[END_REF]'s exploration of modeling the disfluency, there are features found to be useful in the detection of disfluency on the syntactic side: the linguistic length, the syntactic category, the construction types, the location of interruption, the repair onset, and the repair offset. These features could be useful in our examination of disfluency in our corpus. In [START_REF] Tseng | Repairs and repetitions in spontaneous mandarin[END_REF] 's research about repairs and repetitions in spontaneous Mandarin, the editing term (an indication of speech repair such as "well" "I mean" or filled pauses) is found to be useful in the detection of repetition and repairs.

Methodology

A large quantity of training data is necessary for machine learning tasks. But labeled data are not easy to get. Snorkel (Ratner et al., 2017b) provides a solution to this bottleneck by using labeling functions to generate a large amount of labeled data. As stated in (Ratner et al., 2017b), based on theories and experiments, Snorkel has proven effective in training high-accuracy machine learning models, even using potentially lower-accuracy inputs. It has been recently applied to high-level NLP such as discourse parsing in [START_REF] Badene | [END_REF].

Weakly supervised tools like Snorkel allows for quickly labeling extensive data with minimal but expert manual involvement. The use of Snorkel is to write some labeling functions (LF) to produce some useful training data with labels. A labeling function is a rule that attributes a label for some subset of the training data set. Using Snorkel, it will train a model that combines all the rules defined written to estimate their accuracy, along with the overlaps and conflicts among different labeling functions.

The workflow of Snorkel distinguishes from traditional machine learning approaches; it is based on a data programming paradigm. Briefly, it is composed of two phases, and the first is to produce estimated labels using a generative model, the second is using these labels to train the ultimate model, a discriminative model. Within this design philosophy, the system design of Snorkel can be divided into three phases: first, pre-processing of the data to have the reorganized data for later use, such as word segmentation and POS tagging. Second, writing labeling functions. Labeling functions do not need to be entirely accurate or exhaustive and can be correlated. Snorkel will automatically estimate their accuracies and correlations in a provably consistent way, as introduced in (Ratner et al., 2016). Third, after the evaluation and calibration of the LFs, we decide on an optimal set of LFs to produce a set of labels to train a model.

Data and Manual labelling

Extensive conversational data are limited in numbers. We are interested in the real-time conversational data in talking form transcribed in textual form instead of texts generated in instant-messaging tools. The data we used in this study is from LDC's CALLHOME Mandarin Chinese collection. This is a telephonic conversation corpus, with audio files and transcriptions. The language was in Mandarin even though the participants are from different provinces of China. The corpus includes 120 transcripts in total, and each is a five or ten-minute segment from the telephone speech files. From the description on the website1 , the transcripts are already tokenized automatically using a tool called the Chinese Lexical Analysis System (ICTCLAS). The results were further corrected manually.

In this paper, the corpus concerned is already segmented. In long sentences, an NSU component may appear in the middle, but we won't label it as NSU if it doesn't stand independently. Suppose we deal with a raw corpus not segmented yet. In that case, we will decide the utterance boundary first based on our research question(s) and the conversation context, including syntax, prosody, and pragmatic effect. However, it's also possible to define NSU and describe it first and then extract them or locate them in the corpus.

The original data includes the start time and end time of every segment, the speaker, the textual content of the utterance. In the text transcription, there are also examples of annotation as enrichment of information as illustrated in example 2.

(2) Examples of annotation2 {text}: sound made by the talker. e.g. {laugh} {breath noise} //text//: aside (talker addressing someone in background) e.g.// 来 说 English Hello, 您好 . (Come say Hello, hello).//

We processed the data and transformed it into Pandas DataFrame [START_REF] Mckinney | Data structures for statistical computing in python[END_REF] in order to manipulate it into Jupyter Notebooks [START_REF] Pérez | [END_REF]. They are transformed as a table, and the information is divided by columns. The original information is separated into four columns: Start time, End time, Speaker, and Text transcription. Based on these, we added other columns (illustrated in figure 1):

• Conversation code: the original code of the file • Duration : how long the utterance lasts

• Same Speaker: if the utterance is produced by the speaker of the previous utterance (BOOLEAN)

• Latency : a gap between two turns, the Start time minus the previous End time (we only consider the positive value cases)

• Overlap : the duration when more than one person speaks (we only consider the positive value cases)

• Word count: How many units are there in the utterance (depending on the segmentation method, one unit may not necessary correspond to one Chinese character, and the punctuation can be included as well)

• Tagged: the POS tagged text used in this study is attributed by the tool Zpar [START_REF] Zhang | Syntactic processing using the generalized perceptron and beam search[END_REF] We have 33485 utterances in total in combining 120 files. Combined with the tagged results, we omit the ones untagged, so we deal with 33431 utterances (229 412 tokens).

We selected around 5% of the whole data as a sample to tag manually to know the difference between data with NSU tags and the complete data. Only one annotator does the manual annotation for convenience and cost. Then we have another annotator to annotate 7% of the sample data (0.35% of the whole data) to compare with the first annotator's result. We get a kappa score of 0.54 for all the NSU categories and a kappa score of 0.57 for the four most frequent NSU classes((PLAIN ACKNOWLEDG-MENT, REPEATED ACKNOWLEDGEMENT, CHECK QUESTION, and INTERJECTION), a kappa score of 0.58 for the four first-level NSU classes (AC-KNOWLEDGMENT,QUESTION, ANSWER and COM-PLEMENT).

Through a qualitative analysis of the NSU categories in our corpus, we made some adjustments of the classification in [START_REF] Wong | Classifying Conversations[END_REF], the results are shown in table 1.

Labelling Functions

When writing labeling functions, there are several strategies: keyword matches, regular expressions, arbitrary heuristics, and third-party models.

In our case, we use the first two strategies combined with three types of cues: the Textual cues, the Timing cues, and the Contextual cues. For each type of signal, we look at the relevant features. There are two variables in [START_REF] Schlangen | Towards finding and fixing Fragments-Using ML to identify nonsentential utterances and their antecedents in multiparty dialogue[END_REF], the structural features and the lexical/utterance-based features. In [START_REF] Fernández | [END_REF], as mentioned in section 2, there are three sets of features: NSU features, Antecedent features, and Similarity features. In (Dragone, 2015), the baseline feature set is the same as in [START_REF] Fernández | [END_REF], but with extended features at different levels: POS tags, phrase-level, dependency features, turn-taking features, and similarity features. We have chosen these features as presented in the figure 2 based on the characteristics and available information of our corpus.

In our case, the features are used in the writing of labeling functions. Based on the result of LF performance, which is undoubtedly influenced by the majority's classes, the more frequently used features are the keywords, such as feedback/ backchannel word, followed by wh-question word and ques-Figure 1: Head of the pre-processed corpus dataframe tion final particles. Features used to detect the Sentential Utterances and Disfluency also have good performance. Some features may be not so effective because of some shared words among different NSUs, thus less frequent due to major classes' existence. For instance, "嗯"(um) is typical in PLAIN ACKNOWLEDGEMENT. Still, it can also appear in INTERJECTION or questions, so that we may need a combination of features such as POS tag features and other corpus-related cues.

Our labeling functions can be divided into three types: Keyword-based LF combined with sizerelated LF, POS tagging LF, Context-related LF. For the three classification models, we set the sizerelated limitation such as counted words and we used frequent words for each NSU category in the LF, and also frequent POS tag or tag combination, such as demonstrated in figure 3. We also compare the number or promotion of shared patterns between the utterance and its precedent. For the SU class, we also have LF targeting at disfluency with sizerelated LF, such as Duration and Word count, contextual cues (two consecutive utterances produced by the same speaker) and POS tag cues.

Modelling and Classification

Our goal is to build a model to classify all the NSU classes, we also build two extra classification models for comparison, one with the four first-level It should be noted the final set for each model only includes the LFs without serious incorrectness. Otherwise, it will only harm the model so that if an LF has more incorrect than the correct cases, we tend to exclude them, especially when the ratio is significant. Based on the result and after the error analysis, this problem could not be solved; we do not have LFs for each NSU. For the main classes model, we didn't get a proper LF for the class REPEATED ACKNOWLEDGEMENT, for the first-level classification model, the ANSWER class, and COMPLE-MENT class LF don not enter in the final set. For all-class model, only PLAIN ACKNOWLEDGMENT, CHECK QUESTION, and INTERJECTION) entered in the final set.

The results are presented in table 3. For each model, we run the experiment in three conditions:

• Baseline: with the definite majority class acknowledgment (the most frequent one) with 58% in our sample data frequency;

• System: with all the classes in each model, no use of punctuation (the training label difference in these three conditions can be seen in [START_REF] Wong | Classifying Conversations[END_REF] Figure 2: Features and description

• Topline: also with all the classes in each model, including punctuation (provided by the transcript) as cues.

Snorkel's Label Model can learn the dependency among the LFs, and its output is an array of single probabilistic training labels. As explained in (Ratner et al., 2016), there are four types of dependency among the LFs: "similar, fixing, reinforcing, and exclusive." A dependency graph will be calculated and established. Overall, the model will give a more data-balanced decision for the data points where there are conflicting LFs.

The Majority Label Voter of Snorkel takes the majority vote for each data point; each LF will cover a portion of data. Its inadequacy is that each vote of the LF are considered of equal efficiency, but this is not the case. Snorkel's Label Model deals with the correlation among LFs when combining all the outputs of the LFs.

As we have mentioned the workflow of Snorkel in section 3, Snorkel's Label Model's output is then used to train the ultimate discriminative model, such as a Scikit-Learn classifier.

The Label Model Accuracy is not always higher than the Majority Vote Accuracy. In (Ratner et al., 2017b), it's explained that for very sparse label matrices (almost no conflicts among LFs) or very dense label matrices (a lot of conflicts among LFs) will probably lead to this result. The F1 score is a Micro average for the multiclass setting, that "calculates metrics globally across classes, by counting the total true positives, false negatives and false positives", as explained in [START_REF] Sasaki | The truth of the Fmeasure[END_REF].

Evaluation

So the result of a task to detect just the majority class ACKNOWLEDGMENT from the Sentential Utterace (SU) and the rest of the NSU classes is acceptable, but the abstain votes from the other NSU classes can explain the gaps with the system condition. The small difference among all these three conditions can be attributed to the outcome of the final labeling function sets. Because we omit the LFs with apparent imprecision, we are left with an LF set targeting classes for some major classes like AC-KNOWLEDGMENT and a few effective others for the rest. The all-class classification model's performance can be attributed to the number of classes and the affiliation relation between them. The 24 tags are mutually exclusive, but some can be grouped under a first-level category. Besides, the SU class is the opposite of all the other classes. With its relatively high frequency, in a binary situation, when we only need to distinguish SU and NSU. Still, in our multi-class setting, one class's negative classification is not yet realized in Snorkel. For some classes, even though we have posed some limits on the counted word number and duration, the LF still targets many SU (including disfluency cases). Consequently, there are many false-positives for some LFs, especially for some minority categories, such as for different sub-categories under ANSWER. Extremely unbalanced data as reference, they do not have a single case present in the labeled data set.

Also, the similarity between ANSWER and AC-KNOWLEDGEMENT makes it hard to classify the ANSWER and its sub-classes. They have shared words and sometimes similar scope of counted words; the most credible way is by solving whether the previous utterance is a question. But when we do without the punctuation, the performance is not so good, neither. Some INTERJECTION words are also confused with the ACKNOWLEDGEMENT.

It's exceptionally delicate when dealing with some classed heavily depending on the semantic relationship. For the all-class model, we haven't come up with LFs for BARE MODIFIER PHRASE and COR-RECTION who are hard to capture.

Conclusion

In this article, we present our work regarding nonsentential utterances automatic classification. NSUs are utterances partial syntactically but convey integral meaning semantically. We chose one classification for Chinese Mandarin and test it with a telephone conversation corpus, using a weak supervision method to build a model for automatic labeling.

From a broader perspective, the approach adopted shows interesting results. It constitutes an efficient way to combine domain experts (here linguists) with state-of-the art machine learning techniques.

Future development For classes with barely any coverage in the reference data set, such as the subcategories in ANSWER, we can put more data of these classes for the model training and use some data augmentation method so that we can test and find the LF for these classes.

Dealing with classes easily confused with majority class, such as INTERJECTION and ACKNOWL-EDGEMENT, we may need audio-related information to distinguish them, such as intensity and energy of utterances. Prosodic information has appeal in separating question from declarative with the rising tone at the end for the Mandarin.

To find the semantic connection for a particular utterance in cases, especially when there are no repeated patterns, we need tools to present the relatedness not only for two consecutive utterances but with a flexible contextual window.

  classes ACKNOWLEDGMENT,QUESTION, ANSWER and COMPLEMENT, and another with the four most frequent NSU classes(PLAIN ACKNOWLEDGMENT, REPEATED ACKNOWLEDGEMENT, CHECK QUES-TION, and INTERJECTION).

table 2

 2

	);

Table 1 :

 1 Classification of NSU in

Table 2 :

 2 Comparison of training labels in baseline, system and topline situations in Majority class classification model

Table 3 :

 3 Performance of three models in three conditions

https://catalog.ldc.upenn.edu/LDC2008T17

http://shachi.org/resources/661

Acknowledgments

We would like to thank Pierre Magistry for helping with the POS-tagging as well as anonymous reviewers for extremely valuable comments. All remaining errors are ours.


Nacera Bouldja
email: nacera.bouldja@centralesupelec.fr

Marc Sciamanna

Delphine Wolfersberger

Improved slow light performances using photorefractive two wave mixing

Improved slow light performances using photorefractive two-wave mixing

Nacera Bouldja, Marc Sciamanna, Delphine Wolfersberger

v g = d ∆τ = c n(ω) + ω∂n/∂ω (1)
where d is the thickness of the material, ∆τ is the time delay, n(ω) is the refractive index, ω∂n/∂ω is the material dispersion and ω the frequency detuning between the pulse and the pump. Another key parameter is the so-called fractional delay (FD), i.e the pulse delay ∆τ divided by the full width at half maximum (FWHM) [START_REF] Gehring | Tunable optical time delay of quantum signals using a prism pair[END_REF] at the slowlight system output. Since the pulse FWHM is inversely proportional to the signal bandwidth, the fractional delay is related to the so-called delay-bandwidth product (DBP) [START_REF] Gehring | Fiber-based slow-light technologies[END_REF].

Ideally, applications seek significant reduction of v g with a large DBP value,or in other words, a significant delay for short input pulses and with little distortion of the pulses at the material output. Slow light has been observed in numerous physical systems [START_REF] Horn | Slow and fast light in photorefractive sbn: 60[END_REF][START_REF] Thévenaz | Slow and fast light in optical fibres[END_REF][START_REF] Bortolozzo | Slowlight through nonlinear wave-mixing in liquid crystal light-valves[END_REF][START_REF] Camacho | Wide-bandwidth, tunable, multiple-pulse-width optical delays using slow light in cesium vapor[END_REF]. A milestone was achieved in 1999 [START_REF] Hau | Light speed reduction to 17 metres per second in an ultracold atomic gas[END_REF] when Hau et al. reported a dramatic reduction of light speed down to 17 m/s in an ultracold gas using the Electromagnetically Induced Transparency (EIT). Four years later, Podivilov et al. [START_REF] Podivilov | Light pulse slowing down up to 0.025 cm/s by photorefractive two-wave coupling[END_REF] demonstrated speed light reduction to 0.025 cm/s through a two wave mixing process in a BaTiO 3 photorefractive crystal at room temperature. However, the material dispersion that leads to reduction of v g also significantly broadens the output pulse, hence limiting the FD value. In [START_REF] Podivilov | Light pulse slowing down up to 0.025 cm/s by photorefractive two-wave coupling[END_REF], FD is of the order of 0.4 for a pulse duration of 1.3 s in BaTiO 3 . Slowing down of 100 ms pulses was also obtained in a SPS crystal with v g = 40cm/s and FD = 0.5. Simultaneously, several other physical mechanisms including Brillouin [START_REF] Thevenaz | Flexible slow and fast light in optical fibers[END_REF][START_REF] Yi | Delay of broadband signals using slow light in stimulated brillouin scattering with phase-modulated pump[END_REF] or Raman [START_REF] Liang | Slow light produced by stimulated raman scattering in solid hydrogen[END_REF] scattering process in the optical fiber or propagation close to band-edge in photonic crystals [START_REF] Baba | Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide[END_REF] have shown the possibility to enhance the FD in a slow light system. For example, T. Baba et al. [START_REF] Baba | Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide[END_REF] measured to our knowledge the highest value of FD in the order of 57 in a photonic crystal coupled waveguide (PCCW). In these systems however the group velocity remains large (v g = 11000 km/s in photonic crystal [START_REF] Baba | Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide[END_REF] and v g = 12000 km/s in optical fiber [START_REF] Okawachi | Tunable all-optical delays via brillouin slow light in an optical fiber[END_REF]) since an optimal pulse delay typically requires long material interaction length and this in addition introduces significant losses for the light pulses being slow-down.

It therefore appears current approaches remain unsuccessful in offering slow-down of short input light pulses while maintaining a small v g , a large FD or, equivalently, little output pulse distortion.

In this letter, wCe optimize the experiment of two wave mixing in photorefractive material at room temperature. We specifically address the question of the slow light performance in terms of group velocity reduction, FD and input pulse duration. The choice of the SPS photorefractive crystal is justified by its large and broadband gain and its faster response time [START_REF] Bach | Tailoring of infrared photorefractive properties of sn 2 p 2 s 6 crystals by te and sb doping[END_REF] compared to other ferroelectrics materials. SPS was also previously used for two-wave mixing experiments and slowing down of light [START_REF] Sturman | Slowdown and speedup of light pulses using the selfcompensating photorefractive response[END_REF][START_REF] Shumelyuk | Slowing down of light in photorefractive crystals with beam intensity coupling reduced to zero[END_REF]. While v g decreases monotonously with increasing the input pulse duration, the FD shows a maximum in a range of input pulse duration from 10 ms to 200 ms and remains large in a range of pulse durations spanning three orders of mag- nitude. Therefore, 100 ms pulses are slowed down with v g ∼ 8 cm/s and FD ∼ 0.8, hence showing a significant improvement of slow-light performances when compared to [START_REF] Podivilov | Light pulse slowing down up to 0.025 cm/s by photorefractive two-wave coupling[END_REF]. Furthermore, our experience shows that the pulse is less distorted at the SPS crystal output than in BaTiO 3 .

Fig. 1 shows the experimental setup using a SPS crystal. The laser beam (λ = 638nm) with an intensity of 3.8 W/cm 2 is split into two coherent beams, a signal S and a pump P with different powers, 17 mW and 40 mW for the signal and the pump respectively. The amplitude of the signal is modulated by an electro-optical modulator (EOM) placed before the mirror M 2 . We use a signal generator and an amplifier as driver for the EOM to generate a Gaussian optical pulse shape. An attenuator (A) is placed before the modulator to vary the signal power at the crystal input face from 2 µW to 3 mW . The two-wave mixing gain is then measured for different input intensities I 0 = I s (z = 0) + I p , where I p and I s (z = 0) are respectively the pump and signal input pulse intensities and I p I s . The pump and the signal pulses enter on the SPS crystal through the zface an intersection angle 2θ. This SPS crystal with a thickness of d = 5 mm, is grown in Institute of Solid State Physics and Chemistry, Uzhgorod National University by the conventional vapor-transport method [START_REF] Nitsche | Crystal growth of metalphosphorus-sulfur compounds by vapor transport[END_REF]. It is known that the SPS crystal is characterized by a faster photorefractive build up time (of the order of ms) when compared to photorefractive BaTiO 3 or LiNbO 3 [START_REF] Grabar | Photorefractive effects in sn 2 p 2 s 6[END_REF]. Finally, the input and output pulses are detected by two amplified silicon photodiodes (D 1 ) and (D 2 ).

The interference of two coherent waves in a photorefractive crystal induces the formation of a refractive index grating with a period (Λ). When the light pulse and the pump pass through the SPS, they diffract on the grating and following Eq.( 2) it results in the transfer of a part of the pump energy in the signal direction [START_REF] Podivilov | Light pulse slowing down up to 0.025 cm/s by photorefractive two-wave coupling[END_REF]:

∂As ∂z = -i πn 3 r λ EA p ∂Ap ∂z = ∓i πn 3 r λ E * A s (2)
where A s and A p are respectively the amplitudes of the signal and the pump, n is the refractive index of the crystal, r is the effective electro-optical coefficient, E is the complex amplitude of the space charge field, λ is the wavelength of the laser and z is the propagation direction.

The measurement of the resulting amplification of the signal beam allows estimating the so-called photorefractive gain and relating this to the slow light performance. Indeed, if we call γ = I s (d)/I s (0) the amplification factor, where I s (0) [I s (d)] is the signal intensity at the entrance (output) of the crystal. and if we call m = I p (0)/I s (0) the ratio of pump to signal intensity at crystal input, the photorefractive gain Γ is related to γ through the following Eq. (3), or equivalently Eq. ( 4) from Kukhtarev et al [START_REF] Khuktarev | Holographic storage in electrooptic crystals. ii. beam coupling-light amplification[END_REF]:

γ = I s (d) I s (0) = 1 + m 1 + me -Γd (3)
Γ = 1 d ln I s (d) I p (d) + 1 d ln I p (0) I s (0) (4)
In our experiment, we fix I p (0) and vary I s (0) from 3 mW to 2 µW . Fig. 2 (a) plots γ versus m for the corresponding Γ in the optimal experimental conditions corresponding to Λ = 1.9 µm. Fig. 2 (b) plots Γ for increasing m. The photorefractive gain is therefore a quantity that varies with the operating conditions, in particular with m. In the following we operate at m ≥ 10 4 which corresponds to what is called the undepleted pump approximation, for which the operating conditions are in the plateau of Fig. 2 (a).

As shown in Fig. 2(c) the measured photorefractive gain Γ is related to the slow light performance and first of all to the pulse delay. We fix the input pulse duration to 10 ms and we measure the time delay ∆τ (time delay between the maximum of the input and the output pulse) for different Γd.As shown in Fig. 2(c), the time delay increases with the photorefractive gain. for Γd = 4.7, the delay ∆τ = 9.4 ms is almost equal to the full input pulse duration t 0 at half level.

After characterizing the photorefractive gain and delay for an input pulse duration of 10 ms, we perform a serie of measurements to determine the time delay, the output pulse duration and the delay-bandwidth product as a function of the input pulse duration in the optimal conditions. We fix the gain to Γ = 13 cm -1 corresponding to the maximum delay. Fig. 3 illustrates the temporal envelopes of the normalized output and input pulses as function of the time. For three input pulse durations t 0 of (a) 1.2 ms (shorter than the photorefractive response time τ = 10 ms), (b) 165 ms and (c) 3.5 s (longer than the photorefractive response time), delays of 0.4 ms, 132 ms and 550 ms are measured respectively. The corresponding effective group velocities v g are computed from Eq.( 5) and we obtain 12.5 m/s, 2.1 cm/s and 0.9 cm/s respectively.

v g = d(cm) ∆τ (s) (5)
By varying input pulse width between 0.3 ms and 3.5 s, we can plot the experimental time delay and output pulses duration (FWHM) in Fig. 4(a) and (b) respectively. As show in Fig. 4(a), the time delay ∆τ increases with the input pulse duration.The comparison of Fig. 4(a) with from [START_REF] Shumelyuk | Light pulse manipulation in sn2p2s6[END_REF] tells us that: 1) we can slow-down pulses of durations smaller than 1 ms (here 300 µs) and of duration up to 3.5 s. In [START_REF] Shumelyuk | Light pulse manipulation in sn2p2s6[END_REF] the shortest pulse for which slow light was recorded is of duration smaller than 150 ms, and moreover fast and not slow light is observed for pulse duration above 200 ms, 2) we achieve a larger delay than in [START_REF] Shumelyuk | Light pulse manipulation in sn2p2s6[END_REF] for pulse duration from 10 ms to 3.5 s. For comparison, Ref [START_REF] Podivilov | Light pulse slowing down up to 0.025 cm/s by photorefractive two-wave coupling[END_REF] measured a group velocity of 40cm/s and Ref [START_REF] Shumelyuk | Light pulse manipulation in sn2p2s6[END_REF] achieved a delay ∆τ = 22 ms for a pulse duration of 150 ms. For the same pulse duration we measure a delay of 78 ms which corresponds to a group velocity of the order of 6.4 cm/s; hence confirming an overall improvement of the slow light performances.

As mentioned earlier, it is interesting to analyze also the FD performance. According to previous studies, slowingdown of the group velocity and reaching a large FD simultaneously is difficult because of the output pulse distortion. Fig. 4(c) plots the FD versus the input pulse duration. Although the experimental data are scattered significantly, the FD remains of the order of 0.5 in a broad range of input pulse duration. While scanning the input duration, a max FD of 0.79 is achieved for a pulse duration of 165 ms (corresponding to Fig. 3(b)). In Fig. 4(c), we compare the achieved FD with the one retrieved from the data of ref [START_REF] Shumelyuk | Light pulse manipulation in sn2p2s6[END_REF]. Although the dependency of FD on the pulse duration remains qualitatively the same, the FD is systematically larger in the full range of pulse durations under analysis and spanning four orders of magnitude. Typically the FD is improved by a factor 2 when compared to [START_REF] Shumelyuk | Light pulse manipulation in sn2p2s6[END_REF]. In addition, we extend the analysis of [START_REF] Shumelyuk | Light pulse manipulation in sn2p2s6[END_REF] to light pulse durations below the millisecond time-scale. Now, if we compare the output pulse shape to the input one, the result in Fig. 5 shows that the two-wave mixing in the SPS enables the slowdown of the output pulses without much distortion even for a strong gain. Fig. 5 tells us that the output pulse durations t measured experimentally is close to ideal case (t = t 0 ). Also, we note for some pulse durations, the compression of the pulse when it passes through the crystal.

We explain the small distortion by 1) the fact that gain is smaller than that used in [START_REF] Podivilov | Light pulse slowing down up to 0.025 cm/s by photorefractive two-wave coupling[END_REF], 2) the presence of two charge carriers in SPS that are responsible for a fast and a slow grating whose interplay allows to reduce the broadening of the output pulse [START_REF] Sturman | Slowdown and speedup of light pulses using the selfcompensating photorefractive response[END_REF]. By changing the rotation c-axis of the crystal, we modify the dispersion sign and the delayed light pulse can be accelerated. This result is shown in Fig. 6.

To conclude, the photorefractive two-wave mixing experiment presented in this letter allows combining significant slow down of light pulses (below cm/s) and large fractional delay (close to 1) or equivalently large. We detail the dependency of both delay and FD on several experimental parameters such as the input intensity, the photorefractive gain and the duration of the pulse to be delayed. A large Γd induces typically a temporal deformation of the output pulses which reduces FD. The distortion observed in our SPS crystal is however small compared to the one measured in other photorefractive crystals such as BaTiO 3 .

The successful simultaneous achievement of a small group velocity below cm/s and a FD close to 1 at room temperature is a significant improvement when compared to other slow-light systems.

We identify two paths for further improvement. First, the results are obtained at visible wavelengths, but the photorefractive gain in SPS is shown to be broadband up to at least 1.55 µm [START_REF] Mosimann | High-speed photorefraction at telecommunication wavelength 1.55 µm in sn 2 p 2 s 6: Te[END_REF]. The transparency window goes up to 8 µm but there is not data yet of beam coupling experiences beyond 1.55 µm. We therefore expect similar performances can be achieved for slowing down light pulses at telecom wavelengths for large Γd. Secondly, Ref [START_REF] Bach | Optical phase conjugation of picosecond pulses at 1.06 µ in sn 2 p 2 s 6: Te for wavefront correction in high-power nd-doped amplifier systems[END_REF] makes use of a pulses train to increase the overall interval intensity hence reducing the photorefractive response time and making it possible to slowdown very shorter pulses down to ps. It will be interesting to analyze FD performances for those short pulse durations.

Figure 1 :

 1 Figure 1: Slow light experimental setup ; EOM is the electrooptic modulator, Di are the detectors, Mi are the mirrors, BS are the beamsplitters.

Figure 2 :

 2 Figure 2: (a) Dependence Is(d)/Is(0) on the input intensities ratio (Ip(0)/Is(0)) for different photorefractive gain values. are the operating points shown in (b). (b) Dependence of photorefractive gain Γ input intensities ratio (Ip(0)/Is(0)) for grating period Λ = 1.9 µm and total input power P0 = 35 mW . (c) Delay as a function of Γd for a crystal length d = 5mm and input pulse duration of 10 ms.

Figure 3 :

 3 Figure 3: Temporal envelopes of the normalized input pulse (dotted line) and output pulse (red line) for three input pulse durations, (a) = 1.2 ms, (b) t0 = 165 ms and (c) t0 = 3.5 s corresponding to group velocities of 12.5 m/s, 2.1 cm/s and 0.9 cm/s respectively, Γ = 13 cm -1 , Λ = 1.9 µm and d = 5 mm.

Figure 4 :

 4 Figure 4: Pulse delay ∆τ (a), full output width at half maximum t (b) and delay bandwidth product (c) as function of the full input duration at half maximum t0, Γd = 6.6, Λ = 1.9 µm, d = 5 mm, τ = 10 ms. Red dot curve has FD calculated from the time delay values and output pulse durations of the publication [23].

Figure 5 :Figure 6 :

 56 Figure5: Output pulse duration t (red triangle) as function of the input pulse duration t0, Γd = 6.6, Λ = 1.9 µm, τ = 10 ms. A curve with blue squares plots the output pulse with no coupling in the crystal and therefore t = t0.

Acknowledgements

The authors thank the founders of the Chair in Photonics: Ministry of Higher Education and Research, European Union (FEDER), Region Grand Est, Departement de la Moselle, Metz Metropole, Airbus-GDI Simulation, Centrale-Supélec and Fondation Supélec. The authors also thank A.A. Grabar from the University of Uzhgorod for the SPS sample.