Zhi-Xiang Liu

Pei Yang

Yuan Zhang

Zong-Bo Li

Finn Kjellberg

Antennae and the role of olfaction and contact stimulation in mate recognition by males of the pollinating fig wasp Ceratosolen gravelyi (Hymenoptera: Agaonidae)

Keywords: Mating behaviour, olfactory cues, contact chemicals, cuticular hydrocarbon, chemoreceptor

Antennae and the role of olfaction and contact stimulation in mate recognition by males of the pollinating fig wasp Ceratosolen gravelyi (Hymenoptera:

Agaonidae)

Introduction

A set of signals (e.g. pheromones, coloration, displays) is attractive to the opposite sex, and is thus involved in mating pair formation. Several studies suggest that sympatric taxa show stronger mating discrimination than do allopatric taxa of the same genetic distance [START_REF] Butlin | Species, speciation, and reinforcement[END_REF][START_REF] Noor | Reinforcement and other consequences of sympatry[END_REF][START_REF] Ortiz-Barrientos | The genetics of speciation by reinforcement[END_REF][START_REF] Lukhtanov | Reinforcement of pre-zygotic isolation and karyotype evolution in Agrodiaetus butterflies[END_REF]. This enhanced species discrimination in sympatry appears to be the result of natural selection for pre-zygotic reproductive isolation, such that females preferentially mate with conspecific males in many species [START_REF] Noor | Reinforcement and other consequences of sympatry[END_REF][START_REF] Lukhtanov | Reinforcement of pre-zygotic isolation and karyotype evolution in Agrodiaetus butterflies[END_REF][START_REF] Langerhans | Sexual selection paves the road to sexual isolation during ecological speciation[END_REF]. This pattern is typically beneficial to both sexes. Females that mate preferentially with their own species can produce more offspring than those that mate at random. Males also benefit from mating preferentially with conspecific females rather than investing time and resources on heterospecifics. Hence, selection for non-random mating will favour the evolution and maintenance of species isolation among sympatric species [START_REF] Noor | Reinforcement and other consequences of sympatry[END_REF][START_REF] Smadja | On the scent of speciation: the chemosensory system and its role in premating isolation[END_REF][START_REF] Langerhans | Sexual selection paves the road to sexual isolation during ecological speciation[END_REF]. This is particularly true for taxa that breed simultaneously on the same site. Fig wasps constitute such an example as sometimes thousands of individuals from multiple species occur within a single breeding arena constituted by a fig [START_REF] Weiblen | How to be a fig wasp[END_REF]Kjellberg et al. 2005b;[START_REF] Krishnan | Finding hidden females in a crowd: mate recognition in fig wasps[END_REF]. [START_REF] Bain | Geographic structuring into vicariant species-pairs in a wide-ranging, high-dispersal plant-insect mutualism: the case of Ficus racemosa and its pollinating wasps[END_REF][START_REF] Sutton | Local coexistence and genetic isolation of three pollinator species on the same fig tree species[END_REF]. Pollinating fig wasps are all members of the chalcidoid family Agaonidae and have similar life cycles [START_REF] Weiblen | How to be a fig wasp[END_REF]Kjellberg et al. 2005b). The other group includes parasitic non-pollinators that provide no apparent benefit to their associated fig species. They include gall inducing wasps, cleptoparasites and parasitoids. Some studies have shown that most non-pollinating fig wasp species are each associated with a single fig species, whereas a single fig species typically hosts multiple non-pollinator wasp species [START_REF] Weiblen | How to be a fig wasp[END_REF][START_REF] Cook | Mutualists with attitude: coevolving fig wasps and figs[END_REF]. Non-pollinating fig wasp species belong to several chalcidoid families and show a diversity of life cycles. Nevertheless, regardless of the species of parasite that oviposits inside the fig, the offspring of both pollinators and nonpollinators attain sexual maturity simultaneously in the cavity of the enclosed, urn-like fig. In pollinating wasps and some parasitic lineages, males emerge from their galls before females and mate with females still enclosed in their natal galls, while in other non-pollinator fig wasps, matings occur in the fig cavity or even outside figs. In such a close-knit nursery system, mate discrimination is a crucial step for the lifecycle of each species and finding females can be challenging. Efficient mechanisms facilitating sexual recognition within species are of particular importance in such systems. Indeed, in fig wasps, the wingless and shortlived (24-48 h) [START_REF] Ghara | Comparative life-history traits in a fig wasp community: implications for community structure[END_REF] males have to rapidly and accurately locate the conspecific femalecontaining galls. The signals and cues involved in mate discrimination in fig wasps are probably primarily chemical as locating receptive females probably involves an olfactory-guided approach associated with contact confirmation. Indeed, male fig wasps live in the restricted, dark cavity of the fig and have a pair of reduced eyes; therefore, unlike males of many other insect species, male fig wasps do not rely on visual cues to find potential mates in close proximity and they have to gnaw a hole into galls to reach the females [START_REF] Greeff | Dispersal and fighting in male pollinating fig wasps[END_REF]Kjellberg et al. 2005b;[START_REF] Krishnan | Finding hidden females in a crowd: mate recognition in fig wasps[END_REF][START_REF] Ohyama | A multilevel multimodal circuit enhances action selection in Drosophila[END_REF]. Nevertheless, using acoustic songs to locate receptive females from a distance is particularly challenging in a fig as several hundreds of conspecific receptive females may be present within the enclosed cavity. Hence the males have might evolved an odour reception system that avoids the risk of saturation of olfactory receptors and of olfactory confusion and still allows location of receptive females. Conversely the females have had to evolve a mode of signalling that can be adequately perceived in the fig cavity.

If male fig wasps rely on chemicals to recognise conspecific mates, then individual females must possess species-specific chemical signatures that allow males to discriminate among conspecific and heterospecific females that reach sexual maturity concurrently inside the fig.

The cuticular hydrocarbons of the insect epicuticle compose a group of lipid compounds that contain various numbers of carbon atoms. These cuticular hydrocarbons are important in insect chemical communication and function in mate discrimination, kin discrimination and sexual discrimination in numerous insect taxa, including fig wasps [START_REF] Howard | Ecological, behavioral, and biochemical aspects of insect hydrocarbons[END_REF][START_REF] Nagamoto | Discrimination of conspecific individuals via cuticular pheromones by males of the cricket Gryllus bimaculatus[END_REF][START_REF] Krishnan | Finding hidden females in a crowd: mate recognition in fig wasps[END_REF][START_REF] Ranganathan | A coat of many scents: cuticular hydrocarbons in multitrophic interactions of fig wasps with ants[END_REF]. Cuticular hydrocarbons are relatively heavy and hence have limited volatility, a feature which is probably a favourable trait for efficient signalling within the closed fig cavity. Typically, antennae are the main receptors involved in insect perception [START_REF] Schneider | Insect antennae[END_REF]. Male fig wasps might therefore depend on antennal sensation to detect the cuticular hydrocarbons on the surfaces of females or female-containing galls. For this hypothesis to be supported, behavioural and chemical evidence for the role of such chemicals must be found and a chemoreception system that allows the perception of such chemicals through chemoreceptors must be identified in the antennae of these species. However, no information regarding chemoreceptors on the antennae of male wasps is available. Ultrastructural analyses of such chemoreceptors, which could provide insight into behavioural characters and possible physiological functions, are lacking.

In this contribution we test the hypothesis that mate location and recognition by males is olfactory and involves a more focused sensing system than for instance the olfactory system of the female wasps that is used to locate figs from a distance. To demonstrate this, we conducted a series of mating observations to investigate the mating behaviour of the pollinating fig wasp Ceratosolen gravelyi, including the male's mating sequence, duration, and number of rounds. We test the behavioural reactions of males to stimuli from virgin and mated females as well as from extracts of femalecontaining galls and empty galls (from which females had been removed; see below). We then investigated the male's chemoreceptors at the ultrastructural level to gain insight into their functional morphology as they are likely involved in olfactory and tactile perception within the dark cavity of the fig.

We provide evidence that mate discrimination is mediated by the olfactory and contact perception of an as yet unidentified chemical message originating from the body surface of females. The ultrastructure of male antennal chemoreceptors is consistent with highly directional chemosensory function.

Materials and methods

Species biology and source

Ceratosolen gravelyi Grandi pollinates the dioecious fig Ficus semicordata and develops only within the male figs of this plant. As all fig pollinating wasps, the species is sexually dimorphic. Female pollinators have functional wings and large eyes and are responsible for colonising new figs. Male pollinators are wingless, are typically restricted to the cavity of their natal fig, and were observed to exhibit fighting behaviour with conspecific males (Supplementary materials). Although fighting behaviour was not quantified in the present study, this is the first report of fighting between males of the genus Ceratosolen. Males of fighting species move more rapidly than those of non-fighting species, which can facilitate behavioural monitoring [START_REF] Greeff | Dispersal and fighting in male pollinating fig wasps[END_REF]. The figs of F. semicordata are also parasitised by four species of non-pollinating fig wasps that belong to the subfamilies Sycophaginae (Sycophaga cunia) and Sycoryctinae (Philotrypesis dunia, Sycoscapter trifemmensis and Apocrypta sp.); these species show sexual dimorphism similar to that of the pollinator species. Males of all of these wasp species die inside their natal figs except for some male pollinator individuals that cut a hole through the fig bracts, thus allowing the mated female fig wasps to emerge from the fig.

To obtain galls containing only Ceratosolen wasps and no non-pollinating fig wasps, we manipulated figs to prevent non-pollinating fig wasps from ovipositing within them. This was done by enclosing developing figs of F. semicordata in mesh nylon bags. Five Ceratosolen females were introduced per receptive fig, as an average of five foundresses were found within individual, naturally visited figs. We then collected these figs at the stage at which male wasps had exited their galls but female wasps were still within their galls. We cut the figs open to obtain male and female (virgin and mated) pollinating fig wasps as well as female-containing galls and empty galls.

Mating behaviour observations

For the mating behaviour observations, one quarter of each of the collected predispersal figs was individually placed on the object stage of a dissecting microscope (SteREO Discovery V20, Zeiss, Heidelberg, Germany) under cold-light illumination and observed on a computer screen. Observations were focused on analysing the sequence of behaviours of male individuals that led to mating as well as the subsequent behavioural sequence. When a male reached a femalecontaining gall, we observed whether the male individual contacted the surface of the gall and how it made contact. We monitored the male's sequence of behaviour leading to mating. In figpollinating wasps, once a male has reached a female containing gall, the male probes the gall with its antennae. Then, the male chews a hole into the gall and, while maintaining its hold on the gall, extends its elongated genitalia under its body and inserts them through the hole in the gall and copulates with the female [START_REF] Weiblen | How to be a fig wasp[END_REF]Kjellberg et al. 2005b). Mating duration was calculated as the time from the initiation of chewing a hole in the gall to the removal of the male's genitalia from the gall. Mating duration and number of mating round was recorded for each male. Each male was continually observed for at least 30 min. Data from a total of 38 males were recorded.

Bioassay

To determine whether male Ceratosolen wasps recognise conspecific females using olfactoryguiding and tactile-confirming chemicals that are emitted by females, we employed three biological tests using a method similar to that of [START_REF] Krishnan | Finding hidden females in a crowd: mate recognition in fig wasps[END_REF]. Each male was individually placedin themiddleof a cell cultureplate filled with 1% agarose gel and presented with a choice between two galls or extracts placed symmetrically on either side of the male at a distance of 3 mm. Each male was allowed 5 min to respond to odours. A choice of side was scored when the wasp approached one side. Meanwhile we recorded the male's behaviours, noting what part of the male's body first made contact and whether genital elongation occurred. A scoring system based on a dichotomous variable 'behaviour exhibited' or 'behaviour not exhibited' was used. If the behaviour was exhibited within 5 min, a score of 1 was recorded; if not, a score of 0 was recorded. All of the tests were performed using an activity recorder for studies of insect behaviour (SN2000, Camsonar, London, UK) under red light conditions (set value 100%) at 25 ± 1°C, 70-80% RH. Observations were made using a selfadaptive camera for the pairwise choices and with a stereoscope for the male behaviours. Preliminary experiments with the control of solvent hexane showed males equally chose to either side. Choice tests included 40-58 replicates, and at least 35 individuals made a choice. Each male individual was used only once in the bioassay tests.

Experiment A: male response to different types of galls. Individual males were randomly assigned to one of the following four treatments: (1) a female-containing gall, (2) a malecontaining gall, (3) an exited gall, or (4) a washed gall (control). The different types of galls were determined on the basis of their external morphology. Washed galls were obtained by washing male/female-containing gall surfaces in 500 µl of hexane in a 2 ml glass vial for 10 min.

Experiment B: male response to different types of female wasps. These treatments were similar to those of Experiment A. Individual males were randomly assigned to (1) a virgin female, (2) a mated female, or (3) a washed female (control). The virgin females were obtained by directly collecting females from intact female-containing galls. Mated females and males were separately collected in the fig cavity. The stimuli wasps were freeze-killed by exposing them to -80°C for 10 min. Washed wasps were obtained by washing the body surface with hexane, a method similar to that described in Experiment A.

Experiment C: male response to insect extracts. Males were presented with a washed empty gall covered with female extracts, gall extracts, or an equivalent amount of solvent. Individual males were randomly assigned to (1) a washed gall with female-containing gall extracts, (2) a washed gall with female extracts, (3) a washed gall with empty gall extracts, or (4) a washed gall covered with hexane (control). Extracts were obtained by dipping 30 object individuals into 500 µl of hexane for 10 min at room temperature, condensing the solution under nitrogen to a total volume of 50 µl, and then maintaining the sample at -20°C until needed. Extracts (5 µl) were directly added to the gall surface using a micropipette, and the solvent was allowed to evaporate for 15-20 min.

Ultrastructural analysis

Scanning electron microscopy (SEM) was used to determine the presence and location of antennal sensilla that may perceive chemicals for mate discrimination, and a transmission electron microscope (TEM) was used to examine the ultrastructure of these sensilla. For scanning electron microscopy, intact male individuals were washed with an ultrasonic cleaner and fixed in 2% glutaraldehyde. The samples were dehydrated in a graded ethanol series to 100%, CO2-dried using a critical point dryer, sputter-coated with gold and examined at an accelerating voltage of 10 kV using a Zeiss EVO LS10 SEM. For transmission electron microscopy, the antennae were removed from living male individuals and immediately immersed in 2.5% glutaraldehyde containing 0.1 M phosphate buffer (pH 7.4) and 4% paraformaldehyde and maintained at 4℃ for at least 4 h. The antennae were then briefly washed in 0.2 M PBS (overnight) and postfixed with 1% osmium tetroxide mixed with PBS at 4℃ for 2 h. After dehydration in a graded series of ethanol, the antennae were embedded in Epon 618. Ultrathin sections were cut with a diamond knife using a Leica-U ultramicrotome and collected on copper grids. The samples were then contrasted with 4% uranyl acetate and 1% lead citrate and finally observed using a Hitachi JEM-1010 TEM. The sensillar terminology adopted follows [START_REF] Schneider | Insect antennae[END_REF], [START_REF] Barlin | Multiporous plate sensilla in antennae of the Chalcidoidea (Hymenoptera)[END_REF], [START_REF] Ochieng | Functional morphology of antennal chemoreceptors of the parasitoid Microplitis croceipes (Hymenoptera: Braconidae)[END_REF], [START_REF] Van Baaren | Antennal sensilla of hymenopteran parasitic wasps: variations linked to host exploitation behavior[END_REF] and [START_REF] Li | Ultrastructure of antennal sensilla of female Ceratosolen Solmsi Marchali (Hymenoptera: Chalcidoidea: Agaonidae: Agaoninae)[END_REF].

Data analysis

All data analyses were performed in R version 3.5.0 (R Core Development Team 2018, www.Rproject.org). Graphs were produced using Sigmaplot 10.0 (Systat Software, San Jose, CA, USA). The null hypothesis was that the pairwise choices or behavioural displays occurred at equal proportions between the two sides (odour sources). A Fisher's exact test was used to test whether males responded to the odours of conspecific females significantly more often than to the stimulus on the other side. If the male showed 'no choice', this result was excluded from the analyses but reported in the results. For the exhibited behaviours, the dichotomous (0, 1) variables were analysed with a Cochran's Q test. Post hoc pairwise comparisons were performed using McNemar's tests, and the p-values were adjusted with the Bonferroni procedure.

Results

Mating behaviour

The males were very active, with most of the observation time spent moving and interacting with females. All 38 males showed the following sequence of behaviour (Supplementary material). After emerging from its natal gall, the male held the natal gall with its fore legs and mid legs and extended its body, with its antennae oriented forward and its head up, slightly rocking and appearing to be continuously sensing environmental cues, a behaviour we called 'olfactory detection'. Once the male started to move, it moved directly towards a gall. Upon reaching the gall, the male would first touch the surface of the gall with its antennae, which was in most cases (96%) a female-containing gall, and then it moved forward and grasped the tip of the gall with its head down and touched the surface of the gall with its antennae. The contact could elicit 'contact confirmation' and then the male would start chewing a hole. Alternatively, generally for galls that did not contain a conspecific female, the abovedescribed subsequent behaviour did not occur following the antenna touching the surface of the gall; instead, the male moved away from the gall to search for a new nearby gall. Although most of the male individuals (67%) chewed holes prior to copulation, some individuals (33%), particularly those copulating multiple times with the same female, used holes that had been chewed for previous copulation events. Following contact confirmation and chewing of the mating hole, the male moved forward slightly, adjusted the position of its body, held the tip of the gall with its fore legs and mid legs, and attempted copulation by elongating its gaster and inserting it into the femalecontaining gall; we referred to this behaviour as 'genital touch'. Genital touch was followed by copulation. During the observation sequence, one male copulated with 1-11 different females, and the same individual copulated 1-7 times with the same female. However, over its successive matings with the same female, mating duration gradually decreased (Figure 1).

Fighting was typically observed when male individuals competed for the same femalecontaining gall, particularly for galls located closest to the fig cavity, where female containing galls are more accessible [START_REF] Yu | Moving your sons to safety: galls containing male fig wasps expand into the centre of figs, away from enemies[END_REF]. When two males encountered each other, they pushed each other away, or one would directly attack another using its mandibles or bite the opponent's mid leg or hind leg from behind and pull them backward. We also observed one case in which two males competing for the same female showed no aggression towards one another. The duration of fighting was variable and ranged from 5 s to 258 s. No injuries resulting from fighting were recorded for any of the observed individuals, but the victors almost always copulated with the contested female.

Figure 1. Duration of male Ceratosolen gravelyi copulation events with a single female.

Bioassay

Experiment A: Male C. gravelyi individuals showed a significant preference for femalecontaining galls (p = 0.0032) or male-containing galls (p = 0.0091) over washed galls. Five of 42 individuals chose the empty galls, but none responded to the washed galls. When given a choice between female-containing and male-containing galls, males tended to prefer female-containing galls, but the difference was not significant (p = 0.469) (Figure 2(a)). In the behavioural analysis, a significant difference in the frequency of contact confirmation was observed among the four different types of galls (Q = 78.172, p < 0.0001). This behaviour was exhibited toward female-containing galls and male-containing galls at rates of 82% and 69%, respectively. However post hoc pairwise comparison showed that the difference was not (χ 2 = 3.368, p = 0.199). Similarly, a significant difference in the frequency of genital touch among the treatments following antennal contact was observed (Q = 93.571, p < 0.0001), with males showing no response to washed or empty galls. Post hoc pairwise comparison showed that the galls containing females were much more likely to elicit this behaviour (95% response rate) than were the male-containing galls (5% response rate) (χ 2 = 12.410, p = 0.0013). Experiment B: Most male individuals distinguished between mated or virgin females and washed females (p < 0.01), but they did not distinguish virgin from mated females (p = 0.387; Figure 2(b)). The Cochran's Q test revealed a significant difference in antennal contact (Q = 51.209, p < 0.0001) and genital touch (Q = 50.167, p < 0.0001) among the three types of stimulus females we presented. A post hoc pairwise comparison revealed that virgin and mated females were equally likely to elicit these behaviours (antennal confirmation: χ 2 = 3.125, p = 0.231; genital touch: χ 2 = 3.20, p = 0.221).

Experiment C: A significantly larger proportion of males chose the gall treated with femalecontaining gall extracts (p = 0.023) or female extracts (p = 0.001) over the control galls covered with solvent (Figure 2(c)). Nine of 52 male individuals chose the washed gall treated with the extract from empty galls, and no males responded to the control galls. Males did not distinguish between the galls treated with female-containing gall extracts and those treated with female extracts (p = 0.776). A Cochran's Q test revealed a significant difference in the frequency of contact confirmation elicited among the three types of extracts (Q = 37.852, p < 0.0001). This behaviour was exhibited by 72% and 83% of male individuals in response to the galls treated with female-containing gall extracts and those treated with female extracts, respectively. A post hoc comparison showed that the female-containing gall extracts and the female extracts elicited similar frequencies of contact confirmation (χ 2 = 4.0, p = 0.137). A significant difference was observed among the extract treatments in the frequency of genital touch following antennal contact (Q = 39.931, p < 0.0001), as the males did not display this behaviour in response to empty gall extracts or to the control solvents. A post hoc pairwise comparison showed that the washed galls treated with female wasp extracts were more likely to elicit copulation attempts than were the control galls (χ 2 = 12.0, p = 0.0016). A further result is that males attracted to female gall extracts and to female extracts against washed gall extracts in treatment C mostly continued the sequence of behaviour up to genital touch, i.e. exhibited the whole sequence of behaviour leading to mating in 48 instances out of 58.

Ultrastructural analysis

The flagellum of the male antennae is composed of three flagellomeres (Figure 3(a,b)), but only the distal part of the terminal flagellomere (the third flagellomere, F3) presents antennal sensilla (Figure 3(c)). We identified three types of sensilla: multiporous plate sensilla (MPS) and basiconic sensilla types 1 (BS-1) and 2 (BS-2). These sensilla were considered to be chemosensory receptors on the basis of their external morphology (Figure 3(a-c)) and ultrastructure (Figure 3(d-i)).

Multiporous plate sensilla: MPS are botuliform and surrounded by a groove and a cuticular ridge (Figure 3(c)). These sensilla are slightly raised from the antennal surface and distributed between rows of BS-1 and BS-2. They are generally aligned in parallel with the longitudinal axis of the flagellomere segment. The dimensions of these plates vary little, with a length and width of approximately 10 μm and 4 μm, respectively. Each plate is innervated by numerous dendrites. These neurons are situated proximally in the hemolymph space of the antenna and project distally into the sensillum lymph along the sensillum axis. The dendrites expand quickly once they reach the distal end, which contains multiple cuticular pores (Figure 3(d,g)) that are suggestive of olfactory function. showing the scape (Sc), pedicel (Pe) and flagellum (F). (c) High magnification image of the terminal flagellomere (the 3rd flagellomere, F3) showing the three types of chemoreception sensilla: multiporous plate sensilla (MPS) and basiconic sensilla types 1 (BS-1) and 2 (BS-2). Note the terminal indentation (De) in the BS on the insets in the lower left corner. (d) Longitudinal section of a multiporous plate sensillum showing dendritic branches (DB) running parallel to the sensillar lymph (SL) and ending with cuticular pores (Po) at the sensillum surface. (e) Longitudinal section of the basal area of a basiconic sensilla type 1 inserted into a socket surrounded by a raised cuticular ring (CR). (f) Longitudinal section of the basal area of a basiconic sensilla type 2. (g-i) Cross-sections of a multiporous plate sensillum and basiconic sensilla types 1 and 2. The sensillar wall (SW) of BS-1 and BS-2 is non-porous at this level.

Basiconic sensilla type 1: BS-1 are short and peg-like in shape, with a blunt tip and a flexible socket (Figure 3(c)). Each sensillum has a thick, nonporous cuticular wall surrounding the inner lumen and is innervated by several dendritic branches (Figure 3 (e,h)). BS-1 length varies from 2.2 μm to 3.3 μm, and their basal diameter ranges from 0.9 μm to 1.1 μm. The tips of BS-1 presents multiple indentations (Figure 3(c), inset) that may allow some chemicals access to the sensillar lymph, and they are thus considered to have a contact chemoreception function.

Basiconic sensilla type 2: BS-2 are robust and project more obviously with respect to the antennal axis compared with BS-1 (Figure 3(c)). A thick, nonporous cuticular wall surrounds an inner lumen innervated by numerous dendritic branches (Figure 3(f,i)). The length of these sensilla varies from 7.2 μm to 8.9 μm, and the width ranges from 1.8 μm to 2.3 μm. Because of their orientation and size (Figure 3(c)), the tips of BS-2 extend substantially beyond the other sensilla, suggesting a contact chemoreception function.

Discussion

Aggressive male behaviour is rare among pollinating fig wasps. Due to the femalebiased offspring sex ratio, males face little competition in accessing potential mates. [START_REF] Greeff | Dispersal and fighting in male pollinating fig wasps[END_REF] reported that males of the Agaonidae genera Alfonsiella, Nigeriella, Allotriozoon, Pegoscapus, Platyscapa and Courtella can engage in aggressive behaviour and exhibit several fighting-related traits, including falcate mandibles, a large head, a long antennal scape, and modified legs and thorax. The present study is the first to report fighting between Ceratosolen males competing for an individual female; however, the morphology of C. gravelyi males is not consistent with the fighting traits of aggressive males [START_REF] Greeff | Dispersal and fighting in male pollinating fig wasps[END_REF]. Conversely, C. gravelyi males move more rapidly than males of the non-aggressive C. fusciceps, which move slowly when searching for females in the dark cavity of the fig [START_REF] Krishnan | Finding hidden females in a crowd: mate recognition in fig wasps[END_REF]. During our observations of male behaviour, we observed that fighting between males typically occurred in the centre of figs (Supplementary material), where access to females is easy, and females have larger body-size, suggesting higher reproductive value and more mating opportunities, while fighting was not observed for the fertilisation of females in galls of difficult access located close to the fig wall [START_REF] Dunn | Longevity, early emergence and body size in a pollinating fig wasp-implications for stability in a fig-pollinator mutualism[END_REF][START_REF] Yu | Moving your sons to safety: galls containing male fig wasps expand into the centre of figs, away from enemies[END_REF][START_REF] Peng | Fig wasps from the centre of figs have more chances to mate, more offspring and more female-biased offspring sex ratios[END_REF]. Therefore, several males often compete for the same gall in the fig centre, leading to a localised malebiased operational sex ratio that favours male-male fighting. This fighting can lead to an arms race among relatives [START_REF] Dawkins | Arms races between and within species[END_REF] if males gain more benefits from the particular ecological situations. Dispersal is an effective means for decreasing competition intensity [START_REF] Greeff | Dispersal and fighting in male pollinating fig wasps[END_REF]; however, in our experience, C. gravelyi males have never been observed to disperse; e.g. males have not been observed to leave the natal fig and enter another fig on the same tree as was observed for males of some other Agaonidae [START_REF] Greeff | Dispersal and fighting in male pollinating fig wasps[END_REF]. Within C. gravelyi, therefore, the arms race must be restricted. The intensity of competition between brothers can be partially or fully eliminated through the precise adjustment of the offspring sex ratio by foundresses [START_REF] Herre | Fig-associated wasps: pollinators and parasites, sex-ratio adjustment and male polymorphism, population structure and its consequences[END_REF]; however, several factors, such as multiple foundresses [START_REF] Herre | Fig-associated wasps: pollinators and parasites, sex-ratio adjustment and male polymorphism, population structure and its consequences[END_REF], male mortality [START_REF] Hardy | Patterns of sex ratio, virginity and developmental mortality in gregarious parasitoids[END_REF][START_REF] Greeff | Dispersal and fighting in male pollinating fig wasps[END_REF]) and parasitic wasps [START_REF] Kathuria | What fig wasp sex ratios may or may not tell us about sex allocation strategies[END_REF][START_REF] Pereira | Non-pollinating wasps distort the sex ratio of pollinating fig wasps[END_REF] can increase the male-to-female sex ratio. Because of a strategy to ensure sufficient numbers of males involving both laying more males and laying them in locations protected against parasites (Kjellberg et al. 2005a;[START_REF] Yu | Moving your sons to safety: galls containing male fig wasps expand into the centre of figs, away from enemies[END_REF], the fine adjustment of the sex ratio in fig wasp clutches may be regarded as a trade-off in the reproductive strategy [START_REF] Scharf | Reproductive trade-offs and direct costs for males in arthropods[END_REF].

Another important finding of this study is that individual male pollinators may mate several times with the same female. This condition could result in a more female-biased sex ratios if sperm is limiting [START_REF] Hamilton | Wingless and fighting males in fig wasps and other insects[END_REF][START_REF] Ramírez-Benavides | Sex ratio in two species of Pegoscapus wasps (Hymenoptera: Agaonidae) that develop in figs: can wasps do mathematics, or play sex ratio games?[END_REF][START_REF] Peng | Fig wasps from the centre of figs have more chances to mate, more offspring and more female-biased offspring sex ratios[END_REF], since more gametes might be transferred over the successive matings. Occurrence of a male mating successively several times with the same female has also been documented to occur in the two pollinators of Ficus ottoniifolia in Gabon. In that situation, the species mating most rapidly was also the one that remated females more frequently, suggesting that quantity of sperm transferred can be limiting [START_REF] Michaloud | The co-occurrence of two pollinating species of fig wasp and one species of fig[END_REF]. Females being mated several times has also been recorded for a number of fig pollinating wasp species, but in those cases the males tried to find other females to mate before coming back and remating a female [START_REF] Greeff | Dispersal and fighting in male pollinating fig wasps[END_REF]. For example, males of C. solmsi marchali, which is associated specifically with the fig Ficus hispida, can repeatedly mate four [START_REF] Peng | Fig wasps from the centre of figs have more chances to mate, more offspring and more female-biased offspring sex ratios[END_REF] to ten times [START_REF] Murray | Comparative morphology and mate competition of flightless male fig wasps[END_REF]). In Kradibia tentacularis, only offspring of a single male were found in single female broods, a result the authors attributed to lack of multiple matings but which could alternatively be due to sperm replacement [START_REF] Zavodna | Do fig wasps produce mixed paternity clutches?[END_REF]. In this study, we found that C. gravelyi males participated in up to seven rounds of mating, and some individuals used previous mating holes chewed by themselves or other individuals to mate. Hence number of mating holes can underestimate the number of mating events [START_REF] Greeff | Dispersal and fighting in male pollinating fig wasps[END_REF][START_REF] Peng | Fig wasps from the centre of figs have more chances to mate, more offspring and more female-biased offspring sex ratios[END_REF]. Regarding mating duration, considerable time may be invested in moving nutrients or compounds other than sperm from the male to its mate. These substances may be beneficial for increasing clutch size or offspring viability, thereby increasing the female's reproductive success. For example, male pollinating fig wasps have higher nitrogen levels and lower phosphorus levels than do females [START_REF] Zhang | N:P stoichiometry in Ficus racemosa and its mutualistic pollinator[END_REF], and mating duration may be influenced by the transfer of these substances to their partners [START_REF] Kay | Toward a stoichiometric framework for evolutionary biology[END_REF]. However, over multiple mating events with the same male, the provision of such substances may decrease over time, leading to decreased mating duration. Foundresses have short lifespans, and their eggs are mature upon adult emergence [START_REF] Ghara | Comparative life-history traits in a fig wasp community: implications for community structure[END_REF]. This may limit the role of a male resource donor; nonetheless, male provisioning may be vital in prolonging foundress lifespan, as adult females do not feed.

Consistent with the mating systems of other species in which the encounter of the sexes is mediated by cuticular chemicals [START_REF] Howard | Ecological, behavioral, and biochemical aspects of insect hydrocarbons[END_REF][START_REF] Nagamoto | Discrimination of conspecific individuals via cuticular pheromones by males of the cricket Gryllus bimaculatus[END_REF]) and in agreement with previous results of fig pollinating wasps [START_REF] Krishnan | Finding hidden females in a crowd: mate recognition in fig wasps[END_REF], we found clear evidence for a role of cuticular surface chemicals originating from C. gravelyi females. In pollinator fig wasps, females develop and remain in their galls until males chew holes that allow them to escape. Females, in turn, are responsible for the pollination that maintains the stability of the fig-wasp mutualism [START_REF] Weiblen | How to be a fig wasp[END_REF]Kjellberg et al. 2005b). In such a system, selection favours females producing cuticular chemicals that facilitate their recognition by conspecific males and limiting fertilisation by heterospecific males, thus ensuring pre-zygotic isolation through assortative mating [START_REF] Lukhtanov | Reinforcement of pre-zygotic isolation and karyotype evolution in Agrodiaetus butterflies[END_REF][START_REF] Smadja | On the scent of speciation: the chemosensory system and its role in premating isolation[END_REF][START_REF] Langerhans | Sexual selection paves the road to sexual isolation during ecological speciation[END_REF]. In our experiments, the males were very active and moved more rapidly than do males of the non-aggressive, pollinating fig wasps [START_REF] Krishnan | Finding hidden females in a crowd: mate recognition in fig wasps[END_REF]. This allowed monitoring of numerous choices made by the males. Males were clearly attracted by cuticular chemicals emitted by the females, and their encounters with females involved olfactorydirectional and tactile-confirmation cues. Our data also shows that female-emitted cuticular chemicals are sufficient to initiate the whole sequence of male behaviour leading to mating attempt. Hence, while we cannot exclude that males can use such cues as vibrations produced by females as previously suggested [START_REF] Krishnan | Finding hidden females in a crowd: mate recognition in fig wasps[END_REF] we can state that such cues are not required to elicit the full sequence of male behaviour.

Males of C. gravelyi showed no differences in their attraction toward wasp-containing galls (either females or males) and types of females (virgin and mated), although some males did not respond to empty galls treated with extracts from these objects. Their responses thus suggest the existence of a chemical or a combination of chemicals common to both sexes, similarly to what has been observed in Drosophila spp. [START_REF] Howard | Ecological, behavioral, and biochemical aspects of insect hydrocarbons[END_REF], that does not allow the sex of conspecific individuals to be discriminated. In fig pollinating wasps, as females are much more numerous than males and as males rapidly emerge from their galls, males have limited opportunities to encounter galls containing males. There is therefore limited selection on them to rapidly detect that a gall contains a male. Nevertheless, the males did not chew mating holes into galls containing males, showing that in a second phase they detected the sex of the individual enclosed in the gall.

In most agaonid wasps, females do not avoid mating more than once (for exceptions see [START_REF] Greeff | Dispersal and fighting in male pollinating fig wasps[END_REF]. This is a direct consequence of females waiting in their galls until the fig reaches the appropriate stage for their emergence into the fig cavity. Nevertheless while unmated females only produce sons [START_REF] Weiblen | How to be a fig wasp[END_REF][START_REF] Cook | Alternative mating tactics and fatal fighting in male fig wasps[END_REF]Kjellberg et al. 2005b), our data indicate that virgin and mated females are equally attractive to males.

Our results are consistent with the detection at a distance of cuticular compounds, allowing the males to reach a gall containing a female, followed by contact chemical stimulation. Detection at a distance and contact stimulation should be mediated by the multiporous plate sensilla and the basiconic sensilla (types 1 and 2), since no other chemoreceptors were observed on the antennae. Numerous pores of MPS occur along the botuliform plate, allowing the entry of the volatile molecules into the sensillar hemolymph space, which fulfil the morphological criteria of olfactory chemoreceptive mechanism underlying the olfactory function of the sensory neurons [START_REF] Barlin | Multiporous plate sensilla in antennae of the Chalcidoidea (Hymenoptera)[END_REF][START_REF] Ochieng | Functional morphology of antennal chemoreceptors of the parasitoid Microplitis croceipes (Hymenoptera: Braconidae)[END_REF][START_REF] Van Baaren | Antennal sensilla of hymenopteran parasitic wasps: variations linked to host exploitation behavior[END_REF]). Much fewer sensillar sensory neurons were observed here in male C. gravelyi individuals than had been observed previously in females of another agaonid wasps species [START_REF] Li | Ultrastructure of antennal sensilla of female Ceratosolen Solmsi Marchali (Hymenoptera: Chalcidoidea: Agaonidae: Agaoninae)[END_REF]) and more generally comparatively to other chalcidoid wasps [START_REF] Barlin | Multiporous plate sensilla in antennae of the Chalcidoidea (Hymenoptera)[END_REF]. However, within a fig, males could easily be confused by the chemical messages produced by the several hundreds of females. The simplified male antennae (Figure 3(a,b)), with olfactory distance and contact receptors located only at the tip of the distal flagellomere, may be an adaptation to easily manipulate the precise position of the chemoreceptors in a complex sensory environment. Male Ceratosolen can readily retract their antennae into their typical more or less closed antennal grooves, and they steadily move around the tip of their antennae, probably probing their environment for the precise location of particular chemical cues at rather low distances. In such situations, a highly sensitive detection mechanism would probably be inefficient as it would systematically become saturated. We may suggest that MPS plays an important role for detection at a distance, while basiconic sensilla (see below) would be more involved in short distance or contact stimulation. It is probable that the MPS plays a similar role in the behaviour of the different fig wasp species that reproduce in Ficus racemosa, given that male nonpollinating fig wasps have been shown to exhibit olfactory discrimination between conspecifics and heterospecifics [START_REF] Krishnan | Finding hidden females in a crowd: mate recognition in fig wasps[END_REF].

The two subtypes of BS that were present on the distal flagellomere concurrently are quite common on the antennae of hymenopteran parasitoids [START_REF] Slifer | Sense organs on the antenna of a parasitic wasp, Nasonia vitripennis (Hymenoptera, Pteromalidae)[END_REF][START_REF] Ochieng | Functional morphology of antennal chemoreceptors of the parasitoid Microplitis croceipes (Hymenoptera: Braconidae)[END_REF][START_REF] Van Baaren | Antennal sensilla of hymenopteran parasitic wasps: variations linked to host exploitation behavior[END_REF][START_REF] Li | Ultrastructure of antennal sensilla of female Ceratosolen Solmsi Marchali (Hymenoptera: Chalcidoidea: Agaonidae: Agaoninae)[END_REF]). The BS-1 have a similar morphology to the thinwalled chemoreceptor in the pteromalid Nasonia vitripennis [START_REF] Slifer | Sense organs on the antenna of a parasitic wasp, Nasonia vitripennis (Hymenoptera, Pteromalidae)[END_REF], and to the sensilla basiconica B in braconid Microplitis croceipes [START_REF] Navasero | Sensilla on the antennae, fortarsi and palpi of Microplitis croceipes[END_REF], or multiporous BS in female agonids [START_REF] Li | Ultrastructure of antennal sensilla of female Ceratosolen Solmsi Marchali (Hymenoptera: Chalcidoidea: Agaonidae: Agaoninae)[END_REF]. The shape of BS-2 was similar to the previously described sensilla in some parasitoids including sensilla basiconica A [START_REF] Navasero | Sensilla on the antennae, fortarsi and palpi of Microplitis croceipes[END_REF], thickwall chemoreceptor [START_REF] Slifer | Sense organs on the antenna of a parasitic wasp, Nasonia vitripennis (Hymenoptera, Pteromalidae)[END_REF], and uniporous BS [START_REF] Li | Ultrastructure of antennal sensilla of female Ceratosolen Solmsi Marchali (Hymenoptera: Chalcidoidea: Agaonidae: Agaoninae)[END_REF]). Yet the two subtypes of BS are smooth and present a nonporous surface (Figure 3(e,f,h,i)). In spite of remarkable differences in size and cuticular attachment, both BS-1 and BS-2 had similar numbers of neurons and apical pores, suggesting a similar function of perceiving the contact signals, since they stood out above the antennal surface so that they must contact the gall surface when the male touches it with the tip of its antennae [START_REF] Ochieng | Functional morphology of antennal chemoreceptors of the parasitoid Microplitis croceipes (Hymenoptera: Braconidae)[END_REF][START_REF] Van Baaren | Antennal sensilla of hymenopteran parasitic wasps: variations linked to host exploitation behavior[END_REF]). More generally, the distribution pattern, size and orientation of both types of BS are consistent with a contact chemoreceptive role in several parasitic wasps [START_REF] Navasero | Sensilla on the antennae, fortarsi and palpi of Microplitis croceipes[END_REF][START_REF] Ochieng | Functional morphology of antennal chemoreceptors of the parasitoid Microplitis croceipes (Hymenoptera: Braconidae)[END_REF][START_REF] Van Baaren | Antennal sensilla of hymenopteran parasitic wasps: variations linked to host exploitation behavior[END_REF][START_REF] Li | Ultrastructure of antennal sensilla of female Ceratosolen Solmsi Marchali (Hymenoptera: Chalcidoidea: Agaonidae: Agaoninae)[END_REF].

In conclusion, males of C. gravelyi are aggressive, but they lack the suite of fighting traits exhibited by classical fighting male agaonid wasps. These results suggest that morphological adaptation to fighting in C. gravelyi may be limited by the necessity to access the females enclosed in galls located close to the fig wall, a localisation that also decreases the level of male-male competition. Males showed a fixed sequence of behaviour leading to mating, including olfactory direction, contact confirmation and genital touch. This species uses distinctive olfactory directional and tactile-confirmed cues to recognise conspecific females. An analysis of the major components of the cuticular chemicals, a test of single sensilla response to these chemicals and a direct assessment of their roles in mate recognition is now needed to confirm our interpretation of how male fig pollinating wasps locate females still enclosed in their galls.

  Fig wasps are hymenoptera that only develop inside the urn-shaped inflorescences of fig trees (called figs or syconia). Fig wasp species can be divided into two functional groups. One group consists of mutualistic pollinators that are specifically responsible for the pollination of fig trees: the fig trees completely depend on the pollinators for pollen dispersal between figs. The species-specific mutualism between the pollinators and fig trees is generally obligatory interaction, particularly in local region, although some exceptional cases, such as a fig tree hosting two (or more) pollinators and several pollinators sharing a fig, have been documented in recent years

Figure 2 .

 2 Figure 2. Choice experiment with male Ceratosolen gravelyi responding to cues from different types of galls (a) and wasps (b) as well as insect extracts (c). WG, washed galls; FCG, femalecontaining galls; MCG, male-containing galls; WF, washed females; MF, mated females; VF, virgin females; WGS, washed galls covered with solvent; FGE, female-containing gall extracts; FE, female extracts. Males that did not respond within 5 min were excluded from the chi-square test. The number following the abbreviation indicates the percentage of times that each side was chosen. NC = no choice, n.s = non-significant difference (p > 0.05), * p < 0.05, ** p < 0.01, *** p < 0.001, N indicates the total number of the tested wasps.

Figure 3 .

 3 Figure 3. Micrographs of the antennae and chemosensory sensilla of male Ceratosolen gravelyi. (a) Scanning electron micrograph of the head and antennae, showing an exposed area of the 2nd-3rd flagellomeres (F2-F3). (b) Scanning electron micrographs of an excised antenna,

Acknowledgements

We would like to thank Mr Cao Li (Xishuangbanna Tropical Botany Garden, CAS, China), and Ms Tang Ying (Kunming Medical University, China) for technological assistance with electron microscopy. We also thank Su Rui and Xie Hua (Southwest Forestry University, China) for fieldwork. We appreciate the support of the Central Laboratory of Xishuangbanna Tropical Botanical Garden and Key Laboratory for Forest Resources Conservation and Utilisation in the Southwest Mountains of China.

Funding

This work was supported by the Natural Science Foundation of Yunnan Province [2014FB183]; Young top-notch talent of Ten Thousand Talent Program in Yunnan Province ; National Natural Science Foundation of China [31760107, 31560116,31100279].


domain: spi phys phys.cond.cm-ms

text:
A Pugliara

M Bayle

C Bonafos

R Carles

M Respaud

K Makasheva
email: kremena.makasheva@laplace.univ-tlse.fr

Predictive modelling of the dielectric response of plasmonic substrates: application to the interpretation of ellipsometric spectra

Keywords: plasmonic substrates, modelling, spectroscopic ellipsometry, AgNPs embedded in SiO 2 layers

A predictive modelling of plasmonic substrates appropriate to read ellipsometric spectra is presented in this work. We focus on plasmonic substrates containing a single layer of silver nanoparticles (AgNPs) embedded in silica matrices. The model uses the Abeles matrix formalism and is based on the quasistatic approximation of the classical Maxwell-Garnett mixing rule, however accounting for the electronic confinement effect through the damping parameter. It is applied on samples elaborated by: (i) RF-diode sputtering followed by Plasma Enhanced Chemical Vapor Deposition (PECVD) and (ii) Low Energy Ion Beam Synthesis (LE-IBS), and represents situations with increasing degree of complexity that can be accounted for by the model. It allows extraction of the main characteristics of the AgNPs population: average size, volume fraction and distance of the AgNPs layer from the matrix free surface. Model validation is achieved through comparison with results obtained from transmission electron microscopy approving for its applicability. The advantages and limitations of the proposed model are discussed after eccentricity-based statistical analysis along with further developments related to the quality of comparison between the model-generated spectra and the experimentally-recorded ellipsometric spectra.

Introduction

The properties and potentialities of nanocomposite materials are nowadays widely studied aiming at a very broad spectrum of applications. It is difficult to deny the usefulness of nanocomposite materials for electronic devices and electrical engineering solutions, as flame retardant of natural and synthetic textile polymers or for medical purposes as antibacterial agents [1-6 and the references therein]. Moreover, nanostructures containing a layer of gold or silver nanoparticles (AgNPs) embedded in silica matrices close to the free surface have strong potential for plasmonic devices. The main advantage of these structures is the possibility to manipulate, localize and enhance the electromagnetic field at their surface [START_REF] Maier | Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides[END_REF][START_REF] Hartland | Optical studies of dynamics in noble metal nanostructures[END_REF]. The Localized Surface Plasmon Resonance (LSPR) of metallic NPs is widely explored for enhanced optical spectroscopies of molecules [START_REF] Nie | Probing single molecules and single nanoparticles by surface-enhanced Raman scattering[END_REF][START_REF] Jeon | Nanostructured plasmonic substrates for use as SERS sensors[END_REF], photothermal therapy [START_REF] Baffou | Thermo-plasmonics: using metallic nanostructures as nano-sources of heat Laser[END_REF], photovoltaics [START_REF] Atwater | Plasmonics for improved photovoltaic devices[END_REF], or more recently in plasmoelectronics [START_REF] Warren | Plasmoelectronics: coupling plasmonic excitation with electron flow[END_REF] and photocatalysis [START_REF] Cacciato | Enhancing carrier generation in TiO 2 by a synergistic effect between plasmon resonance in Ag nanoparticles and optical interference[END_REF].

Presently, visualisation and characterisation of nanocomposite materials is mostly accomplished by using well-established microscopy techniques, including Atomic Force Microscopy (AFM), Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM) and their derivative modes. Although being extremely performant these characterisation methods remain 'local', intrusive, and unsuitable for real-time and in-line monitoring of the processes, especially on the surface/interfaces modifications. To guarantee the performance of plasmonic structures when integrated in devices one needs to characterize their dielectric response during the elaboration phase. A good way is to use reliable non-destructive diagnostic methods. Many fundamental and functional properties of nanocomposites can be conveniently probed using several variants of optical spectroscopy. In particular, using polarized light in ellipsometric measurements proves to be highly efficient. Spectroscopic ellipsometry (SE) actually turns out to be the most appropriate among various tools for characterization of nanocomposite materials [START_REF] Losurdo | Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-ofthe-art, potential, and perspectives[END_REF][START_REF]Handbook of Ellipsometry[END_REF][START_REF]Ellipsometry at the Nanoscale[END_REF]. The SE is a non-destructive, non-intrusive, and noninvasive, contactless optical technique that has been developed and applied extensively over many years now. The SE is widely used for measurements of the thickness and optical constants of semi-transparent dielectric, semiconductor, and metal thin films. It is a very powerful diagnostic method not only for optical characterization of bulk materials and thin films, but also for in situ real-time measurements of multilayered film structures, interfaces, and composites, during fabrication and processing. However, to fully benefit the advantages offered by SE an appropriate modelling necessary for interpretation of the recorded spectra is highly demanded. The application of SE, especially on the sub-100 nm thickness range and/or on absorbing heterogeneous structures like plasmonic substrates, should be carefully performed in order to limit the errors in the interpretation of the recorded spectra. A critical review discussing how to reduce the correlation between film thickness and optical constants was recently provided in the literature [START_REF] Hilfiker | Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry[END_REF]. It gives an assessment of advantages and limitations in applying optical diagnostic methods when dealing with very thin and absorbing films.

In this work we report on development, test and application of a predictive model appropriate for interpretation of ellipsometric spectra recorded on plasmonic substrates containing AgNPs. It is based on the quasistatic approximation of the classical Maxwell-Garnett mixing rule applied with Abeles formalism and accounts for the electronic confinement effect through the damping parameter. Model validation is achieved through comparison with results obtained from transmission electron microscopy. The intended application of the model is related to fast tracking of plasmonic substrates needed to study the underlying mechanisms for adhesion of biological targets (proteins/cells) on dielectric matrices containing AgNPs with specific attention paid to the controlled release of silver from those structures [START_REF] Pugliara | Assessing bio-available silver released from silver nanoparticles embedded in silica layers using the green algae Chlamydomonas reinhardtii as bio-sensors[END_REF].

Experimental

Sample description

The plasmonic substrates reported here consist of a delta-layer of AgNPs embedded in silica matrix at a wellcontrolled nanometric distance from the free surface. Their total thickness was selected in a way that for specific wavelengths the reflectance is at minimum and consequently the electric field at the free surface is at maximum, as accounted for by modelling the propagation of electromagnetic waves in stratified media [START_REF] Carles | Three dimensional design of silver nanoparticle assemblies embedded in dielectrics for raman spectroscopy enhancement and dark-field imaging[END_REF][START_REF] Bayle | Experimental investigation of the vibrational density of states and electronic excitations in metallic nanocrystals[END_REF]. In the current study a total thickness of 100 nm of the nanocomposite structures was intended. The selected samples actually represent situations with increasing degree of complexity that can be accounted for by the model. The reason for such presentation is limited to practical issues. The presented samples were elaborated by using two different but complementary physical deposition methods: (i) RF-diode sputtering followed by Plasma Enhanced Chemical Vapor Deposition (PECVD) for samples S1 and S2, and (ii) Low Energy Ion Beam Synthesis (LE-IBS) for samples S3 and S4, called hereafter 'plasma deposited' and 'implanted' samples, respectively. The two final structures are schematically represented on figure 1.

Several differences in the resulting plasmonic structures induced by the corresponding elaboration technique are intentionally put forwards on the pictures for clarity. In general, the plasma deposition processes are known to be conformal to the surface on which the layer is deposited. This surface conformity allows coatings of patterned substrates. In this study, as the plasma deposited SiO 2 cover layer is very thin, it envelops the AgNPs and spreads between them, finally imposing a slight waviness on the surface (figure 1(a)). The ion implantation process preserves the composition of the host matrix and respects the planarity of the surface of the final structure. However, for some synthesis conditions it may give rise to a secondary plane of smaller in size AgNPs placed deeper in the silica matrix in comparison to the main layer of AgNPs (figure 1(b)). Detailed description of the methods, elaboration procedure and characterisation of the sample properties are given elsewhere [START_REF] Despax | Deposition of 'polysiloxane' thin films containing silver particles by an RF asymmetrical discharge Plasma Process[END_REF][START_REF] Pugliara | Controlled elaboration of large-area plasmonic substrates by plasma process[END_REF][START_REF] Makasheva | Dielectric engineering of nanostructured layers to control the transport of injected charges in thin dielectrics[END_REF][START_REF] Carles | The synthesis of single layers of Ag nanocrystals by ultralow-energy ion implantation for large-scale plasmonic structures[END_REF][START_REF] Benzo | Stability of Ag nanocrystals synthesized by ultra-low energy ion implantation in SiO 2 matrices[END_REF][START_REF] Benzo | Controlled synthesis of buried delta-layers of Ag nanocrystals for near-field plasmonic effects on free surfaces[END_REF]. The two synthesis methods and the operating conditions are summarized in supplementary information (SI) which is available online at stacks.iop.org/MRX/5/035027/mmedia.

Structural and optical characterization of the plasmonic substrates

Structural characterization of the deposited nanostructured layers was carried out by applying various diagnostic methods. Visualization of the plasmonic substrates was achieved by TEM in cross-sectional (XS-TEM) and plane view (PV-TEM). Specimens transparent to electrons have been prepared according to a standard procedure: mechanical polishing and Ar + ion milling. The observations were performed using a field emission TEM, FEI Tecnai™ F20 microscope operating at 200 kV, equipped with a spherical aberration corrector and the Gatan Imaging Filter (GIF) TRIDIEM.

The experimental ellipsometric spectra were acquired with a SOPRA GES5 spectroscopic ellipsometer in the wavelength range from 250 to 850 nm at incidence angle of 75°.

Systematic comparison of the obtained results from ellipsometry with results from TEM analyses allows identification of real situations that can be considered by the model.

Description of the theoretical model used for simulation of plasmonic structures

The optical frequency range (3×10 11 Hz<ω/2π<3×10 16 Hz) extends from far-infrared (FIR) to vacuum-ultraviolet (VUV) spectral regions with longest and shortest wavelength of 1 mm and 10 nm, respectively. At the optical frequencies and below (microwave and radiofrequency range) matter behaves as continuum since the atomic dimensions are of the order of 0.1 nm. The response at macroscopic level is smooth and usually detected by light probes in the optical range although the discrete atomic structure of matter and the induced strong spatial variations of the quantities describing the optical fields. The nanostructured materials can be considered as a mixture of individual components each of them possessing their own continuum-like optical response. The advantage of treating a nanostructured material as a mixture having continuum behavior is the possibility to find the macroscopic (averaged) field quantities by using approximate treatment (effective media approximation, EMA). If the composite material consists of dissimilar regions that are small compared to the wavelength of probing light but large enough to express their own dielectric identity, the local fields and the subsequently obtained averaged quantities are impacted by the presence of screening charge that develops at the boundaries between the regions [START_REF] Aspnes | Plasmonics and effective-medium theories[END_REF]. The screening charge modifies locally the electric field which yields modifications in the averaged macroscopic polarization. However, under certain conditions we can find the dielectric function, but the one that describes the macroscopic response of the nanocomposite material to the applied field. If the geometry of the nanostructured material is sufficiently simple so that we can solve the Maxwell equations analytically, we can obtain expression relating the averaged dielectric function to the structural parameters of the nanocomposites on the basis of EMA. We have performed such treatment on the nanocomposites elaborated in this work and described the above plasmonic structures by using the prototype of EMA, the one developed by Garnett [START_REF] Garnett | Colours in metal glasses and in metallic films[END_REF].

The physical situation that we describe consists of an ensemble of AgNPs inserted in a silica matrix at a given distance from the free surface. Following the EMA rules, and in particular the Maxwell-Garnett approximation, we convert this heterogeneous system in a homogeneous effective media. To describe the interaction between the AgNPs and the electromagnetic wave we limit the case to the quasi-static approximation. This consideration is based on the fact that the size of AgNPs in the system is much smaller than the wavelength of the external electric field in the visible range. Additional condition is that the density of AgNPs inclusions (their volume fraction) remains small so that their impact on the system can be considered as a perturbation only. Accordingly, the electromagnetic field does not experience the detailed structure of the nanocomposite. The effective permittivity of the media ε eff is then available according to the Clausius-Mossotti relation where N is the number of NPs with volume V, the volume of one particle, and ε m is the dielectric permittivity of the host matrix: For sufficiently small volume fractions ( f=1), i.e. far from percolation threshold, the effective permittivity of the media ε eff takes the form: When scaling down to nanometer size, the optical response of metals is affected by three main features: size, shape and surrounding medium of the metal [START_REF] Kreibig | Optical Properties of Metal Clusters[END_REF][START_REF] Maier | Plasmonics-a route to nanoscale optical devices[END_REF]. The complex dielectric function of metal nanoparticles develops size dependency for nanoparticles of dimensions in the nanometer range. The size dependency of the dielectric function stems from both interband transitions and damping contributions. The impact of interband transitions is related to local changes in the properties, like electron density and atomic distances, close to the particle surface, for example. The damping contribution involves changes in the electronic mean free path due to the scattering of conduction electrons against the nanoparticle surface. Usually, the latter contribution exceeds the former one by far more [START_REF] Coronado | Surface plasmon broadening for arbitrary shape nanoparticles: a geometrical probability approach[END_REF]. Consequently, when the nanoparticle size is smaller than the bulk electronic mean free path l b (52 nm for silver [START_REF] Kreibig | Optical Properties of Metal Clusters[END_REF]), the damping increases and can be written as:

f 3 2 . 3
D g v D , 4 NP b s F NP g g = + ( ) ( )
where γ b is the bulk dumping parameter accounting for collisions of electrons with other electrons, crystal lattice (phonons), lattice defects, or impurities; γ b =1/τ where τ is the time between two consecutive collisions (known as the relaxation time of the free electron gas), g s is a dimensionless parameter depending on the surface scattering [START_REF] Baida | Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO 2 nanoparticles[END_REF][START_REF] Carles | Plasmon-resonant Raman spectroscopy in metallic nanoparticles: surface-enhanced scattering by electronic excitations[END_REF], taken as a constant (g s =1) in the present modelling, v F is the Fermi velocity, and D NP is the nanoparticle size. In the visible frequency range, the condition ω?γ (D NP ) remains valid and the real NP e w ¢ ( )

and
= ¢ @ ¢ - ( ) ( ) ( ) ( ) D g v D , . 6
NP NP p s F NP 2 3
e w e w w

w  @  + ( ) ( ) ( )
Consequently, the size dependency of the dielectric function is negligible for the real component of the dielectric function (which is equal to the bulk value) meanwhile it significantly influences its imaginary part.

Finally, the complex dielectric function of spherical metallic nanoparticles ε NP (ω, D NP ) can be written as:

D i D , , 7
NP NP IB p NP 2 2
e w e w w

w g w = - + ( ) ( ) ( ) ( )
where ε IB (ω) is the part of the complex dielectric function due to the interband transitions in bulk metals.

Considering the dielectric permittivity of the nanoparticles as given by equation [START_REF] Maier | Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides[END_REF] in the expression of effective permittivity of the media (equation ( 3)) allows for accounting the size effects imposed by the AgNPs in the theoretical model of plasmonic structures.

Numerical procedure for the simulations

Schematic representation of the modeled plasmonic structures is given in figure 2. The plasmonic structures are considered as multi-layer systems. Each of the layers is described by its own dielectric permittivity. The layers containing AgNPs are considered as effective media in the frame of the above described Maxwell-Garnett approximation and represented by the corresponding effective dielectric permittivity (equation ( 3)). As can be noticed on figure 2 such consideration of the plasmonic structure offers the possibility to describe double layer of NPs with different size and volume fractions. This stratified structure is well adapted to account for different physical situations that can arise in the stack representation according to the type of applied elaboration method.

The dielectric properties of the Si-substrate were taken from [START_REF] Palik | Academic)[END_REF] for the whole wavelength range, those of the SiO 2 layer from SOPRA Database [START_REF]SOPRA Database[END_REF] and the AgNPs dielectric function was calculated according to equation (7) by using the optical properties of bulk silver [START_REF] Palik | Academic)[END_REF]. As input parameters in the model we start with guesses for the thicknesses of different layers in the structure and the corresponding volume fractions of AgNPs. After convergence of the model calculations the output parameters of the simulation are as listed in figure 2 along with the calculated ellipsometric spectra (tan (Ψ) and cos (Δ)) in the 250-850 nm wavelength range, corresponding to the considered structure. Those theoretically-obtained spectra are compared with experimentally-recorded ellipsometric spectra on the same sample.

The developed numerical code runs on Matlab software [START_REF]The MathWorks Version R[END_REF] and uses Abeles formalisms for calculations of the electric field in multilayer systems. The Abeles formalism is a transfer-matrix method mainly used in computational optics to easily calculate the specular reflectivity of stratified media. The reflection and transmission of light at the interfaces are calculated using Fresnel equations. More information on the basis and the adopted hypotheses is given elsewhere [START_REF] Bayle | Experimental investigation of the vibrational density of states and electronic excitations in metallic nanocrystals[END_REF][START_REF] Larivière | Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsometry[END_REF][START_REF] Poinsotte | Son et matière nanostructurée: diffusion Raman et acoustique picoseconde[END_REF].

Systematically the parameters of tested plasmonic structures obtained from modelling were compared with results extracted from TEM observations of the same sample.

Before going further in the modelling of plasmonic substrates we have used a 90 nm thick SiO 2 layer thermally grown on Si-substrate as a model benchmark. The obtained from modelling results are shown in figure 3(a) along with the experimentally recorded spectra. The obtained from modelling thickness of the SiO 2 layer is 89.8±0.5 nm. The XS-TEM image of the studied benchmark sample is shown in figure 3(b) as complementary indicator for comparison of the obtained SiO 2 layer thickness. It confirms the theoretically obtained thickness after modelling. Additional verification for the benchmark sample was performed by using the EMA model for ellipsometric spectra processing on WinElli Software available by SOPRA [START_REF]SOPRA Database[END_REF]. This testsample approves the theoretical model and the selected numerical procedure.

Several indicators were used to estimate the sensitivity and uniqueness of the model. The first estimate is related to quality of the comparison between the model-generated ellipsometric spectra and the experimentally obtained ones in the entire spectral range. In particular, the results interpretation is related to the theoretical model sensitivity. This includes calculation of the mean square error (MSE) curve that quantifies the difference between model and experience for all regressed quantities according to: minimum when compare theoretical and experimental ellipsometric spectra. The normalized MSE versus thickness for the benchmark SiO 2 sample is given on figure 4. Similar uniqueness tests were performed on the other parameters extracted from the model of plasmonic structures like size of the AgNPs, their volume fraction, the cover layer thickness, etc. The obtained limits are reported in the next section when discussing the studied plasmonic structures.

MSE L M L M 1 2 1 2 , 8 i L i i i i i i 1 mod exp , exp 2 mod exp , exp 2 2 å y y s s c = - - + D -D = - y = D ⎡ ⎣ ⎢ ⎢ ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎤ ⎦ ⎥ ⎥ ( ) where

Results and discussion

Advantages of the model describing the dielectric response of plasmonic structures

Two physical methods were used to elaborate the plasmonic structures. They are different regarding their basic principles but complementary in terms of final results. The advantage is above all the possibility to cover different architectures of the nanostructures, evolution of the size, density and shape of the AgNPs and the nanometric distance from the sample free surface. respectively. The parameters characterizing the plasmonic structure obtained from modelling and those extracted from TEM-image processing are summarized in table 1.

The planarity of the AgNPs layer in this case allows for model-generated ellipsometric spectra identical to the experimentally recorded ones. The very slight waviness of the sample surface imposed by the plasma deposition method does not lead to depolarization of the probe light in the entire wavelength range. This particular situation is common for the plasma deposition method and inevitable when the cover layer is very thin, as in the present case. However it can be considered by the model.

The represented plasmonic structure on figure 6 corresponds to the implanted sample S3. A strong particularity of sample S3 is the presence of a second plane of AgNPs in-depth of the sample. It arises frequently in the LE-IBS. In this case the constituent layers of the modeled structure are five, as represented in figure 2. This sample testifies for the appropriateness of the developed theoretical model with respect to the stratified structure comprising effective media with different size and volume fraction of the AgNPs.

One can notice the excellent agreement between the parameters describing the two plasmonic structures (S1 and S3) obtained from modelling of the ellipsometric spectra and those extracted from TEM measurements (table 1). The common point of these two examples is that their structural parameters completely satisfy the hypotheses of the Maxwell-Garnett approximation. The AgNPs are spherical in shape. They are well aligned in a plane so that they form a single layer in which the thickness of the effective media can be considered equal to the diameter of the AgNPs. The AgNPs volume fraction is small enough and can be considered as perturbation only.

Abrupt variations of the experimentally-recorded ellipsometric spectra (as can be noticed on the figures) arise around 400 nm. It is related to the fact that for an isolated spherical AgNP embedded in silica, the plasmon response (mainly absorption) consists in a sharp line centered at 410 nm. When the shape of the AgNPs undergoes evolution, like for example, from spherical to prolate spheroid, or when the AgNPs interact forming dimers or elongated structures, the 3-fold plasmon mode degeneracy is split in a transverse (at lower wavelength) and longitudinal (at higher wavelength) modes, conveying a shift of the plasmon resonance. When the AgNPs touch the free surface, the dielectric permittivity through the refractive index of the effective surrounding medium is lowered presenting a value in between the ones of silica and air, also leading to a shift of the plasmon response towards the shorter wavelengths. Finally, it is important to note that the presence of very small in size AgNPs is accompanied by a broadening of the plasmonic response, according to equation (4). It is thus expected that the ellipsometric spectra express strong variation in the corresponding wavelength range between 340 and 440 nm. The above described experimental features are considered, to different extent, by the model-generated spectra and the differences are accounted for by the error bars calculated for each parameter of the plasmonic structure (table 1), however remaining in the 10% confidence limit (equation ( 8)) for all calculated parameters.

One can notice on the results obtained for the implanted sample S3 that under condition of narrow AgNPs size distribution, a small departure from the plane organization of AgNPs in the silica layer can be absorbed by the modelling however remaining in the 10% limit of MSE for all defined parameters. As it is considered in the model that the size of the spherical AgNPs equals the thickness of the mixed layer, the obtained from SE AgNPs size is slightly larger than the one obtained from TEM. In consequence this overestimation leads to a slightly smaller volume fraction determined by the SE compared to the TEM observations and to an increase of the incertitude of the thickness of both the cover layer and the SiO 2 under layer. Another important issue to consider is the effect of mutual interactions of the AgNPs which in the case of very small particles remains rather low and does not lead to violation of the model hypotheses, because the optical response is essentially dominated by absorption and not at all by scattering [START_REF] Kreibig | Optical Properties of Metal Clusters[END_REF]. For bigger particles the correction has to be taken into account and contributes to the explanation of the discrepancies observed between model-generated and experimentally recorded spectra. The obtained excellent agreement confirms that the sensitivity and the limits of the developed predictive modelling of the dielectric response of plasmonic substrates are fully dependent on the model hypotheses when related to the AgNPs size and the thickness of the effective medium (t Ag:SiO2 ).

Critical assessment of the applicability of the model

Departure from the hypotheses of the Maxwell-Garnett approximation used in the modelling leads to a strong discrepancy between the model-generated and the experimentally-obtained ellipsometric spectra. This is demonstrated on figure 7 for the plasma deposited sample S2 and on figure 8 for the implanted sample S4.

The discrepancy occurs mainly in the wavelength range around 400 nm where the localized surface plasmon resonance response is detected. It results from the evolution in shape of the AgNPs from spherical to prolate spheroid for the plasma deposited sample S2 and from dispersion of AgNPs in a band that cannot be represented The parameters describing samples S2 and S4 obtained from model-generated ellipsometric spectra and those extracted from TEM images are given in table 2. The largest error stems from the AgNPs size as obtained from the model for the corresponding SE spectra and TEM measurements which prevents from correct description of the thickness and dielectric function of the effective media and further reflects on the calculation of the thickness of SiO 2 layer on which the AgNPs rely. Additional error results from the poor calculation of the SiO 2 cover layer thickness. Finally, some of the errors accumulate to attain more than 10% difference in the total thickness as for the sample S2 or compensate as for sample S4 but the uniqueness of the solution is not guaranteed. As given in table 2, convergence on few parameters, for which the error bars are reported, can be achieved for the plasma deposited sample S2 but the obtained results are fare from the results obtained after TEM observations. As far as the implanted sample S4 is concerned, no error bars are reported in table 2 as the structure is beyond the one that can fulfill the model hypotheses and convergence cannot be obtained in this case. The SE reported values for sample S4 should be considered only as indicative.

Eccentricity-based statistical analysis of the two plasma deposited samples (S1 and S2) and the two implanted samples (S3 and S4) based on TEM-image processing gives additional information on the influence of the AgNPs shape evolution and size distribution on the theoretically-generated spectra. It underlines the departure from the model hypotheses. The analysis was performed on a large ensemble of AgNPs and is shown in figure 9 for the four situations discussed here. Statistics on more than 1000 AgNPs have been considered for each sample. The level of eccentricity refers to different shapes of the NPs starting from zero for ideally spherical NPs and evolving to 0.8 for a prolate spheroid shape for which the minor axis is 40% smaller than the major axis (figure 9(a)).

The observed excellent agreement between theoretically-obtained and experimentally-recorded ellipsometric spectra is for plasmonic structures (samples S1 and S3) containing AgNPs with shape close to spherical one. The permitted level of eccentricity of AgNPs appears to be limited to 0.4 in order to fulfill the hypotheses of Maxwell-Garnett approximation. This statement is clearly demonstrated on figures 9(b) and (d) corresponding to samples S1 and S3. Eccentricity level higher than 0.4 is experienced by a very small number of AgNPs: only 29 AgNPs for the plasma deposited sample S1 and only 5 AgNPs for the implanted sample S3. The influence of these AgNPs on the calculation of the effective dielectric function remains limited. Moreover, the size distribution of AgNPs should be quite narrow. As can be seen on figures 9(b) and (d), the plasma deposited sample S1 and the implanted sample S3 for which the theoretical model describes correctly the plasmonic structures express a narrow size distribution. As far as the plasma deposited sample S1 is concerned, the size distribution of AgNPs in this sample obeys a normal (Gaussian) law with more than 66% of the AgNPs having size in the only ±1 nm span around the mean value. The implanted sample S3 presents a size-distribution in good agreement with the theoretical distributions predicted by the Lifshitz-Slyosov-Wagner (LSW) theory for Ostwald ripening, as observed in previous works [START_REF] Carles | The synthesis of single layers of Ag nanocrystals by ultralow-energy ion implantation for large-scale plasmonic structures[END_REF][START_REF] Benzo | Stability of Ag nanocrystals synthesized by ultra-low energy ion implantation in SiO 2 matrices[END_REF][START_REF] Benzo | Controlled synthesis of buried delta-layers of Ag nanocrystals for near-field plasmonic effects on free surfaces[END_REF]. 72% of the AgNPs in this sample have size in the ±2 nm window around the mean value.

When the evolution in shape becomes important for a large number of AgNPs, like for samples S2 (plasma deposited) and S4 (implanted), their dielectric function ε NP (ω, D NP ) does not fulfill any more the model assumptions. In sample S2 (figure 9(c)) this percentage is extremely high, 97%. It means that almost all of the AgNPs in sample S2 change in shape with clearly pronounced evolution towards prolate spheroid. For 8% of the AgNPs in this sample the eccentricity level higher than 0.5. In sample S4 (figure 9(e)) 10% of the AgNPs have eccentricity level equal or larger than 0.4. Large size distribution of AgNPs leads to ill-defined effective dielectric permittivity of the corresponding layer. This is further confirmed by the analysis presented in figures 9(c) and (e). In the deposited sample S2 not only the shape is prolate spheroid but more than 80% of the AgNPs are in the ±4 nm span around the mean value. Although the shape of AgNPs in the implanted sample S4 is close to spherical one (eccentricity level less than 0.4 for the majority of AgNPs) their size distribution evolves to a log-normal one. High eccentricity level combined with large size distribution violates two of the main hypotheses of the model. The AgNPs shape cannot be considered spherical and the thickness of the SiO 2 layer containing AgNPs cannot be taken equal to the size of the nanoparticles as they are not well aligned.

When the large size distribution is accompanied by eccentricity level over 0.4, the error accumulation in the calculated ellipsometric spectra leads to a large discrepancy of the obtained parameters of plasmonic structures compared to TEM observations and the MSE that quantifies the difference between theoretically-obtained and experimentally-recorded spectra is out of range. These problems that arise from NPs distribution and eccentricity could be taken into account into our model in order to reproduce the reality of the samples [START_REF] Giordano | Effective medium theory for dispersions of dielectric ellipsoids[END_REF][START_REF] Battie | Extended Maxwell-Garnet-Mie formulation applied to size dispersion of metallic nanoparticles embedded in host liquid matrix[END_REF]. However, the corrections would imply the addition of other adjustment parameters, which may lead to artificially accurate results. The relevance of the developed model relies also on its simplicity and on the limited number of geometrical parameters to describe the plasmonic structures.

Conclusions

The results presented in this work concern development, test and application of a predictive modelling appropriate for interpretation of ellipsometric spectra recorded on plasmonic structures. The model is based on the quasistatic approximation of the classical Maxwell-Garnett formalism and accounts for the electronic confinement effect through the damping parameter. It is found that excellent agreement between theoreticallycalculated and experimentally-recorded ellipsometric spectra can be achieved for quasi-spherical AgNPs with volume fraction in the host matrix up to 15%-17%. Eccentricity-based statistical analysis of the samples reveals that a level of 0.4 of the eccentricity of AgNPs should not be exceeded in order to remain in the frame of Maxwell-Garnett approximation. Additionally, a narrow size distribution of the AgNPs is required to allow truthful representation of the thickness of the effective media layer by the diameter of the AgNPs. The simplicity of the proposed model, with a very limited number of adjustment parameters, prevents from artificially accurate results and guarantees the uniqueness of the solution. Possible extension of the model can be envisaged towards consideration of shape evolution and size dispersion of the AgNPs in the description of the dielectric response of plasmonic substrates.

Table S4

Parameters used to elaborate the SiO2 plasma cover layer by PECVD.

Sample

SiO2 plasma deposition conditions

(

Table S5

Parameters used to elaborate the plasmonic samples by ion implantation.

Sample

Ag +

Implantation conditions

Energy,

Figure 1 .

 1 Figure 1. Schematic representation of the studied plasmonic structures prepared by: (a) RF-diode sputtering followed by PECVD and (b) LE-IBS.

  components of ε NP (ω, D NP ) read:

  , exp s y D are the experimental error bars, L and M are the number of ψ, Δ pairs and the number of fit parameters, respectively. Moreover, an uniqueness test of the model was performed to guarantee the less than 10% Unique Range which spans above and below the best fit that provides 10% variance on the global MSE

Figure 2 .

 2 Figure 2. Schematic representation of the stratified structure considered for modelling and the parameters of the plasmonic substrates extracted from the simulation.

Figure 5 (

 5 a) represents the obtained from modelling and the experimentally recorded ellipsometric spectra on the plasma deposited sample S1. The XS-TEM and PV-TEM of this sample are shown in figures 5(b) and (c),

Figure 3 .

 3 Figure 3. Benchmark of the model: (a) ellipsometric spectra of 89.8±0.5 nm thick pristine SiO 2 layer grown on Si substrate as recorded experimentally (dots) and as obtained from modelling (red line), and (b) XS-TEM Bright Field image of the pristine SiO 2 layer.

Figure 4 .

 4 Figure 4. Normalized MSE versus thickness for the benchmark SiO 2 sample grown on Si substrate.

Figure 5 .

 5 Figure 5. (a) ellipsometric spectra as recorded experimentally (dots) and as obtained from modelling (red line), and (b) XS-TEM and (c) PV-TEM Bright Field images of the plasma deposited sample S1.

Figure 6 .

 6 Figure 6. (a) ellipsometric spectra as recorded experimentally (dots) and as obtained from modelling (red line), and (b) XS-TEM and (c) PV-TEM Bright Field images of the implanted sample S3.

Figure 7 .

 7 Figure 7. (a) ellipsometric spectra as recorded experimentally (dots) and as obtained from modelling (red line), and (b) XS-TEM and (c) PV-TEM Bright Field images of the plasma deposited sample S2.

Figure 8 .

 8 Figure 8. (a) ellipsometric spectra as recorded experimentally (dots) and as obtained from modelling (red line), and (b) XS-TEM and (c) PV-TEM Bright Field images of the implanted sample S4.

Figure 9 .

 9 Figure 9. Eccentricity of the AgNPs in the studied samples. Analysis based on minimum 1000 AgNPs per sample. Evolution of the NPs shape for different eccentricity levels in (a); Eccentricity on the left and histogram on the right axis for the plasma deposited samples S1 and S2 in (b) and (c) and for the implanted samples S3 and S4 in (d) and (e).

Table 1 .

 1 Parameters describing the studied samples S1 and S3 as obtained from spectroscopic ellipsometry and from TEM observations.

	Sample S1	Sample S3

Table 2 .

 2 Parameters describing the studied samples S2 and S4 as obtained from spectroscopic ellipsometry and from TEM observations.

	Sample S2	Sample S4

Acknowledgments

This work is financially supported by the program IDEX Transversalité of Université Fédérale de Toulouse (ANR-11-IDEX-0002-02), under project ADAGIO and the CNRS project MI Inter-Instituts. A P acknowledges PhD-grant from Université Paul Sabatier, Toulouse under AO3-project BioNAg.

Supplementary Information

Predictive modeling of the dielectric response of plasmonic substrates: application to the interpretation of ellipsometric spectra A. Pugliara, 1,2 M. Bayle, 3 C. Bonafos, 2 R. Carles, 2 M. Respaud 4,5 and K. Makasheva

Sections

S1. Plasma deposition process

The plasma deposition process employed for elaboration of plasmonic structures consists of an axially-asymmetric RF capacitively-coupled discharge maintained at 13.56 MHz at low gas pressure that successfully combines metal sputtering (PVD) and plasma polymerization (PECVD) [S1]. It allows a fine control over the size and density of the metal nanoparticles along with homogeneous dispersion for metallic concentrations from a few percent up to 100% (continuous metallic nanolayer). Detailed description of this plasma process used for deposition of plasmonic substrates alongside with the general trends in the structure variation for different operating conditions and the method versatility are given elsewhere [S2, S3].

Here we summarize the operating conditions for the elaboration of the plasmonic substrates in interest.

The AgNPs single layer was deposited on thermally grown SiO2 thin films on Si substrates by means of Ag sputtering of the powered electrode (silver target) in argon plasma sustained at low gas pressure. It was subsequently covered by a high quality very thin SiO2 plasma layer during the plasma polymerization step to form the stack. The selected plasma operating conditions for the sputtering process leading to the deposition of AgNPs are presented in Table S1. As mentioned above after the PVD step, the AgNPs plane was covered by a very thin SiO2 layer deposited in the same plasma reactor. In the latter deposition step, the plasma is obtained in a mixture of argon (Ar)-hexamethyldisiloxane (HMDSO,

]. The deposition of SiO2 is performed for a fixed deposition time t (to always achieve the same thickness as the deposition time controls the layers thickness according to the established deposition rate), at constant RF power P and total pressure p (Table S2). A strong particularity of our plasma process, which makes it original and highly efficient, is the pulsed introduction of the HMDSO-precursor. Combined with an appropriate amount of O2 and relatively high applied power for the plasma polymerization phase it ensures deposition of high quality plasma silica layers.

S2. Low Energy Ion Beam Synthesis (LE-IBS)

The ion implantation has been performed on a recently developed synthesis technique based on implantation of Ag + ions with low kinetic energy (few keV) and doses of few 10 16 ions/cm 2 . Under those conditions a layer of AgNPs is embedded near the free surface of a 3

SiO2 layer thermally grown on a Si wafer [S4 -S6]. A specifically modified Varian 200A2

implanter was used in order to work in the low energy range. The layers have been implanted at fixed energy E of the Ag + ions and with two ion doses D (see Table S3). The ion density current I plays a key role for the silver diffusion in the silica matrix and has been fixed to 5 µA for all implantations. In the present case the nucleation of AgNPs takes place during the implantation process due to the high diffusivity of Ag in SiO2 [S7, S8] without the need of any annealing step [S4, S9, S10].

To recover the matrix damage and protect the AgNPs from fast oxidation [S5] a postimplantation rapid-thermal-annealing (RTA) was carried out under N2 atmosphere at 500°C for 30 minutes. The choice of the annealing time and temperature was restricted as to maintain unchanged the AgNPs size distribution and their position inside the SiO2 matrix.

Therefore, it was demonstrated that by ion implantation technique one can achieve an accurate tuning of the AgNPs average size, surface density and position with respect to the free surface. Nevertheless, for implanted doses larger than 3 × 10 16 ions/cm 2 , sputtering and diffusion effects towards the free surface limit the amount of Ag that can be introduced in the dielectric and thus the final average diameter of the formed nanocrystals, that cannot exceed 15 nm [S6].

Tables Table S3

Parameters used to elaborate AgNPs by sputtering deposition process (PVD).

Sample

AgNPs deposition conditions