Pauline Quémart

The Role of Morphology in Literacy Acquisition in Dyslexic Readers

recognition despite a non-verbal level of reasoning in the norm; an absence of sensory or neurological deficit; and a favorable social, cultural and psychological environment (International Dyslexia Association 2002;World Health Organization 2011). A diagnosis is made after eliminating other potential sources of difficulty in learning to read, and after confirming a reading delay of a minimum of 18 months (or 24 months in children over nine years of age) [START_REF] Casalis | Written spelling in French children with dyslexia[END_REF]. According to an epidemiological study of children from White Island [START_REF] Yule | Over and under achievement in reading: distribution in the general population[END_REF], dyslexia affects 5 percent of school-age children, i.e., approximately one per school class [START_REF] Sprenger-Charolles | Lecture et dyslexie: approche cognitive[END_REF].

The difficulties encountered by dyslexic students stem from a disorder which affects the recognition of written words, a skill that children must master to become proficient readers [START_REF] Gough | Decoding, reading and reading disability[END_REF]. Although several hypotheses have been proposed to explain these difficulties, currently, the most accepted is that of a phonological deficit interfering with the development and/or access to phonological representations [START_REF] Boets | Intact but less accessible phonetic representations in adults with dyslexia[END_REF][START_REF] Ramus | Neuroimaging sheds new light on the phonological deficit in dyslexia[END_REF][START_REF] Saksida | Phonological skills, visual attention span, and visual stress in developmental dyslexia[END_REF][START_REF] Snowling | Dyslexia[END_REF]. This phonological deficit disrupts the phonological decoding process, which consists of matching graphemes to their corresponding phonemes. According to the hypothesis of self-teaching proposed by [START_REF] Share | Phonological recoding and self-teaching: sine qua non of reading acquisition[END_REF], the development of the orthographic lexicon is based on the successful decoding of words. This decoding allows the reader to associate the orthographic form of words with their phonological representations. Consequently, the orthographic lexicon cannot develop correctly in dyslexic students [START_REF] Share | Phonological recoding and self-teaching: sine qua non of reading acquisition[END_REF], which prevents the automatization of written word recognition and disrupts performance in written production [START_REF] Share | Phonological recoding and orthographic learning: A direct test of the self-teaching[END_REF][START_REF] Shahar-Yames | Spelling as a self-teaching mechanism in orthographic learning[END_REF]. These difficulties are likely to lead to problems in written comprehension [START_REF] De Oliveira | Reading component skills in dyslexia: word recognition, comprehension and processing speed[END_REF] and to limit vocabulary growth [START_REF] Stanovich | Matthew effects in reading: Some consequences of individual differences in the acquisition of literacy[END_REF][START_REF] Ziegler | Modelling reading development through phonological decoding and self-teaching: Implications for dyslexia[END_REF].

Strategies in dyslexic readers

Despite a persistent phonological deficit, some people with dyslexia develop reading skills that exceed expectations, given their difficulties with phonological decoding, and go on to pursue studies at the postsecondary level [START_REF] Bruck | Persistence of dyslexics' phonological awareness deficits[END_REF]. These dyslexic students likely rely on skills that partially bypass their phonological deficit and which allow them to read reasonably proficiently.

Among the hypotheses put forward to explain how dyslexic readers compensate for their phonological deficit, [START_REF] Stanovich | Toward an Interactive-Compensatory Model of Individual Differences in the Development of Reading Fluency[END_REF] proposed that they rely more heavily on contextual cues contained in written texts than normally-developing readers, which enables them to read the words by guessing. Reading is an interactive activity that involves low-level (e.g., decoding) and high-level (e.g., knowledge mobilization, semantic anticipation, context use) processes that operate in parallel and allow written messages to be understood. Several sources of informationphonological, orthographic, semantic and syntacticare synthesized simultaneously. Difficulties in low-level processing (i.e., decoding difficulties) can therefore be compensated for by higher-level processing, via context activation.

Several studies have shown that weak decoders rely more on contextual information to recognize words [START_REF] Ben-Dror | Word identification in isolation and in context by college dyslexic children[END_REF][START_REF] Bruck | Word-recognition skills of adults with childhood diagnoses of dyslexia[END_REF][START_REF] Nation | Individual differences in contextual faciliation: Evidence from dyslexia and poor reading[END_REF][START_REF] Stanovich | A longitudinal study of sentence context effects in second-grade children: Tests of an interactive-compensatory model[END_REF].

Dyslexic readers also draw on their greater sensitivity to the orthographic characteristics of words. In fact, dyslexic readers score higher than children with the same reading level for orthographic awareness, defined as "knowledge of the actual spelling of particular words and higher level conceptual skills, such as the recognition of the properties of words and sequences and typical positions of letters" (Siegel, Share, & Geva, 1995, p. 250). They are also more competent than their peers at judging between two plausible pseudowords which could be a word from the letters that constitute it, while remaining less proficient at decoding them. In addition, dyslexics' spelling skills are sometimes superior to those of reading-matched children, especially in dyslexic children whose difficulties cannot be explained by a lack of exposure to writing [START_REF] Stanovich | Converging evidence for phonological and surface subtypes of reading disability[END_REF]. They have been found to recognize the letters presented in a text more quickly and accurately [START_REF] Steinhauser | Scanning times through prose and word strings for various targets by normal and disabled readers[END_REF], according to Siegel et al., 1995). Finally, they are faster than children matched for reading ability at selecting the correct spelling of a word when presented with a pseudo-homophone (e.g., rain vs. rane) [START_REF] Olson | Specific Deficits in Component Reading and Language Skills: Genetic and Environmental Influences[END_REF]. Although there are few of these studies, they indicate that, despite their difficulties in manipulating the phonological structure of the language, dyslexic students develop a sensitivity to the probabilities of association between letters and store the orthographic form of words in memory.

Dyslexic readers thus seem able to compensate for their phonological deficits by relying more on contextual clues to read, and/or paying more attention to the sequences of letters of words. Another type of reading strategy based on the processing of written morphemic units was proposed by [START_REF] Elbro | The role of morpheme recognition and morphological awareness in dyslexia[END_REF]. Most alphabetic systems encode not only phonological information, but also morphological information. According to [START_REF] Elbro | The role of morpheme recognition and morphological awareness in dyslexia[END_REF], dyslexic children could preferentially orient to these units to process written language. The aim of this chapter is to present a set of studies that suggest that dyslexic students develop morphological knowledge, that they can manipulate oral morphemic units, and that they process these units when recognizing and producing words in writing.

From a methodological point of view, the study of morphological processing in dyslexic students involves comparing their performance with two control groups: a group of children matched for chronological age, and a group of children matched for reading and/or spelling level (according to the dimension studied, [START_REF] Casalis | Morphological awareness in developmental dyslexia[END_REF]. The use of the age-matched control group determines whether the performance of dyslexic children is within normal parameters or delayed for their age. The use of a control group matched for the studied dimension (reading/writing) makes it possible to determine whether difficulties are the consequence of their reading delay (in which case there would be no significant differences between the two groups' performance) or the consequence of a deficit (in which case the scores of dyslexic children would be lower than those of the control group). The studies presented in this chapter will therefore be organized according to the comparison group used. To highlight possible developmental effects in dyslexic children's morphological processing (e.g., effect of age and/or exposure to written language), findings will also be presented according to the age group under study (children, adolescents, and adults).

Morphological awareness and dyslexia

Morphological awareness is defined as the "conscious awareness of the morphemic structure of words and their ability to reflect on and manipulate that structure" (Carlisle, 1995, p. 194). It influences different domains of literacy acquisition, including: children's ability to read both morphologically simple words [START_REF] Carlisle | Phonological and morphological awareness in first graders[END_REF][START_REF] Casalis | Morphological analysis, phonological analysis and learning to read French: A longitudinal study[END_REF][START_REF] Roman | Toward a comprehensive view of the skills involved in word reading in Grades 4, 6, and 8[END_REF] as well as morphologically complex words [START_REF] Carlisle | Awareness of the structure and meaning of morphologically complex words: Impact on reading[END_REF][START_REF] Nagy | Contributions of morphology beyond phonology to literacy outcomes of upper elementary and middle-school students[END_REF]; the reading of pseudowords [START_REF] Deacon | Morphological awareness: Just 'more phonological'? The roles of morphological and phonological awareness in reading development[END_REF][START_REF] Mann | Linking morphological knowledge to English decoding ability: Large effects of little suffixes[END_REF]Singson, Mahony & Mann, 2000), written comprehension [START_REF] Carlisle | Morphological awareness and early reading achievement[END_REF][START_REF] Casalis | Morphological analysis, phonological analysis and learning to read French: A longitudinal study[END_REF][START_REF] Deacon | Morphological awareness: Just 'more phonological'? The roles of morphological and phonological awareness in reading development[END_REF], written production [START_REF] Casalis | How specific is the connection between morphological awareness and spelling? A study of French children[END_REF][START_REF] Fejzo | The contribution of morphological awareness to the spelling of morphemes and morphologically complex words in French in students from low socioeconomic backgrounds[END_REF] and vocabulary acquisition (McBride-Chang, Wagner, Muse, Chow, & Shu, 2015).

Development of morphological awareness in dyslexic readers: hypotheses

Two hypotheses have been proposed regarding the development of morphological awareness in dyslexic readers [START_REF] Casalis | Morphological awareness in developmental dyslexia[END_REF]. According to the first hypothesis, the phonological deficit of dyslexic readers could hinder the development of oral morphological representations. This hypothesis is based on the idea that phonological awareness is inextricably linked with the development of morphological awareness [START_REF] Carlisle | Phonological and morphological awareness in first graders[END_REF][START_REF] Carlisle | Morphological awareness and early reading achievement[END_REF][START_REF] Casalis | On the relationship between morphological and phonological awareness: Effects of training in kindergarten and in first-grade reading[END_REF][START_REF] Casalis | Morphological analysis, phonological analysis and learning to read French: A longitudinal study[END_REF]Fowler & Liberman, 1995).

According to a second hypothesis, morphological awareness could develop at least partially independently from phonological awareness [START_REF] Casalis | Morphological awareness in developmental dyslexia[END_REF]. Although it is difficult to disentangle these two types of metalinguistic knowledge, regression analyses show that morphological awareness explains a portion of the variance in reading scores that is distinct from the portion explained by phonological awareness [START_REF] Carlisle | Phonological and morphological awareness in first graders[END_REF][START_REF] Carlisle | Morphological awareness and early reading achievement[END_REF][START_REF] Shankweiler | Cognitive profiles of reading-disabled children: Comparison of language skills in phonology, morphology, and syntax[END_REF]. Moreover, phonological training has no impact on the ability to produce as suffixed form when given a base form (e.g., young: "the man remembers his ___(youth)") in French prereaders [START_REF] Casalis | On the relationship between morphological and phonological awareness: Effects of training in kindergarten and in first-grade reading[END_REF]. This result confirms the hypothesis that the overlap between phonological and morphological skills is only partial [START_REF] Casalis | On the relationship between morphological and phonological awareness: Effects of training in kindergarten and in first-grade reading[END_REF]. In addition, children with repeated mild otitis (which theoretically decreases auditory acuity thereby causing phonological processing disorders) can process the morphological structure of words to the same extent as children who are not struggling with this type of problem (Breadmore & Carroll, 2016). This finding reinforces the idea that phonological and morphological processing are at least partially independent from each other. Therefore, morphological knowledge could influence the acquisition of written language in individuals who have a deficit in phonological awareness, such as children with dyslexia.

Several authors have hypothesized that dyslexic children's oral comprehension skills allow them to develop knowledge of the morphological structure of language via the meanings of morphemes [START_REF] Casalis | Morphological awareness in developmental dyslexia[END_REF][START_REF] Elbro | The role of morpheme recognition and morphological awareness in dyslexia[END_REF]. If the development of morphological representations is based on mapping units that systematically share form and semantic properties [START_REF] Rastle | Morphological decomposition based on the analysis of orthography[END_REF][START_REF] Schreuder | Modeling morphological processing[END_REF][START_REF] Verhoeven | Morphological processing in reading acquisition: A cross-linguistic perspective[END_REF], in order for dyslexic readers to develop morphological representations, they may rely more heavily on their preserved sensitivity to the semantic context. Their development of morphological awareness could also be mediated by vocabulary development, since the ability to develop vocabulary also remains intact in dyslexics (Cavalli, Duncan, Elbro, El Ahmadi, & Colé, 2016[START_REF] Vellutino | Semantic and phonological coding in poor and normal readers[END_REF].

Morphological awareness in dyslexic readers: comparison with age-matched controls

From an empirical point of view, most studies that compare dyslexic children with chronically age-matched children indicate a delay in the development of morphological awareness. Dyslexic children encounter difficulties with tasks involving the activation of knowledge related to morpheme association rules [START_REF] Berthiaume | Are dyslexic children sensitive to the morphological structure of words when they read? The case of dyslexic readers of French[END_REF], as well as tasks involving manipulation of morphemes [START_REF] Casalis | Morphological awareness in developmental dyslexia[END_REF][START_REF] Siegel | Morphological awareness skills of English language learners and children with dyslexia[END_REF], but not in tasks that involve memorizing morphologically complex words [START_REF] Service | Recall of morphologically complex forms is affected by memory task but not dyslexia[END_REF].

Dyslexic adolescents also experience more difficulties than their peers of the same chronological age when performing morphological awareness tasks. At the age of 13, English-speaking dyslexic adolescents make more mistakes when attempting to complete sentences with a derived form (e.g., care. The road is narrow here, so please be _____ (careful)) or with a base (e.g., weakness. After being sick for many days, he was very _____(weak)) [START_REF] Tsesmeli | Derivational morphology and spelling in dyslexia[END_REF]. Hebrew-speaking dyslexic adolescents also make more mistakes than age-matched adolescents when choosing the correct form in an analogy task (reading : reader (textbook); the washing : ________ (cleanliness / reader (person) / laundry/ restriction / laundress)) [START_REF] Schiff | Auditory morphological knowledge among children with developmental dyslexia[END_REF]. Finally, Chinese-speaking dyslexic adolescents score lower than the normal readers of the same chronological age when completing a sentence with a word consisting of two morphemes [START_REF] Chung | Cognitive skills and literacy performance of Chinese adolescents with and without dyslexia[END_REF], see also [START_REF] Shu | Understanding Chinese developmental dyslexia: Morphological awareness as a core cognitive construct[END_REF].

Finally, in dyslexic adults, different results were reported according to language. In English, the performance of dyslexic university students is lower than that of students of the same age [START_REF] Law | Morphological awareness and its role in compensation in adults with dyslexia[END_REF]. For French, dyslexic students' level of morphological awareness is not significantly different from that of students of the same age but not dyslexic in terms of accuracy [START_REF] Cavalli | Vocabulary skills are well developed in university students with dyslexia: Evidence from multiple case studies[END_REF][START_REF] Martin | Morphological awareness in dyslexic university students[END_REF] whereas their scores on phonological awareness tasks are lower. However, they are slower to perform certain tasks involving the deletion of suffixes [START_REF] Martin | Morphological awareness in dyslexic university students[END_REF] and the detection of suffixed words [START_REF] Cavalli | Vocabulary skills are well developed in university students with dyslexia: Evidence from multiple case studies[END_REF].

Morphological awareness in dyslexic readers: comparison with reading-matched controls

Comparison of dyslexic readers' morphological awareness with that of children with the same level of reading yields more contrasting results. Dyslexic readers' scores depend on the skills required to perform the task. For tasks which rely heavily on phonological skills (e.g., manipulating pseudowords, "a little trine is a ____ trinette"), the scores of dyslexic children are lower than that those of children matched for reading level (average chronological age: 7 years 3 months, [START_REF] Casalis | Morphological awareness in developmental dyslexia[END_REF]. The influence of phonological skills is further confirmed when the dyslexic children are divided into two subgroups according to the extent of their phonological disorder ("phonological" type dyslexia and "delay" type dyslexia). In this case, dyslexics with the most pronounced phonological deficit experience more difficulty in producing morphologically complex pseudowords [START_REF] Casalis | Morphological awareness in developmental dyslexia[END_REF].

On the other hand, when morphological awareness tasks do not involve maintaining a pseudoword in short-term memory or producing one, the performances of dyslexic children are no different from than those of children matched for reading level [START_REF] Berthiaume | Are dyslexic children sensitive to the morphological structure of words when they read? The case of dyslexic readers of French[END_REF][START_REF] Casalis | Morphological awareness in developmental dyslexia[END_REF], Fowler & Liberman, 1995). For example, on tasks involving vocabulary that is accessible to dyslexic children, their performances are equivalent to or better than those of children with the same level of reading. When they must produce derived words (e.g., fivefifth), they are no more penalized by the phonological and orthographic modifications of the base form than their reading-matched peers [START_REF] Casalis | Morphological awareness in developmental dyslexia[END_REF]Fowler & Liberman, 1995;[START_REF] Shankweiler | Cognitive profiles of reading-disabled children: Comparison of language skills in phonology, morphology, and syntax[END_REF]. In a morphological fluency task which requires the child to orally produce as many words of the same morphological family as they can think of, dyslexic children produce more morphologically related words than their reading-matched peers [START_REF] Casalis | Morphological awareness in developmental dyslexia[END_REF].

Their performance is also superior when it comes to finding the derived pseudoword that does not fit with the others (e.g., médaille-muraille-bataille-mangeaille (medal-wallbattle-grub), médaille being the intruder)) or a suffixed word where the meaning of the suffix is different depending on the derived word (e.g., arrosage-bavardage-voisinagenettoyage (watering-chatting-neighborhood-cleaning) (the suffix -age in voisinage means "a set" compared to "the action of" in the other words) [START_REF] Casalis | Conscience morphologique chez des lecteurs tout venant et en difficultés[END_REF]. In summary, these studies show that the oral morphological skills of dyslexic children depend on the nature of the task and on the processes underlying the task.

The performance patterns of dyslexic adolescents are similar to those of dyslexic children.

There is no distinction between their performance and the performance of younger children of the same reading level on a sentence-completion task involving a derived form (e.g., care. The road is narrow here, so please be ______ (careful)) or a base word (e.g., weakness. After being sick for many days, he was very _____ (weak)) [START_REF] Tsesmeli | Derivational morphology and spelling in dyslexia[END_REF]. Similar results have been reported for Chinese [START_REF] Chung | Cognitive skills and literacy performance of Chinese adolescents with and without dyslexia[END_REF] and Hebrew [START_REF] Schiff | Auditory morphological knowledge among children with developmental dyslexia[END_REF]. However, the frequency of target words strongly influences dyslexics performances on these tasks [START_REF] Tsesmeli | Derivational morphology and spelling in dyslexia[END_REF]. This reinforces the idea that the morphological abilities of dyslexics are strongly related to their level of vocabulary.

In dyslexic adults, the results depend on the language under study. In French, their morphological skills are superior to what would be expected given their reading level. They are faster and more accurate than reading-matched peers (who are also matched for phonological awareness) at performing a task where they must identify prefixed words (e.g., endive -envolenclume: envol (endive -flightanvil)) and suffixed words (e.g., lanière -tanièreglacière: glacière (lanyard -dencooler)) [START_REF] Martin | Morphological awareness in dyslexic university students[END_REF].

However, this strong effect for morphological structure has not been observed in dyslexic adults in Hebrew: in a study using the same analogy task as [START_REF] Schiff | Auditory morphological knowledge among children with developmental dyslexia[END_REF][START_REF] Schiff | Morphological analogies in Hebrew-speaking university students with dyslexia compared with typically developing gradeschoolers[END_REF] showed that dyslexic adults make more mistakes than younger children of the same reading level.

Influence of morphological awareness on literacy in dyslexic readers

The influence of morphological knowledge on dyslexic readers' literacy acquisition has been the subject of very few studies. To our knowledge, only [START_REF] Law | Morphological awareness and its role in compensation in adults with dyslexia[END_REF] took an interest in this issue. In their study of dyslexic university students, morphological awareness was a better predictor of reading, spelling and reading comprehension levels than vocabulary or phonological awareness [START_REF] Law | Morphological awareness and its role in compensation in adults with dyslexia[END_REF].

To summarize, these results indicate that dyslexic readers demonstrate a higher degree of morphological sensitivity than one might expect given their phonological deficit, at least when tasks are not too costly in terms of phonological manipulation. The findings indicate that the skills of dyslexic readers are equivalent to, or better than, those of reading-matched children, suggesting that to some extent, morphological skills operate independently form phonological awareness. Dyslexic readers' morphological awareness appears to be particularly developed when it comes to using vocabulary and / or knowledge about the meaning of morphemes. In adulthood, contradictory results were reported according to language. Studies found that performances of French-speaking adults with dyslexia continued to improve into adulthood: their performances were indistinguishable from those of age-matched readers. For other languages, dyslexic adults were less proficient than their age-matched peers at manipulating the morphological structure of oral words. In the case of Hebrew, dyslexic adults also scored lower than their reading-matched peers. Finally, consistent with findings for normally-developing readers, morphological skills were also found to predict reading level.

Morphemes as reading units in dyslexics

Recognizing written words is a process that requires the reader to use written stimulus to map visual representations with their corresponding representations stored in memory.

Over the past 40 years, many studies conducted among expert readers have shown that the recognition of morphologically complex words involves their decomposition into morphemic units [START_REF] Frost | Cross-linguistic perspectives on morphological processing: An introduction[END_REF][START_REF] Longtin | Morphological priming without morphological relationship[END_REF][START_REF] Rastle | Morphological and semantic effects in visual word recognition: A time-course study[END_REF][START_REF] Schreuder | Modeling morphological processing[END_REF][START_REF] Taft | Recognition of affixed words and the word frequency effect[END_REF]. Children's ability to process the morphological structure of words appears rather early in reading development [START_REF] Beyersmann | Morphological processing during visual word recognition in developing readers: evidence from masked priming[END_REF][START_REF] Burani | How early does morpholexical reading develop in readers of a shallow orthography?[END_REF][START_REF] Carlisle | Exploring the role of morphemes in word reading[END_REF][START_REF] Colé | Stem and derivational-suffix processing during reading by French second and third graders[END_REF][START_REF] Deacon | Seeing the harm in harmed and harmful: Morphological processing by children in Grades 4, 6, and 8[END_REF][START_REF] Quémart | Exploring the Role of Bases and Suffixes When Reading Familiar and Unfamiliar Words: Evidence From French Young Readers[END_REF], even before the mastering of phonological decoding (Marec-Breton, [START_REF] Marec-Breton | Traitements morphologiques lors de la reconnaissance des mots écrits chez des apprentis lecteurs[END_REF].

Since morphological processing of writing is not based solely on phonological decoding skills, dyslexic readers may benefit from the presence of morphemic units in word recognition. [START_REF] Elbro | Differences in dyslexia. A study of reading strategies and deficits in a linguistic perspective[END_REF], reported by Elbro & Arnbak, 1996) was the first to propose the idea that dyslexic readers' morphological knowledge could be used to compensate for their difficulties in manipulating phonological units when recognizing spoken words. The possibility of identifying groups of letters associated with meaningmorphemescould improve the reading skills of dyslexic children by facilitating access not only to lexical representations [START_REF] Burani | Morpheme-based reading aloud: Evidence from dyslexic and skilled Italian readers[END_REF] but also to the meaning of words [START_REF] Elbro | The role of morpheme recognition and morphological awareness in dyslexia[END_REF]. This hypothesis is supported by research which indicates that dyslexic readers do develop morphological representations [START_REF] Casalis | Morphological awareness in developmental dyslexia[END_REF][START_REF] Martin | Morphological awareness in dyslexic university students[END_REF]. It is also supported by studies which have shown that morphological awareness explains a significant portion of variance in reading scores, above and beyond the variance explained by phonological awareness [START_REF] Carlisle | Phonological and morphological awareness in first graders[END_REF][START_REF] Casalis | Morphological analysis, phonological analysis and learning to read French: A longitudinal study[END_REF][START_REF] Deacon | Morphological awareness: Just 'more phonological'? The roles of morphological and phonological awareness in reading development[END_REF].

Morphology and young dyslexic readers

To test this hypothesis in dyslexic children, most studies have used a task of naming (i.e. to read aloud) of morphologically simple and complex pseudowords. In a study involving French-speaking dyslexic children and reading-matched children, [START_REF] Casalis | Apprentissage de la lecture et dyslexies de l'enfant[END_REF] administered a task which involved reading three types of items: derived words (e.g., classement (ranking)); pseudowords made up of a base and a suffix (e.g., écolerie); and pseudowords made up of a pseudobase and a suffix (e.g., elocerie). Participants in both groups read more morphologically complex pseudowords (e.g., school) than pseudowords with no base form (e.g., élocerie). Morphological construction also had a more pronounced influence on the performances of dyslexic children than the performances of readingmatched controls. These results suggest that when dyslexic children encounter pseudowords (i.e., new words), they are able to identify prominent units in them, i.e., the morphemes, on which to rely for easier access to the lexicon. An effect for pseudoword construction has also been demonstrated for words with more transparent spellings. For instance, dyslexic Italian-speaking children (aged between 11 and 12) read pseudowords composed of a base and suffix (e.g., donn-ista) more quickly and more accurately than simple pseudowords (e.g., denn-osto, [START_REF] Burani | Morpheme-based reading aloud: Evidence from dyslexic and skilled Italian readers[END_REF] ; see also [START_REF] Traficante | How do roots and suffixes influence reading of pseudowords: A study of young Italian readers with and without dyslexia[END_REF]. A similar effect has been observed in children matched on reading level and chronological age. On the other hand, only dyslexic children and reading-matched controls benefit from the presence of morphemes in terms of reading speed [START_REF] Burani | Morpheme-based reading aloud: Evidence from dyslexic and skilled Italian readers[END_REF]. The presence of morphemes also facilitates the reading of pseudowords in Spanish-speaking children with dyslexia. The presence of more than one morpheme allows them to read pseudowords constructed with two morphemes (e.g., plateza) more quickly than morphologically simple pseudowords (e.g., astoza), and this effect is stronger in dyslexic children (aged from 7 to 10 years) than in children matched on chronological age (Suárez-Coalla & Cuetos, 2013).

Morphology and adolescent dyslexic readers

Elbro and Petersen (1993, reported by [START_REF] Elbro | The role of morpheme recognition and morphological awareness in dyslexia[END_REF] used another method to investigate the role of morphological processing in word recognition by Danish dyslexic adolescents (aged 15 years on average). The researchers asked them to scroll through text on a computer screen using the mobile window method. They could scroll the text either syllable by syllable, morpheme by morpheme, or word by word. The results showed no significant differences between dyslexic children and reading-matched controls in terms of text scrolling speed in the word by word condition. On the other hand, dyslexic adolescents scrolled faster than normo-readers in the morpheme by morpheme condition, and this pattern was reversed for the syllable by syllable condition. These results demonstrate dyslexic adolescents' preference for processing morphemic units as opposed to written syllabic units.

Morphology and adult dyslexic readers

Although effects of the morphological structure have been observed for children and adolescents, the same effects have not been demonstrated for English-speaking dyslexic adults attending university. In a lexical decision task, it was normo-readers matched for reading comprehension, and not dyslexic adults, who had faster response times for morphologically complex words (e.g. musical) than for morphologically simple but pseudo-derived words (e.g., metal, where met-and -al are respectively a base and a suffix in English) [START_REF] Deacon | Processing of Derived Forms in High-Functioning Dyslexics[END_REF]. However, these results were not compared to results for a control task involving morphologically simple words. However, as [START_REF] Burani | Morpheme-based reading aloud: Evidence from dyslexic and skilled Italian readers[END_REF] propose, dyslexic readers could benefit from the presence of morphemes as lexical units irrespective of their meaning, whether they are morphologically constructed or pseudoderived. Only comparing results with those obtained for a task involving simple words would have provided insight into the emergence of this type of processing. Thus, it is difficult to draw a clear conclusion from this study.

All these findings suggest that dyslexic readersat least until adolescenceprocess words and pseudowords in terms of their morphological structure, and that they are able to do so with no additional processing costs in terms of observed speed.

Nature of morphological processing in dyslexic readers

Two sources of information encoded in morphemes could influence how dyslexic readers process the morphological structure of words: the semantic properties and/or the form properties of morphemes [START_REF] Quémart | Visual processing of derivational morphology in children with developmental dyslexia: Insights from masked priming[END_REF]. If dyslexic readers draw principally on the semantic properties of morphemes, the way in which morphological representations are organized in the lexicon may be determined by the semantic links between words of the same morphological family. In this case, an effect would be observed when readers process words belonging to the same morphological family (e.g., helper-helpful) and that effect would vary according to the size (number of members) and frequency of this family.

If dyslexic readers rely essentially on the form properties of morphemes, the organization of morphological representations in the lexicon would be influenced by the identification of lexical units formed by the same set of graphemes at the same position independently of their meaning overlap. In this case, if presented with a set of words that share a lexical unit but do not share a semantic link (e.g., flag-flagon), dyslexic readers would erroneously decompose the longer word into smaller units (i.e., flag-on).

The nature of the morphological processes that dyslexic readers use to recognize written words has been demonstrated through the use of test items that vary according to word transparency. The morphological construction of words is not always transparent: it varies on a continuum from transparent to opaque. When the construction is semantically transparent, the meaning of the derived form can be predicted by its component morphemes, such as nageur in French (swimmer in English). However, some words are composed of a base and a suffix, but their meaning cannot be clearly inferred from its component morphemes. These words are semantically opaque. For example, the word rideau (curtain) is constructed with the base ride and the suffix -eau, but the meaning of rideau is no longer related to that of ride. Other words, "pseudoderived", include accidentally morphemic units that are not related to the word either from a semantic or etymological point of view (e.g., baguette). Morphological derivation can also lead to a form (orthographic or phonological) modification of the lexical base, which produces formally opaque words. For example, the phonological and orthographic form of the base hôpital (hospital) becomes hospitalier (hospitable) in its derived form. Dyslexic readers are influenced by the semantic transparency of morphemes during morphological processing. Danish dyslexic adolescents read semantically transparent words (e.g., sunburn) more quickly and more accurately than semantically opaque compound words (e.g., window) [START_REF] Elbro | Differences in dyslexia. A study of reading strategies and deficits in a linguistic perspective[END_REF][START_REF] Elbro | The role of morpheme recognition and morphological awareness in dyslexia[END_REF]. Such an effect for transparency is not observed in children matched on reading level. These findings suggest a reading profile for dyslexic readers that is distinct from children of the same level of reading and which is characterized by a greater sensitivity to the semantic properties of morphemes. More recently, in a study involving French-speaking dyslexic children and children matched on reading and chronological age, [START_REF] Quémart | Visual processing of derivational morphology in children with developmental dyslexia: Insights from masked priming[END_REF] administered a lexical decision task based on the masked priming paradigm. In this paradigm, the target is preceded by another stimulus, the prime, to observe its effect on how the target is processed. The prime is said to be "masked" when its presentation time is so short that it cannot be processed explicitly by the participant, which in turn reveals which properties of the prime are processed automatically. To examine how the semantic properties of morphemes are processed by dyslexic children, the authors proposed primes and targets that share a morphological link (e.g., saladier-SALADE (salad bowl -salad), a link of pseudoderivation (e.g., mortier-MORT (deadman-DEAD)), a purely orthographic link (e.g., vendredi-VENDRE, (Friday-SELL)) or a purely semantic link (e.g., bouillon-SOUPE (broth-SOUP)). The researchers found that patterns for effects of priming were different in the three groups: while children from the two control groups benefitted from the prime under the morphological and pseudoderived conditions, dyslexic children benefitted from the prime only in the morphological condition. The only difference between these two conditions lies in the semantic link between the prime and the target in the morphological condition. A surface morphological link between the prime and the target (such as that of the condition pseudoderivation) is not sufficient for dyslexic children to benefit from the presence of morphemes to recognize written words: the activation of the semantic properties of morphemes underlies this type of processing.

Dyslexic children are also affected by the form transparency of lexical bases. In a second study using the masked priming paradigm, [START_REF] Quémart | Visual processing of derivational morphology in children with developmental dyslexia: Insights from masked priming[END_REF] examined the processing of the form properties of morphemes. Targets and primes could share four relationships: morphological and transparent (e.g., amoureux-AMOUR (lover-LOVE)), morphological with only phonological modification (e.g., bergerie-BERGER (sheepfold-SHEEP)), morphological with phonological and orthographic modification (e.g., aviateur-AVION (aviator-AIRPLANE) or purely orthographic (e.g., fourmi-FOUR (ant-OVEN).

While the groups of children matched on reading and on chronological age benefitted from the prime only in the transparent morphological condition, dyslexic children benefitted from the prime in all three conditions despite form modifications of the lexical base between the prime and the target. Dyslexic children, therefore, tolerate more form modifications of the lexical base when recognizing written words.

These studies indicate that constituent morphemic units contained in words are activated when dyslexic readers (especially children and adolescents) are recognizing them.

Activation of these units facilitates the recognition of written words with respect to a control condition where no morphemic unit is locatable. To achieve this processing, dyslexic readers seem to preferentially rely on the semantic properties of morphemes, a strategy which distinguishes them from normo-readers, who are more sensitive to the form properties of morphemes.

Morphemes as writing units in dyslexics

The ability to locate morphemic units in words makes it easier not only to recognize them, but also to recover their spelling from memory to produce them in writing. Most alphabetic systems represent not only phonological information, but also morphological information.

From the age of 6, young writers take into account the presence of a base when choosing the orthography of a suffix (e.g., smarter vs. corner), or the presence of a suffix to choose the spelling of graphemes that constitute the lexical base (e.g., turn in turning vs. turnip) [START_REF] Casalis | How specific is the connection between morphological awareness and spelling? A study of French children[END_REF][START_REF] Deacon | What young children do and do not know about the spelling of inflections and derivations[END_REF], 2006). The ability to activate words from the same morphological family also makes it easier to spell words that are not morphologically complex but which end with a silent letter (e.g., bavard vs. foulard (chatterbox vs. scarf)) [START_REF] Sénéchal | Morphological effects in children's spelling of French words[END_REF].

There are few studies on the role of morphology in the written production of dyslexics.

Dyslexic writers seem to draw on morphological information in the same way as children of the same reading age. In a study involving dyslexic adolescents, and groups of children matched for reading and chronical age respectively, Tsesmeli andSeymour (2006, 2009) asked English-speaking participants to spell either morphologically complex words (e.g., finally) or their lexical base (e.g., final). They measured morphological consistency, i.e. the percentage of graphemes that were spelled exactly the same way in the base word and in the morphologically complex word. The researchers found that dyslexic writers rely on morphological consistency to the same extent as younger children with the same level of reading, despite the scores of dyslexic writers being generally lower than that of the other two groups. Dyslexic children thus benefit from the morphological structure of words during their production. Similar results have been reported by Breadmore and Carroll (2016) in another study in English. In their study, participants had to complete written sentences with a pseudoword that was either morphologically simple (e.g., He called his pet rat Paoma) or morphologically complex (e.g., A person who soams is a soamer). The performance of dyslexic students did not differ from that of the reading controls, which confirms the results reported by Tsesmeli andSeymour (2006, 2009).

In other studies, the performances of dyslexic children were compared to those of children matched on spelling. In a written production task where participants had to recall the spelling of words that ended with final consonant clusters in English (e.g., bars), dyslexic children and spelling-matched children omitted fewer graphemes when those graphemes were part of a morphologically complex word (e.g., "r" in bars, where "bar" and "s" are two distinct morphemes) than when they were part of a simple word (e.g., "r" in Mars) [START_REF] Bourassa | Use of morphology in spelling by children with dyslexia and typically developing children[END_REF]. Moreover, both groups of children made fewer mistakes when choosing the spelling of a grapheme that can be pronounced in several ways (e.g., "d" or "t", which can be pronounced /t/ or /d/ according to the words in which they appears) when the grapheme was part of a morphologically complex word (e.g., waiting) than when it was part of a morphologically simple word (e.g., beauty). Therefore, there are no meaningful differences between dyslexic children's and younger spelling-matched children's ability to use morphological knowledge to spell words [START_REF] Bourassa | Use of morphology in spelling by children with dyslexia and typically developing children[END_REF].

In another study involving dyslexic children whose spelling level corresponded to the 2 nd year of primary school, [START_REF] Bourassa | Children with dyslexia have sophisticated spelling strategies[END_REF] cited by [START_REF] Bourassa | Spelling development and disability in English[END_REF] asked participants to spell morphologically simple words and morphologically complex words. The words all started with the same lexical base (e.g., trick) but had different endings: the morphologically complex words ended with a suffix (e.g., tricked; tricky) whereas the morphologically simple words ended with a sequence of letters not corresponding to a suffix (e.g., trickle). All participants (dyslexic and controls) spelled morphologically complex words more accurately than morphologically simple words. This result indicates once again that dyslexic writers take morphological information into account when they produce words, and that they do so in ways that are similar younger spelling-matched children. This effect for the morphological structure was replicated in Greek by [START_REF] Diamanti | Spelling of derivational and inflectional suffixes by Greek-speaking children with and without dyslexia[END_REF] with dyslexic children between 10 and 13 years old and age-matched controls. They asked participants to write morphologically constructed adjectives. As in the studies by [START_REF] Bourassa | Use of morphology in spelling by children with dyslexia and typically developing children[END_REF][START_REF] Bourassa | Children with dyslexia have sophisticated spelling strategies[END_REF], dyslexic children scored lower than age-matched children, but similarly to children of the same spelling level. Since Greek spelling is very transparent, this result suggests that morphemic processing in written production is also observed in instances when phonemegrapheme correspondences are consistent.

Dyslexic writers may rely on the morphological structure of words when writing to a greater extent than expected, given their level of reading and spelling. [START_REF] Quémart | Morphology and spelling in French students with dyslexia: the case of silent final letters[END_REF] asked dyslexic children and adolescents (aged 10 to 15 years) and younger children matched on reading and spelling to produce words ending with a final silent letter. In the morphological condition, the choice of the final, silent letter could be disambiguated by using morphologically related words (e.g., tricot (knit), where the final "t" is pronounced in morphologically related words such as tricoter (to knit), and tricoteur (knitter)). In the control condition, the selected words did not belong to a morphological family (e.g., effort, "effort"). The results show that while dyslexic children scored lower overall than children in the control group, they performed similarly to children of the same level of reading and spelling when they could draw on morphologically related words.

In addition, the ability of dyslexic writers to use the morphological structure of words sometimes exceeds expectations given their lexical level. [START_REF] Angelelli | Morpheme-based Reading and Spelling in Italian Children with Developmental Dyslexia and Dysorthography[END_REF] have shown that Italian dyslexic children benefit as much as children of the same chronological age from the morphological structure of words in their written production. They produce fewer errors when producing pseudowords constructed with two morphemes (e.g., lampad-ista) than pseudowords in which it is not possible to locate morphemic units (e.g., livonosto). This same effect is observed in dyslexic children and children of the same chronological age. It is also observed when the participants have to produce infrequent words constructed from frequent morphemic units (e.g., brut-ezza (ugliness)) in relation to words constructed from rarer morphemic units (e.g., agrum-eto, (citrus grove)). Thus, despite their delays in reading and spelling, dyslexic children perform similarly to children of the same chronological age when asked to produce morphologically complex words in writing.

To sum up, data on the written production of morphologically complex words indicate that the performances of dyslexic children match and sometimes exceed those of children matched on reading and / or spelling. These findings are particularly encouraging and coherent with those highlighted in the word recognition studies. These studies deserve to be replicated, especially in adult dyslexics, for whom spelling difficulties are persistent and quite resistant to intervention.

Conclusion

The objective of this chapter was to review how people with dyslexia process the morphological structure of words in different languages and in different domains related to the acquisition of written language: morphological awareness, reading, and written production. Studies in this field are still rare, particularly in the field of reading and spelling production.

Given the variability observed between the different studies, it is difficult to formulate clear and unambiguous conclusions about the ability of dyslexics to process the morphological structure of the language. Nevertheless, the results are broadly convergent and indicate that people with dyslexia do not present specific deficits in this area. They can manipulate the morphological structure of the language orally, especially when the task draws on their vocabulary and/or semantic skills. The effects are also influenced by task requirements in terms of phonological manipulation.

The possibility of locating morphemic units in words also facilitates the reading of complex words compared to words that are morphologically simple. In addition, the nature of the processing used by dyslexic readers differs from that of normally-developing readers.

Dyslexic readers preferentially rely on the semantic properties of morphemes to benefit from the morphological structure of words. In contrast, for normally-developing readers, the activation of morphological representations in memory seems to be based primarily on the form (orthographic and/or phonological) properties of morphemes. This pattern is consistent with findings from investigations of morphological awareness in the dyslexic population: the data indicate that dyslexic participants are particularly competent when performing tasks which require them to use their vocabulary [START_REF] Casalis | Morphological awareness in developmental dyslexia[END_REF]. Further studies are needed to confirm this difference in processing between groups. They could also clarify the differential role of vocabulary and semantic skills in the processing of the morphological structure of words by those with dyslexia.

Finally, the fact that dyslexic students' lexicons are structured around morphological representations facilitates the recovery of word spellings when they are asked to produce them in writing. Dyslexic writers can therefore partially overcome their spelling difficulties by relying on the morphological structure of the words. These data have important implications at the theoretical level. Dyslexic readers' difficulties are best explained by their phonological disorders [START_REF] Boets | Intact but less accessible phonetic representations in adults with dyslexia[END_REF][START_REF] Ramus | Neuroimaging sheds new light on the phonological deficit in dyslexia[END_REF][START_REF] Saksida | Phonological skills, visual attention span, and visual stress in developmental dyslexia[END_REF][START_REF] Snowling | Dyslexia[END_REF]. These disorders prevent them from implementing the grapho-phonemic conversion procedure, which disturbs the development of the orthographic lexicon [START_REF] Share | Phonological recoding and self-teaching: sine qua non of reading acquisition[END_REF]. However, the studies presented in this chapter also show that the development of literacy does not rest solely on phonological skills: morphological skills are also important contributors. Thus, the size of the units activated when processing written language varies not only according to orthographic consistency [START_REF] Ziegler | Reading acquisition, developmental dyslexia and skilled reading across languages: a psycholinguistic grain size theory[END_REF], 2006) but also according to the reader's level of expertise with oral and / or written language. When dyslexic readers are unable to effectively establish grapho-phonemic correspondences, they turn to larger units: morphemes. This processing does not necessarily involve a fine coding of the exact letters in each morpheme, which leads them to be less sensitive than normally-developing readers to the inversions and / or transpositions of letters within a given morpheme (e.g., bain/baignoire (bath / bathtub); hôpital/hospitalier (hospital / hospitalable)) [START_REF] Quémart | Visual processing of derivational morphology in children with developmental dyslexia: Insights from masked priming[END_REF].

From a methodological point of view, these studies reinforce the need to compare the performances of dyslexic students with those of students matched on the dimension studied (reading and / or spelling level). This comparison group makes it possible to highlight the nature of the difficulties encountered by dyslexic students, but also the domains in which they have developed abilities that exceed expectations given their level of reading / spelling. Another important point concerns the type of task used to assess morphological abilities. Tasks that involve a strong phonological awareness component penalize dyslexics whereas their morphological abilities become evident when tasks solicit their vocabulary.

Practical implications

These data are particularly encouraging because they provide pathways for managing the difficulties of dyslexic students. The processing of morphological units is obviously not sufficient to completely overcome dyslexic students' disorders in reading and spelling.

Nevertheless, training that targets the morphological skills that they do have is likely to be a good alternative to the traditional phonic method, which aims to develop the skills that are at the heart of dyslexic readers' challenges [START_REF] Mcarthur | Phonics training for Englishspeaking poor readers[END_REF]. For example, Arnbak and Elbro (2000, see also [START_REF] Tsesmeli | Morphological structure of the derived words and spelling performance of dyslexic students: An intervention study[END_REF] carried out a study aimed at improving the morphological awareness of dyslexic readers through targeted training and examined the impact of that training on reading and spelling. The results are promising since participants showed an improvement in morphological awareness compared to control groups that did not receive training, as well as improvements in reading and spelling. [START_REF] Goodwin | A meta-analysis of morphological interventions: Effects on literacy achievement of children with literacy difficulties[END_REF] have also shown that training that targets morphological skills is of benefit to struggling readers, and favors the development of phonological awareness, morphological awareness and vocabulary.

In a meta-analysis published in 2010, Goodwin and Ahn proposed a synthesis of key factors contributing to the improvement of morphological skills in struggling readers. They found that interventions with the greatest effect lasted between 10 and 20 hours minimum and that the most effective exercises involved manipulations of the morphological structure of words in relation to reading, vocabulary acquisition, and writing. Tasks involving the manipulation of morphemes without linking to these domains were much less effective.

Finally, the type of intervention (group or individual) has no significant influence on the effectiveness of training. These recommendations may guide practitioners who wish to offer morphological activities to their dyslexic students.


Gauthier Roubaud

Sébastien Bidault
email: sebastien.bidault@espci.fr

Sylvain Gigan

Samuel Grésillon
email: samuel.gresillon@espci.fr

†institut Langevin

Statistical Nonlinear Optical Mapping of Localized and Delocalized Plasmonic Modes in Disordered Gold Metasurfaces

Keywords: disordered media, plasmonics, metasurfaces, nonlinear luminescence, wave-

come   L'archive ouverte pluridisciplinaire

front shaping

The complex interplay between localized and delocalized plasmonic modes provides disordered metallic metasurfaces with remarkable optical properties. [START_REF] Shalaev | Optical Properties of Nanostructured Random Media[END_REF][START_REF] Stockman | Localization versus Delocalization of Surface Plasmons in Nanosystems: Can One State Have Both Characteristics?[END_REF][START_REF] Seal | Coexistence of Localized and Delocalized Surface Plasmon Modes in Percolating Metal Films[END_REF] Not only do they feature deeply subwavelength optical field enhancements [START_REF] Gresillon | Experimental Observation of Localized Optical Excitations in Random Metal-Dielectric Films[END_REF][START_REF] Seal | Near-Field Intensity Correlations in Semicontinuous Metal-Dielectric Films[END_REF][START_REF] Awada | Experimental Study of Hot Spots in Gold/Glass Nanocomposite Films by Photoemission Electron Microscopy[END_REF][START_REF] Losquin | Experimental Evidence of Nanometer-Scale Confinement of Plasmonic Eigenmodes Responsible for Hot Spots in Random Metallic Films[END_REF] -or hotspots -with applications in surface enhanced Raman scattering, 8 nonlinear optics [START_REF] Beversluis | Continuum Generation from Single Gold Nanostructures through Near-Field Mediated Intraband Transitions[END_REF][START_REF] Anceau | Local Second-Harmonic Generation Enhancement on Gold Nanostructures Probed by Two-Photon Microscopy[END_REF][START_REF] Stockman | Enhanced Second-Harmonic Generation by Metal Surfaces with Nanoscale Roughness: Nanoscale Dephasing, Depolarization, and Correlations[END_REF][START_REF] Chettiar | FDTD Modeling of Realistic Semicontinuous Metal Films[END_REF][START_REF] Haug | Hot-Electron Intraband Luminescence from Single Hot Spots in Noble-Metal Nanoparticle Films[END_REF] or Purcell effects; [START_REF] Biteen | Enhanced Radiative Emission Rate and Quantum Efficiency in Coupled Silicon Nanocrystal-Nanostructured Gold Emitters[END_REF][START_REF] Krachmalnicoff | Fluctuations of the Local Density of States Probe Localized Surface Plasmons on Disordered Metal Films[END_REF][START_REF] Canneson | Strong Purcell Effect Observed in Single Thick-Shell CdSe/CdS Nanocrystals Coupled to Localized Surface Plasmons[END_REF][START_REF] Castanie | Distance Dependence of the Local Density of States in the Near Field of a Disordered Plasmonic Film[END_REF] but their coupled plasmonic modes, delocalized over micrometer scales, [START_REF] Stockman | Localization versus Delocalization of Surface Plasmons in Nanosystems: Can One State Have Both Characteristics?[END_REF][START_REF] Seal | Coexistence of Localized and Delocalized Surface Plasmon Modes in Percolating Metal Films[END_REF][START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] permit a far-field optical modulation of the optical response by wavefront shaping. [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF][START_REF] Gunn | Polarization and Phase Control of Remote Surface-Plasmon-Mediated Two-Photon-Induced Emission and Waveguiding[END_REF][20][START_REF] Aeschlimann | Nano-Optical Control of Hot-Spot Field Superenhancement on a Corrugated Silver Surface[END_REF][START_REF] Roubaud | Far-Field Wavefront Control of Nonlinear Luminescence in Disordered Gold Metasurfaces[END_REF] In particular, we recently demonstrated that this combination of near-and far-field phenomena allows the nonlinear photoluminescence (NPL) of gold metasurfaces to be locally increased by more than 2 orders of magnitude, using a femtosecond excitation with a phase profile optimized by an iterative random algorithm. [START_REF] Roubaud | Far-Field Wavefront Control of Nonlinear Luminescence in Disordered Gold Metasurfaces[END_REF] These optical properties are strongly sensitive to the level of structural disorder of the samples: the strength and density of optical hotspots, [START_REF] Awada | Experimental Study of Hot Spots in Gold/Glass Nanocomposite Films by Photoemission Electron Microscopy[END_REF] the observed Purcell factors [START_REF] Krachmalnicoff | Fluctuations of the Local Density of States Probe Localized Surface Plasmons on Disordered Metal Films[END_REF] and the length of the delocalized modes [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] all depend on the filling fraction ff of gold on the metasurface. In practice, all processes are maximized when the surface is close to the electrical percolation threshold and features the highest morphological complexity, leading to the most efficient wavefront control of nonlinear optical properties. [START_REF] Roubaud | Far-Field Wavefront Control of Nonlinear Luminescence in Disordered Gold Metasurfaces[END_REF] However, it is currently difficult to associate the deeply subwavelength dimensions of optical hotspots [START_REF] Gresillon | Experimental Observation of Localized Optical Excitations in Random Metal-Dielectric Films[END_REF] and the micrometer scales of delocalized modes [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] in full-field electrodynamic calculations [START_REF] Chettiar | FDTD Modeling of Realistic Semicontinuous Metal Films[END_REF] in order to analyze the optical properties of disordered plasmonic surfaces. Getting an experimental insight into the spatial distributions of localized and delocalized modes is therefore essential to fully exploit such disordered nanophotonic systems.

The analysis of optical hotspots typically requires subwavelength imaging techniques such as near-field optical microscopy, [START_REF] Gresillon | Experimental Observation of Localized Optical Excitations in Random Metal-Dielectric Films[END_REF][START_REF] Seal | Near-Field Intensity Correlations in Semicontinuous Metal-Dielectric Films[END_REF] photoemission electron microscopy (PEEM) [START_REF] Awada | Experimental Study of Hot Spots in Gold/Glass Nanocomposite Films by Photoemission Electron Microscopy[END_REF][START_REF] Aeschlimann | Nano-Optical Control of Hot-Spot Field Superenhancement on a Corrugated Silver Surface[END_REF] or spatially resolved electron energy loss spectroscopy (EELS). [START_REF] Losquin | Experimental Evidence of Nanometer-Scale Confinement of Plasmonic Eigenmodes Responsible for Hot Spots in Random Metallic Films[END_REF] However, far-field techniques such as 2 NPL [START_REF] Beversluis | Continuum Generation from Single Gold Nanostructures through Near-Field Mediated Intraband Transitions[END_REF] or second harmonic generation imaging [START_REF] Anceau | Local Second-Harmonic Generation Enhancement on Gold Nanostructures Probed by Two-Photon Microscopy[END_REF] are also strongly sensitive to the spatial distribution of local field enhancements. Interestingly, it is possible to observe a direct correlation between NPL images and the spatial distribution of optical near-fields [START_REF] Ghenuche | Spectroscopic Mode Mapping of Resonant Plasmon Nanoantennas[END_REF] as long as the number of optical hotspots per diffraction limited area is below 1. This low hotspot density is typically observed in disordered gold metasurfaces as experimentally evidenced in PEEM. [START_REF] Awada | Experimental Study of Hot Spots in Gold/Glass Nanocomposite Films by Photoemission Electron Microscopy[END_REF] On the other hand, an accurate mapping of disordered plasmonic modes remains an open issue. For instance, images obtained by measuring widefield scattering or nonlinear photoluminescence combine intertwined information on both localized and delocalized modes.

The intensity measured in a given diffraction-limited area is due to both the strength of local optical hotspots and constructive or destructive interference effects between propagating plasmonic modes. [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF][START_REF] Roubaud | Far-Field Wavefront Control of Nonlinear Luminescence in Disordered Gold Metasurfaces[END_REF] Therefore, we propose here a novel imaging approach that counterbalances this complexity by a statistical analysis of a large number of widefield NPL images obtained with random wavefronts. In particular, we demonstrate that average intensities provide an image of localized plasmonic hotspots with a diffraction-limited resolution; while relative standard deviations yield a map of areas with large densities of interfering delocalized modes, which allow an efficient modulation of nonlinear optical properties by far-field wavefront shaping.

Methods

Disordered gold metasurfaces are obtained by surface dewetting of a few nanometers of gold deposited on a glass coverslip using an electron-beam (E-Vap Maktek Mighty Source) in a vacuum chamber (Oerlikon). The structural morphology of the surface is characterized in transmission electron microscopy by the filling fraction of gold: ff = s m /(s m + s g ), with s m and s g the surfaces covered by gold and glass, respectively. When the filling fraction reaches a threshold value ff t = 0.65, electrical percolation is reached. [START_REF] Seal | Near-Field Intensity Correlations in Semicontinuous Metal-Dielectric Films[END_REF][START_REF] Gadenne | Optical Properties of Nanostructured Random Media[END_REF] The photoluminescence As shown in Fig. 1-a, a collimated femtosecond laser (Mira 900, Coherent, 200 fs, 80 MHz, 790 nm) is reflected by a spatial light modulator (SLM, LCOS 10468-02, Hamamatsu, 792×600 pixels, 20 µm pixel size) before being conjugated by a lens L1 with the gold metasurface using a 1.4 NA (60×) objective in an inverted microscope (Eclipse Ti, Nikon). To ensure that the excitation intensity is homogeneous over the sample, the laser is focused by L1 on the Fourier plane of the objective (typical intensity of 1 kW/cm 2 , 5 orders of magnitude below the damage threshold of the metasurface). NPL images are retrieved on a sCMOS camera (Edge 5.5, PCO, 2560×2160 pixels, 6.5 µm pixel size) after spectral filtering between 450 nm and 650 nm. The interest of using nonlinear photoluminescence compared to linear photoluminescence lies in the higher sensitivity of NPL to plasmonic hotspots, [START_REF] Beversluis | Continuum Generation from Single Gold Nanostructures through Near-Field Mediated Intraband Transitions[END_REF] which allows a direct correlation of far-field NPL images to electrodynamic simulations (convoluted by the resolution of the imaging system) when there is less than one hotspot per diffraction-limited area. [START_REF] Ghenuche | Spectroscopic Mode Mapping of Resonant Plasmon Nanoantennas[END_REF] Reference measurements are performed on a homogeneous fluorescein sample (1 wt% in a 1 µm thick polyvinyl alcohol film) to analyze experimental fluctuations of the excitation intensity due, in particular, to spherical aberrations experienced by the shaped wavefront when passing through the limited numerical aperture of the objective.

The excitation wavefront is chosen randomly and modified 100 times to measure corresponding NPL images over a 90 seconds period (Fig. 1-a-b). Within these images a 10µm×10µm area is selected, corresponding to 10 4 pixels, in which the excitation intensity is homogeneous when considering a constant wavefront. For each (i, j) pixel, it is possible to measure the NPL intensity fluctuations during the iteration process (Fig. 1-c) and, thus, the intensity distribution when excited by random wavefronts (Fig. 1-d). For each pixel of the image, an average nonlinear photoluminescence intensity <I N P L > ij (using a logarithmic scale for the NPL as shown on Fig. 1-d) and a normalized standard deviation σ ij (standard deviation of the distribution std(I N P L ) ij divided by <I N P L > ij ) are defined. These measurements clearly evidence the ability of far-field wavefront shaping to modulate the emitted NPL with strong intensity variations, more than 5 times larger than the average signal (see Fig. 1-c).

We use the normalized standard deviation σ ij so that the fluctuations of the NPL intensity can be compared between gold metasurfaces with different ff values that typically feature very different luminescence signals. Indeed, as shown on Fig. 2, intensity distributions for the different pixels vary significantly as a function of the gold filling fraction ff . To illustrate this effect, we selected two filling fractions: one well below percolation, for which the surface is essentially composed of isolated gold particles with nanoscale spacings (ff =0.29, Fig. 2-a); and one close to percolation that corresponds to a fractal morphology with a combination of complex-shaped gold islands and air nanogaps (ff =0.58, Fig. 2-b). For the percolated film, we expect significantly larger NPL intensities as optical hotspots are much stronger.

Results and discussion

Because of the structural complexity of disordered gold metasurfaces, the characterization of their optical properties can only be performed by a statistical analysis. [START_REF] Seal | Coexistence of Localized and Delocalized Surface Plasmon Modes in Percolating Metal Films[END_REF][START_REF] Awada | Experimental Study of Hot Spots in Gold/Glass Nanocomposite Films by Photoemission Electron Microscopy[END_REF][START_REF] Losquin | Experimental Evidence of Nanometer-Scale Confinement of Plasmonic Eigenmodes Responsible for Hot Spots in Random Metallic Films[END_REF][START_REF] Krachmalnicoff | Fluctuations of the Local Density of States Probe Localized Surface Plasmons on Disordered Metal Films[END_REF][START_REF] Castanie | Distance Dependence of the Local Density of States in the Near Field of a Disordered Plasmonic Film[END_REF][START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] For instance, delocalized plasmonic modes were evidenced by analyzing the variance of the scattered optical near-field 3 and their spatial extent was estimated by studying the variance of the scattered far-field intensity for different illumination conditions. [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] The influence of localized plasmonic modes can also be observed in the normalized variance of measured Purcell factors. [START_REF] Krachmalnicoff | Fluctuations of the Local Density of States Probe Localized Surface Plasmons on Disordered Metal Films[END_REF] In general, these statistical analyses are performed over the entire sample by studying different positions on the surface 3,6,7,15,18 but our aim here is to provide spatially resolved information. This is why we excite the surface with 100 random wavefronts in order to per-form a statistical analysis of the NPL intensity at any given diffraction-limited position of the sample. Compared to previous studies where wavefront-shaping was used to optimize the NPL intensity in a given area of the plasmonic metasurface in a phase-dependent fashion, [START_REF] Roubaud | Far-Field Wavefront Control of Nonlinear Luminescence in Disordered Gold Metasurfaces[END_REF] this study instead exploits a statistical analysis to infer wavefront-independent information on the sample.

In practice, analyzing the fluctuations of NPL images allows us to map independently areas with strong optical hotspots and areas that feature a large number of interfering delocalized modes. As already mentioned, a widefield nonlinear photoluminescence image mixes the two phenomena. To recover information over the amplitude of optical hotspots, we analyze the average NPL intensity < I N P L > ij . Indeed, averaging over 100 excitation conditions cancels out the influence of constructive or destructive interference effects between delocalized plasmonic modes. An image of <I N P L > ij is therefore similar to the image obtained when scanning the surface with a diffraction limited excitation [START_REF] Beversluis | Continuum Generation from Single Gold Nanostructures through Near-Field Mediated Intraband Transitions[END_REF] and provides the relative amplitude of the corresponding excited optical hotspot [START_REF] Ghenuche | Spectroscopic Mode Mapping of Resonant Plasmon Nanoantennas[END_REF] as there is typically one hotspot per diffraction-limited area in these gold metasurfaces. [START_REF] Awada | Experimental Study of Hot Spots in Gold/Glass Nanocomposite Films by Photoemission Electron Microscopy[END_REF] In order to map the local density of delocalized modes on any given point of the sample, it is essential to correct the fluctuations of the NPL signal with respect to its average value.

The normalized NPL standard deviation σ ij then becomes independent of the strength of local optical hotspots and depends only on interference effects between delocalized plasmonic modes. However, the statistical analysis does not provide quantitative information over the number of localized or delocalized modes. Overall, this statistical imaging scheme recovers, in any diffraction-limited area of the disordered surface, the relative amplitude of optical hotspots and the relative density of interfering delocalized modes.

Apart from interference effects between delocalized modes, several experimental factors can also influence the measured NPL fluctuations. On top of typical experimental noise sources, the sharp phase modulations produced by the SLM introduce small fluctuations of the excitation intensity. Indeed, the magnification of the microscope objective means that the phase jumps between SLM pixels are well below the diffraction limit and produce small diffraction fringes. [START_REF] Roubaud | Far-Field Wavefront Control of Nonlinear Luminescence in Disordered Gold Metasurfaces[END_REF] To characterize these intensity fluctuations convoluted by other measurement noise, we measure two-photon fluorescence (TPF) images of a homogeneous fluorescein-doped film with random phase profiles. These fluctuations are mainly due to the excitation, identical for NPL and TPF, and to the detection path. While there are minute differences in the detection path due to the spectral profiles of NPL and TPF, analyzing the fluctuations of TPF from a homogeneous fluorescein film remains a very good estimate of the excitation fluctuations when measuring NPL from the disordered gold samples. Reference measurements on the gold metasurfaces (ff =0.29 and 0.58) and the fluorescein film are also performed using the same incoming wavefront repeated 100 times.

Fig. 3 provides the distributions of normalized standard deviations for the 10 4 pixels of the selected area during these measurements. We observe that distributions of σ ij are significantly larger for both metasurfaces under random illuminations compared to all reference measurements, clearly indicating the influence of the sample complexity on the fluctuations of NPL intensities. This is confirmed by the much larger standard deviations for the surface close to the percolation threshold (Fig. 3-b).

Our measurements indicate that the normalized standard deviations observed on the fluorescein film σ f luo (Fig. 3-c and Fig. 3-d) are a good estimator of fluctuations due to both diffraction-induced artefacts of the incoming excitation and to other experimental noise. If the σ ij value corresponding to a given pixel in the NPL image of the metasurface is significantly larger than the average <σ f luo > value for fluorescein, then the NPL fluctuations at this position are due to efficient wavefront shaping of the electromagnetic field distribution on the metasurface and, thus, to strong interference effects between delocalized modes.

To estimate with a 98% fidelity whether a given (i, j) pixel on the NPL images features a large number of interfering delocalized modes, we define a threshold standard deviation value as <σ f luo > plus twice the standard deviation std(σ f luo ). This threshold is represented in Fig. 3 by a dashed line: it shows that all the pixels, and therefore the entire percolated (d) σ ij distributions for the three samples when the same random wavefront is repeated 100 times, used to define our measurement limit. The purple dotted vertical line on all probability distributions corresponds to our measurement limit defined as <σ f luo > +2std(σ f luo ).

metasurface (ff =0.58), can be modulated by wavefront shaping, while only a limited part of the low-ff surface will be sensitive to far-field phase fluctuations due to delocalized plasmonic modes. This is not surprising as, for ff =0.29, the sample mostly features isolated gold nanoparticles (see Fig. 2-a) for which plasmon polariton propagation is only feasible by plasmon coupling when interparticle gaps are smaller than the particle radii, 25 a parameter that is not controlled with dewetted gold films. On the other hand, fractal percolated metasurfaces exhibit both elongated particles, on which plasmon polaritons can propagate, and smaller dielectric nanogaps to allow plasmon coupling. This is confirmed by the typical length of delocalized modes, which is more than 2 times larger close to percolation when ff =0.58 (more than 4 µm) than for ff =0.29 (less than 2 µm), [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] explaining the typically lower density of such modes for the sample far from percolation.

To more quantitatively characterize the areas of the metasurface that feature a large number of delocalized modes, we propose a relative standard deviation Σ ij as a figure of merit of the strength of the NPL fluctuations compared to experimental artefacts as: As also demonstrated by the distribution of Fig. 3-a, not all the low-ff sample surface features optical properties that are tunable by wavefront shaping. In practice, about 20% of the surface does not exhibit a large enough density of delocalized modes (0< Σ ≤1), meaning that NPL fluctuations can be attributed to experimental artefacts. While the rest of the surface is sensitive to far-field phase modifications, the fluctuation figure of merit Σ remains below 5, indicating that a limited number of delocalized modes can effectively interfere to modulate the nonlinear luminescence signal. For all samples close to the percolation threshold or above it, we observe that the figure of merit, Σ, is larger than 1 for the entire metasurface. This means that far-field wavefront shaping is possible anywhere on samples around or above the percolation threshold. However, we observe that the largest normalized NPL modulations are reached close to the percolation threshold. This is where fluctuations of the nonlinear luminescence can be one order of magnitude larger than those observed on a homogeneous fluorescent layer (10< Σ). It is in excellent agreement with previous studies demonstrating longer decay lengths of delocalized modes for metasurfaces close to percolation [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] or showing that these samples provide the highest NPL enhancement factors after wavefront optimization. [START_REF] Roubaud | Far-Field Wavefront Control of Nonlinear Luminescence in Disordered Gold Metasurfaces[END_REF] The ability of the disordered gold metasurface to feature large local field enhancements, i.e. optical hotspots, and high densities of delocalized plasmonic modes are effectively characterized by the average nonlinear photoluminescence intensity <I N P L > ij and fluctuation figure of merit Σ ij for any given position on the sample associated with the (i, j) pixel of the sC-MOS camera. Fig. 5-a-d provides typical examples of 10µm×10µm images of <I N P L > and Σ for gold metasurfaces with ff =0.29 and ff =0.58. We recover the main trends of Fig. 234: close to the percolation threshold, both the average nonlinear photoluminescence intensities and the strength of the fluctuations due to wavefront shaping are larger. Since NPL images are diffraction-limited, there is statistically one optical hotspot per measurement area. [START_REF] Awada | Experimental Study of Hot Spots in Gold/Glass Nanocomposite Films by Photoemission Electron Microscopy[END_REF] This explain why the minimum values of <I N P L > in Fig. 5-a Direct comparison between <I N P L > and Σ images do not clearly indicate a spatial correlation between strong optical hotspots (Fig. 5-a-b) and large densities of delocalized modes (Fig. 5-c-d). The calculated 2D correlation coefficients for ff =0.29 and ff =0.58 are 0.65 and 0.59, respectively. For instance, the <I N P L > image in Fig. 5-b indicates optical hotspots with higher amplitudes on the right side of the sample while there are large values of the fluctuation figure of merit Σ on the left side of the same area (Fig. 5-d). This demonstrates that the two quantities are not always spatially correlated and highlights the interest of mapping localized and delocalized modes independently.

Σ ij = σ ij /[<σ f luo > +2std(σ f luo )].
However, the 50% of pixels with the largest average NPL intensities have more than a 70% Strong optical hotspots and large densities of interfering delocalized modes are therefore linked. One possible interpretation for this spatial correlation arises from nanoscale air gaps.

Indeed, these gaps generate local field enhancements but also favor efficient plasmon coupling for polariton propagation. In practice, the brightest areas of the metasurface have a significant chance of featuring the largest densities of delocalized modes : the 5% of pixels with highest <I N P L > ij have a 30% or 65% chance of having Σ ij in the top 5%, for ff =0.29 and ff =0.58, respectively.

This statistical analysis thus highlights how areas of the disordered gold metasurface can exhibit concurrently strong optical hotspots and large densities of delocalized plasmonic modes. On the other hand, a bright NPL signal does not always ensure efficient wavefront modulation. It is therefore interesting to combine the independent maps of <I N P L > and Σ as shown on Fig. 5-e,f. Areas that colocalize strong optical hotspots and large densities of delocalized plasmonic modes (which are an essential combination for efficient wavefront shaping) are thus denoted as yellow pixels. On the contrary, mostly red/orange pixels correspond to large average NPL intensities that are weakly sensitive to wavefront shaping, and green pixels indicate large densities of delocalized plasmonic modes with relatively weak optical hotspots.

As discussed above in the statistical analysis of <I N P L > ij and Σ ij , the areas with the largest average NPL signals generally feature large wavefront modulation. This is especially true for a disordered surface close to the percolation threshold as there is a limited number of bright red pixels in Fig. 5-f. However, it is interesting to note that we observe a number of green-only areas in Fig. 5-e and Fig. 5-f indicating that, for a given excitation polarization and wavelength, parts of the sample that feature interfering delocalized modes will not exhibit the largest NPL intensities, even after wavefront optimization. Statistical imaging can therefore pinpoint areas of the metasurface (denoted here as bright yellow pixels) that are the most likely to provide optimized nonlinear optical properties after wavefront shaping.

Conclusions

In this report, the fluctuations of nonlinear luminescence produced by disordered gold metasurfaces under a phase-modulated femtosecond excitation were analyzed to provide independent images of areas with large optical hotspots and areas with large densities of interfering delocalized plasmonic modes. The nanoscale morphology of the surface is shown to strongly influence both the average and relative standard deviations of the NPL signal, evidencing the relative strengths of localized and delocalized modes for different filling fractions of gold.

In particular, we demonstrate that the amplitude of the localized modes, but also the densities of delocalized modes, are maximized close to the percolation threshold. Importantly, combined images of the average intensities and of the fluctuation figure of merit clearly map areas of the metasurface that should provide the highest nonlinear responses after optimizing the phase of the excitation. These results thus demonstrate how statistical imaging schemes can become an essential characterization technique for metasurfaces used in the far-field wavefront control of optical responses, not only to select favourable areas for given excitation conditions, but also to study polarization-and wavelength-dependent memory effects in complex nanophotonic systems.

For Table of Contents Use Only

Figure 1 :

 1 Figure 1: Principle of the experiment. (a) Experimental setup: a spatially filtered and linearly polarized (λ/2: half-wave plate) femtosecond laser is reflected by a spatial light modulator (SLM) before being conjugated to the sample plane and focused on the Fourier plane of the microscope by L1. Nonlinear luminescence (NPL) is focused on a sCMOS camera by L2. A set of spectral filters and a dichroic mirror are used to minimize stray laser light on the camera. (b) NPL images are measured for 100 different random phase patterns on the SLM. (c) Typical NPL intensities for a given (i, j) pixel of the camera when changing the wavefront 100 times. (d) Distribution of NPL intensities for a given (i, j) pixel, allowing the definition of the average intensity, < I N P L > ij , and the corresponding standard deviation, std(I N P L ) ij . (e) Distribution of normalized standard deviations σ ij = std(I N P L ) ij / <I N P L > ij for 10 4 pixels of the camera.

6

 6

  s] I NPL[cts/s]

Figure 2 :

 2 Figure 2: Influence of the gold filling fraction of the disordered metasurface, ff , on the measured fluctuations of the nonlinear luminescence (NPL) signal. Typical transmission electron microscopy (left) and NPL (right, bar is 1µm) images for ff =0.29 (a) and ff =0.58 (b). Distributions of NPL intensities for three pixels, highlighted by white circles in (a,b), for ff =0.29 (blue data, c) and ff =0.58 (red data, d).

Figure 3 :

 3 Figure 3: Distributions of normalized standard deviations σ ij when exciting gold metasurfaces with ff =0.29 (a) and ff =0.58 (b) and a homogeneous fluorescein film (c) using 100 different random wavefronts.(d) σ ij distributions for the three samples when the same random wavefront is repeated 100 times, used to define our measurement limit. The purple dotted vertical line on all probability distributions corresponds to our measurement limit defined as <σ f luo > +2std(σ f luo ).

Fig. 4 Figure 4 :

 44 Figure 4: Influence of the gold filling fraction on the percentage of the metasurface that features large values of the fluctuation figure of merit Σ, ie large fluctuations of the NPL signal with respect to experimental artefacts.

  -b are non-zero. It is also interesting to notice that the largest average NPL intensities in Fig. 5-a-b are significantly lower than the maximum NPL signals in Fig. 2-a-b. As already mentioned, the intensity in widefield NPL images shown in Fig. 2 are due both to local field enhancements and to interference effects between delocalized modes. But in the analysis of Fig. 5 with a large enough number of random wavefronts, the average intensities <I N P L > become independent of interference effects and provide an effective map of the relative intensities of optical hotspots, for a given excitation polarization and wavelength, with diffraction-limited resolution.

Figure 5 :

 5 Figure 5: Nonlinear optical mapping of the average NPL intensity < I N P L >, associated with local field enhancements (a,b), of the fluctuation figure of merit Σ, associated with large densities of interfering delocalized plasmonic modes (c,d) and combined images (e,f) for metasurfaces with a low gold filling fraction, ff =0.29 (a,c,e), and one close to percolation, ff =0.58 (b,d,f). Bar is 1µm.

Statistical

  Nonlinear Optical Mapping of Localized and Delocalized Plasmonic Modes in Disordered Gold Metasurfaces Gauthier Roubaud, Sébastien Bidault, Sylvain Gigan and Samuel Grésillon £¤ ¥¦ 0 T 450 §¨© ©© <I NPL > [cts/s] Schematic representation of a disordered gold metasurface excited by random wavefronts generated using a spatial light modulator (SLM, left). Statistical optical map of a percolated gold surface combining an image of the average nonlinear photoluminescence intensity <I N P L >, corresponding to localized plasmonic modes, and an image of the fluctuation figure of merit Σ, corresponding to delocalized plasmonic modes (right).

Acknowledgement

This work was supported by the French Direction Générale de l'Armement (DGA) under project 2017706. Work at Institut Langevin was supported by LABEX WIFI (Laboratory of Excellence within the French Program "Investments for the Future") under references ANR-10-LABX-24 and ANR-10-IDEX-0001-02 PSL*. Work at Laboratoire Kastler Brossel was supported by the European Research Council (ERC) under project 278025. S.G. is a member of the Institut Universitaire de France (IUF).