Monica Heintz

REPUBLIC OF MOLDOVA VERSUS ROMANIA: THE COLD WAR OF NATIONAL IDENTITITES

In their project of forging a Moldovan identity that would justify the existence of the economically distressed Republic of Moldova as an independent state, the officials search for the symbols commonly used for forging nationhood. As these symbols are the same or not significantly different from those of the neighbouring Romanian state due to their common history (same official language, though differently labelled, same tricolor, similar coat-of-arms), the Moldovan officials perceive Romania as a threat. My analysis based on anthropological fieldwork pays special attention to the political declarations of the Moldovan government and questions their capacity of strengthening citizenship in a country in which ethnic minorities form more than 30% of the population and which experiences severe economic problems and massive emigration. The analysis draws also attention to the evolution of NATO and EU borders, which have accelerated the identity problems of Moldova, which does not wish to follow 'neither Russian, nor Romanian' ways.

Rep. of Moldova Romania

Rep. of Moldova Romania

The issues at stake in the identity conflict For understanding the complex relationship between the two neighbouring states of Romania and the Republic of Moldova, one should necessarily go back to the history that unfolded on the physical territory on which these two states are constituted. Two thousand years ago the region was inhabited by Dacians, who were conquered by the Romans in 106 A.C. The population resulting from the mix of Dacians and Romans spoke a distinctive language, of clear Latin influence, which was already recognized towards the 17 th century as 'Romanian'(first mentioned as 'Romanian' by the Metropolitane Varlaam in 1643, quoted in Literatura si Arta, 13.11.2003). Later the wave of migratory people, especially the Slavs, influenced the language and mixed with the local population. From the 14 th to the 19 th century, the region was politically divided into three main kingdoms: Moldova, Walachia and Transylvania.

(from [START_REF] Treptow | A History of Romania[END_REF] The three kingdoms have been under the influence of three empires: the Austro-Hungarian Empire (Transylvania and from the 18 th century the northern parts of Moldova), the Ottoman Empire (Walachia and Moldova) and the Russian empire (the eastern part of the kingdom of Moldova, baptized by Russians Bessarabia, from the 19 th century). In the 19 th century two of the kingdoms, Moldova, without Bessarabia, and Walachia benefited from favourable geopolitical circumstances to unite under the name of Romania.

(from [START_REF] Treptow | A History of Romania[END_REF] After the First World War, due to the politics of nationhood promoted by Wilson and with the support of Western allies, Transylvania and Bessarabia voted for unification with Romania. The ensuing Greater Romania encompassed the current territories of Romania and the Republic of Moldova, and other territories now in Ukraine (Northern Bukovina, Maramures and Southern Bessarabia) and Bulgaria (the Quadrilater).

(from [START_REF] Treptow | A History of Romania[END_REF] The German-Russian non aggression pact Ribbentrop-Molotov of 1939 allowed the Soviet Union to claim Bessarabia without the intervention of German forces. On the 28 th of June 1940, after an ultimatum, the Romanian army and administration retired from Bessarabia and the Soviet army took over. The 'annexation' or 'liberation' of Bessarabia, depending on whose point of view is expressed, was accompanied by massive movements of people: the Romanian elite (teachers, priests, administration) sought refuge in Romania; those who did not manage to flee were subject to massive deportations in Siberia [START_REF] Bulat | After the Folkloric Movement: Traditional Life in Post-Socialist Moldova[END_REF]Fruntasu, 2003). One year later, in 1941, Romania joined the German forces, now in conflict with the USSR, with the aim of recovering Bessarabia. (Eyal and Smith, 1998). The Moldovans were conceived as a separate ethnic group from Romanians and hold to speak a different language, the Moldovan, which started being written with Cyrillic to further differentiate it from Romanian, written with Latin characters. The story of the birth of the 'Moldovan' language has been amply documented by Western social scientists, who found it of particular political interest (see Hegarty, 2001;Eyal and Smith, 1998;[START_REF] King | The Moldovans. Romania, Russia and the politics of Culture[END_REF]. To render more complex the picture and prevent future territorial claims, Stalin also redesigned boundaries. He gave some of the Bessarabian territories to the Ukrainian Soviet Socialist Republic and incorporated into the MSSR 'in exchange' a long border territory just across the Dniestr, Transnistria, which was existing since its creation by Stalin in 1924 under the name of the 'Moldovan Autonomous Soviet Socialist Republic'. This strip of land, which had never belonged to the kingdom of Moldova and had only 40% ethnic Romanians (in the 1989 census), became the main industrial and energy producer of the MSSR (Troebst, 2003). During the whole socialist period, the two socialist republics of Moldova and Romania had few contacts and the circulation of information concerning their common past was prohibited in both states. Maps in Romania would juxtapose the map legend on the MSSR's territory, indicated only as 'USSR'. The Romanian intellectuals in MSSR had been massively deported, as all those who had contacts with the Romanian administration before the war. Moldovans had their own schools, but those wishing further education had to gain proficiency in Russian.

Russian specialists were brought in the Republic, mixed marriages were encouraged and the Homo Sovieticus was almost born. Meanwhile the Moldovan history and literature had been reduced to those parts of the history exclusively linked to the kingdom of Moldova and to its Russian relations, while in Romania, Romanian history and literature excluded everything linked to the existence and products of the Moldovan territory.

Despite this policy, at the end of the 80s, a new formed generation of Moldovan intellectuals started claiming language and national rights. In a few years, facilitated by the Perestroika and the general 1989 movements in Eastern Europe, Moldovans obtained the recognition of their national language as unique official language in the country (31 august 1989), of their ethnic name, of the Romanian national anthem and political rights [START_REF] Cojocaru | The Politics of Language in Moldova[END_REF]. At the time, the Republic featured a mixed ethnic population, including 64,5% Moldovans (Romanians), 13,8% Ukrainians, 13% Russians, 3,5% Gagaouz and other groups (from 1989 census, the last census available). Two years afterwards, on the 27 th of August 1991, after the putsch against Gorbatchev, the republic declared its independence from the Soviet Union under the name 'Republic of Moldova'. But the national rights gained in 1989 are gradually vanishing away due to the desire of Moldovan officials to base the legitimacy of their new state on the uniqueness of their nation. Thus the name of the official language was named 'Moldovan' again, the anthem was changed to a text written by a Romanian born on the Bessarabian territory, Alexe Mateevici, history textbooks are periodically threatened to be changed (in 2004 in the majority of schools the History of Romanians is taught) and the old Stalinist doctrine of the difference between the two ethnic groups is embraced, the officials refusing to consider the Republic of Moldova as a Romanian state within different state borders.

Identities are always defined in two ways: through their intrinsic characteristics and in opposition. Similarities between the national characteristics and symbols of Romania and Moldova render the first option difficult. This is the main reason why the officials had to appeal to the second and develop an identity against the Romanian identity, by denigrating both Romanians and Romania as a state.

The anti-Romanian campaign in the Republic of Moldova

The antipathy of Moldovan officials towards the Romanian state has grown after the 2001 elections in which the Moldovan Communist Party won a vast majority. The Communist officials promised to return to a territorial administration that would differentiate their countries' organization from Romania's organization (in judete as opposed to raioane), to change history curricula from Romanian History to Moldovan history and to introduce Russian as a second official language in the state. While the first administrative measure mentioned was implemented in 2003 1 , the attempt to change the history and to introduce Russian as official language met with massive demonstrations especially from students. In 2002 a sitting was organized in Chisinau city center, organized by a pro-unionist party and supported by young people, to prevent the rewriting of history and to ask for the recognition of the Bessarabian Metropolitanate, a 1 The organisation in judete was dating from 1999.

Romanian Orthodox structure that was not authorized to function since its revival in 1992. The rewriting of history was temporally abandoned but a vast campaign is still made in its favour. In 2003 new 'integrated' histories of Moldova started being taught in several schools in the Republic as an experiment and the state supported the publication and promotion of a Moldovan-Romanian dictionary (2003), of a History of Moldova (2003), written by Vasile Stati, who not only claim that there is a difference between the two ethnic groups, Romanian and Moldovan, but also state that Romania annexed Moldova in the 19 th century, subjecting it to 'roumanisation' and that the eastern part of the Moldovan kingdom, the actual republic of Moldova, is the only part that survived, preserving its name and language. The books have a map of a 'Greater Moldova' on the cover. The intention to include Romanians as a separate ethnic group in the census planned for 2004 was stated by Victor Stepaniuk, leader of the Communist Parliamentary fraction in October 2003 (Timpul, 19.12.2003). The idea was that by getting the majority of people to assert their Moldovan identity, the reason for teaching Romanian literature and history in school will disappear. Also this introduces a division inside the Romanian-Moldovan population (estimated at 70% of the entire population in the Republic of Moldova minus Transnistria), between those who would declare themselves Romanians (mostly the elite) and those who would declare themselves Moldovans-mostly the rural population, whom, in the opinion of Iulian Fruntasu (2003), have never acquired identities larger than their very local identities, which on the one hand helped them preserve their customs and language, but on the other hand hindered the process of integration into the Romanian nation, during the interwar period. This policy of division of the majority group has been actively employed by the officials: an alternative Writers' Union who would promote an anti-Romanian stance was created, as well as an alternative

The competition of national identities at local levels

There are several societal factors that catalyse the positive reception of moldovenism at local levels. The first is the ethnic composition of the country, which has 30% minorities, more than half of them born on the Moldovan territory, many of them better educated than Moldovans (Skvortsova:169) and often in leading economic positions. The russophones minorities have constantly supported a policy closer to Russia and the CIS and feared policies bringing nearer Romania. For maintaining good relations with minorities who speak poor Romanian (there had been initially an obligation for administrative staff to learn the official language of the country, but this was finally not reinforced), Moldovans continue using Russian in public spaces, as during the Soviet period. If they complain later in their personal environments about themselves being the only bilingual citizens (Romanian/Russian) in the republic, this is seldom echoed in other places than independent newspapers and among Moldovan/Romanian intellectuals (who are actually also the most proficient in Russian). Mixed marriages are frequent; constituting 21% of all marriages in rural areas and 36% in urban areas (the statistics from the socialist period includes Transnistria, where the rates are higher, Skvortsova, 2002:172). Children from mixed marriages are often sent to school in Russian schools-as many of them told me in a broken Romanian, the reason being that "the (Russian) mother wanted me to speak Russian and the (Moldovan) father was indifferent". Language is the main distinctive feature between ethnic groups in Moldova, who otherwise have the same religion (Orthodoxy). Given that most of the labour migration from Moldova has Russia as a destination (Western Europe is more inaccessible due to visa regulations), children are encouraged to learn Russian as their perspective of future employment are linked to it. Russia is the country that offers employment to large parts of the Moldovan population, especially those leaving in the eastern parts of the Republic. Discrepancies in wealth, economic opportunities and Romanian or Russian sympathies could be seen between the western parts of Moldova, more Romania-oriented and the eastern part, more former Soviet Union-oriented.

The second factor is the perception of the 1989 national revival movement in the light of the present economic distress of the Republic of Moldova. Moldova is an agricultural country with no energetic resources, with 40% of its industry today in the secessionist Transnistria. When USSR collapsed, it was the end of the 'good old times', bolshevita-the communist voting in the 2001 election is an expression of communist nostalgia and trust in a communist regime. Or many communist voters in the countryside believe their national aspirations to be the cause of the failure of the USSR and thus the cause of their present economic distress. In their despair face to the economic situation in the country, they regret the national movements and blame their current economic problems on their elites and on Romanians in general (the Moldovan/Romanian elites claim to be Romanian).

A third related factor comes from the ideologisation that took place during the socialist period. Moldovans learnt in school that the Soviets had liberated them from fascist Romanians (during the war from 1941 to1944 Romania was allied with nazi Germany), from bourgeois Romanians (some educated people in the village in which I worked ignored even the fact that Romania was a socialist country). The Soviet past with the series of deportations from the 40s did not come under public criticism as in the Baltic States. After 1989, when due to the mobilisation of urban elites in a series of demonstrations for national language and national symbols, Romanian was recognised as an official language in schools and history books became Romanian history books (on the recommendation of the Council of Europe), parts of the population saw this as a form of Romanian invasion. The policy of the Communist Party in power, 'neither with Russians, nor with Romanians', makes Moldovans see in equal terms their national relation with Russians and their relation with Romanians. This is mainly due to lack of information: isolated from the 1989 demonstrations and uninformed due to the lack of alternative nongovernmental television and radio stations that would reach the countryside (the journals are quite elite oriented and difficult to read by people who had to switch from Cyrillic to Latin characters at an adult age). Thus many rural people do not know that their Romanian national revival took place independently from the country with the same name, Romania, which at the time was under the personal dictatorship of Ceausescu. Also they do not seem to know that later movements of self declared 'Romanians' in the republic were not led by Romania as a country or by Romanians born in Romania.

To mix things up further, a new type of Romanians appeared in the Republic of Moldova. These are Moldovans (and not only of Romanian ethnic origin) who obtained Romanian citizenship in the past ten years. Given Romania's perspective for EU integration, the possibility to obtain Romanian citizenship is more and more appealing to Moldovans, who have tremendous difficulties to travel abroad and who are in their great majority seeking work abroad (official statistics count that 650 000 people, i.e.17% of the total population, work abroad). The minister of External Affairs of the Republic of Moldova drew the attention of EU authorities to the danger that "more and more citizens of the Republic of Moldova will be tempted to acquire Romanian citizenship for travelling in the Schengen space and thus the Republic of Moldova risks becoming a state with more and more Romanian citizens" (Jurnal, 23.01.2004). Romania, which is otherwise extremely shy in fraternity declarations towards the neighbouring Moldova (and this holds for the parties in power and in the opposition, except for the ultranationalists of 'Greater Romania Party', 8% of the electoral options in the June 2004 elections), has a very special citizenship policy that allows ex-Romanian citizens and their descendents to re-obtain Romanian citizenship without having to comply with residence requirements. Interestingly, this citizenship offer is what bothers less the moldovenists I have met, who in their great majority were seeking means to obtain Romanian citizenship while simultaneously blaming Romanians for stealing them their songs, authors, historical figures etc. (The story told by Ilascu, a former prisoner in Transnistria now senator in the Romania, in the Opposition press is that the promoter of moldovenism and of Greater Moldova, Vasile State, has also solicited to become 'Romanian with the right papers'.) At local levels, the confusion regarding national and ethnic identity fosters negative feelings towards Romanians, who are known to live in a more prosperous country and thus thought to afford taking over everything: Moldovan national poets, the tomb of Saint Stefan the Great and all the churches he built, the literary figures of Eminescu, Creanga, Alecsandri (it so happens that an impressive number of Romanian literature classics come from the Romanian part of Moldova, so they have been recognised also as Moldovan authors, even during the Soviet period, but being born in Romanian Moldova, are indisputably Romanian). The strongest promoters of these negative feelings are people more aware than the average of their ethnic identity and proud of their Moldovan identity, as opposed to Russian and Ukrainian identity. Imagine their disappointment face to an ethnic Romanian from Romania (such as myself) who would use the same Romanian sayings, know the same popular songs and recite the same poems, probably even better than the Moldovans, because of her/him being socialised uniquely in the Romanian culture (and knowledge of the folklore is promoted as major marker of ethnic identity, see Cash 2002). My host in Moldova, a Romanian/Moldovan pro-communist, told me one day when the TV cable was installed to catch Romanian State Television in the village, that one Romanian program was even too much! Until then, one could watch around five Ukrainian TV programs, and only with difficulty the Moldova State program (who runs for a few hours per day, in Romanian)-while there were no Ukrainian speakers in the village and there are quite a few arguments about how similar Russian (that villagers understand) and Ukrainian languages are… Clearly the unique Romanian program was seen as a danger, because it would risk becoming the unique source of information for the Moldovans in the village (the Romanian Radio is already the most listened to radio and my pro-communist host won't actually listen to anything else. One day he caught a different program, he claimed to be a Chisinau program, because of the slight Moldovan accent and music transmitted, to discover later that it was Radio Iasi, Iasi being the capital of Romanian Moldova. He did not appreciate my witnessing of his confusion).

Conclusion

In this paper I wanted to show some of the difficulties of legitimising a country on exclusively national bases. The Republic of Moldova is a multiethnic country, born out of USSR collapse in 1991, which tries to found its independence and legitimacy on the national identity of its majority, the Moldovans (Romanians). As this majority shares the same ethnic belonging, language and history as the majority of the neighbouring country, Romania, due to its springing from the same core, the only available policy for Moldovan identity creators appeared to be an aggressive denial of the common features, which was accompanied by accusatory political declarations towards the neighbouring state. While this policy appears absurd to the Romanian elites of the Republic of Moldova and to the Romanian leaders and press, it does not go without consequences at the local levels. The doctrine of 'moldovenism' is embraced by uninformed, confused sympathisers of the Communist Party, who become hostile to Romania and Romanians due to it. The cold war of declarations could thus generate more far-reaching animosities than would be expected.

  From 1941 to 1944 the Bessarabian region had a joint German-Romanian administration. On the 17 th of March 1944, the Soviet troupes crossed the Dniester and incorporated the Bessarabian region and Northern Bukovina in the USSR. Parts of the territory (Northern Bukovina and Southern Bessarabia) were incorporated into Ukraine and the remaining central part was consolidated as a new republic, the Moldavian Soviet Socialist Republic (MSSR). The frontier between the Socialist Republic of Romania and the Moldavian Soviet Socialist Republic was reinforced and the history of the two countries was rewritten from a Soviet perspective: in order to justify the new borders, Stalin created a new nation, the Moldovans, an action necessary for respecting the USSR policy of incorporating only nation states in the USSR

(

  CIA World Factbook 2003) (from the CIA-World Factbook 2003) Romania was the first state to recognise Moldova's independence, an act often invoked today by Romanian politicians to defend themselves from the accusations of expansionism made by Moldovan officials. Fear of reunification with Romania was invoked by the eastern part of the republic, Transnistria, for justifying its secession, after a short war in 1992. Though technically separated from the Republic of Moldova (frontiers, other currency, own government etc), Transnistria still belongs officially to the Republic of Moldova, not being recognized as an independent state by the international community. For twelve years negotiators seek a solution to this conflict, which often distracts the attention of international press and population from other internal problems faced by the Republic of Moldova (the most important being emigration and Romanian/Moldovan identity problems). From 1991 onwards the two states of Romania and Moldova have coexisted peacefully and engaged in cultural and economic contacts.

  Journalists' union etcLooking at the external Moldovan-Romanian relations, the year 2003 was marked by the accusation made by the Ambassador of Moldova in Paris to the City Council of Europe that Romania did not revise its history of the Holocaust (the Council of Europe formally replied to assure Moldova that Romania is in the process of revising it with supervision from the Council of Europe), by president Voronin's declaration that 'Romania is the last empire in Europe', by a letter to the Commissar for European Enlargement stating that Romania was interfering in the internal affairs of the Republic of Moldova and spending huge amounts of money on its territory without coordinating it with the officials. A practical consequence of this declaration is the fact that since the communists are in power, the educational agreements promoting student exchange and the allocation of scholarships by the Romanian state to Moldovan citizens were suspended and have still not been resumed. Despite this, the Romanian state offers scholarships to Moldovan citizens who apply for, on an individual basis, at Romanian high schools and universities. The Romanian officials defend themselves from the accusations of interference by reminding that the Romanian state was the first to recognize the independence of the Republic of Moldova and by supporting 'the European destiny of the Republic of Moldova'. Meanwhile, Romanian officials persistently state the 'special relation' between the two countries, two Romanian states, a formula strongly resisted by their Moldovan counterparts. The mass media in Romania is generally indifferent to the actions and movements of the neighbouring country. This apparent indifference of Romanian official and press is easily explainable by the fear to compromise Romania's integration into the European Union, scheduled for the 1 st of January 2007. Here is an example of the confrontation of symbols and declarations between the two states and the press in the two countries. The 2nd of July 2004 was the anniversary of 500 years since the death of Saint Stefan the Great, important historical figure of the medieval kingdom of Moldova, canonised saint at the beginning of the 90s. Both Romania and the Republic of Moldova had declared 2004 as the Year Stefan the Great. Saint Stefan the Great was celebrated with great pomp at a gathering of hundred of thousands of people at the Putna Monastery, in Romania, where the king is buried. Moldovan Opposition newspapers announced that the president of Moldova conditioned his presence at Putna in Romania, where he had been invited by the Romanian president, to the recognition of the difference between Romanian and Moldovan language. The Romanian president denied that there has been such a discussion and stated that their relations with the Moldovan president were good. The Romanian press was indifferent to the matter. The Moldovan president Vladimir Voronin organized a counter celebration of Stefan the Great in Chisinau on the same date. The presidential discourse insisted that history has rewarded Stefan with the preserve of his (Moldovan) state, language and people. His party newspaper, the Communist (2 iulie 2004), published on its front page a poem with clear territorial allusions, supported on the second page by an article entitled 'For a Unique Moldova', thus advocating the incorporation of Romanian Moldova into the Republic of Moldova. The 2 nd of July is the Saint Day of Stefan in the Romanian Orthodox Calendar. In his eagerness, the president celebrated Saint Stefan on this day, while the Republic of Moldova uses the old orthodox calendar of the Russian Orthodox Church, thus Saint Stefan's day is 13 days later than in Romania, on the 15 th of July. While the Moldovan Opposition press considers this with hilarity and contempt, as it also looks down on most of the anti-Romanian manifestations of the communists in power, I would like to argue in this paper for a much more serious consideration of the declarations, symbols and policy lead by the communists. The material that I have collected in my 2003/2004 fieldwork in the Moldovan countryside show that 'moldovenism' has an impact on the Moldovan population. Its impact ranges from confusion towards one's own identity, to competition between Moldovans and Romanians and up to hate towards Romanians.


R Lefort

SPATIO-TEMPORAL WEIGHTING FOR UNDERWATER SOURCE LOCALIZATION IN THE CONTEXT OF COHERENCE LOSS*

INTRODUCTION

In the field of underwater source localization, inversion remains the reference baseline. This approach consists of making a comparison between an analytical model of the expected acoustic pressure measured by an array antenna and the real captured one. By definition, the models are however limited to the knowledge available on the propagating medium while the propagated acoustic signal is subject to natural unpredictable ocean fluctuations. For instance, the internal waves may create spatio-temporal dynamics of the sound velocity, which introduces strong perturbations of the wave front 1 . The unpredictable acoustic wave echo due to a random seabed may produce such wave perturbations as well. The difficulty to integrate the random aspects of these natural phenomena into a physical model is the main source of the coherence loss observed in practice between sensors of a same antenna. In the literature, a lot of studies characterize a region in the ocean by analyzing the observed loss of coherence [START_REF] Carey | The determination of signal coherence length based on signal coherence and gain measurements in deep and shallow water[END_REF][START_REF] Collis | Observed limiting cases of horizontal field coherence and array performance in a time-varying internal wavefield[END_REF][START_REF] Duda | Horizontal coherence of low-frequency fixed-path sound in a continental shelf region with internal wave activity[END_REF] . Some experiments have also been carried out in a tank to reproduce the loss of coherence on a measured signal, with the objective of proposing new processing methods 12,13 .

In this paper, we are interested in the investigation of some processing methods that automatically correct the loss of coherence from the interpretation of the observed signal in situ. Among the various approaches we can think of, machine-learning techniques stand for an appropriate solution to deal with any losses of coherence 10 as they do not require any prior knowledge on the propagating medium but learn it instead. These techniques however require consistent training databases that may prevent their use in embedded acquisition systems. In this paper, we propose a new inversion method exploiting statistical knowledge on the acquired pressure field. If the perturbation is considered to be a stationary random process, the random characteristics are not depending on the time or, equivalently, the snapshot index. In that case, we can infer some parameters of the process, under an additional Gaussian assumption. Knowing the covariance matrix, it is consequently possible to cancel out any effects of the coherence loss [START_REF] Gershman | Matrix fitting approach to direction of arrival estimation with imperfect spatial coherence of wavefront[END_REF][START_REF] Paulraj | Direction of arrival estimation by eigen structure methods with imperfect spatial coherence of wave fronts[END_REF] . But, the random ocean fluctuations make this random process not stationary in practice, leading to both spatial and temporal perturbation of the acoustic field. As a consequence, the coherence loss will not be the same from one snapshot, e.g. one time, to another. In a recent paper, this problem is addressed by a mixture model that classifies each snapshot according to two classes: "coherent" or "not coherent" 7 . This can be interpreted as a snapshot weighting method which gives a higher weight to those coherent snapshots. The problem may also be addressed from the point of view of sub-antenna processing [START_REF] Cox | Line array performance when the signal coherence is spatially dependent[END_REF] . In such a case, we suppose that each sub-antenna of each snapshot is locally coherent, thus, each sub-antenna independently applies a conventional localization method, such as a beamforming method.

In this paper, we propose a decision model that combines both the idea of sub-antenna processing and the concept of snapshot weighting. Unlike Cox's works 4 , our sub-antenna structure is not based on adjacent antenna pieces, each sub-antenna results from a sliding Gaussian function instead. In addition, unlike Ge's works 7 , we make the hypothesis that we know neither the signal power nor the noise power, and also, that we do not know the prior probability distribution of a coherent snapshot. Instead, we make use of the so-called "Mutual Coherence Function" to identify how coherent is a measured snapshot. In order to model the loss of coherence, we exploit a multiplicative noise, as recommended by Flatté 5 . This type of noise is indeed well-suited to model a perturbation attached to an incoming wave, noticing that a multiplicative noise on the expected pressured field leads to an additive noise on the incoming wave phase. In the experiments, we show that our spatio-temporal weighting approach may outperform a conventional beam-former and some other baselines.

The paper is organized as follows. In section 2 we present the model used to characterize the coherent loss, in section 3 we present the model of source localization, in section 4 we propose experimental comparisons with baseline references, and we finally conclude in section 5.

MODEL OF LOSS OF COHERENCE

In this paper, we restrict our study to a single monochromatic source. Formally, let f be the emitting frequency of the source and θ its position. Note that this position may be the direction of arrival of plane waves or the {range, elevation} coordinates of spherical waves. Let " # (%) ∈ ℂ be the Fourier representation of the emitted signal at the frequency ) at time +. Considering an array composed of , sensors, the model of a coherent received signal usually takes the following form:

-# = " # (%)/(%) + 1 # (1)
Where -# ∈ ℂ 2×4 denotes a snapshot, i.e. a Fourier representation of the captured signal at frequency ) at time +, and /(%) ∈ ℂ 2×4 denotes a physical model of -# . For instance, when the source is far enough, we consider that the acoustic propagation can take the form of a plane wave: /(%) = 56 7 89:∆ <=>(?) , 6 7 89:8∆ <=>(?) , … , 6 7 89:2∆ <=>(?) # $

Where . $ stands for the transpose operator, & denotes the sound celerity and ∆ the distance between two consecutive sensors. The white additive noise 1 # ∈ ℂ 2×4 represents some electrical noise that follows a multivariate complex normal distribution: '(1 # ) = ()(*, + # 8 , 2 ), with zero mean and a diagonal covariance matrix + # 8 , 2 , with + # ∈ ℝ proportional to the noise power and , 2 ∈ ℝ 2×2 the identity matrix. In this paper, we assume that we do not know + # .

Let . # ∈ ℂ 2×4 be a random vector modeling the loss of coherence due to the fluctuations of the propagating medium. We assume that it is distributed according to a zero-mean multivariate complex normal distribution of covariance matrix / # ∈ ℝ 2×2 : '(. # ) = ()(*, / # ). In comparison to the white noise 1 # that has independent components, the components of . # are assumed to be statistically dependent. Formally, it is implemented into the observation model (1) as a multiplicative noise:

-# = " # (%)0/(%) × . # 1 + 1 # (3) Where the operator × denotes an element-by-element vector multiplication.

Let us now consider some more interpretations. The model of multiplicative noise is not new in the literature. Flatté has considered this model to study and statistically characterize different regimes of fluctuations 5 . De facto, multiplicative complex noise is well-suited to model additive phase noise (and some kind of attenuation) on incoming waves. Here, we assume a not-diagonal covariance matrix / # , such that we are able to statistically model the sensor dependencies. In practice, it is possible to relate the elements of / # to the local coherence length of the fluctuation, say 2 , so that it validates the effectively observed correlation between two sensors of the array, depending on their distance. Hence each element / # (3 4 , 3 8 ) of the covariance matrix is Gaussian-like expressed as:

/ # (
The way the signal is coherent in time and space is then directly modeled by the way the sensors are correlated. In figure 1, we show three realizations of three different random processes that we have simulated. In this figure, we plot the phase of the coherence loss arg (. # ) for each sensor of each snapshot. For instance, in figure 1-a, by changing the covariance matrix / # at each snapshot, we have been able to generate a loss of coherence that is not stationary, the coherence loss being spatially constant. In figure 1-b, we have simulated a loss of coherence from a single covariance matrix / # , making the realization stationary, but the loss of coherence is not spatially constant in the array: the first part of the antenna is more coherent than the second part. In figure 1-c, we combine the two previous cases: the random process that generate . # is not stationary and the loss of coherence is not spatially constant. This paper takes place in the context of the general scenario of figure 1-c that involves losses of coherence that are not constant in both space and time. (c) Figure 1. We plot the phase of the loss of coherence arg (. # ) as a function of both the sensor index and the snapshot index. Figure 1-a: the random process . # is depending on time and the loss of coherence is spatially constant. Figure 1-b: the random process . # is not depending on time and the loss of coherence is not spatially constant. Figure 1-c: the random process . # is not depending on time and the loss of coherence is not spatially constant.

MODELS OF SOURCE LOCALIZATION

Conventional beamforming

The conventional beamforming is used for any source signal which is modelled from the expression (1). It consists in finding the source position that maximizes the estimated source signal intensity:

% ? = arg max ? B|"̂#(%)| 8 $ #E4 (5)
Where F denotes the number of snapshots. The optimization problem ( 5) is greedy solved by grid search. The estimated source signal intensity is the solution of the square error minimization problem: "̂#(%) = arg min I J (?)

‖-# -" # (%)/(%)‖ 8 (6) The solution of (6) being given by "̂#(%)=/(%) M -# /(%) N /(%) ⁄ , the conventional beam-former thus takes the form of:

% ? = arg max ? B P /(%) M -# /(%) N /(%) P 8 $ #E4 (7)

Temporal weighting

In this part, we consider that the source signal is subject to some loss of coherence accordingly to expression (3). In addition, we consider that the loss of coherence . # is random sampled from a random process that is not stationary but spatially constant. Examples of such realizations are given in figure 1-a. Ge has proposed a method to weight each snapshot contribution 7 , but it requires to know some environmental parameters such as the signal power, the white noise power, and also, the prior probability that a snapshot is coherent. Instead, in this paper, the method we investigate is not depending of such crucial parameters. We just extend the expression [START_REF] Dashen | Sound Transmission through a Fluctuating Ocean[END_REF], by adding a weighting variable Q # that indicates how coherent a snapshot is:

Vol. 38. Pt. 3. 2016 % ? = arg max ? B Q # P /(%) M -# /(%) N /(%) P 8 $ #E4 (8)
The weighting parameter is expressed as follows:

Q # = R|S 7 (-# )| T3 (9)
Where S 7 (-# ), also called the "Mutual Coherence Function"

3,12,13

, measures the averaged statistical correlation in the complex domain between two sensors separated by 3 sensors:

S 7 (-# ) = ∑ -# (V) N -# (V + 3) W X∑ |-# (V)| 8 W X∑ |-# (V + 3)| 8 W (10)
For a given measured snapshot, if all the sensors are coherent, thus |S 7 (-# )| = 1 for all 3 and thus Q # = 1. On the contrary, in the presence of coherence loss, we observe that |S 7 (-# )| tends toward 0 when 3 is increasing, by consequence Q # tends toward 0.

Spatial weighting

In this section, we design a sub-antenna model from a weighting vector Z 7 ∈ ℝ 2×4 , where:

Z 7 = [6 45.6\ 744 ] ^9, … , 6 45.6\ 742 ] ^9 _ $ (11)
The shape of each sub-antenna is therefore drawn from a Gaussian-like function, the parameter ` being setting the sub-antenna length. Doing so, we aim to mimicking the front distortion of the incoming waves induced by some fluctuations modeled as in (3), the parameter ` playing a similar role as the coherence length 2 . . We ensure that each sensor is a centroid of coherence by making the Gaussian sliding along the antenna. There are consequently as many sub-antennas as there are sensors in the antenna. The beam-former therefore takes into account the contribution of each snapshot of each sub-antenna:

% ? = arg max ? B Ba"̂7 ,# (%)a 8 $ #E4 2 7E4 (12)
Where "̂7 ,# (%) ∈ ℂ denotes the Fourier representation of this signal in % from the point of view of the sub antenna. In addition, we make the major assumption that the sensors are locally coherent. In other words, we consider that there is not any loss of coherence in a sub antenna drawn by Z 7 .

Accordingly, the model (3) can be rewritten in its coherent form: 0b 7 × -# 1 = " 7,# (%)/(%) + 1 # (13) The estimated source signal intensity is the solution of the square error minimization problem:

"̂7 # (%) = arg min I J (?) c0b 7 × -# 1 -" 7,# (%)/(%)c

Spatio-temporal weighting

The method we investigate in this section combines both the spatial weighting of section 3.3 and the temporal weighting of section 3.2. The proposed beam-former is a combination of equations ( 8) and ( 15 (c) (d) Figure 4. We compare the localization performance of the methods presented in section 3. In figure, 4-a, the average localization error is reported as a function of the Signal to Noise Ratio (SNR) of the white noise 1 # . In figure 4-b, it is reported as a function of the proportion of coherent sensors in the first snapshot. In figure 4-c, it is reported as a function of the number of snapshots. In figure 4-d, it is reported as a function of the coherence length 2 in equation (4).

Discussion and perspectives

On the first hand, the simulation results we have obtained are very encouraging and promising. Figure 4 indeed shows that our proposed method outperforms some well-known baselines in the scenario that we have considered. On the second hand, it raises numerous questions about both the applicability and the perspective of the approach.

The methods, called "spatial weighting" and "spatio-temporal weighting", respectively presented in sections 3.3 and 3.4, are roughly based on sub-antenna processing. The consequence of such a smaller antenna is a reduction of the spatial resolution. This may be an issue in multi-source cases. Especially, the averaging effect may, if not increase, at least fail to improve the localization error in the case of low SNR. As an example, in figure 4-a, in the case of low SNR, there is no improvement by using these sub-antenna approaches. We therefore encourage the development of high-resolute versions of sub-antenna processing. For instance, a techniques exploiting more prior information on the sources, as sparsity, may be adapted in that specific case 9 .

In this paper, the free parameter ` has been set empirically. Instead, this could be addressed from the point of view of an optimization problem that consists of finding the best parameter value, the one that matches the best with the data. For instance, a dynamic parameter `7,# that depends on both the sensor index and on the snapshot index would be interesting. In the example of figure 1-b, a low value should be reached in the noisy part of the antenna, while a high value should be reached in the coherent part. Moreover, it should be possible to define the vector Z 7 as a discrete vector, the objective being to directly optimize its components. For instance, the objective function to optimize could be dependent on the Mutual Coherence Function integration (17).

8 ( 14 )

 814 This leads to the following sub-antenna beam-former:

  According to section 3.2, the weight Q 7,# is a coherence indicator of the +th snapshot received by the 3th sub-antenna, drawn by the Z 7 weighting:Q 7,# = RaS 7 (-7,# )a T3(17)

Proceedings of the Institute of AcousticsVol. 38. Pt. 3. 2016

This work has been supported by the DGA/MRIS.

Proceedings of the Institute of Acoustics

Vol. 38. Pt. 3. 2016 Where S 7 (-7,# ) is defined as in equation [START_REF] Lefort | Direct regressions for underwater acoustic source localization in fluctuating oceans[END_REF]. This approach allows us to weight each sub-antenna according to its observed intrinsic loss of coherence.

In figure 2-b, we give the evaluated dQ 7,# e, for all 3, +, for the particular realization of the sampled noise . # given in figure 2-a. In this experiment, we have random sampled a snapshot before we have added the coherent noise f. # g and computed dQ 7,# e by using equation ( 17). The signal-tonoise ratio related to the additive white noise 1 # is infinite (noiseless case). As expected, the more the coherence loss . # , the closer to 0 the weighting parameter Q 7,# . On the contrary, when the loss of coherence is constant between some sensors, the corresponding weighting parameter is close to 0.

arg (. # )

) Figure 2. In figure 2-a, we show arg (. # ) the phase of a dynamic random loss of coherence as a function of both the snapshot index and the sensor index. In figure 2-b, we show the corresponding weighting parameter Q 7,# .

EXPERIMENTS

Simulation protocol

We consider the problem of assessing the direction of arrival (DOA) of a plane wave. The distance ∆ between two consecutive sensors is chosen such that the Shannon property remains valid: ∆= 8: .

In this context, the replica /(%) is given by model [START_REF] Carey | The determination of signal coherence length based on signal coherence and gain measurements in deep and shallow water[END_REF]. We consider an antenna composed of , = 32 sensors. The inverse problem is solved by searching in a grid 128 possible DOA in j 49 k , 9 k l. We consider m = 5000 Monte Carlo iterations to compute an average localization error. More precisely, at each iteration p ∈ f0, … , mg, we random sample a DOA % q ∈ j 49 k , 9 k l. Let % ? q be the estimated DOA, we then compute the normalized localization error and we deduce the mean localization error from:

∑ a% q -% ? q a r qE4

.

We generate the received pressure field according to model (3). We consider the following scenario where the first snapshot is assumed to be the only one "partly coherent". This is illustrated in figure 3-a and b by the covariance matrices used to draw the coherence losses of the snapshots. More precisely, the loss . 4 of the first snapshot is generated from the covariance matrix / 4 that is shown in figure 3-a. This covariance matrix is such that the coherence loss is weak (the coherence length equals 2 = 10 sensors) on the first part of the antenna, while it is strong on the other part of the antenna, with a coherence length of 2 = 0.1 sensors. For the other snapshots, the loss of coherence is assumed also strong, with a coherence length of 2 = 0.1 sensors along the antenna. The covariance matrix / # , for all + ≠ 1, is shown in figure 3-b. Note that, in order to random sample . # , we must ensure that the covariance matrix / # is positive definite. We therefore replace / # by a nearest positive one:

Proceedings of the Institute of Acoustics

Vol. 38. Pt. 3. 2016

In this paper, the free parameter ` in ( 11) is empirically set to `= 4 sensors, whatever the coherence length 2 . In this regard, it is worth noticing that the link between both parameters 2 and ` is not obvious. The first one is part of a probabilistic model, and as such, will be representative of an average behavior of the coherence loss, while the other set deterministically the weights given to each sensor within the sub-antennas. In practice, this choice of `= 4, although clearly not optimal, was sufficient to get the good results presented in the next subsection. We discuss further possible optimization developments of parameter ` in section 4. In figure 4-a, the average localization error is reported as a function of the SNR of the random white noise 1 # . As expected, the less the SNR the more the localization error, but in a favorable case of positive SNR, we find that the spatio-temporal weighting outperforms the other approaches by a factor of two. We also notice the improvement brought by a spatial weighting and a temporal weighting that both outperform a conventional beam-forming.

Results

In figure 4-b, the localization error is reported as a function of the proportion of coherent sensors in the first snapshot. When the proportion is set to 0, none of the sensors are coherent in the first snapshot, making the localization task very tough and the error very high. On the contrary, we observe a very low localization error when this proportion tends toward one, all the sensors being consequently coherent. In between, when the proportion between the number of coherent and not coherent sensors is more balanced, the spatio-temporal approach is able to identify the informative part which makes the localization error decreased.

In figure 4-c, the localization error is reported as a function of the number of snapshots. We note that the spatio-temporal processing drastically outperforms any other approach even if the localization error increases when the number of snapshots increases. The reason why the error increases as the number of snapshots increases is that all the snapshots we add are fully not coherent, as describes in section 4.1.

In figure 4-d, the localization error is reported as a function of the coherence length 2 (equation ( 4)) in the coherent part of the first snapshot. Similarly to the previous results, we note that the proposed spatio-temporal outperforms by a factor of two.

Proceedings of the Institute of Acoustics

Vol. 38. Pt. 3. 2016

Finally, it would be of interest to evaluate the proposed approach on a real dataset acquired in situ. The data measurements carried out by Badiey et. al. reveal a huge temperature dynamics and, consequently, a spatio-temporal variation of the sound velocity profile 1 . The effects of such observed losses of coherence could be dealt with our proposed approach. To complete this task, it is possible to extend the model (2) to broadband signal as well as to multi modal propagated signals in shallow water.

CONCLUSION

We have proposed a method to deal with the problem of spatio-temporal dynamic fluctuation of a propagation channel. This method combines the optimality of the sub-antenna processing as well as the idea of weighting the snapshots according to their degree of coherence.

The approach is assessed through various synthetic experimentations paving the way of promising developments. Future work will in particular focus on introducing more prior information on each sub-antenna processing in order to deal with the multi-source case.


Prachi Rastogi

$ Audrey Chu

Charlie Gréboval

Junling Qu

Ulrich Nguétchuissi Noumbé

Sang-Soo Chee

Mayank Goyal

Adrien Khalili

Xiang Zhen Xu

Hervé Cruguel

Sandrine Ithurria

Bruno Gallas

Jean-Francois Dayen

Lenart Dudy

Mathieu G Silly

Gilles Patriarche

Aloyse Degiron

Gregory Vincent

Emmanuel Lhuillier

Pushing Absorption of Perovskite Nanocrystals into the Infrared

Keywords: Perovskites, Formamidinium lead iodine, nanocrystal, short-wave infrared, light matter-coupling, resonator

To date defect-tolerance electronic structure of Lead halide perovskite nanocrystals is limited to optical feature in the visible range. Here, we demonstrate that IR sensitization of formamidinium lead iodine (FAPI) nanocrystals array can be obtained by its doping with PbS nanocrystals. In this hybrid array, absorption comes from the PbS nanocrystals while transport is driven by the perovskite which reduces the dark current compared to pristine PbS. In addition, we fabricate a field-effect transistor using a high capacitance ionic glass made of hybrid FAPI/PbS nanocrystal arrays. We show that the hybrid material has an n-type nature with an electron mobility of 2 x 10 -3 cm 2 V -1 s -1 . However, the dark current reduction is mostly balanced by a loss of absorption. To overcome this limitation, we couple the FAPI/PbS hybrid to a guided mode resonator, that can enhance the infrared light absorption.

Beyond their bright luminescence in the visible, nanocrystals (NCs) have raised interest for the design of optoelectronic devices and especially for infrared (IR) sensors. [START_REF] Hafiz | Colloidal Quantum Dots for Thermal Infrared Sensing and Imaging[END_REF][START_REF] Lhuillier | Recent Progresses in Mid Infrared Nanocrystal Optoelectronics[END_REF][START_REF] Tang | Dual-Band Infrared Imaging Using Stacked Colloidal Quantum Dot Photodiodes[END_REF] Particularly, lead chalcogenides have attracted much attention for the design of solar cells collecting the near infrared (NIR) part of the solar spectrum. [START_REF] Nozik | Quantum Dot Solar Cells[END_REF][START_REF] Chuang | Improved Performance and Stability in Quantum Dot Solar Cells through Band Alignment Engineering[END_REF][START_REF] Carey | Colloidal Quantum Dot Solar Cells[END_REF] However, over the recent years, solar cells based on PbS colloidal quantum dots (CQDs) have been challenged by the growing competition of perovskite materials. While PbS CQD solar cells achieved competitive short circuit current, the trap states lead to a reduced open circuit voltage [START_REF] Chuang | Open-Circuit Voltage Deficit, Radiative Sub-Bandgap States, and Prospects in Quantum Dot Solar Cells[END_REF][START_REF] Pradhan | Origin of the Below-Bandgap Turn-On Voltage in Light-Emitting Diodes and the High VOC in Solar Cells Comprising Colloidal Quantum Dots with an Engineered Density of States[END_REF] (0.6 V which is half of the band gap), limiting their power conversion efficiency.

Lead halide perovskites present a defect-tolerant electronic structure, which accommodate the presence of dangling bonds on the NC surface. This property facilitates solar cells with large open circuit voltage [START_REF] Suri | Enhanced Open-Circuit Voltage of Wide-Bandgap Perovskite Photovoltaics by Using Alloyed (FA1-XCsx)Pb(I1-XBrx)3 Quantum Dots[END_REF][START_REF] Swarnkar | Quantum dot-induced phase stabilization of α-CsPbI3 perovskite for highefficiency photovoltaics[END_REF][START_REF] Akkerman | Strongly Emissive Perovskite Nanocrystal Inks for High-Voltage Solar Cells[END_REF] (>1 V) and leads to high photoluminescence efficiencies without shells passivating the surface. [START_REF] Swarnkar | Colloidal CsPbBr3 Perovskite Nanocrystals: Luminescence beyond Traditional Quantum Dots[END_REF][START_REF] Protesescu | Nanocrystals of Cesium Lead Halide Perovskites (CsPbX3, X = Cl, Br, and I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut[END_REF] In spite of this success, the band gap of lead halide perovskite solar cells remains large which prevents the absorption of the NIR part of the solar spectrum. Alternatively, replacing lead by tin allows to reduce the band gap, but it also reduced the material stability. [START_REF] Jellicoe | Synthesis and Optical Properties of Lead-Free Cesium Tin Halide Perovskite Nanocrystals[END_REF] So far, reducing the band gap of perovskite materials to enable their absorption in the IR range appears as a major limitation in the field.

To address the IR spectrum using formamidinium lead iodine (FAPI) perovskite NCs we incorporate PbS NCs. The strategy of mixing PbS CQDs with thin films (bulk) of perovskite has already been explored, [START_REF] Masi | Chemi-Structural Stabilization of Formamidinium Lead Iodide Perovskite by Using Embedded Quantum Dots[END_REF][START_REF] Ning | Quantum-Dot-in-Perovskite Solids[END_REF][START_REF] Yang | Colloidal Quantum Dot Photovoltaics Enhanced by Perovskite Shelling[END_REF] either to push the absorption [START_REF] Yang | Mixed-Quantum-Dot Solar Cells[END_REF][START_REF] Zhao | Efficient Visible-Near-Infrared Hybrid Perovskite:PbS Quantum Dot Photodetectors Fabricated Using an Antisolvent Additive Solution Process[END_REF][START_REF] Manekkathodi | Solution-Processed Perovskite-Colloidal Quantum Dot Tandem Solar Cells for Photon Collection beyond 1000 nm[END_REF][START_REF] Zhu | Enhanced Efficiency of Perovskite Solar Cells by PbS Quantum Dot Modification[END_REF][START_REF] Ngo | PbS Quantum Dots as Additives in Methylammonium Halide Perovskite Solar Cells: The Effect of Quantum Dot Capping[END_REF][START_REF] Yang | Effects of Incorporating PbS Quantum Dots in Perovskite Solar Cells Based on CH3NH3PbI3[END_REF] of the material toward the IR or as a way to achieve NIR light emitting diodes. [START_REF] Zhang | PbS Capped CsPbI3 Nanocrystals for Efficient and Stable Light-Emitting Devices Using p-i-n Structures[END_REF] Here, we use an all-nanocrystals-based approach and push the final material absorption up to the short-wave IR (1.5 µm at the absorption peak). By pushing the IR sensitization toward longer wavelength (1.7 µm) compared to previous work (around 1.2 µm ), we can anticipate a higher role of the interface band offset between the two materials. [START_REF] Masi | Chemi-Structural Stabilization of Formamidinium Lead Iodide Perovskite by Using Embedded Quantum Dots[END_REF][START_REF] Ning | Quantum-Dot-in-Perovskite Solids[END_REF][START_REF] Yang | Colloidal Quantum Dot Photovoltaics Enhanced by Perovskite Shelling[END_REF][START_REF] Yang | Mixed-Quantum-Dot Solar Cells[END_REF][START_REF] Zhao | Efficient Visible-Near-Infrared Hybrid Perovskite:PbS Quantum Dot Photodetectors Fabricated Using an Antisolvent Additive Solution Process[END_REF][START_REF] Manekkathodi | Solution-Processed Perovskite-Colloidal Quantum Dot Tandem Solar Cells for Photon Collection beyond 1000 nm[END_REF][START_REF] Zhu | Enhanced Efficiency of Perovskite Solar Cells by PbS Quantum Dot Modification[END_REF][START_REF] Ngo | PbS Quantum Dots as Additives in Methylammonium Halide Perovskite Solar Cells: The Effect of Quantum Dot Capping[END_REF][START_REF] Yang | Effects of Incorporating PbS Quantum Dots in Perovskite Solar Cells Based on CH3NH3PbI3[END_REF] In addition, coupling of PbS CQD with perovskite (bulk) matrix was achieved via epitaxial connection between two materials [START_REF] Ning | Quantum-Dot-in-Perovskite Solids[END_REF] ; and thus wave function in the PbS was leaking into the perovskite, affecting the optical spectrum. Here, by mixing two population we can independently tune their band gap. To benefit from such hybrid structures, the loss of absorption originated from the FAPI needs to be balanced by lower dark current. To reach this goal, we demonstrate that the ratio of FAPI needs to be above the percolation threshold of the PbS CQDs. In this case, the transport is driven by the "wide" band gap of FAPI that reduces the dark current with respect to pristine PbS.

To probe transport in this hybrid material, we use a field-effect transistor (FET) configuration. However, so far there is no report for perovskite NCs based FET. Conventional dielectrics have been unsuccessful to displace the Fermi level close to the valence and conduction band likely due to the Fermi level position located at the middle of the gap. [START_REF] Mir | Strategy to Overcome Recombination Limited Photocurrent Generation in CsPbX3 Nanocrystal Arrays[END_REF][START_REF] Amelot | Revealing the Band Structure of FAPI Quantum Dot Film and Its Interfaces with Electron and Hole Transport Layer Using Time Resolved Photoemission[END_REF] Alternative attempts based on electrolyte gating result in the dissolution of the ionic perovskite NCs. Here, we use a high capacitance gate made of ionic glass, enabling us for the first time to extract the field effect mobility of a perovskite NCs film. Finally, we introduce a plasmonic resonator based on guided modes to improve the IR absorption in FAPI/PbS hybrid film. Introduction of such guided mode resonators [START_REF] Chu | Near Unity Absorption in Nanocrystal Based Short Wave Infrared Photodetectors Using Guided Mode Resonators[END_REF] (GMRs) not only enhances the absorption of the film above the one of pristine PbS, but also generates electrical gain. [START_REF] Konstantatos | Colloidal Quantum Dot Photoconductive Photodetectors: Transport, Traps, and Gain[END_REF] We are thus able to improve the detectivity by one order of magnitude, compared to the film of pristine PbS.

We demonstrate IR sensitization of a perovskite NC array by doping them with PbS NCs. FAPI has been selected as the perovskite host matrix. This choice is a good trade-off between the material stability and the band gap value. The latter needs to be larger than the one of the IR absorbing PbS NCs to reduce the thermally activated carrier density associated with dark current. However, a wide band gap will prevent an efficient charge transfer from the IR sensitizer to the perovskite host matrix due to the presence of large energy offset. FAPI is synthesized using the procedure given by references [START_REF] Zhang | PbS Capped CsPbI3 Nanocrystals for Efficient and Stable Light-Emitting Devices Using p-i-n Structures[END_REF][START_REF] Fu | Unraveling Exciton-Phonon Coupling in Individual FAPbI3 Nanocrystals Emitting near-Infrared Single Photons[END_REF] , leading to a 750 nm (1.65 eV) band edge energy, with a bulk like absorption spectrum, see Figure 1b. The FAPI particles show a cubic shape according to transmission electron microscopy (Figure 1a).

PbS NCs are grown [START_REF] Moreels | Size-Dependent Optical Properties of Colloidal PbS Quantum Dots[END_REF] with a band edge appearing at 1.5 µm (0.82 eV), which is slightly bluer than the targeted detection wavelength (1.55 µm) to account for the redshift occurring when the material is processed under film form and its ligands are stripped off. PbS NCs have a spherical shape, see transmission electron microscopy (TEM) image in Figure 1c.

When a fresh solution of FAPI is mixed with PbS NCs, we observe an absorption (Figure 1e) which presents contribution from the two materials with both an edge in the short wave infrared (SWIR) at 1.5 µm and a slope disruption resulting from the FAPI host matrix around 750 nm. This confirms that the two materials are preserved after mixing. Electron microscopy (Figure 1d) and energy dispersive X-ray spectroscopy (Figure S1 andS2) results also support the mixing of the two materials at the nanoscale.

Figure 1 a Transmission electron microscopy (TEM) image of FAPI NCs. b. Absorption spectra of FAPI and PbS NCs . c TEM image of PbS NCs with a band edge at 1500 nm (after synthesis). d. High angle annular dark field TEM image of a FAPI/PbS mixture. FAPI have a characteristic square shape, while PbS are small spheres. e. Absoprtion spectra of FAPI/PbS mixture with various PbS ratios. f. Photoemission signal relative to the valence band for FAPI, PbS and FAPI/PbS (35% PbS content). Inset is a band diagram for FAPI and PbS NCs. The Fermi energy is set at 0 eV.

To further explore the electronic structure of the hybrid material, we use X-ray photoemission spectroscopy. A complete analysis of the core levels for the pristine material and the hybrid material is given in Figure S3-8. No shift of the core level binding energy has been noticed, revealing that (i) material integrity is preserved after mixing and (ii) no charge transfer occurs between the two materials under dark condition.

The PbS prepared under such condition is found to be quasi n-type degenerated [START_REF] Chu | HgTe Nanocrystals for SWIR Detection and Their Integration up to the Focal Plane Array[END_REF] (i.e. Fermi level lies very close to the conduction band), while for FAPI the Fermi level is deep into the band gap. [START_REF] Zhang | PbS Capped CsPbI3 Nanocrystals for Efficient and Stable Light-Emitting Devices Using p-i-n Structures[END_REF] We determine it here to be located on the n-side (i.e. upper part of the conduction band) suggesting some degree of fluctuation from sample to sample. The band alignment between PbS and FAPI is found to be type I, see the inset of Figure 1f. The probing of the valence band state by photoemission clearly indicates that the valence band state in the mixture corresponds to PbS, see Figure 1f.

We then deposit the materials onto electrodes in order to measure their transport properties and demonstrate the IR sensitization of the perovskites. The ligands of the hybrid material are exchanged by dipping the film into a solution of lead acetate in ethyl acetate. [START_REF] Swarnkar | Quantum dot-induced phase stabilization of α-CsPbI3 perovskite for highefficiency photovoltaics[END_REF][START_REF] Yang | Effects of Incorporating PbS Quantum Dots in Perovskite Solar Cells Based on CH3NH3PbI3[END_REF] I-V curves under illumination at 1.55 µm are given in Figure 2a-c for various PbS content. As expected from its band gap value, the pristine PbS is photoconductive under IR illumination (Figure 2c). Similarly, when the PbS ratio becomes low, almost no current modulation is obtained in the IR (Figure 2a). This picture is consistent with the photon energy (0.8 eV) being smaller that the band gap of the perovskite (1.65 eV). For intermediate PbS content, we observe a clear IR photocurrent modulation (Figure 2b). The PbS content also affects the material time response and we found that the very low PbS content has a slow response, consistent with bolometric effect. Once PbS is introduced, the response fastens, see Figure S9 and S10, but while the pristine PbS also presents a slow contribution (likely from traps), the hybrid response only presents a single fast contribution. To confirm that the response is induced by the PbS absorber, we measure the photocurrent of the hybrid material for various PbS contents and we clearly observe that the IR photoconduction follows the absorption of PbS, see Figure 2d. In Figure 2e and f, we follow how the dark conduction, the responsivity and the light to dark current ratio are influenced by the PbS content in the FAPI host matrix. Two regimes are clearly observed. When FAPI is introduced into pure PbS, we observe a reduction of the dark conductance, due to the wider band gap nature of FAPI which has less thermally activated carriers. The material also contains less absorbers which lead to a decrease of the responsivity. Nevertheless, responsivity does not drop as fast as the dark current. At very low PbS content, the IR absorption becomes too weak due to the lack of absorbing dopants. As a result, there is an optimal doping value, maximizing the light to dark current modulation, see Figure 2f. The latter being around 35%. In the following, this PbS ratio will be used for the hybrid material.

To further understand the electronic structure and charge transfer into this hybrid material, we then design a FET configuration. While FET has been reported for perovskite thin films, [START_REF] Senanayak | Understanding Charge Transport in Lead Iodide Perovskite Thin-Film Field-Effect Transistors[END_REF][START_REF] Chin | Lead Iodide Perovskite Light-Emitting Field-Effect Transistor[END_REF][START_REF] Li | The Effect of Thermal Annealing on Charge Transport in Organolead Halide Perovskite Microplate Field-Effect Transistors[END_REF] this tool is still lacking for perovskite NCs. To obtain a high capacitance gate we use an approach based on ionic glass. In such glass, the application of an electric field on the substrate can displace vacancies to the surface of the material and generates a polarization. [START_REF] Biscaras | Onset of Two-Dimensional Superconductivity in Space Charge Doped Few-Layer Molybdenum Disulfide[END_REF] Here, we utilize a LaF3 glass which has been successful for the gating of 2D materials [START_REF] Wu | A Two-Dimensional MoS2 Catalysis Transistor by Solid-State Ion Gating Manipulation and Adjustment (SIGMA)[END_REF][START_REF] Wu | Gate-Induced Metal-Insulator Transition in MoS2 by Solid Superionic Conductor LaF3[END_REF][START_REF] Noumbé | Ionic Glass-Gated 2D Material-Based Phototransistor: MoSe2 over LaF3 as Case Study[END_REF] and narrow band gap NCs films. [START_REF] Gréboval | Field-Effect Transistor and Photo-Transistor of Narrow-Band-Gap Nanocrystal Arrays Using Ionic Glasses[END_REF][START_REF] Noumbé | Reconfigurable 2D/0D p-n Graphene/HgTe Nanocrystal Heterostructure for Infrared Detection[END_REF] This gating approach combines two key advantages with respect to the colloidal perovskite material. First, it is a high capacitance (400 nF.cm -2 ) method, [START_REF] Wu | A Two-Dimensional MoS2 Catalysis Transistor by Solid-State Ion Gating Manipulation and Adjustment (SIGMA)[END_REF] with a sheet capacitance 30 times larger than the one of a conventional dielectric and only a factor 2-5 weaker than the one obtained from electrolyte gating. It consequently allows to strongly modulate the relative position of the band with respect to the Fermi level. Second, it is an all solid-state approach which prevents the perovskite from any exposition to dissolving solvent.

Using this approach, we obtain a FET which scheme is depicted in Figure 3a and whose channel is made of a perovskite NC film doped with IR absorber. The hybrid material appears to have the n-type nature according to the transfer curve, see Figure 3b and c and S11. The on-off ratio reaches four orders of magnitude. For the sake of comparison, for pristine PbS NCs with the same gate, an ambipolar behavior was reported with a two orders of magnitude current modulation. [START_REF] Wu | A Two-Dimensional MoS2 Catalysis Transistor by Solid-State Ion Gating Manipulation and Adjustment (SIGMA)[END_REF] This change indicates the filtering effect of the perovskite which allows the electron transfer while preventing the hole transfer. This picture is consistent with the band alignment obtained from photoemission. The Schottky barrier for the electron transferred into the perovskites is weaker than that of the hole. We have determined also the electron mobility to be 2x10 -3 cm 2 .V -1 s -1 . Such value was still lacking for perovskite NC arrays. It gives an idea of the inter-nanoparticle coupling in a ligandexchanged array of perovskites NCs. The obtained value is close to the one obtained for conventional solidstate metal chalcogenides NCs, [START_REF] Lhuillier | Mid-Infrared HgTe/As2S3 Field Effect Transistors and Photodetectors[END_REF][START_REF] Liu | Dependence of Carrier Mobility on Nanocrystal Size and Ligand Length in PbSe Nanocrystal Solids[END_REF] but remains weaker than state of the art value obtained for phase transfer ligand exchanges using ionic surface chemistry. [START_REF] Nag | Metal-Free Inorganic Ligands for Colloidal Nanocrystals: S 2-, HS -, Se 2-, HSe -, Te 2-, HTe -, TeS3 2-, OH -, and NH2as Surface Ligands[END_REF][START_REF] Kovalenko | Colloidal Nanocrystals with Molecular Metal Chalcogenide Surface Ligands[END_REF] Interestingly, not only the dark conductance can be modulated thanks to the gate but also does the photocurrent. The magnitude of the photocurrent can be tuned by a factor of 5 with the gate bias, see Figure 3d. Also note that the magnitude enhancement of the photoresponse comes at the price of a slower response, see the inset of Figure 3d. In this sense, the tunability of the photoresponse is made at quasi constant gainbandwidth product as commonly observed in NCs-based phototransistors. [START_REF] Wu | Gate-Induced Metal-Insulator Transition in MoS2 by Solid Superionic Conductor LaF3[END_REF][START_REF] Lhuillier | Electrolyte-Gated Colloidal Nanoplatelets-Based Phototransistor and Its Use for Bicolor Detection[END_REF] We have developed a hybrid material absorbing in the IR, where the dark current is reduced compared to the pristine IR material. However, the absorption of the hybrid material is reduced (typically by a factor of 3) compared to the pristine IR material. To overcome this absorption drop, we introduce a plasmonic resonator, [START_REF] Tong | Surface Plasmon Enhanced Infrared Photodetection[END_REF][START_REF] Le-Van | Electrically Driven Optical Metamaterials[END_REF] whose role is to enhance the incident electromagnetic field onto the thin slab of absorbing material. We choose to use a guided mode resonator (GMR). [START_REF] Chu | Near Unity Absorption in Nanocrystal Based Short Wave Infrared Photodetectors Using Guided Mode Resonators[END_REF][START_REF] Massiot | Metal Nanogrid for Broadband Multiresonant Light-Harvesting in Ultrathin GaAs Layers[END_REF][START_REF] Verdun | Guided-Mode Resonator for Thin InGaAs p-i-n Short-Wave Infrared Photo-Diode[END_REF] The resonator will generate a mode which propagates along the film thus enabling multi passes of the light through the absorbing semiconductor which enhances the light absorption.

Our GMR is composed of a back-side mirror, which role is particularly to generate a second pass of the light. On the top of the mirror a dielectric spacer and a gold grating are deposited, see Figure 4a for a scheme of the device. The gold grating plays a dual role. First (i), it generates a resonance for a wavelength equal to the period of the grating times the optical index of the semiconductor. Here the targeted wavelength is 1.55 µm, which corresponds to a grating period of ≈1 µm assuming an optical index of 1.6 for the hybrid material, see supporting information for more details about the design (Figure S12-15 and S17) and fabrication (Figure S16) of the grating. Note that the value of 1.6 reflects the presence of the perovskite host matrix since the value of 2 is better fitting in the case of pristine PbS. Secondly, (ii) this grating is used as interdigitated electrodes for transport. We design the GMR electrodes to maximize the absorption of the TM mode at 1.55 µm. The obtained spectra (Figure 4d, Figure 5b andS9) present two clear resonances in the TM mode at 1.55 µm and at 1.3 µm. There is another resonance in TE mode at 1.25 µm. In Figure 4e, we have evaluated the absorption within the NCs film at 1.55 µm as a function of PbS content into the hybrid material. For 35% PbS content, the ratio maximizing the light to dark current, we are able to obtain an absorption around 65%, which is three times higher than the one from the pristine PbS. In other words, the introduction of GMR not only balances the reduction the IR absorber number but even overcomes its initial value. Another important element to examine spatial mapping of the absorption. The absorption in the lossy metal will generate heat but no photocurrent. Because the anti-node of the field are located within the hybrid IR absorbing NC layer, 74% (resp 96 %) of the absorption occurs in the semiconductor for the TM mode at 1.55 µm (resp for the TE mode at 1.25 µm), as shown by the map of the electromagnetic field in Figure 4b andc.

We have then quantized the effect of the GMR electrode on the IR detection properties. Figure 5a compares the simulated absorption spectra for the pristine PbS, the hybrid material with optimal PbS content (35%) and the latter material coupled to the resonator. As expected, the hybrid material is less absorbing than the pristine PbS, but the hybrid material coupled to the resonator is more absorbing than the pristine PbS. In Figure 5b andc, we compare the simulated spectra with the experimental photocurrent data. We clearly show in both cases a polarized response with a main resonance in TM mode at 1.55 µm and a second one in TE mode at 1.25 µm. Marginal deviation from the experiment with respect to simulation especially in the peak linewidth results from the acceptance angle of the FTIR setup used to conduct the experiment. We can then quantize the effect of the hybrid material and GMR electrode onto the device responsivity, see Figure 5d. As we compare the pristine PbS with the hybrid perovskite/CQD coupled to GMR, we identify a strong enhancement in the photoresponse (x100), which is beyond the absorption enhancement (x6). The latter is the result of electrical gain. In the GMR electrodes, the inter electrode spacing is ≈1 µm, while it is 30 µm for the regular electrodes used for PbS. As a result, the transit time, duration to transport carriers from one electrode to another, is reduced, which results in electrical gain (recirculation of the majority carriers during the lifetime of the minority carriers). The noise in the system has been defined as 1/f limited, [START_REF] Liu | 1/f Noise in Semiconductor and Metal Nanocrystal Solids[END_REF][START_REF] Lai | Low-Frequency (1/f) Noise in Nanocrystal Field-Effect Transistors[END_REF] see Figure S 18. Regarding signal-to-noise ratio (detectivity) we found that PbS and hybrid FAPI/PbS give rise to similar values of the detectivity (≈10 [START_REF] Suri | Enhanced Open-Circuit Voltage of Wide-Bandgap Perovskite Photovoltaics by Using Alloyed (FA1-XCsx)Pb(I1-XBrx)3 Quantum Dots[END_REF] Jones at room temperature and 1 kHz). In other words, loss in the absorption is balanced by the noise reduction for the hybrid material. Once coupled to the GMR electrode, the detectivity of the device has been found to be one order of magnitude higher reaching 10 10 Jones at room temperature (at 1 kHz), see Figure S 18. A second key advantage of the hybrid material is the faster time response. Pristine PbS is well known to have a slow time response due to the presence of traps, [START_REF] Amelot | Revealing the Band Structure of FAPI Quantum Dot Film and Its Interfaces with Electron and Hole Transport Layer Using Time Resolved Photoemission[END_REF] whereas perovskite is able to show fast time response. [START_REF] Yang | Effects of Incorporating PbS Quantum Dots in Perovskite Solar Cells Based on CH3NH3PbI3[END_REF] Here, the time response is typically around 5 µs, Figure S 18.

To summarize, we demonstrated that hybrid perovskite NC arrays can be sensitized by the introduction of PbS NCs for photoconduction in the short-wave infrared. An optimal PbS content is identified for which the PbS content is low enough to prevent the percolation between PbS grains and let the transport occurring within the perovskite array. The mixing of the two materials preserve their integrity and show no evidence for charge transfer between them in dark condition. The band alignment is found to have a type I nature with states in the vicinity of the Fermi level being PbS-like. Thanks to the ionic glass gating, we build an FET and demonstrate an n-type nature with an effective electron mobility of 2 x 10 -3 cm 2 .V -1 s -1 for the doped NCs array. Last, we proposed that the light matter coupling within the hybrid material can be improved with GMR electrodes. The resonator can enhance the absorption up to 3 times compared to pristine PbS. The final device made of IR sensitized perovskite presents a detectivity more than a decade higher than pristine PbS and a significantly faster time response (5 µs compare to the 200 µs for the PbS only). This work paves the way for the integration of perovskite for infrared optoelectronics, which will bring the benefit of the defect tolerance toward longer wavelengths.

ACKNOWLEDEGMENTS

The project is supported by ERC starting grant blackQD (grant n° 756225) and Ne2Dem (grant n° 853049). The photoluminescence experiments are part of a project that has received funding from the European Research Council (ERC CoG FORWARD n°771688). We acknowledge the use of clean-room facilities from the "Centrale de Proximité Paris-Centre". This work has been supported by the Region Ile-de-France in the framework of DIM Nano-K (grant dopQD). This work was supported by French state funds managed by the ANR within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02, and more specifically within the framework of the Cluster of Excellence MATISSE and also by the grant IPER-Nano2, Copin (ANR-19-CE24-0022), Frontal (ANR-19-CE09-0017), Graskop (ANR-19-CE09-0026). JQ thanks Chinese Scholar council for PhD grant while AC thanks Agence innovation defense. U.N.N. thanks DGR h-pero for funding.

ASSOCIATED CONTENT

Figure 2 a

 2 Figure 2 a. I-V curves under illumination for a low (10%) PbS content film made of FAPI/PbS NCs. The inset provides the power dependence of the photocurrent. b. I-V curves under illumination for an intermediate (35%) PbS content film made of FAPI/PbS NCs. The inset provides the power dependence of the photocurrent. c. I-V curves under illumination for a PbS NC film. The inset provides the power dependence of the photocurrent. d Photocurrent spectra for films made of FAPI/PbS NCs with various PbS contents. e. Dark current and responsivity as a function of the PbS content for films made of FAPI/PbS NCs. f. Ratio of the photocurrent over the dark current for films made of FAPI/PbS nanocrystals as a function of the PbS content. For part a-c, e and f, the illumination is done by a 1.55 µm laser diode.

Figure 3 a

 3 Figure 3 a Scheme of a field effect transistor based on a LaF3 substrate used as gate and channel made of a FAPI/PbS (35% PbS content) NC thin film. b Transfer curves (drain and gate current as a function of the applied gated bias under a constant drain source bias set equal to 0.5 V) for the device described in part a. c. I-V curves with different gate biases for the device described in part a. d. Photocurrent (λ = 1.55 µm-P= 4 mW) as a function of the applied gate bias for the device described in a. The inset is plot of the current as a function of time as the light is turned on and off for two values of the applied gate bias. The drain source bias is set at 0.5 V.

Figure 4 a

 4 Figure 4 a. Scheme of a period of the guided mode resonator (GMR). b. Absorption map associated with the TM mode at 1.55 µm for a mix containing 35% of PbS. c. Absorption map associated with the TE mode at 1.25 µm for a mix containing 35% of PbS. d Simulated absorption spectra for the TM mode for various content of PbS in a FAPI/PbS mixture (0 corresponds to pure FAPI). e Absorption within the NC at 1.55 µm for the TM mode as a function of the PbS content in the FAPI/PbS NC mixture.

Figure 5 a

 5 Figure 5 a. Simulated absorption for a film of PbS and FAPI/PbS mixture (35% PbS content) onto regular electrodes and FAPI/PbS mixture (35% PbS content) onto GMR electrodes. b. Simulated absorption spectra for FAPI/PbS mixture (35% PbS content) onto GMR electrodes in the TM mode, TE mode and for unpolarized light. c. Experimental photocurrent spectra for FAPI/PbS mixture (35% PbS content) onto GMR electrodes in the TM mode, TE mode and for unpolarized light. d. Responsivity at 1.55 µm as a function of the incident irradiance for PbS and FAPI/PbS mixture (35% PbS content) onto regular electrodes, as well as FAPI/PbS mixture (35% PbS content) onto GMR electrodes.

SUPPORTING INFORMATION

The Supporting Information is available free of charge on the ACS Publications website at DOI: Material synthesis and characterization, investigation of the electronic structure using photoemission, details about device fabrication and characterization, additional information about GMR electrodes design, fabrication and characterization.

COMPETING INTEREST

The authors declare no competing financial interest.