Annie Lannuzel

Jean-Louis Ferge

Quentin Lobjois

Aissatou Signate

Benoit Roze

Benoit Tressières

Yoann Madec

Pascale Poullain

Cécile Herrmann

Fatiha Najioullah

Long-Term

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Long-term Outcome in Neurozika: When Biological Diagnosis Matters

Background:

Zika virus (ZIKV) postnatal infection has been associated with both central and peripheral neurological manifestations. The full spectrum, relative frequency and prognosis of these neurological manifestations have yet to be described. Design/Methods: We conducted an observational study in consecutive ZIKV-infected patients presenting with neurological manifestations during the French West Indies 2016 outbreak.

Results: Eighty-eight patients, including six children, were enrolled. Ninety-five percent of all cases required hospitalization. Guillain-Barré syndrome was the most frequent manifestation (46.6%) followed by encephalitis or encephalomyelitis (20.5%), isolated single or multiple cranial nerve palsies (9.1%), other peripheral manifestations (6.8%), and stroke (1.1%). Fourteen patients (15.9%) including one child, developed a mixed disorder involving both the central and peripheral nervous system. Mechanical ventilation was required in 21 cases all of whom had ZIKV RNA in at least one biological fluid. Two adult patients died due to neuroZika. Clinical follow-up (median 14 months; interquartile range, 12-17) was available for 77 patients. Residual disability (modified Rankin scale ≥2) was identified in 19 (24.7%) patients, in 6 cases (7.8%), disability was severe (modified Rankin scale ≥4). Amongst patients with ZIKV RNA detected in one biological fluid, the risk of residual disability or death was higher (odd ratio, 9.97; CI, 1.22 to 81.21; P=0.032).

Conclusions:

NeuroZika spectrum represents a heterogenous group of clinical neurological manifestations.

During an outbreak, clinicians should consider neuroZika in patients presenting with cranial nerve palsies and a mixed neurological disorder. Long-term sequelae are frequent in NeuroZika. ZIKV reverse-transcription PCR status at admission can inform prognosis and should therefore be taken into consideration in the management of hospitalised patients.

  To characterize the full spectrum, relative frequency and prognosis of the neurological manifestations in Zika virus (ZIKV) postnatal infection.


Isabelle Pasquet

Lionel Presmanes

Yohann Thimont

Corine Bonningue

N Venkataramani

Shiva Prasad

Valérie Baco-Carles

Philippe Tailhades

Antoine Barnabé

Effect of synthesis method and morphology on the enhanced C0 2 sensing properties of magnesium ferrite MgFe 2 0 4

Ferrite Oxlde

Gas sensor CO.

The synthesis and characterization of rnagnesium ferrite Mgl'e2') 4 prepared by co-precipitation and sol gel combustion is reported. Structural characterization showed that ail the samples have single spinel phase. The co precipitated sample exhibits smaller grains and twioe higher BET surface than the sol gel combustion samples. The powder was shaped to dedicated chemo-resistive home-made sensors devices. The electrical properties and sensing properties towards carbon dioxide of both Mgl'e2') 4 powders were studied. The type of charge carriers were analysed on the basis of the change in resistanoe in the presenoe of air and argon. The sensing response towards CO 2 was found tn be dependent on the morphology of the powder sample and the C � concentration. A high response of 36% towards 5000 ppm of CO 2 was reached which is good for this gas. The key rote of the Mg ions modulating the electrical pr operti es is discussed.

Introduction

Carbon dioxide is a greenhouse gas, which affects adversely the health and the environment and henoe should be monitored. Carbon dioxide sensing is also interesting as it is useful for proximity sensing for incorporating with the indoor air quality maintenance. This requires the installation of CO 2 sensors in large number. However, the currently available commercial sensors are based on infrared optics and are costly. The use of metal oxide semiconductor (MOS ) based sensor would alleviate this issue. But the lower reactivity of CÜ2 towards MOS makes it difficult for practical implications.

Reoently there have been reports on the use of silicon nanowires for CÜ2 sensing [START_REF] Naama | CO 2 gas sensor based on silicon nanowires modified with metal nanoparticles[END_REF]. In addition to this, metal oxide and graphene corn posites have also been found useful for CÜ2 sensing [START_REF] Lee | A sensitive electrochemical sensor using an iron oxide/graphene composite for the simultaneous detection of heavy metal ions[END_REF]. There have been many reoent reports on the use of single oxides for CO 2 sensing like copper oxide [START_REF] Tanvir | Work function based CO 2 gas sensing using metal oxide nanoparticles at room temperature[END_REF], tin oxide [START_REF] Wang | CO 2 -sensing properties and mechanism of nano-SnO 2 thick-film sensor[END_REF], perovskites (5 9], zinc oxide [START_REF] Dhahri | ZnO:Ca nanopowders with enhanced CO 2 sensing properties[END_REF][START_REF] Kannan | CO 2 gas sensing properties of DC reactive magnetron sputtered ZnO thin film[END_REF] and other single phases (12 19]. Composite or functionalized oxides have also been reported as potential candidates for CO 2 sensing ( 20 26 ] . Our group has reported using copper oxide copper ferrite composite thin films and powder composites as CO2 sensors (27 29].

• Corresponding author.

Even if ferrite have been widely studied for many different application s (30 34] including gas sensing (35 40 ] , the use of single spinel ferrite phases for 002 detection has rarely been e:xplored before. Among the various ferrites, magnesium ferrite was chosen for studying the CO 2 response. Magnesium ferrite is a magnetic material and finds applica tion in deflection yokes (Mg Zn ) , microwave devices (Mg Mn ) , catalysis and biomedical applications and chemical sensing ( 41 45]. The che mica! sensing properties of magnesium ferrite have been studied to wards various gases like LPG, ethanol, carbon monoxide, hydrogen sulfide, petrol, ch lorine and aoetylene [ 46 51 ] . However, as compared to the conventional single metal oxide materials, the chemical sensing properties of complex metal oxides towards weakly reactive gases like carbon dioxide is not well e:xplored. Among these mixed oxides, the CÜ2 sensing properties of magnesium ferrite have not yet been studied.

In this paper, we report the synthesis of magnesium ferrite by two techniques, co precipitation using oxalate precursor route and sol gel combustion. The effect of synthesis techniques on the structural, mor phological, electrical and carbon dioxide sensing properties is reported.

E-mail address: barnabe@chimie.ups-tlse.fr ( A. Barnabé ) .

https://doi.org/10.1016/ j .oeramint.2018.07.082

Methodology and materials

Materials and fabrication process

Magnesium ferrite was synthesized by two techniques; co pre cipitation with oxalate precursor route and sol gel combustion. For co precipitation route magnesium chloride and ferrous chloride were mixed in 1.8:1 ratio (theoretical 1:2 ratio does not yield stoichiometric magnesium ferrite due to the preferential washing away of the Mg ions related to a quite high solubility product of magnesium oxalate com pared to iron oxalate) in a mixture of water (60%) and ethylene glycol (40%) to form a 2 M solution. Hydrochloric acid (1%) was added to prevent the oxidation of metal salts. The mixture was stirred using a magnetic stirrer. In order to precipitate metal ions, this solution was added to the solution of oxalic acid (10% extra to the total metal ion content) with 0.5 M ethanol using a peristaltic pump. The entire mix ture was stirred mechanically for 30 min. The resultant suspension was washed by centrifuging (3500 rpm, 10 min) followed by mechanical stirring (30 min) for 3 times using de ionized water. This was followed by a washing with ethanol. The obtained oxalate precursor was dried at 80 °C in oven for 8 h. The oxalate was then decomposed in air at 350 °C at a heating rate of 50 °C/h and was then calcined at 600 °C for 1 h. This powder was further calcined at 800 °C for 1 h for having the same calcinations temperature as that of the sol gel combusted sample.

For sol gel combustion, metal nitrates of magnesium and iron was taken in 1:2 ratio and dissolved in de ionized water using a magnetic stirrer equipped with a hot plate at 60 °C. Citric acid was added to this solution in 1:1 ratio of the total metal ion content. The pH of solution was brought to 7 by adding ammonium hydroxide. The mixture turned in to a thick solution, a transparent gel and then to a thick gel with time. At this point the temperature of the hot plate was increased to 80 °C. This initiated the combustion which continued until all the citric acid has been burned. A fluffy powder was obtained after the combustion which was then ball milled using yttrium stabilized zirconia balls for 24 h. The powder was then calcined at 800 °C to obtain pure phase of magnesium ferrite.

The phase of the synthesized powder was checked using X Ray Diffraction (XRD) using a D4 Endeavor Bruker diffractometer equipped with a copper anode and LynxEye 2D detector. The lattice parameter of the phase was calculated from Rietveld refinement using Fullprof software. The surface area of the particles was measured using BET single point Micromeritics Automate 23 surface area analyser. The morphology of both the powders was studied by JEOL JSM 6400 Scanning Electron Microscope (SEM). The powder was fabricated to a device on alumina substrate without any change of the microstructure of the sample. The elaboration of powder in the form device requires achieving a proper contact between the active material and the elec trode. This was done by the use of silver oxalate as the precursor for contact. A paste made with the magnesium ferrite powders and ethy lene glycol was coated on the substrate with electrode. This was again kept in vacuum for 24 h and was then heated to 780 °C for 1 h with a heating rate of 150 °C/hour and was allowed to cool normally in the furnace. The detailed procedure is mentioned elsewhere [START_REF] Sumangala | Study on the effect of cuprite content on the electrical and CO 2 sensing properties of cuprite-copper ferrite nanopowder composites[END_REF].

Experimental set up

The CO 2 sensing properties of the device were studied using a chemical sensor set up. The schematic of this set up is given in Fig. 1.

The sensing was performed using a Linkam cell attached with a thermal controller. The CO 2 sensing was measured by alternately pas sing dry air and 5000 ppm CO 2 in dry air. The flow rate of both the gases was controlled using separate Brooks 5800S mass flow controllers (MFC). The flow rate and duration of gas through these mass flow controllers were further controlled using a pneumatic valve (PV) which in turn was controlled using an electro valve (EV). The incorporation of two mass flow controllers made it possible to change the concentration of the test gas from 5000 ppm to 1000 ppm. A ball valve (BV) was added to the line to prevent a back streaming of the gas. The resistance in the presence of air and CO 2 was measured using Keithley 2400 source meter. The set up consisted of a computer which was connected to the temperature controller of the Linkam cell, the mass flow con trollers, electro valve and the Keithley source meter. The interfacing and controlling was executed using LabVIEW software. The response towards CO 2 was calculated using Eq. (1)

= R(%) R -R R x 100
Air CO2

Air

(1)

Results and discussion

Structural characterization

Fig. 2 gives the XRD patterns of magnesium ferrite prepared by co precipitation and sol gel combustion methods. All the peaks could be indexed with magnesium ferrite spinel phase. This indicates that both the powders corresponds to single phase magnesium ferrite (space group F d3 ̅ m). The lattice parameter of both samples was calculated by performing Rietveld refinement implemented in the Fullprof program. The obtained lattice parameters were 8.385 (1) Å and 8.383 (2) Å for the co precipitated and combusted powder respectively. It could be noted that the lattice parameters of both samples are nearly the same. It is therefore not possible to make differences related to a small change in magnesium content and/or cationic distribution on these samples. Magnesium ferrite is normally 90% inverse ferrite in bulk form and the lattice parameter of bulk material is 8.36 Å [START_REF] Smit | Ferrites : physical properties of ferrimagnetic oxides in relation to their technical applications[END_REF]. The lattice parameter obtained on the synthesized magnesium ferrite powder samples is higher than the bulk and indicates that the inversion factor is lower than 0.9. A calculation of inversion factor based on Poix's method [START_REF] Poix | Liaison interatomique et propriétés des composés minéraux[END_REF][START_REF] Poix | Study of parameter cell variation with cation distribution in YFe 3 O 4 , (1-y) FeCr 2 O 4 and YFe 3 O 4 , (1-y) Fe 2 SnO 4 system using invariants method[END_REF] indicates that it is in between 0.7 and 0.75 for the samples. In this method, lattice constants were calculated using cation oxygen distances listed in Table 1 deduced from the effective ionic radii ac cording to R.D. Shannon [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF].

The lattice constant of a spinel oxide M[M′ 2 ]O 4 is then defined by Eq. ( 2):

= + - a 2.0995 A [5.8182 B 1.4107 A ] 2 2 1 / 2 (2)
where A = ∑ n i (M i O) Td and B = 0.5 ∑ n j (M′ j O) Oh represents the ca tion to oxygen average distances in tetrahedral and octahedral sub lattices respectively. In this calculation, n i and n j are the respective quantities of M and M′ cations per formula unit, and (Mi O) Td and (M′i O) Oh are the cation oxygen distances in tetrahedral and octahedral sites. Thus the XRD patterns confirm that the samples have the same structure irrespective of the synthesis technique adopted.

Microstructural analysis

The XRD patterns in Fig. 2, indicated the similarity in the structure of both samples. However, it could be observed from Fig. 2 that the peak broadening is not the same in case of both samples. The peaks of co precipitated powder are broader than that of the combusted powder. This indicates that there is a difference in the crystallite size between the two samples. The crystallite size of both samples was calculated following the Williamson and Hall method approach. The obtained crystallite sizes were 22 nm and 126 nm for the co precipitated and combusted samples respectively. This shows that the combusted sam ples consist of crystallites which are nearly 5 times bigger than the co precipitated sample.

To confirm the difference in the microstructure, the samples were observed by SEM. Fig. 3(a) and Fig. 3(b) gives the SEM images of both the magnesium ferrite powders. At lower magnification, Fig. 3(c) and Fig. 3(d) show SEM images of both powders coated onto the porous silver electrode.

From Fig. 3, it is observed that the morphology of both powders is different. Magnesium ferrite synthesized by co precipitation method has elongated particles and forms a porous assembly. The average length of these particles was 0.9 ± 0.2 µm and breadth 0.18 ± 0.06 µm. This indicates that each particle contain many crys tallites. The width of a single particle is greater than that the crystallite size and this shows that the elongated particles are formed by in dividual crystallites which are arranged along their length and breadth to form a needle like structure. Magnesium ferrite by sol gel combustion has spherical particles which are bound to each other to form hard clusters. The average particle size estimated from the SEM image is 0.21 ± 0.07 µm. This shows that the particles consist of either one or two crystallites.

The SEM observation yields that the samples with the same com position results in different microstructure. This is important for the application of these materials in gas sensing because sensing capability depends of the specific surface. This is due to the fact that the chemical sensing is dependent on the number of active sites available for che mical reaction. Thus, to quantify the available surface sites, a BET surface area analysis was performed on both the samples. The surface area obtained was 16.2 and 9.0 m 2 /g, for the co precipitated and combusted powder respectively. This shows that the surface area of the co precipitated powder is nearly twice of the combusted one. The particle size of the combusted powder evaluated from SEM is smaller than the co precipitated one. This means the surface area of the com busted powder should be higher. But, this case would be applicable only if both the samples have the same morphology and microstructure. The higher surface area of the co precipitated particle could be due to the needle like morphology and a high porosity resulting from the de composition process of the starting oxalate, which in the end yields more surface area than corresponding spherical particle with the same dimension. In addition to this, the lower surface area of the combusted particles could also be assigned to the presence of agglomerates which considerably reduces the available active surface.

Electrical properties

In the mechanism proposed by Verwey, electrical conduction occurs by charge hopping between transition metal cations from the same element, with different oxidation state, and located in the same sub lattice [START_REF] Verwey | Electronic conduction of magnetite (Fe 3 O 4 ) and its transition point at low temperatures[END_REF]. MgFe 2 O 4 is a n type semiconductor [START_REF] Liu | Simple synthesis of MgFe 2 O 4 nanoparticles as gas sensing materials[END_REF] and the conduc tion is then due to electron hopping mechanism: Fe 3+ + e ↔ Fe 2+ in octahedral site. The temperature dependence of the conductivity in ferrites at a high temperature can be expressed as:

= 1 R A T e - E k T a B ( 3
)
where R is the electrical resistance, A a constant, T the absolute tem perature, E a the hopping activation energy and k B the Boltzmann's constant.

The electrical properties of the sample were studied by heating the sample in the 100 300 °C range. Arrhenius plots (ln T/R versus 1/k B T) given in Fig. 4 are almost linear which confirm the hopping type con duction. We can also observe that the resistance values of both samples are quite closed. The slight difference observed between the two de vices may be the consequence, on the one hand, of the coarser

Table 1

Cationoxygen distance according to R.D. Shannon effective ionic radii [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF].

Cation (M i -O) Td (Å) (M′ j -O) Oh (Å) Fe 2+ 2.003 2.154 Fe 3+
1.855 2.020 Mg 2+ 1.990 2.106 microstructure of the ferrite obtained by combustion, and on the other hand, of the variation of the geometrical characteristics (distance be tween the electrodes and the thickness of the sensitive layers) which is due to the method of preparation used. The slope of the plot gives the hopping activation energy (E a ) and was calculated to be 0.79 and 0.72 eV for co precipitated and sol gel combusted samples respectively. This shows that the activation energy is in the same range for the both preparation.

Using the resistance variation during Air Ar alternations it is pos sible to define if the material has a p type or n type semiconducting behavior.

The change in resistance (R/R 0 ) of both magnesium ferrite samples was studied under air and argon alternations (Fig. 5). This experiment, gives an idea about the charge carrier present in the sample. When an n type semiconducting oxide is put in contact with air, the adsorption of oxygen species (mainly O 2 and O ) occurs at the surface, which in turn mobilizes electrons, causing depletion in number of carriers at its surface and thus leading to an increase of the electrical resistance. In the case of p type oxide, it is the opposite phenomenon, which occurs and the mobilization of electrons causes an increase in the hole con centration at the surface and thus lead to a decrease in the resistance. When the oxide samples are brought under argon, the desorption of oxygen species releases the initially trapped electrons which lead to a recovery of the electrical properties by a decrease in the resistance for the case of a n type or conversely an increase in the case of a p type. It is clear from Fig. 5 that the resistance of magnesium ferrite increases in air while it decreases with the insertion of argon. That demonstrates the n type behavior of both magnesium ferrite samples. We can notice that the ratio R/R 0 is much higher in the case of co precipitated sample, which can be due to the higher specific surface area of the ferrite particles prepared by this route.

Carbon dioxide sensing

CO 2 sensing tests carried out with both magnesium ferrite samples are reported in Fig. 6. In Fig. 6(a), we can observe that the resistance decreases with the insertion of 5000 ppm of CO 2 for both samples. The experiments performed with a step size of 10 min indicate that this time is sufficient for the co precipitated sample to saturate. However, the combusted sample has not reached saturation in the same time interval as the co precipitated sample. Fig. 6(a) shows the repeatability over 10 cycles with co precipitated and sol gel combusted samples. The signal remains almost the same over multiple cycles in both test devices which is in agreement with a complete reversibility of the CO 2 mechanism adsorption. The noisy data in case of co precipitated sample can be attributed to the higher resistance (up to 11 GΩ) in comparison with the combusted powder (2.5 GΩ) which leads to instrumental limit. This result demonstrates the sensitivity of both samples towards 5000 ppm of CO 2 . The response and the response transients (response time and recovery time) towards 5000 ppm of CO 2 are given in Table 2.

It can be observed from Table 2, that magnesium ferrite samples prepared by both techniques are sensitive to CO 2 . However, the re sponse of magnesium ferrite obtained by co precipitation is higher than that with sol gel combustion. In addition to this, the magnesium ferrite co precipitated sample has faster transient response (faster response and recovery time) in comparison with the sol gel combusted one. The change in the response of both magnesium ferrite samples towards CO 2 could be attributed to the different microstructure. The co precipitated sample had more surface area and elongated particles which would have led to more chemically reactive surface sites.

The CO 2 sensing response of devices made with both magnesium ferrite powders was also studied by varying the concentration to 5000, 3000 and 1000 ppm. The change in response with CO 2 concentration for magnesium ferrite sol gel combusted sample is shown in Fig. 6(b). The response obtained at each concentration for both samples is com pared in Fig. 6(c). The response of both samples increase linearly with the concentration of CO 2 . This result confirms that the response is de pendent on the concentration of CO 2 .

The dynamic responses of both co precipitated and sol gel magne sium ferrite samples towards 5000 ppm of CO 2 (R = 36% and R = 24% respectively) are highly increased in comparison with those of co pre cipitated copper ferrite (CuF) samples (R = 10%) measured in the same experimental conditions [START_REF] Wang | Origin of extraordinarily high catalytic activity of Co3O4 and its morphological chemistry for CO oxidation at low temperature[END_REF]. Chemoresistive CO 2 sensing perfor mances of other various oxide based materials [57 59] are reported in Table 3 for similar experimental conditions, i.e. for 4000 5000 ppm of CO 2 in dry air and various operating temperatures. We can notice from this data that the dynamic response of 36% obtained with the co pre cipitated magnesium ferrite powder sample is of the same order of magnitude as SnO 2 based and/or ZnO based doped nanostructured materials. In our previous study [START_REF] Wang | Origin of extraordinarily high catalytic activity of Co3O4 and its morphological chemistry for CO oxidation at low temperature[END_REF], CuF samples showed typical n type gas sensing properties with 1) a decrease in the resistance upon Ar exposure and 2) an increase of the resistance upon CO 2 exposure into the air. The increase in resistance value when n type sample is exposed to a CO 2 pulse can be explained by the reaction of adsorbed oxygen ions with the CO 2 gas leading to the extraction of electrons from the con duction band [START_REF] Kannan | CO 2 gas sensing properties of DC reactive magnetron sputtered ZnO thin film[END_REF]. The most probable assumption is that sensing me chanism of MgFe 2 O 4 layer could be controlled by the work function variations due to adsorption of carbonate at the surface of the grains. In our case, the use of dry air in our experiment can lead to the formation of iron and/or magnesium carbonates activated both by oxygen and carbon dioxide.

In this work, n type MgF samples showed identical behavior than CuF ferrite upon Ar exposure but the resistance of the samples de creased when CO 2 gas is introduced. This unexpected result suggests that, in presence of Mg, the operating sensing mechanism is likely to be different from that observed for copper ferrite. This result was pre viously observed on others n type semiconducting active materials as for instance LaOCl ZnO [START_REF] Xiong | Effective CO 2 detection based on LaOCl-doped SnO 2 nanofibers: insight into the role of oxygen in carrier gas[END_REF], SnO 2 [START_REF] Hoefer | CO and CO 2 thin-film SnO 2 gas sensor on Si substrates[END_REF]. When comparing ZnO and Ca doped ZnO materials, R. Dhahri et al. [START_REF] Dhahri | ZnO:Ca nanopowders with enhanced CO 2 sensing properties[END_REF] observed similar behavior, i.e. an opposite direction of resistance changes with the Ca doping. They highlighted the key role of Ca addition on the ZnO surface in the sensing mechanism: Ca acts as basic center and therefore is able to absorb more strongly the acid CO 2 gas molecules compared to a pristine ZnO surface. Through the formation of adsorbed carbonates and bi carbonates, electrons are releasing and consequently strongly decrease the resistance. Similarly, our results suggest that, in ferrite surface, Mg ions plays a similar key role in the CO 2 adsorption and enhance the CO 3 or HCO 3 or any complex ligands formation rather than change in depletion region (Debye layer) which strongly impact the carrier transport in particular at grain boundary. Thus the direction of the change in resistance is opposite.

Conclusion

In summary, magnesium ferrite nanoparticles were synthesized by two chemical routes; co precipitation with oxalate precursor and sol gel combustion. Both these samples had similar composition and lattice parameter. However, the microstructure of both samples was different. The BET surface area of co precipitated sample was greater (nearly twice) than that of sol gel combusted sample and consisted of elongated grains. The Air Ar measurement performed on both samples showed that the samples contained n type charge carriers. Both these samples showed significant response towards CO 2 . The sensing response of co precipitated sample was greater (36%) than the sol gel combusted sample (24%). The response of the sample was dependent on the powder morphology and the sample microstructure, which were in turn dependent on the synthesis technique used. An opposite direction of resistance change was observed for the Mg ferrite in comparison with Cu ferrite or other conventional n type semiconducting materials. This suggests that, as in the case of Ca in zincite material, Mg generates different reaction mechanisms with gas in spinel ferrite. These results show that MgFe 2 O 4 material is a good candidate for low cost CO 2 sensing device.

Fig. 1 .

 1 Fig. 1. Schematic of the CO 2 sensing set up.

Fig. 2 .

 2 Fig. 2. X-ray diffraction of magnesium ferrite synthesized by co-precipitation and sol gel combustion routes.

Fig. 3 .

 3 Fig. 3. SEM micrograph of magnesium ferrite powders prepared by co-precipitation [a), c)] and sol gel combustion [b), d)] coated on porous silver electrode for electrical and gas sensing measurements.

Fig. 4 .

 4 Fig. 4. Arrhenius plot of magnesium ferrite co-precipitated and combusted sample.

Fig. 5 .

 5 Fig. 5. Variation of the response R/R 0 at 300 °C of magnesium ferrite samples co-precipitated and sol-gel combusted in the presence of air and argon.

Fig. 6 .

 6 Fig. 6. (a) Change in resistance at 300 °C of co-precipitated and sol gel combusted magnesium ferrite samples in the presence of 5000 ppm CO 2 . (b) Variation of the resistance at 300 °C with concentration for Mg ferrite sol-gel combusted sample. (c) Variation of the resistance at 300 °C as a function of the CO2 concentration for both samples.

Table 2

 2 Response, response time and recovery time towards 5000 ppm CO 2 of magnesium ferrite samples prepared by both routes.

	Sample	Response (%)	Response time	Recovery time
			(min)	(min)
	MgF Co-precipitation	36 ± 2	2	4
	MgF Sol-gel	24 ± 2	5	5
	combustion

Table 3

 3 Comparative chemoresistive CO 2 sensing performances of various oxide-based materials reported in the literature as well as the magnesium ferrite of the present study.

	Material	Response (R CO2 -R air )/R air (%)	Operating conditions	Ref.
	BaTiO 3 -CuO-LaCl 3	+ 2.4	5000 ppm CO 2 at 550 °C in dry air	[57]
	LaOCl	+ 300	5000 ppm CO 2 at 260 °C in dry air	[58]
	BaTiO 3 -CuO	+ 4	5000 ppm CO 2 at 300 °C in dry air	[25]
	Ca₁₀(PO₄)₆(OH)₂	+ 200	5000 ppm CO 2 at 165 °C in dry air	[16]
	CdO	20	5000 ppm CO 2 at 250 °C in dry air	[18]
	SnO 2 -LaOCl	85	4000 ppm CO 2 at 250 °C in dry air	[21]
	La 0.8 Sr 0.2 FeO 3	+ 36	4000 ppm CO 2 at 380 °C in dry air	[6]
	ZnO-LaOCl	75	4000 ppm CO 2 at 400 °C in dry air	[22]
	Sm 2 O 3	6	4000 ppm CO 2 at 400 °C in dry air	[14]
	CuFe 2 O 4 -CuO	40	5000 ppm CO 2 at 250 °C in dry air	[28]
	ZnO:Ca 5% at	30	5000 ppm CO 2 at 450 °C in dry air	[10]
	SnO 2	8	5000 ppm CO 2 at 240 °C in dry air	[4]
	ZnO:La 50% at	+ 65	5000 ppm CO 2 at 400 °C in dry air	[20]
	SnO 2 -LaFeO 3	+ 170	4000 ppm CO 2 at 250 °C in dry air	[24]
	Co 3 O 4	+ 20	5000 ppm CO 2 at 150 °C in dry air	[59]
	SnO 2 -LaOCl	76	5000 ppm CO 2 at 300 °C in dry air	[23]
	CuFe 2 O 4	+ 10	5000 ppm CO 2 at 450 °C in dry air	[29]
	MgFe 2 O 4	+ 36	5000 ppm CO 2 at 450 °C in dry air	This work

Acknowledgments

This work was supported by the ANR France [grant number 13 IS08 0002 01] and DST India [grant number 14IFCPAR001] MonaSens project.


Rabih Haddad

Eunika Mercier-Laurent

Decision Support Systems Aiming in Reducing Globalization Burdens in Education

Keywords: Higher Education, Automated Admission System, International Students, Knowledge Management, Text Mining, and Speech Recognition

The potential drawbacks that globalization might have on education are increasing and becoming a main worry. The number of international students is increasing and students' mobility is becoming a crucial phenomenon to obtain a good degree and secure a decent job. Universities have tripled their efforts to recruit and attract international students but their educational ecosystem is still missing some fundamentals. Ensuring that all international students are admitted using an adapted automated admission system, receiving assistance and decent welcome from international faculty and staff, and building their career after are factors that reduce the negative impacts of globalization in education. This paper presents our Decision Support System using knowledge management (KM) approach and AI techniques contributing to achieve those fundamentals and reduce its impacts.

Introduction

Globalization consisting in the integration of markets, cultures, industries and economies around the world (FT, 2019) affects numerous sectors of human life. One of them is education and more precisely higher education. Regardless of the controversial aspects of its influence on countries, developed or developing, positive or negative it can be an important asset in higher education if it is used in an effective method. In fact, nations, regions, country and cities should manage their intellectual capital (Ordonez, Edvinsson (2015).

Globalization phenomena has been risen in the last 20 years due to increasing of internet penetration rate in the world, the easiness and availability of electronic communications (social media, mobile applications, electronic newsletters…) the growth of the low-cost transportation means and the trend for mobility, included into the EU strategy.

Since globalization involves an integration of various cultures then naturally there should be procedures that govern the impact of globalization in higher education to avoid or at least minimize its drawbacks. This paper presents an analysis on how decision support system using knowledge base assessment can help reducing the following weaknesses:

• Selection and admission of international students.

• Services provided for international students to overcome the cultural differences while pursuing their academic programs. • Success of international programs, not only among international students but also for the international faculty and staff and the absorption of the potential graduates in the desired markets.

This paper discusses these important drawbacks. Also, it contains our analysis of admission process, brief state of the art, presentation of research method, proposed architecture of DSS (Decision Support System) positioned in the context of educational ecosystems.

Process of Admission of International Students

With the number of international students increasing globally and the mobility of students is becoming a condition to secure a good job and to gain a shining career, evaluating candidates' prerequisites is becoming challenging (Nguyen, Haddawi, 2007;Bahtiari, 2011). We address this challenge using a methodology based on knowledge management approach powered by adequate AI techniques to help academic institutions in the evaluation of international students' profiles. This methodology should provide multicriteria evaluation of candidates by considering also their cultural background.

Today applying to any degree seeking program anywhere in the world nationally or abroad requires that candidates should undergo an admission procedure to assess the profile of candidates and to take the final decision (admission/refusal of candidates). Admission systems vary from one country to another and from one institution to another. The whole process is mainly done manually by specialized persons (Min Edu, 2019;Szymankiewicz, 2005) and we did not find any information about a fully automated admission system. The characteristics of each country and institution shape the admission system; most of them require the traditional documentation, evaluation, information: admission and languages proficiency exams, interviews, CVs, transcripts, motivation and recommendations letters.

In some countries the first factor of admission is the ability to pay for courses.

An adequate evaluation of students will shorten the gap between the student, the desired country and its educational system. Academic program in any country is designed based on specific cultural aspects and the universal contents of curriculum. Creating an adapted assessment of profiles can predict the eligibility of students to attend an academic program in a multicultural environment.

Admission Process

All recruiting institutions require the candidate information and exams results to decide its admission status. The general admission procedure can be described as follows:

• Students apply online on the institution website by supplying all requested and relevant documents.

Components of Proposed System

As an entry point to understanding the admission system, we consider two major knowledge blocks contributing to the relevant evaluation of students' profiles: Curriculum Vitae (CV) and the online interview. The CV still is an important document that helps the admission committee identifying important information about the candidates and provides knowledge on student's academic and career path. The online interviews help detecting motivation and validate the consistency and genuineness of the candidates' in line with their CVs and profiles. For this purpose, the online interviews will be recorded and rerun for the offline evaluation.

Curriculum Vitae (CV)

This block is very essential in the evaluation process. In the current systems the CV students are not taken into consideration as the evaluation logic only depends on the profiles of previous students who have succeeded a certain curriculum. Hence it depends on a comparative mechanism that might be valid for students coming from the same background but might fail for a diversified group of students. CV should provide the following information about each candidate:

• Basic: to detect the country of origin of each candidate, age and gender. The country will be a crucial factor in the adapted evaluation since a cultural impact matter here. • Academic background: to detect the institution attended by the candidate and the highest degree obtained and the number of academic years after high school. This will bring elements for a base of academic institutions worldwide that will be ranked based on students' success after enrollment and pursuing of classes. • Professional experience: to verify the experience and skills acquired and its relevancy to the degree obtained. This will bring elements for a base of companies worldwide that will be ranked based on students' success after enrollment and pursuing of classes.

Beside the direct knowledge that will be extracted from CVs, text mining will be applied to discover knowledge from the unstructured text by merging all the above listed information.

Online Interview

The online interview will be used to evaluate the English language level of candidates, their motivation, their capability to present themselves and present a coherent project of life, and some easy behavioral aspects. The video interviews will serve to:

• Detect the candidates' oral ability by evaluating the first couple of minutes of their interview. • Analyze the candidates' behavior in terms of self-confidence and consistency.

• Evaluate the candidates' answers to detect their motivation and relevance.

The integrated system of student's evaluation using knowledge management approach is presented in Figure 1. The main aim is to assess how KM can help in such system. By presenting and analyzing the 2 major components of the evaluation system, we will be able to obtain an architecture that leads to an adequate evaluation of candidates. Also, this analysis will help us to validate the proposed solution on real cases and integrate feedback. Such evaluation is beyond the traditional one assessing the experience, the skills acquired and the behavior in a multinational environment.

Figure 1. Proposed architecture of decision support system for student admission

This admission system should provide universities with qualified profiles who are adapted to the desired programs and countries and hence reduce the risk of having students integrating international institutions abroad but never managing to validate the academic conditions to get their degree and missing the main objective of coming to these countries.

Innovating Educational Ecosystem -added values and benefits

As per the UNDP (United Nation Development Program) by following the 4 learning principles (to live together, to know, to do, and to be) many globalization problems such as meeting current social challenges and acquiring new skills in a fast-moving technological environment can be resolved (UNDP 2019). By using decision support systems that produces educational system in line with the students' profiles the objective of each of these learnings can be achieved.

Academic Adaptation

Learning to live together

Based on historical information and students' knowledge and intelligent algorithms, this system can provide an adequate environment to the student to work their projects together and interact positively. The workgroups can be generated based on cultural complementarities. Also, system can provide professors with conflict resolution practices based on the students' background or culture.

Learning to know

The decision support system can provide students with many success stories that have been implemented in the sector of the activity related to the student specialization. Those stories can have a dual task. First by motivating the students to work during their academic program to validate the condition to obtain the degree. Second by forcing the students to think out of the box and innovate while conducting their projects and acquiring experiences.

Learning to do

Learning enough or learning to do enough is not enough. Students should be able to apply the acquired knowledge in complex situations. By using the decision support systems and by analyzing the available information, students can be provided simulators that produce real situation and real-life examples.

Learning to be

The system also should be students centric to detect their soft skills and provide them with Learning what and how to learn should be added to these four (Mercier-Laurent, 2011).

Logistic Services

In aim preserving balance of educational ecosystem, in addition to the academic support and adaptation, the welcome services should be provided to overcome the problems that might affect the academic track of students. Also, there should be a strong connection with the real life. This logistics support should include pre-arrival, on arrival and post arrival services to facilitate the integration of students in the desired country and reduce homesickness. The pre-arrival services should include finding accommodation, visa procedures guidance, organizing the airport pickups. On arrival is to make sure students are well settled down and have already all the administrative procedures related to the desired country.

Our decision support system includes the base of problem solving that have been addressed with previous batches/countries to learn from the previous experience. A mentorship system based on cultural affinity could be produced to assure the different groups of students coming from different cultures [START_REF] Bakhtiari | Globalization and Education: Challenges and Opportunities[END_REF]. Also, events should be organized to help the international student meet national students to exchange experiences at the language level, academic level, political level and cultural level as well. Such type of communication can diminish international student strains and help national student accept and understand the behavior of international students.

By applying those best practices, the number of international students in any country will grow and the possibility of having more comfortable international environment will be higher. This will reduce directly the risks and drawbacks that might be produced to globalization in education.

Elements of Success of International Programs

Ecosystem of Students, Environment & Staff

The designed academic programs that are proposed to international students should be attractive and motivating not only for the students but also for the faculty members who are teaching the programs (Zhou 2018). When a student is seeking a degree in a certain country, the aim is to peruse a degree with an international staff and in an international environment and not only national. This is richer and more beneficial to international students.

The admission system described in section 2 can be used to recruit faculty members as well. The main objective is to have international staff able to adapt the teaching method to the students needs. The faculty members should focus on the success of international students in the desired country and program. By using this approach, we can solve of one the important problems, retaining the maximum number of international faculty and limit the turnover of good and adequate profiles.

This will have also a positive impact on national students as it helps them to be more open to accept cultural differences and to be more efficient in tackling professional life challenges and managing projects in a global environment. There will be an indirect leverage of national students' skills.

Market absorption

Many countries do not manage their intellectual assets, neither they do not have a talents management system. A very dangerous burden of globalization in education is when the economy of the desired country is not able to absorb the potential graduates. The objective is to shorten the distance between the fresh graduates and the recruiters and provide the adequate profiles to the market. This is a result of using an adapted approach with international students. It starts by providing an adapted curriculum lectured by international faculty members and working closely with companies. Also, offering local language courses throughout the whole academic program will help the students' integration easily the professional environment and valorize their degree obtained.

Conclusion and Future Work

Decision Support Systems described above helps recruiting motivated students and reducing risks incurred by globalization. It covers three main areas: admission of international students, the balance of educational ecosystem a nd success of educational program. Apparently, the provided analysis and proposed systems can help in reducing failure in the pursued programs and can reduce the unemployment of students seeking careers abroad, all of that in an acceptable and comfortable environment.

The Future work includes integration of components and testing on hundreds of students' applications to verify their outputs and validate the proposed algorithm. In fine we would like to connect this system with the Intellectual Capital Management in aim of planning the resource for the future, especially in IT field moving very quickly.

  an adapted training program to enhance what is needed.


Romain Dezert

Philippe Richetti

Alexandre Baron
email: alexandre.baron@u-bordeaux.fr

COMPLETE MULTIPOLAR DESCRIPTION OF REFLECTION AND TRANSMISSION ACROSS A METASURFACE FOR PERFECT ABSORPTION OF LIGHT A PREPRINT

Relating the electromagnetic scattering and absorption properties of an individual particle to the reflection and transmission coefficients of a two-dimensional material composed of these particles is a crucial concept that has driven both fundamental and applied physics. It is at the heart of both the characterization of material properties as well as the phase and amplitude engineering of a wave.

Here we propose a multipolar description of the reflection and transmission coefficients across a monolayer of particles using a vector spherical harmonic decomposition. This enables us to provide a generalized condition for perfect absorption which occurs when both the so-called generalized Kerker condition is reached and when the superposition of odd and even multipoles reaches a critical value. Using these conditions, we are able to propose two very different designs of two-dimensional materials that perfectly absorb a plane electromagnetic wave under normal incidence. One is an infinite array of silica microspheres that operates at mid-infrared frequencies, while the other is an infinite array of germanium nano-clusters that operates at visible frequencies. Both systems operate in a deeply multipolar regime. Our findings are important to the metamaterials and metasurfaces communities who design materials mainly restricted to the dipolar behavior of individual resonators, as well as the self-assembly and nanochemistry communities who separate the individual particle synthesis from the materials assembly.

Introduction

When an electromagnetic wave impinges on a single layer of particles or atoms, local currents are generated within the particles that in turn radiate a field that will interfere with the incoming wave to produce a reflection and a transmission [START_REF] David | Classical electrodynamics[END_REF]. The transmission and reflection coefficients, also known as the scattering parameters, of a two-dimensional material are essential observables in physics and chemistry. They are often used to characterize the effective properties of a material. They may also be engineered to target a desired application. In recent years, many two-dimensional materials composed of sub-wavelength polarizable units or scatterers have been designed and modelled to generate extraordinary and tailored reflection and transmission properties. The recent surge in metasurfaces is a good example of arrays of particles designed to control waves both in amplitude and in phase for wave-front shaping [START_REF] Arbabi | Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission[END_REF][START_REF] Decker | High-efficiency dielectric huygens' surfaces[END_REF][START_REF] Khorasaninejad | Metalenses: Versatile multifunctional photonic components[END_REF], filtering [START_REF] Stanislav B Glybovski | Metasurfaces: From microwaves to visible[END_REF] or perfect absorption [START_REF] Alaee | Theory of metasurface based perfect absorbers[END_REF][START_REF] Thongrattanasiri | Complete optical absorption in periodically patterned graphene[END_REF][START_REF] Liu | Experimental realization of a terahertz all-dielectric metasurface absorber[END_REF].

The field radiated by subwavelength individual systems is often decomposed into multipoles. Very recently, multipolar decompositions have become an essential tool in nanophotonics and metamaterials engineering. Alaee et al. provide an interesting perspective on the matter in [START_REF] Alaee | Exact multipolar decompositions with applications in nanophotonics[END_REF]. Here we shall consider the multipolar decomposition on a vector spherical harmonic basis. This is convenient as it reduces the problem to the sole determination of the multipolar scattering coefficients a n,m and b n,m that fully describe how the field is emitted [START_REF] David | Classical electrodynamics[END_REF][START_REF] Craig | Absorption and scattering of light by small particles[END_REF][START_REF] Grahn | Electromagnetic multipole theory for optical nanomaterials[END_REF]. Numerous problems requiring the expression of the field radiated by an infinite array of particles have been treated in the past. As early as 1932, Strachan tried to develop a theory of the light reflected by a monomolecular layer [START_REF] Strachan | The reflexion of light at a surface covered by a monomolecular film[END_REF], though we now know that his theory was incomplete as it neglected the magnetic polarization density [START_REF] Edward F Kuester | Averaged transition conditions for electromagnetic fields at a metafilm[END_REF]. Later arrays were mostly described in terms of electric and magnetic effective dipole moments [START_REF] Tretyakov | Analytical modeling in applied electromagnetics[END_REF][START_REF] Andrey B Evlyukhin | Optical response features of si-nanoparticle arrays[END_REF][START_REF] Pt Bowen | Effective-medium description of a metasurface composed of a periodic array of nanoantennas coupled to a metallic film[END_REF], but also recently including multipolar contributions up to the octupoles [START_REF] Savinov | Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials[END_REF][START_REF] Pavel D Terekhov | Multipole analysis of dielectric metasurfaces composed of nonspherical nanoparticles and lattice invisibility effect[END_REF]. These works are based on expressing the moments in cartesian coordinates but are usually quite involved as the expansions become complex for increasing multipole orders. For this reason, they are usually truncated at low orders, which potentially limits the domain of application of these methods. We may wonder why cartesian coordinates are used in metasurface analysis, since multipolar decompositions up to any order using vector spherical harmonics are widely used and adapted to the study of individual particles.

In this work and in contrast to what has been done thus far, we directly relate the complex reflection and transmission coefficients of a two-dimensional array composed of single subwavelength scatterers of arbitrary shape to the multipolar coefficients of the particles in the array. These coefficients can be directly computed from the currents generated inside a single particle of the array using Grahn's decomposition [START_REF] Grahn | Electromagnetic multipole theory for optical nanomaterials[END_REF]. These currents can be calculated by various numerical methods. This formalism is simple, powerful, totally general and gives a lot of physical insight on the interaction of light with particles of arbitrary complexity. To demonstrate its use, we apply the formalism to absorption, which enables us to derive two generalized conditions that provide the basic recipe to achieve total absorption of an electromagnetic plane wave under normal incidence by an array of multipolar particles. It should be noted that both these conditions have already been given in the literature for arrays composed of dipoles [START_REF] Radi | Full light absorption in single arrays of spherical nanoparticles[END_REF][START_REF] Alaee | Theory of metasurface based perfect absorbers[END_REF]. However, here it is generalized. It turns out that many multipolar systems may act as perfect absorbers which is a definite improvement made possible by our formalism. We are able to provide a generalized interpretation of critical coupling in terms of spherical multipoles as well as provide two examples of perfect absorbing infinite arrays based on very different systems: single silica microparticles that absorb in the far-infrared due to phonon excitations and clusters of germanium particles that absorb at optical frequencies. In this last case, the absorption is obtained via an engineering of the multipolar behavior tailored with the cluster geometry.

Theoretical formalism

The problem we are considering is illustrated on Fig. 1, which depicts a two-dimensional infinite periodic array of particles of period a. Particles are represented as spheres, although the formalism is applicable to particles of arbitrary shape. The array is excited by a plane electromagnetic wave E i with wavevector k. Currents are generated in the volume of each particle due to both the interaction of the incoming wave with the particle as well as its interaction with the wave scattered by all neighbouring particles. These currents are source fields in Maxwell's equations. Each particle emits a scattered field E s in the positive and negative directions. The superposition of all scattered fields in the negative z direction produces a reflected plane wave E r , while the superposition of all scattered fields in the positive z direction interferes with the incoming field and produces a transmitted plane wave E t . The current density field in the unit cell can then be expended using the spherical basis allowing an exact description of the fields with a full account of multipole orders. This enables particles to be both electrically and magnetically polarizable and to sustain multiple resonances (dipole, quadrupole, octupole, etc...). The surrounding medium is considered to be vacuum in what follows for simplicity, but any host medium to the array is applicable.

With these assumptions, the reflection and transmission coefficients of the array can be derived from the expression of the electric field scattered by a single particle of the lattice. Kruk et al. have derived the relationship between the field emitted by an array and the field scattered by a single particle or unit cell of the lattice, using Green's function [START_REF] Kruk | Invited article: Broadband highly efficient dielectric metadevices for polarization control[END_REF]

E a (z) = 2πi|z| kS E s (z) (1)
where S = a 2 is the unit cell area of the array, E a is the field emitted by the array of particles, E s is that emitted by a unit cell, and k is the free-space wavevector. This expression is valid when considering far-field scattering and for a subwavelength square lattice spacing only. Next we expand the field emitted by a unit cell onto vector spherical harmonics using spherical coordinates. The full derivation is available in the appendix (see subsection Reflection and transmission coefficients), but in the interest of conciseness, we directly provide the expressions of the specular reflection and transmission coefficients in terms of symmetric or even (E n ) and anti-symmetric or odd (O n ) multipoles of order n. where the even and odd multipoles can be expressed as a function of the multipole coefficients as follows

r = - π 2k 2 S ∞ n=1 [E n -O n ] (2)
t = 1 - π 2k 2 S ∞ n=1 [E n + O n ] (3)
E n = +1 m=-1 [m(4n + 1)a 2n,m + (4n -1)b 2n-1,m ] (4)
O n = +1 m=-1 [m(4n -1)a 2n-1,m + (4n + 1)b 2n,m ] (5)
Writing the coefficients in this way is quite convenient as a clear distinction can be made in the role of odd and even modes in the reflection and transmission. This role was already underlined by Kruk et al. in the so-called generalized Kerker regime that enables highly transmitting arrays [START_REF] Kruk | Invited article: Broadband highly efficient dielectric metadevices for polarization control[END_REF]. We also note that similar formulas had already been used and discussed in the case of arrays of cylinders by using a cylindrical harmonic decomposition [START_REF] Liu | Generalized magnetic mirrors[END_REF].

Test on a monolayer of high index particles

To illustrate this formalism, we apply it to an infinite square array composed of spherical particles made of a fictitious material with loss that has an index of refraction N = 4 + 0.05i. The surface fill fraction is taken equal to 0.4. The reflectance (R) and transmittance (T ) spectra of the array are represented on Fig. 2(a) as a function of the normalized wavelength (λ/a) and are calculated using eqs. 2 and 3 after decomposing the current fields obtained numerically using the eletromagnetics module of the finite-element based software COMSOL Multiphysics. These quantities are compared to the reflectance and transmittance calculated from the input and output ports in COMSOL through a reflected and

n = b n,1 = b n,-1
). The absorption (A) spectrum is also calculated integrating the ohmic losses in the volume of the particles and the total energy balance is verified by ensuring R + T + A = 1. The example of an array composed of particles that exhibit no symmetry is given in the appendix (see subsection Particle of arbitrary symmetry).

Application to Perfect Absorption

Next, we apply the formalism to the problem of complete absorption of a plane wave under normal incidence on a sheet of particles. Many perfect absorbers have been proposed in recent years that are systematically interpreted in terms of critical dipole coupling. The conditions for perfect absorption with an array of dipoles are given by numerous authors [START_REF] Ra | Thin perfect absorbers for electromagnetic waves: theory, design, and realizations[END_REF][START_REF] Alaee | Theory of metasurface based perfect absorbers[END_REF]. These conditions can be generalized to a multipolar system using eqs. 2 and 3. Complete absorption occurs when both the reflection and transmission coefficients are simultaneously cancelled, that is when

+∞ n=1 O n = +∞ n=1 E n = k 2 S π (6)
This last equation contains two distinct conditions:

1. The generalized Kerker condition. As already noticed by [START_REF] Kruk | Invited article: Broadband highly efficient dielectric metadevices for polarization control[END_REF] in the context of hightly transmitting metasurfaces, this occurs when odd modes are equal to even modes, which we translate here in terms of multipole coefficients as O n = E n . When this condition is realized, we have r = 0. It should be noted that this general condition only requires the sums of odd and even modes to be equal. It does not require that for every n, each symmetric mode be equal to the anti-symmetric odd mode, which would be a much stronger requirement. 2. The zero transmission condition. This occurs when [E n + O n ] = 2k 2 S/π. Since the relation needs to be satisfied in the complex plane it actually means that the overall sum of odd and even modes needs to be a purely real number and reach the exact value that enables a destructive interference with the incoming plane wave. Equation 6 translates into a critical coupling condition equivalent to the classical dipolar critical coupling condition [START_REF] Alaee | Theory of metasurface based perfect absorbers[END_REF].

The power scattered by odd modes is equal to that scattered by even modes and the total scattered power is equal to the absorbed power (see appendix in subsection Critical coupling equivalent formulation with multipole coefficients and optical theorem). An equivalent formulation is that

σ O s = σ E s = σ a 2 (7)
where σ O s (σ E s ) and σ a are respectively the scattering cross-sections of odd (even) modes and the absorption crosssection of a particle within the array. We find two of the main features of perfect absorption, that the total scattering is equal to the absorption and that even and odd modes contribute equally and to half of the total scattering each.

Under the assumption that the multipoles of a single particle are only weakly perturbed by the array, this multipolar description becomes very powerful for design as an initial parameter exploration may be done on an individual particle before resorting to a periodic calculation. To illustrate this concept, we shall now propose two designs of perfect absorbers composed of a periodic arrangement of particles that operate in a multipolar regime in contrast to most absorbers investigated thus far [START_REF] Odebo Lank | Large-scale silicon nanophotonic metasurfaces with polarization independent near-perfect absorption[END_REF][START_REF] Viktar S Asadchy | Broadband reflectionless metasheets: frequency-selective transmission and perfect absorption[END_REF][START_REF] Liu | Experimental realization of a terahertz all-dielectric metasurface absorber[END_REF][START_REF] Tian | Near-infrared super-absorbing all-dielectric metasurface based on single-layer germanium nanostructures[END_REF][START_REF] Valagiannopoulos | Symmetric absorbers realized as gratings of pec cylinders covered by ordinary dielectrics[END_REF][START_REF] Ming | Degenerate critical coupling in all-dielectric metasurface absorbers[END_REF]. First we consider a homogenous microsphere made of SiO 2 with a radius r = 4.12µm. The sphere is initially considered individually through Mie theory and r is tuned in the mid-infrared region to exploit the phonon resonance that occurs near 10 µm. The size is chosen to satisfy the generalized Kerker condition and make sure that the sum of odd modes and the sum of even modes are real and larger than k 2 S * /π, where S * = (2r) 2 . This last requirement may be considered a threshold to reach the zero transmission condition when the particle will be placed in the array as it would correspond to a hypothetical dense square array. We see from Fig. 3(a) that the conditions are reached since both O n and E n (priming denotes that the coefficients are those of the isolated particle) become purely real and go beyond the k 2 S * /π value near 10.1 µm in the red shaded area. Next, an array of these particles is simulated and the pitch is fixed to find a value of S that will satisfy eq. 6 as can be seen on Fig. 3(b). This condition is fulfilled for an array with a fill fraction πr 2 /S = 0.7 . We note that the array influences both the amplitude of the scattering as well as the wavelength at which the conditions are satisfied in comparison to the isolated particle. Figure 3(c) shows the spectra of R, T , and A of the array. As for Fig. 2(a), the parameters calculated directly from COMSOL through planewave projections are compared to those calculated using eqs. 2 and 3. Perfect absorption is reached at a wavelength close to 10.2 µm. We see from the multipole decomposition in the array (Fig. 3(d)) that the perfect absorption condition given by eq. 6 is almost perfectly preserved showing that our assumption is reasonable and our design strategy is valid. As revealed by Fig. 3(d), we find that the system operates in a heavily multipolar regime (see gray region), where at least 8 multipoles are required to account for the perfect absorption behavior. To our knowledge, no multipolar perfect absorber has been proposed up to now. To further reveal the generality of the concept, we also consider a cluster built with spherical particles following an assembly method proposed in [START_REF] Dezert | Isotropic huygens dipoles and multipoles with colloidal particles[END_REF]. Such clusters offer an interesting alternative to spheres made of a homogenous material for which the optical properties are limited by the dispersion of the material. Tuning the volume fraction of inclusions within the clusters enables a tuning of the effective parameters of the cluster. Figure 3(e-h) shows the same quantities as those calculated for the silica system and are computed for a particle cluster composed of thirteen Ge particles that are 75 nm in radius and are pseudo-homogenously distributed in a sphere through repulsive interaction, with a volume fraction of 0.35. The square array made of these clusters has a surface fill fraction of 0.6. Here the resonator is designed to operate at visible frequencies. We see that near perfect absorption is reached at a wavelength close to 790 nm in a heavily multipolar regime once again.

Conclusion

Through a multipolar description of the reflection and transmission coefficients of a monolayer of arbitrary particles, we show that it is possible to infer properties of the metasurface by directly considering heavily multipolar individual particles. We have applied the formalism introduced to perfect absorption theory and given the generalized condition for total absorption of a plane electromagnetic wave under normal incidence on the surface. This phenomenon occurs when the superposition of odd multipoles is equal to that of even multipoles and are equal to the purely real number k 2 S/π, where k is the free-space wavevector of the impinging wave and S is the surface area of a unit period in the array. We use this result to propose two designs of perfect absorbers, one that operates in the mid-infrared region and is made of a infinite periodic array of resonant silica microspheres and another that operates at visible frequencies and is made of an infinite periodic array of germanium clusters. These results are of great interest to the metasurfaces community that has based a lot of its designs on dipolar and sometimes weakly mutlipolar systems. Furthermore it may interest the self-assembly and nanochemistry community who separate the fabrication of individual particles from the two-dimensional or three-dimensional assembly of materials [START_REF] Matthew J Rozin | Colloidal metasurfaces displaying near-ideal and tunable light absorbance in the infrared[END_REF][START_REF] Gómez-Graña | Hierarchical self-assembly of a bulk metamaterial enables isotropic magnetic permeability at optical frequencies[END_REF][START_REF] Baron | Self-assembled optical metamaterials[END_REF][START_REF] Ponsinet | Selfassembled nanostructured metamaterials[END_REF]. two directions, due to the polarization of the incident wave, E s has only one non-zero component along e θ . Our starting point is therefore the expression of the θ-component of the scattered field given in [START_REF] Grahn | Electromagnetic multipole theory for optical nanomaterials[END_REF] expanded in terms of spherical vector wave functions that takes the following form in the far field domain:

E s (θ, φ) =iE 0 e ikr kr ∞ n=1 +n m=-n π(2n + 1) n(n + 1) Q nm × [τ nm (cos θ)a nm + π nm (cos θ)b nm ] e imφ (8)
where Q nm is the normalization constant related to the associated Legendre functions:

Q nm = 2n + 1 4π (n -m)! (n + m)! (9)
τ nm and π nm are the angular scattering functions. They can be expressed using the associated Legendre functions P m n (cos θ) [START_REF] Doicu | Light scattering by systems of particles: null-field method with discrete sources: theory and programs[END_REF]:

π nm (cos θ) = m sin θ P m n (cos θ) (10)
τ nm (cos θ) = d dθ P m n (cos θ) (11)
The angular scattering function evaluated for θ = 0 and θ = π can for example be found in [START_REF] Xu | Electromagnetic scattering by an aggregate of spheres[END_REF] and read:

π n,m (±1) =            (±1) n-1 n(n + 1) 2 m = 1 (±1) n-1 2 m = -1 0 otherwise (12)
τ n,m (±1) =            (±1) n n(n + 1) 2 m = 1 - (±1) n 2 m = -1 0 otherwise (13)
The angular scattering functions cancel for all m / ∈ {1, -1} for both the forward and backward directions. Using these values, the scattered electric field reads in the forward direction:

E s (0, 0) = i E 0 4 e ikr kr ∞ n=1 (2n + 1) [a n,1 -a n,-1 + b n,1 + b n,-1 ] (14)
and in the backward direction:

E s (π, π) = i E 0 4 e ikr kr ∞ n=1 (2n + 1)(-1) n+1 [a n,1 -a n,-1 -b n,1 -b n,-1 ] (15)
Combining 2 and 3 with 8, the field leaving the array can be expressed:

E a (z + ) = - π 2k 2 S ∞ n=1 (2n + 1) (a n,1 -a n,-1 +b n,1 + b n,-1 ) E 0 (16) E a (z -) = - π 2k 2 S ∞ n=1 (-1) n+1 (2n + 1) (a n,1 -a n,-1 -b n,1 -b n,-1 ) E 0 ( 17
)
Inserting these 2 expressions in E t = E i +E a (z + ) and E r = E a (z -) allows us to finally write compactly the reflection and transmission coefficients expressed as a function of the spherical multipole coefficients of a single resonator (or unit cell) of the array:

t = 1 - π 2k 2 S ∞ n=1 m=-1,+1 (2n + 1) (ma n,m + b n,m ) (18)
r = - π 2k 2 S ∞ n=1 m=-1,+1 (-1) n+1 (2n + 1) (ma n,m -b n,m ) (19)
𝝀/𝒂

Particle of arbitrary symmetry

The introduced multipole-based formalism can be used to study periodic arrays of particles with arbitrary shape. To illustrate its large domain of validity, we apply it to arrays of particles consisting of truncated spherical particles with refractive index N = 4 + 0.05i and radius r = 150 nm. Truncations by 2 random planes and a curved surface were used to completely break the symmetry of the final structure as illustrated in the inset of Fig. 4(a). The surface fill fraction is taken equal to 0.4 as in Fig. 2 in the main text. The specular reflectance (R) and transmittance (T ) as well as the absorption spectra (A) of the array are represented on Fig. 4(a) as a function of the normalized wavelength (λ/a). These quantities are well reproduced by the reflectance and transmittance calculated using the extracted multipoles with eqs. 2 and 3 in the main text. The spectra of the modulus of each multipole coefficients of order m = 1 (m = -1) up to the fifth degree are represented on Figure 4(b) (Figure 4(c)).

Critical coupling equivalent formulation with multipole coefficients and optical theorem

In this section we provide the derivation of eq.7 i.e. the energy balance for the metasurface translating the critical coupling of both the symmetric and anti-symmetric excited modes.

By definition, the fraction of incoming power scattered in the backward (forward) direction by the array is equal to |r| 2 (|t -1| 2 ). Using these definitions and the expressions of the reflection and transmission coefficients (i.e. eqs. 18 and 19) the scattering cross sections of even and odd multipoles of a unit cell within the array may be defined by multiplying those quantities by the surface area of a unit cell S, which yields

σ E s = π 2 2k 4 S ∞ n=1 E n 2 (20) σ O s = π 2 2k 4 S ∞ n=1 O n 2 (21)
Assuming perfect absorption, with the condition

+∞ n=1 O n = +∞ n=1 E n = k 2 S
π , the two contributions simply become

σ O s = σ E s = σ a 2 (22)
where the absorption cross-section is actually equal to S since all of the energy impinging a unit cell is absorbed.

We can also show that the optical theorem holds by considering the total absorption A = 1 -R -T , which can be expressed with the multipole coefficients and provides the proportion of absorption due respectively to the symmetric and anti-symmetric modes. Using eqs. 19 and 18 the energy balance then reads:

A = -2 π 2k 2 S 2   ∞ n=1 E n 2 + ∞ n=1 O n 2   + π k 2 S ∞ n=1 Re (E n + O n ) (23)
or equivalently

σ a = -σ s + σ ext (24)
where σ ext is the extinction cross section of the particles in the array, which in the case of an x-polarized incident plane wave becomes [START_REF] Grahn | Electromagnetic multipole theory for optical nanomaterials[END_REF]:

σ ext = π k 2 ∞ n=1 m=-1,+1 (2n + 1)Re (M a n,m + b n,m ) (25)
As for the scattering cross section, the extinction cross section expression can be broken down into even and odd contributions as:

σ E ext = π k 2 ∞ n=1
Re(E n ) (26)

σ O ext = π k 2 ∞ n=1 Re(O n ) (27)
Figure 5: Cross section decomposition in terms of even and odd contributions apply to a cluster-based absorbing metasurface. Each cluster consist of thirteen Ge particles that are 75 nm in radius distributed in a sphere of radius R = 250nm. The square array has a surface fill fraction of 0.6.

In the same way the absorption cross section can be decomposed into even and odd terms obtained by the differences

σ O a = σ O ext -σ O s ( 28
)
σ E a = σ E ext -σ E s ( 29
)
We see that the optical theorem holds for odd and even superpositions independently.

Accessing this decomposition would usually require a configuration with double illumination from both sides of the array as described in [START_REF] Ming | Degenerate critical coupling in all-dielectric metasurface absorbers[END_REF] with co-or cross-polarization allowing for a selective excitation of either the symmetric or anti-symmetric modes of the structure. Instead, using the multipole decomposition allows for a one step procedure to retrieve both the emission and absorption due to the even or odd excited modes.

To illustrate this approach, we present in Fig. 5 the decomposition of the scattering and absorption cross-sections in terms of even and odd multipoles applied to the Ge cluster-based absorber presented in the main text. The absorption σ * a and emission σ * s cross section calculated with respectively the absorbed power obtained via the integration of the ohmic losses and the reflection and transmission coefficients are perfectly reproduced by those reconstructed from the multipole coefficients. In the range of high absorption, the cross sections satisfy:

   σ O s ≈ σ O a ≈ σ 0 2 σ E s ≈ σ E a ≈ σ 0 2 (30)
where σ 0 = S. Strict equalities would be obtained in the case of an absorption reaching 100% while in the present case the maximum absorption exhibited by the metasurface is 98%.

The presented cross sections are quantities of interest as they carry the same information than the scattering, extinction and absorption cross section defined for isolated particles in homogeneous space [START_REF] David | Classical electrodynamics[END_REF][START_REF] Grahn | Electromagnetic multipole theory for optical nanomaterials[END_REF]. Therefore they allow for a direct comparison between the optical properties of particles isolated or placed in a periodic array.

Figure 1 :

 1 Figure1: Artistic rendition of the multipolar decomposition of the field scattered by an array of particles. The particles are reprensented as spheres but the shape can be arbitrary. An electromagnetic plane wave E i with wavevector k is incident on the metasurface. Current densities J are produced within the particles which radiate a scattered field E s in both the top and bottom directions. The interference of the incident field with the scattered field produces a reflected (E r ) and transmitted field (E t ). The current density within a single particle in the array is decomposed on a vector spherical harmonic basis which enables a determination of the multipole coefficients a n,m and b n,m of the unit cell.

Figure 2 :

 2 Figure 2: Test of the multipole decomposition. (a) Reflectance (R), transmittance (T) and absorption (A) spectra of an infinite square periodic array of period a composed of a spherical particle of index N = 4 + 0.05i shown in the inset.The surface fill fraction is 0.4. The continous lines are the spectra calculated from the input and output ports, while the dotted curves are computed from the current decompositions inside the particle and introduced in eqs. 2 and 3. The absorption is caculated directly from the currents. The green curve equal to 1 across the spectrum is R + T + A and ensures energy conservation. (b) Spectra of the magnitude of the multipolar coefficients. Continuous (dashed) lines represent the electric (magnetic) multipoles.

Figure 3 :

 3 Figure 3: Design of perfect absorbers using the multipolar behavior of individual particles. (a) Wavelength dependence of the sum of even and odd multipole coefficients of an individual SiO 2 microsphere in vacuum that is 4.12 µm in radius, calculated using Mie theory. (b) Wavelength dependence of the sum of even and odd multipole coefficients of the SiO 2 microsphere in an infinite square array with a surface fill fraction of 0.7. (c) Spectra of R, T and A calculated for the square array of SiO 2 microspheres, revealing the perfect absorption behavior calculated using the same methods as those used for Fig. 2. (d) Spectra of the modulus of the multipole coefficients retrieved from the current decomposition for the SiO 2 microsphere array.(e-h) are respectively the same quantities as those reprensented on panels (a-d) but for a particle cluster composed of thirteen Ge particles that are 75 nm in redius and are pseudo-homgenously distributed in a sphere through repulsive interaction, with a volume fraction of 0.35. The square array made of these clusters has a surface fill fraction of 0.6. The individual cluster was calculated and explored using the T-matrix method.

a 1 ,1 a 2 ,1 a 3 ,1 a 4 ,1 a 5,1 b 1 ,1 b 2 ,1 b 3 ,1 b 4 ,1 b 5 a 1 ,-1 a 2 ,-1 a 3 ,-1 a 4 ,-1 a 5,-1 b 1 ,-1 b 2 ,-1 b 3 ,-1 b 4 ,-1 b 5 Figure 4 :

 1234123451234123454 Figure 4: Validation of the multipole decomposition with unsymmetrical particles. (a) Reflectance (R), transmittance (T ) and absorption (A) spectra of an infinite square periodic array of period a composed of a 3 times truncated spherical particle. The continuous lines are the spectra of the specular reflection and transmission calculated from the input and output ports, while the dashed curves are computed from the extracted multipoles as introduced in eqs. 19 and 18. The green curve equal to 1 across the spectrum is R + T + A ensuring energy conservation. (b) Spectra of the magnitude of the multipole coefficients of order m = 1. Continuous (dashed) lines represents the electric (magnetic) multipoles.(c) Spectra of the magnitude of the multipole coefficients of order m = -1.

Acknowledgements

The authors aknowledge financial support from the LabEx AMADEus (ANR-10-LABX-42) in the framework of the IdEx Bordeaux (ANR-10-IDEX-03-02).

Appendix Reflection and transmission coefficients

In this section we provide the derivation of eqs. 2 and 3, i.e. the decomposition of r and t as a function of vector spherical harmonic coefficients.

We consider E i , an e x polarized plane wave of magnitude E 0 propagating along the e z direction, normally incident on the metasurface consisting in a square array of particles. Using a multipolar decomposition and spherical coordinates we want to express E s (z) the field scattered by a single particle of the array along the e z axis for both the forward (θ = 0, φ = 0) and backward (θ = π, φ = π) directions , where φ is the azimuthal angle and θ the polar one. For these