The mission took place between November 21st and December the 8th 2017. After formalities in Riyâdh, the team arrived in Jizân to be met with SCTH member H. Mofareh and M. Sabie. They arrived in Farasān, with M. Sabie, on the 23rd of November 2017, where SCTH official A. Aqîli met them. The team stayed in furnished appartments in the center of Farasân city (Nawras), with all the necessary confort. However, a outside courtyard with natural light, essential to the study of the material would be better for next year. SCTH members were accompanying the team at all times and we used SCTH vehicles throughout the mission.

2017 marked the resuming of fielwork activities of the French-Saudi Archaeological Mission. It is the start of a 5-year important programme, as stated in the agreement signed between the project director and the director general of SCTH in November 2017.

The stakes were numerous for this new campaign. On an administrative level, contacts have been reinforced between the project actors and the Saudi partners at SCTH, in Riyâdh, Jizân and Farasân, materialized by the signing of a new agreement.

On a scientific level, the goals were to realize an inventory of the archaeological material collected during previous campaign, to displace it to a adequate place of storage (in the Ṣabya museum for the time being), to complete the study and the documentation of the artefacts thanks to a database elaborated with FileMakerPro. At last, additional fieldwork was to be carried out in Wâdî Shâmî and Wâdî Maṭar.

Introduction Practical Aspects

Prior to the beginning of the mission, on November 22nd 2017, the director met with SCTH Director of Archaeology, Dr. H. Abu-al-Hassan, and the head of research and excavations department, Dr. A. al-Zahrani, to discuss the scientific programme and to sign a new 5-year agreement for the exploration of the Farasan sites in Wâdî Shâmî and Wâdî Maṭar.

The team was visited by SCTH regional director, M. R. Al-Kubaisi on December 5th 2017 on the site (Fig. 1). The latter assured the team of his support to the works of the team in Farasân. He was accompanied by local notables of the Jizân region : the director of the Ṣabya museum, M. H. al-Modare. The latter offered to welcome the archaeological artefacts from the excavations in the museum's stores.

The team has also had the privilege to meet with HRH the Prince of Jizân, Muḥammad Bin Nasser, thanks to the organisation of M. Rustom al-Kubaisi. It took place on December 6th in the Principate's offices and was the occasion to show the most beautiful objets to the prince and to present our work.

The signature of the new agreement was covered in the media in the Kingdom (http://www. arabnews.com/node/1197846/saudi-arabia). The visit to the Prince was also mentioned in several Saudi newspapers (http://www. spa.gov.sa/1695334 ; okaz.com, alriyadh.com, elwatannews.com).

Official visits and media coverage

Work on the archaeological collections

In order to prepare the fieldwork, a database was created with Filemaker Pro©. It will allow centralizing all the data from the project in several tables: sites, iconography (pictures, drawings, maps), stratigraphical units, artefacts & ecofacts, pottery. The 2017 mission was the occasion to record all the data (coordinates and sites characteristics, drawings, pictures, objects and bags of material) collected since 2005, when the project started.

The team also proceeded to rebagging some artefacts in new bags and plastics containers. Some of the material was lost due to poor conservation conditions since 2014. The collection was therefore moved from Farasan to the Sabya museum. Some blocks collected from the sites, during the excavations of the temple WM2-C is in the private museum of SCTH consultant I. Miftah. It would be better if they were kept together with the rest of the artefacts from the excavations. The inventory was carried out on the same occasion.

A student from Paris 1 University, L. Fleury, started a pottery study of the Wadi Matar assemblage. Finally, in 2017, the documentation was resumed: photographs were taken of the artefacts by P.-M. Blanc and drawing were produced by B. Riba (figs. 3,4,5 & 6). The main goal of the survey was to identify a settlement associated with the Late Antique necropolis WS-5 as well as a necropolis associated with the early South Arabic settlement site WS-6.

Thanks to satellites images obtained by G. Davtian from NASA in 2014, a systematic survey was carried out in the region of sites WS-5 and WS-6. An area covering 2 km 2 was covered by foot fro mthe two sites to the east as far as the coast (fig. 7 &8). The perimeter represented two kilometers westeast and one kilometer north-south. The results were numerous. Apart from the goals that were set and attained -those being the discovery of two specific sites associated with WS-5 and WS-6, four new sites were recorded. The density of archaeological remains (about one every 200 m) in the surveyed area allows hoping that a lot more remain to be discovered in the Wâdî Shâmî. New Visit of WS-6 and discovery of new tombs During a new visit on WS-6, ascribable to the ancient South Arabic phase (8 th -6 th c. BCE), additional observations were made, particularly on the large central building of the site. Inside this structure, two large thresholds allow entering the same narrow room (fig. 9). These have suffered from plundering, probably helped by metal detectors. The thresholds are often the target of plundering due to the fact that they can hide foundation deposits.

Wādī Matār 2/B

Survey in Wādī Shāmī

The survey was extended to the norther part of the site, where the landscape consists of large areas of coralline rocks, cracks in the floor create small ravine that are several meters deep (fig. 10). It yielded scattered tombs possibly associated to WS-6. They are small isolated tumuli, that seem unviolated at first glance (fig. 11). A specificity was noted on three of these: it bore a pottery vase neck on top of it (two of them being ancient South Arabic storage jars). The tombs measure 3 to 4 m in diameter. As we moved to the east, the team recorded additional examples. These are in less good condition and don't seem to have been bearing a pottery vase neck. Moreover, they are located close to shell middens. Hence, they could largely predate the other examples.

Immediately to the east of this concentration of prehistorical remains, a 4 meters large rectangular building had monolithic thresholds still visible. A r c h i t e c t u r a l remodeling was observed: doors have been blocked and walls added. The pottery seen on the surface is reminiscent of the one of WS-6 and could therefore indicate a South Arabic date for this site. However, one cannot exclude that these are earlier structures reoccupied during the Ancient South Arabic period. Around this building, several small uncarved stones structures of 1 m meter in diameter could be funerary monuments. To the south of the rectangular building, a little circular ensemble might also represent a finer funerary structure. It is a circle of standing stones planted in the floor, accessible through a door marked by two monolithic doorjambs and a stone ashlar threshold. In the centre of this circle, a dense group of uncarved rocks seems untouched (fig. 12). One of the objectives of the operations in the Wādī Shāmī was to locate the settlement associated with the necropolis WS-5, as WS-6 could not be contemporary judging from the surface material.

Thanks to the systematic surveys led in 2017, it has been located. It is one of the most important discoveries of this year.

The site is 200 m to the north-west of the necropolises (fig. 13). It covers an area of 0,76 ha, in the shape of a rounded rectangle measuring 90 m north-south and 75 m east-west. The visit allowed the observation of a densely built area. The constructions are mostly rectangular measuring 3 x 4 m and of which only one course remains. In some of them, a large storage jars neck show on the surface in the corner of a room. On the southern and western limits of the site, very ashy areas (fig. 14) have been noted, one can see charcoal and charred seeds and a large quantity of material such as a metal plaque (mirror?) (fig. 15). The surface material was collected. Other than the numerous pottery sherds, we also noted an important quantity of glass fragments, a pottery weight, metal fragments, decorated sherds and fragments of decorated incense-burners. The pottery contains local sassemblages as well as imported glazed sherds. The type of material corroborates the hypothesis that this is a domestic settlement, and the comparison of this material with the one from WS-5 allows associated the two sites.

WS-5 and its associated settlement (WS-10)

WS

WS-12

In a glade, close to a modern enclosure wall, a rectangular building in small blocks was recorded (fig. 17). The elevation is preserved up to a several courses. One of its angles has collapse. The date of the structure is most likely quite recent and doesn't seem to overlay an more ancient building. The inside space of this structures and of similar units is never composed of internal walls, backing the hypothesis that these are ephemeral or seasonal buildings for farmers or hunters. Not far from it, an undated dolmen is recorded (fig. 16).

WS-13

To the south of the glade where WS-9 lays, another site was recorded. The architecture is similar to the one observed at WS-11 and WS-15, and therefore allows to propose a dating during recent prehistory. One can see circular units (5 to 6 m in diameter) isolated from one another, very little ceramic is visible on the surface: the rare sherds are very eroded, of a dark red to black colour (fig. 22). Large areas present dense shells concentrations (fig. 23).

Three types of buildings were observed: type I a main circular building on which rests one or several additional units of smaller size (fig. 18).

type II a circular construction with an small area (20 to 30 cm in diameter) delimited by small blocks and resting on the internal facing of the outer wall (fig. 19). This area is slightly higher and is caracterized by the presence of shells (fig. 21).

type III a construction composed of three successive rectangular units, whose sizes diminishes and whose level rises one after the other. The preserved height is 1,50 m (fig. 20). The access between these units is marked by a threshold and two monolithic doorjambs placed in the middle of the wall. This site, discovered during the last campaign, is composed of a few circular structures built with dry masonry of uncarved blocks. They are isolated from one another. Quite dense scatters of pottery (ring bases, vertical lug handles) and of grey-blue gravel may indicate a perishable architecture, especially in the little depression marking the western limit of the site (fig. 24).

A first unit (3,5 m in diameter)shows a threshold with a door socket (fig. 25). The two doorjambs are monolithic blocks. To the north, a circular structure has been recorded. The surface material consists of fine soil covered in dark red sand tempered pottery sherds, one can also observe shells, fragments of basalt grinders and obsidian flakes. This enclosure was called a ḥawṭa by the SCTH representative (fig. 26).

To the east, two standing stones mark the entrance of a small circular structure. In its centre, a small cluster of rocks is still visible. This could possibly be a tomb (fig. 27). A little more to the east, on the site limits, a circle of standing stones has a diameter of 4 m. No threshold is visible there.

In the center, a rocks cluster evokes the unit described above as well as the tombs recorded at WS-11.

To the west of the site, a building is erected on a slight relief. The main unit is built with uncarved blocks and rests on the natural rock, showing on the surface in some places. Neighbouring little units are built against the outer masonry to the south and to the east. In its immediate vicinity, small clusters of smaller blocks are reminiscent of little dolmens (fig. 28). This type of dolmen was also observed in WS-11. This area also yielded a little blade in copper alloy on the surface (fig. 29).

To the north of the two circles of stones, a rectangular construction (2 x 4 m) breaks with the recorded architecture, it could date from a later period, rather modern and probably associated with the modern crop enclosure found in the depression west of the site (visible in the background on figure 24, left). The elevation is preserved up to 1,50 m. An object in basalt was collected on the surface (fig. 30). Finally, to the north of the modern enclosure, a pottery scatter measuring 2,5 m in diameter was observed. New visit of WS-8, first seen in 2011

This site had been surveyed briefly in 2011 by F. Villeneuve and S. Marion de Procé. A second visit allowed completing the surface material collection, description and sketching the site by B. Riba (fig. 31). The masonry is made of small rocks and appears to recover a more ancient structure. The place may have been reoccupied at a recent date, maybe by poachers or farmers according to our guides. The surface observation allowed discovering a coin, that is yet to be identified (fig. 32). Pottery and pozzolano is also observed. The systematic survey carried out in 2017 in the Wadi Shami revealed an unexpected density of sites dating from prehistory to the islamic period. In the coming campaigns, this surveys must be continued in order to realize the archaeological inventory of this largely unknown area. The systematic recording will be carried out by a geomatician, and completed, when deemed necessary, by kite photographs.

Apart from the surveys, the Saudi-French team also considers to excavate some tombs of the late antique necropolis WS-5, in the tumular area of the site (very disturbed by plunderers) as well as in the wider area where untouched tombs still remain. The coming campaigns will focus on establishing a top plan of WS-10, in order to confirm its association with the necropolis and its chronology.

Perspectives on the Wādī Shāmī

Sondages in the Wādī Matar

The team members' time was mainly devoted to the study of the Wadi Matar, started in 2013. The objectives for 2017 were to clarify the plan of the temple and to carry out a test excavation on WM-2/B in order to assess the potential of a larger dig.

A little sondage 1,20 m x 0,90 m was opened in the cella of the temple, at the highest point of the artificial mound in which the building rests. It was located between the north-south walls (M02 and M05), in the narrow room at the eastern extremity of th temple (fig. 33).

It was rapidly confirmed that the circulation levels had all disappeared, as thought since 2013. The sondage in 2017 revealed the presence of a little block apron abutting against the two walls. This apron was showing on the surface (fig. 34). The excavation allowed revealing the eastern facing of the partition wall M02 (fig. 35) as well as the western facing of wall M05 (fig. 36). A coarsed partition wall, M06, appeared on the southern side of the sondage (figs. it.. A surface cleaning to the north of the sondage allows thinking that the apron is contained by another partition wall to the north: one can see on figure 41 that it stops clearly. Two hypothesis can be proposed: the temple cella consists of three rooms (see fig. 43), or this apron materializes a central podium resting on the back wall of the temple. One can also imagine that, if the cella is triple, the central room would be slightly higher. The absence of blocks showing on the surface in line with M02 argues in favor of a podium as well as the very well marked location of the apron (in the middle of M05), but the alignment of blocks on the northern side on the other hand, argues in favor of a triple cella. Given the type of religious buildings known in the region, a dissymetric cella is very unlikely, future excavation will hopefully confirm one hypothesis or the other.

Few material came out of this sounding and there is an important need for the study of the exhumed sherds in order to determine the original date of the apron and of the building. It seems that the apron date from the same construction phase than walls M06 and M02. These two walls are chained whereas wall M05 was built prior to them both. M05 could date from the original building phase but could also be from the same construction phase. It appears logic to first build the outer walls before erecting the internal partition walls and structures such as the apron for a podium. Finally, the slope of the apron and the earth layer beneath it (see the sections fig. 42) probably results from a construction phase destined to erect walls M02 and M05. Once these walls were built, the workmen could fill the space with small blocks as the apron without having to level the earth. mur ?

In the area of WM-2/B, a central location was selected for a test excavation. It was carried out under the responsibility of P.-M. Blanc. M. Sabie (from SCTH -Ṣabya) participated in the excavation and was trained for archaeological activities (fig. 45).

The selected area extended in room (p), on both sides of a monumental threshold located at the southern end of the area (fig. 44). The doorjambs are still in place but they are slightly leaning out of place: the east doorjamb is leaning to the south and the west doorjamb is leaning to the north (fig. 46). This could be resulting from the fall of a lintel that would have crowned the doorjambs. The threshold, once cleared from fallen blocks (fig. 48 et 49), presented a width of almost two meters, like the one found in room (a), which has inscribed doorjambs. The sounding revealed preserved occupation levels (fig . 47) as well as pockets of ash of about 50 cm (fig. 50 and51).

Test excavation in Wadi Matar-2/B (resp. P-M. Blanc)

) c) d) e) f) g) h) i) k) j) l) m) n) o) p) q) s) r) t) v) u) x) y) z) w)
Fig. 44. Location of sounding 2017, room p/ (© MIFA) The remains of the structures and of the layers discovered after the surface cleaning leads to think that the area located north of the threshold must have been an open area, like a courtyard. Small blocks in the ground evoke the blocking of wooden posts (fig. 52), in order to cover the area with that we can imagine being pieces of cloth, leaves and branches or hay. This space is delimited to the east by a crude construction made of blocks laid on a collapse layer characterized by block 1407 (fig. 53), fallen and broken, which may be the door lintel.

Among this year's discoveries, we can mention a small object carved in bone (fig. 54), fines elements made of copper alloy as well as fragments of obsidian tools. The pottery has yet to be studied, it didn't seem to include diagnostic sherds or complete vessels. We can still note that the pottery paste was homogeneous, pink to orange coloured. These discoveries (preservation of occupation layers and a 50-cm stratigraphy to the least) allows planing for more important excavations in the coming seasons as well as one can hope to exhume datable material like charcoal. The 2017 sounding (fig. 55) revealed the archaeological richness of the area and the attention that we shall pay to WM-2/B in the future, in order to clarify its chronology and function. The 2017 season has fully answered this year's questions. The Saudi-French team will therefore continue working in the Wâdî Maṭar 2 area for the excavation of WM-2/B, WM-2/B and WM-2/C. These areas will shed light on the type of site we are studying. There is a need to confirm or not the function of WM-2/A ("crafts area") and define that of WM-2/B as well as its chronology. The temple area is a lot more eroded and future soundings will try to determine the original building period.

The resuming of the works of the Saudi-French archaeological team in Farasan was productive on many levels. In terms of cooperation, this year marked a great enhancement thanks to the help and interest of members of the SCTH in Riyâdh, Ṣabya, Jazân and Farasân. On a scientific level, the archaeological wealth of the islands was confirmed by the surveys and excavations. The test excavations allow a quick assessment of the potential for future digs. This year's results are important and pave the way to more in-depth studies in the coming years, in order to adress the three following regional historical problematics : 1/ Recent prehistory, transition into the South Arabic period; 2/ Antiquity, around the change of era and during the Roman presence; 3/ Late Antique periode. The selection of three areas from three different time periods is explained by the will to shed light on those key-questions and promise encouraging new results for the southern Red Sea.

Perspectives and general conclusions

Fig. 1 .

 1 Fig. 1. Visit of SCTH Jizân regional Director M. R. Al-Kubaisi (© MIFA)

Fig. 2 .

 2 Fig. 2. Object photography in Ṣabya Museum, P-M. Blanc (© MIFA)

Fig. 7 .

 7 Fig. 7. Wādī Shāmī, sites recorded between 2011 & 2017 (© MIFA)

Fig. 9 .

 9 Fig. 9. WS-6, western threshold of the large building, to the south (© MIFA)

Fig. 11 .

 11 Fig. 11. Isolated tombe (WS-11) north of WS-6 (© MIFA)

  Fig. 13. Location of WS-10 (QuickBird, NASA, © MIFA).

Fig. 14 .

 14 Fig. 14. WS-10, ashy areas in the southwestern limit of the site (© MIFA)

Fig. 16 .Fig. 17 .

 1617 Fig. 16. WS-12, rectangular building in the center and a dolmen close-by (© MIFA)

Fig. 18 .

 18 Fig. 18. Type I : circular structure, a second unit (non-visible) is on the left side (© MIFA)

Fig. 24 .

 24 Fig. 24. WS-15, western limit of the site: scatter of grey-blue gravel (close up view on the right), fauna and pottery (© MIFA)

Fig. 27 .

 27 Fig. 27. WS-15, circular construction with a threshold, cluster of rocks in the center, eastern limit of the site (© MIFA)

  Fig. 31. Sketch of WS-8, 2017 by B. Riba (© MIFA)

  Fig. 33. WM-2/C, locaton of the sondages (© MIFA)

Fig. 39 .

 39 Fig. 39. WM-2/C, sondage 2017. Coupe B. Radier comblant l'espace entre M05 et M02 (© MIFA)

Fig. 41 .

 41 Fig. 41. WM-2/C, sondage 2017. Wall M06 and the apron abutt the back wall of the temple (M05). One can see the northern limit of the apron after a surface cleaning. (© MIFA)

Fig. 45 .

 45 Fig. 45. P-M. Blanc and M. Sabie during the excavation of WM-2/B (© MIFA)

Fig. 51 .

 51 Fig. 51. WM-2/B, plan of sounding 2017

Fig. 55 .

 55 Fig. 55. WM-2/B, sounding 2017, aerial view at the end of the season(© MIFA)


Florian Bellafont

Denis Morichon

Volker Roeber

Gaël André

Stéphane Abadie

Stéphane Abadie Infragravity Pe- Riod

Infragravity period oscillations in a channel harbor near a river mouth

Keywords: channel harbor, harbor oscillation, infragravity waves, Boussinesq model, BOSZ, surf zone processes, long waves, wave spectrum

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Harbor entrances are usually designed for protection against wind and swell waves with periods ranging between 5 s and 20 s. However, many harbors experience agitation problems caused by long waves with periods longer than 30 s. In most cases, a harbor is a semi-enclosed water basin located on the coast and therefore an oscillating system. When the period of external forcing is close to the eigen periods of the basin, resonance occurs. With energetic external forcing, a standing wave, associated with vertical oscillations and strong currents, develops: this phenomenon is called coastal seiche [START_REF] Rabinovich | Seiches and harbor oscillations[END_REF].

A stationary system of coastal seiche can hardly develop in river ports, because there is no upstream boundary on which a wave can be reflected. In addition, infragravity waves (IG), when entering the river, can excite the system constituted by the ship at dock and its mooring lines [START_REF] Van Der Molen | Numerical simulation of long-period waves and ship motions in tomakomai port, japan[END_REF]. IG waves are long surface waves with periods between 30 s and 300-600 s (5-10 min) and are generated by two main mechanisms [START_REF] Bertin | Infragravity waves: From driving mechanisms to impacts[END_REF]: non-linear interactions between short waves generate an IG wave which travels phase-locked to the wave groups and is called bound wave [START_REF] Longuet-Higgins | Radiation stress and mass transport in gravity waves, with application to 'surf beats[END_REF]. In addition, the temporal variation of the breaking zone causes a time-variation of the wave set-up and generates free long waves [START_REF] Symonds | Two-dimensional surf beat: Long wave generation by a time-varying breakpoint[END_REF].

Different classes of wave models can be used to simulate the transformation of nearshore waves and their interaction with coastal structures. Spectral wave models are usually applied to describe the characteristics of short waves at the toe of a structure. They include the effects of refraction and breaking processes on wave transformation but they are not adapted to precisely describe wave diffraction by coastal structures which is dominant in harbour environment [START_REF] Booij | The" swan" wave model for shallow water[END_REF][START_REF] Tolman | User manual and system documentation of wavewatch iii tm version 3.14. Technical note[END_REF]. The models based on the mild slope equations, also called Berkhoff model, allow to overcome this limitation by solving explicitly both refraction and diffraction processes for waves propagating over a gentle slope [START_REF] Berkhoff | Computation of combined refraction-diffraction[END_REF]. The mild slope equations were derived for combined refraction and diffraction of linear periodic waves. They are well adapted to describe the interaction of long waves with port structures. They were used in numerous studies to numerically investigate the oscillation of port basins induced by long wave forcing and the conditions for seiche generation [START_REF] Lee | Computer modeling for harbor planning and design[END_REF][START_REF] Okihiro | Excitation of seiche observed in a small harbor[END_REF][START_REF] Thompson | Numerical modeling of harbor response to waves[END_REF]. Boussinesq-type wave models are well suited to simulate the impact of storm waves on harbour oscillations. They allow to simulate both short and long wave interactions with port structure (Thotagamuwage and Pattiaratchi, 2014b;[START_REF] Guerrini | Numerical modelling of long waves amplification at marina di carrara harbour[END_REF][START_REF] Gierlevsen | Wave disturbance modelling in the port of sines, portugalwith special emphasis on long period oscillations[END_REF].

This study aims to study the oscillation in the Port of Bayonne (France) by combining water elevation measurements and numerical simulations results. This port, located near the mouth of the Adour River, frequently faces problems in keeping boats docked during storm conditions and long-period oscillations have led to resonance of an adjacent marina. A field campaign was carried out during a storm event (Hugo) that occurred around March 23, 2018. Offshore wave conditions were typical of a one-year return-period storm (Hs = 6 m and Tp = 15 s) [START_REF] Abadie | Paramètres statistiques de la houle au large de la côte sud-aquitaine[END_REF]. The data collected during this event are used both to characterize the oscillations inside the harbor and the marina and to validate a numerical wave model based on the Boussinesq equations. The model is used to complement the measurements by providing information about the generation processes of IG waves outside the harbor and their behavior inside the river and the marina.

STUDY SITE

Port of Bayonne is located on the south-western shore of France in the Adour river (figure 1). It is composed by two harbors: a channel and commercial harbor that extends up to 6.5 km upstream of the river with an average depth of 14 mCD with respect to chart datum which corresponds to the lowest astronomical tide level. A marina (Port of Brise-Lames), a semi-enclosed water basin with an average depth of 2.5 m, is located on the left shore, 1.4 km from the river mouth. The minimum, average and maximum annual river flow of the Adour are respectively 30, 300 and 2000 m 3 /s. Two breakwaters protect the entrance of Port of Bayonne from lateral currents and swell waves. An underwater sediment deposit made of material from dredging operations of the river is located between 2.5 and 3.5 km from the coast. The minimum depth above the deposit reaches 17 m. The tidal regime of the area is mesotidal with a mean sea level (MSL) and a tidal range during spring tides of 2.53 m and 3.5 m respectively.

DATA AND METHODS

A directional wave buoy, moored in 50 m water depth at 5.3 km from the coastline, records offshore wave conditions and provides a sea and swell directional spectrum every 30 min. The Adour river flow is obtained from the Banque Hydro data base (hydro.eaufrance.fr), and the atmospheric pressure is hourly measured by a weather station located in Biarritz. Four pressure sensors, with a sampling frequency of 1 Hz, were deployed in Port of Bayonne during a storm event. Three sensors were fixed in the channel harbor at 0.3, 2.2 and 3.7 km from the river mouth, and one in the marina (figure 1).

The pressure data are transformed into free surface time series by applying the hydrostatic pressure for-mula whose application range is respected, since the sensors are located outside the surf zone and installed near the free surface at a depth of 1.5 m [START_REF] Bonneton | Recovering water wave elevation from pressure measurements[END_REF].

A spectral analysis of the free surface elevation time series was performed to study the energy distribution in the different frequency bands as well as their spatial and temporal evolution. After removing the tidal contribution by considering a linear deviation of the signal, the significant height (Hs) is calculated from series of 2048 water level data (~34 min) according to the formula (1) [START_REF] Holthuijsen | Waves in oceanic and coastal waters[END_REF].

Hs = 4 √ m 0 (1)
where Hs refers to the significant wave height and m 0 to the zeroth-order moment of the spectrum. Free surface oscillations in the period bands of short (5-30 s) and infragravity (30-300 s) waves can be determined by fixing the integration bounds of m 0 . The power spectral density of the free surface is determined by dividing the signal into 2048 data segments with a 50% overlap between each segment and applying a Hanning window. The mean spectrum being related to the variance of the free surface, the associated confidence interval (CI) follows a Chi-square law (χ 2 ) [START_REF] Thomson | Data analysis methods in physical oceanography[END_REF].

CI = ν.s 2 χ 2 α/2,ν ; ν.s 2 χ 2 1-α/2,ν (2)
where ν denotes the degree of freedom equal to the number of segments minus 1, s 2 the calculated variance and α the confidence coefficient taken at 5%.

NUMERICAL MODEL

The propagation of the waves from the wave buoy to the Adour river during storm Hugo is simulated with the BOSZ numerical model [START_REF] Roeber | Shock-capturing boussinesq-type model for nearshore wave processes[END_REF][START_REF] Roeber | Boussinesq-type model for energetic breaking waves in fringing reef environments[END_REF]. It is a Boussinesq-type model based on the equations of [START_REF] Nwogu | Alternative form of boussinesq equations for nearshore wave propagation[END_REF] expressed in conserved variable formulation. The numerical solution utilizes a low-diffusion Finite Difference scheme for the propagation of the waves towards the surf zone and a robust, shock-capturing Finite Volume scheme for wave breaking and moving boundary (wet/dry) processes.

Model setup

The numerical domain extended 8 km seaward to include the offshore wave buoy (50 mCD of water depth), and covered 8.5 km of coast (centered on the harbor mouth). The upstream boundary is far enough from the area of interest to limit boundary disturbances (figure 2). A sponge condition is applied at the domain boundaries except at the upstream river boundary where a radiation condition is applied to allow for long waves to leave the domain. The mesh is composed of square cells, of which ~50% are wet. Two grid resolutions are chosen, 6.5 and 10 m, to study the effect of mesh size in terms of computation time and convergence of the results (table 1). With a 20˚clockwise rotation of the domain, the western boundary is oriented perpendicular to the peak direction of the incoming swell. The seabed material in the study area is essentially fine sand with some mud deposits in the river. Rocky outcrops have been identified 2 km south of the mouth of the Adour River [START_REF] Augris | Cartographie géologique des fonds marins côtiers: exemples le long du littoral français[END_REF]. Based on this information, a uniform Manning roughness coefficient of 0.015 s/m 3 was applied to the entire domain, corresponding to sand grain with diameter 0.3 mm [START_REF] Arcement | Guide for selecting manning's roughness coefficients for natural channels and flood plains[END_REF]. A factor of 10 is applied to the cells covered by the harbor breakwater to take into account their effect on short waves dissipation due to their rubble-mound armor layers.

The model simulation period is 4 hours, the first 30 minutes are used to ramp up the model and ensure a fully developed wave field. The remaining 3h30 are divided into 30 min segments and their power spectral densities are averaged. Since no phase information is provided in the input spectrum, the BOSZ model assigns a random phase to each spectral component and therefore multiple simulations are required to rule out particular wave-wave interactions due to the set of random wave phases (see [START_REF] Roeber | Destructive tsunami-like wave generated by surf beat over a coral reef during typhoon haiyan[END_REF]). Since the Boussinesq-type equations have only limited dispersion capabilities, the input wave spectrum is truncated near the high-frequency tail. The BOSZ model uses the ratio of wavelength to water depth (µ) to set the threshold of the high frequency tail. The truncated energy is redistributed over the remaining frequency bins to maintain the overall energy of the spectrum. The ratio µ = 1.5 was found appropriate, thus waves with a period of less than ~7 s are not included in the input spectrum (at a depth of 50 m and applying the linear dispersion relation [START_REF] Holthuijsen | Waves in oceanic and coastal waters[END_REF]). Since the individual waves are Grid resolution m 10 6.5 Cells millions 1.5 3.5 Wet cells % 49 47 Computational time days 1 3.5 12 cores: Intel Xeon x5675 @ 3,06 GHz generated for a specific water depth, the bathymetry along the wavemaker is of uniform 50-m depth without friction covering about 100 offshore cells. It is important to notice that the truncation of the input spectrum only affects the waves, which are generated as input. The governing equations are not affected by this method. Essentially, waves of any length -as long as they can be numerically accounted for over the grid -are free to evolve during the computation; e.g. high frequency waves often result in form of super-harmonics of the main carrier frequencies from the shoaling process.

Selected event

The effects of river flow and tide are neglected. To respect this hypothesis, the numerical study focuses on the event of 24 March 2018 from 14:30 to 15:00 (UTC) at low tide: the mean water level was 1.97 mCD with a standard deviation of 0.05 m, and the Adour flow (430 m 3 /s) was slightly higher than the mean annual river flow. The wave characteristics measured offshore were : Hs, peak period (Tp), direction at the peak and directional spreading at the peak equals to 5.7 m, 18 s, 299˚and 19˚respectively. The BOSZ model is forced with a frequency-direction spectrum reconstructed from wave buoy measurements using a parametric directional spreading function (team et al., 2007).

RESULTS

Field data

During the storm event, from 24 to 25 March 2018, the offshore significant wave height and peak period reached maximum values of 6 m and 18 s respectively. Figure 3 shows the response of Port of Bayonne to external forcing: Hs in the channel harbor (b) and in the marina (a). The contribution of short waves (5-30 s) in harbor oscillations is low (Hs S W < 0.15 m) unlike IG waves whose significant heights Hs IG reach values of 0.47 m for an Hs of 0.55 m in the channel harbor and an Hs IG of 0.95 m for an Hs of 1.07 m in the marina. The period band of Hs IG has been extended to 600 s for the marina in order to include the period of basin's fundamental mode (see power spectral density figure 4).

To study the waves transformation during the propagation in the river, power spectral densities (PSD) at the pressure sensors are presented in figure 4 (18h of data). From these densities, significant wave heights are calculated and the contribution of the different period bands to the variance of the free surface is expressed as a ratio of m 0 (R S W = m 0,S W /m 0 ) (table 2). A significant part of the short waves energy is dissipated by the breakwaters: despite an Hs greater than 5 m at the wave buoy, Hs S W is equal to 1 m at the Port mouth (PS0). In the port, the remaining energy dissipates quickly and its contribution to the variance of the free surface is low: Hs S W < 0.10 m and R S W < 5% for PS1 to PS3. The contribution of IG waves to the variance of the free surface is rather low (~30%) at the Port mouth (PS0) but Hs IG is equal to 0.7 m. In the channel harbor, the IG energy is very high (R IG > 80%) and dissipates slightly: only 6 cm in terms of Hs between PS1 (2.2 km) and PS2 (3.7 km), i.e. 20% dissipation. The very long waves (VLW), with a period between 300 and 600 s, have a weak part in the channel harbor oscillations: Hs V LW < 0.15 m and R V LW < 6% for PS0-PS2.

In the marina (PS3), the PSD has several peaks that are characteristic of amplification by basin geometry and correspond to the eigen mode periods of the marina (semi-closed configuration) (Thotagamuwage and Pattiaratchi, 2014a). These periods can be estimated by applying the Merian formula [START_REF] Raichlen | Harbor resonance. Estuary and coastline hydrodynamics[END_REF]. The main peak is related to the fundamental (Helmholtz) mode with period of 330 s, a broad peak is visible at 125 and 80 s, and three peaks are more marked at 45, 27 ans 22 s. The marina geometry causes an amplification of the external forcing, thus an increase of Hs: Hs IG = 0.50 m and Hs V LW = 0.30 m.

Measurement and model result comparison

The power spectral densities from the measured and simulated water level time series are presented in figure 5 for the channel harbor and in figure 6 for the marina.

At PS0, short waves energy is globally underestimated and particularly for periods of less than 12 s. This can be due to the effect of local wind not taken into account in the model and to the cut-off period of 7 s on the input spectrum. For the other sensors (PS1 and PS2), the energy in short wave period band is very low and can neglected: Hs S W < 0.05 m.

Spatial variation and frequency distribution of IG waves (30-300 s) are well reproduced by the model for the channel harbor sensors (PS0 to PS2) and for the two grid resolutions (6.5 and 10 m): the shape of computed spectral energy from BOSZ agree well with the measurements. But, the underestimation of spectral energy for periods higher than 290 s results in a 10% difference in the Hs IG values for the 6.5 m mesh size and for the sensors in the channel harbor (underestimation for PS0 and PS1, and overestimation for PS2): the differences of Hs IG are from 0.03 m to 0.10 m. For the 10 m mesh size, the Hs IG values are underestimated by about 20% for PS0 and PS1 and 10% for PS2: the differences of Hs IG are from 0.03 m to 0.15 m. At PS3 (the marina), the 45 s peak is well reproduced by the model as well as the broad peak between 50 and 200 s. The underestimation of energy at peaks at 290 and 450 s results in significant differences of Hs IG : 20% and 40% for 6.5 and 10 m grid resolution respectively. The sensor PS3 is used to study the impact of the mesh size on simulation results, as the width of the channel between the two basins is 50 m (figure 1). The spectral energy differences between the two meshes are small for periods greater than 40 s.

Comparisons of spectra in the IG period band show that the BOSZ model can reproduce the generation of IG by ocean forcing and their transformation during propagation in the river.

Local nearshore bathymetry effects

The significant wave height is determined at each point of the mesh using the formula 3 [START_REF] Holthuijsen | Waves in oceanic and coastal waters[END_REF]. where σ η is the standard deviation of the free surface elevation η. Thus, only two sums are stored and updated at each time iteration: η and η 2 and not all the time series.

Hs = 4σ η (3)
Hs map is presented in figure 7 in the port mouth area for 10 m grid resolution. With the bathymetry contour lines, the deposit of dredged material is visible at depths between -35.0 and -17.5 mCD. To study its effects on waves transformation, it is removed from the domain and replaced by an uniform slope (the initial bathymetry), all other simulation parameters are the same. The differences of Hs with and without the deposit are in figure 8.

The reduction in water depth by the deposit causes the shoaling of incident waves: Hs increases, the free surface steepens, and non-linearity increases with the possibility of IG waves generation. In addition, the deposit causes the concentration of energy on the port mouth by a refraction phenomenon: in the deposit trail, Hs increases by about 25% and decreases by 15-20% on either side of the deposit. This causes an increase in energy on the port's breakwaters (mechanical stress), and an increase in Hs about 30-35% in the port mouth, navigation operations (in and out of port) can be therefore more difficult.

CONCLUSION

This study based on water level measurements and numerical simulation during a 1-year return period storm event shows that the contribution of short waves (5-30 s) to the oscillations of Port of Bayonne is low: Hs S W = 1 m at the river mouth and Hs S W < 0.15 m in the port. The breakwaters at the port mouth efficiency protect the port against incoming swell and sea waves with a reduction factor of 85% compared to the offshore wave energy. In contrast, a large amount of energy was found in the IG period band (80% of total energy), with a Hs IG reaching maximum values of 0.5 m and 1 m in the channel harbor and the marina respectively. IG waves are generated by oceanic forcing (incident swell). The deposit of dredged material, by a refraction phenomenon, concentrates the energy of incident waves on the port mouth and the breakwaters, which can disturb the ship navigation. It also favors the shoaling of short waves and possibly the generation of IG waves by non-linear interaction phenomenon. As they enter the port, the IG waves propagate freely (without amplification) in the river which acts as a wave guide, and gradually dissipate by friction. However, they conserve enough energy to cause the resonance of the marina (coastal seiche), and to probably excite the moored vessel whose own eigen periods are in the IG period band.

Figure 1 :

 1 Figure 1: Port of Bayonne and positions of the experimental devices: WB waverider buoy, and PS pressure sensors (white dots): PS0 (river mouth), PS1-PS2 (channel and commercial harbor) and PS3 (marina). Zoom on the marina in the lower left corner (white rectangle on the map).

Figure 2 :

 2 Figure 2: Numerical domain and numerical sensor locations. The first 100 offshore cells are flat. Wet cells are in grey.

Figure 3 :

 3 Figure 3: Storm event: (a) Hs and Tp at the offshore wave buoy ; (b) Hs in the channel harbor (PS1) and (c) Hs in the marina (PS3). The red vertical line corresponds to the simulated event.

Figure 4 :

 4 Figure 4: Power spectral densities (PSD) at pressure sensors and confidence intervals (CI).

Figure 5 :

 5 Figure 5: Power spectral densities for measured (FD) and simulated data with the two grid resolutions (10 and 6.5 m), in the channel harbor (PS0 to PS2).

Figure 6 :

 6 Figure 6: Power spectral densities for measured (FD) ans simulated data with the two grid resolutions (10 and 6.5 m), in the marina (PS3).

Figure 7 :

 7 Figure 7: Hs map (m) and contour lines (mCD -dotted lines). Grid resolution = 10 m.

Figure 8 :

 8 Figure 8: Differences of Hs (%) with and without the deposit of dredged material: positive values are increases.

Table 1 :

 1 Numerical domain characteristics and computational time.

Table 2 :

 2 Hs in different period bands calculated from PSD (figure4) and contribution (R) of the different period bands to the variance of the free surface.

	Hs	SW 5-30s		IG 30-300s	VLW 300-600s
	m	Hs (m) R (%) Hs (m) R (%) Hs (m) R (%)
	PS0 1.28	0.99	61	0.72	32	0.16	2
	PS1 0.35	0.07	4	0.31	79	0.08	6
	PS2 0.27	0.02	1	0.25	86	0.06	6
	PS3 0.67	0.12	3	0.53	62	0.28

Table 3 :

 3 Hs in different period bands calculated from PSD (figures 5 and 6).

			Hs	SW (5-30 s) Hs (m)		IG (30-300 s) Hs (m)	Diff (%)
		Meas. 6.5m 10m Meas. 6.5m 10m Meas. 6.5m 10m 6.5m 10m
	PS0	1.62	1.06 1.00	1.22	0.63 0.57	0.94	0.83 0.79	-12	-17
	PS1	0.56	0.44 0.38	0.06	0.03 0.02	0.47	0.42 0.35	-12	-25
	PS2	0.37	0.36 0.30	0.02	0.01 0.01	0.31	0.34 0.29	10	-7
	PS3	1.06	0.68 0.56	0.20	0.05 0.01	0.77	0.62 0.49	-19	-37

SIAME EA 4581, University of Pau and Pays de l'Adour, France

SIAME EA 4581, University of Pau and Pays de l'Adour, France

E2S Chair HPC-Waves, University of Pau and Pays de l'Adour, France

Univ of Hawaii at Manoa, Dpt of Oceanography, USA

Hydrographic and Oceanographic Service of the Navy (SHOM), France

SIAME EA 4581, University of Pau and Pays de l'Adour, France

ACKNOWLEDGEMENTS

The authors thank the technical service of the port of Bayonne for support provided during the design of the measuring devices. The work is co-funded by the Region Nouvelle Aquitaine (France) and the Hydrographic and Oceanographic Service of the Navy (SHOM, France).


Jean Louis Pépin

Jean François Timsit

Renaud Tamisier

Jean Christian Borel

Patrick Levy

Samir Jaber

Prevention and care of respiratory failure in obese patients

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


Johann Berthelot
email: johann.berthelot@fresnel.fr

Nicolas Bonod
email: nicolas.bonod@fresnel.fr

Free-Space Micro-Graphics with Electrically Driven Levitated Light Scatterers

Levitation of optical scatterers provides a new mean to develop free-space volumetric displays. The principle is to illuminate a levitating particle displaced at high velocity in three dimensions (3D) to create images based on persistence of vision (POV). Light scattered by the particle can be observed all around the volumetric display and therefore provides a true 3D image that does not rely on interference effects and remains insensitive to the angle of observation. The challenge is to control with a high accuracy and at high speed the trajectory of the particle in three dimensions. Here we use electrically driven planar Paul traps (PPTs) to control the trajectory of electrically charged particles. A single gold particle colloid is manipulated in three dimensions through AC and DC electrical voltages applied to a PPT. Electric voltages can be modulated at high frequencies (150 kHz) and allow for a high speed displacement of particles without moving any other system component. The optical scattering of the particle in levitation yields free-space images that are imaged with conventional optics. The trajectory of the particle is entirely encoded in the electric voltage and driven through stationary planar electrodes. We show in this paper, the proof-of-concept for the generation of 3D free space graphics with a single electrically scanned particle.

INTRODUCTION

Levitation of nano-objects is a fascinating area of science that aims at trapping and manipulating nano-objects without physical contact. Different techniques can be used to trap nano-objects, among which optical tweezers [1][2][3][4][5] or acoustic traps [6][7][8].

Recently, optical scatterers in levitation reveal as competing alternative to holography to yield volumetric images. Different systems have been proposed to provide free-space 3D imaging [9][10][11][12]. A major breakthrough was achieved in 2018 by the use of photophoretic traps [13]. Such traps use strong gradients in temperature around a lossy particle illuminated by a tightly focused laser beam. This trapping mechanism allows to trap particles in the range of a few micrometers up to hundreds of micrometers. This technique was shown to yield high quality centimeter-sized images. The optical trap is scanned with galvanometric mirrors that rely on a mechanical displacement of optical components. Here we show that immobilized planar point Paul traps can scan particles in a 3D space with AC and DC voltages only. The particle trajectory can be fully driven electrically without requiring any physical displacement of any component of the system.

Radio-frequency (RF) traps have been widely investigated to trap and control ions [14] and they are emerging in nano and microsciences as versatile tools to manipulate nano/microobjects [15][16][17][18][19][20][21]. They rely on the use of a time varying electrical field applied on a special arrangement of electrodes forming an electrostatic potential featuring a saddle shape. RF traps operate with electrically charged nano/micro objects. This step is usually performed with the use of an electrospray ionization system (ESI) [22]. Conventional RF traps are bulky systems that offer low optical access, require high voltages and specific machining facilities. In the 2000's, the extension of this trap configuration into planar geometry has offered novel opportunities with levitation of electrically charged objects [23][24][25]. Besides weaker electric voltages required to trap objects, planar electrodes printed on the same plane offer an open access to easily detect and excite the levitated object with optical beams. Another advantage is related to the fabrication. Such systems are easily fabricated with conventional optical lithography or laser etching. The high stability of PPTs was unveiled in 2016 by translating and rotating PPTs while keeping particles trapped in levitation in air [26]. We show in this study that PPTs are highly suited to yield free-space images by manipulating and displacing individual optical scatterers by plugging the trajectory of particles into AC and DC voltages applied to stationary PPTs.

RESULTS AND DISCUSSION

A typical example of PPT is presented in Fig. 1(a). The dimensions of the different electrodes are 0.7 mm in diameter for the inner electrode and 3 mm in diameter for the outer electrode. They were fabricated on a commercial Printed Circuit Board (PCB). It consists of two inner and outer ring electrodes surrounded by four compensation DC electrodes. The whole PPT has a size of 10 × 10 mm 2 . Typically this PPT geometry requires oscillating fields in the kHz range with an amplitude of hundreds of volts. Connections are made underneath the planar PCB. By polarizing the different electrodes, either with DC or AC voltage, it is possible to trap a single nano-object with a high stability (cf. Fig. 1(b)). The four compensation electrodes add external parameters to displace the object in the plane while the inner electrode controls the out-of-plane displacement. The motion of the object is then driven depending of the configuration and the applied voltage amplitude of the different fields, i.e. AC or DC voltage. An important point is that all the AC voltages must be applied with the same frequency [26]. The circuit configuration used in this study is illustrated in Fig. 1c. Thanks to this system, the trajectory of the particle can therefore be driven by directly encoding the amplitude in function of the position and applied to the electrodes by analog outputs. The speed and the precision of the driven motion are then strictly dependent of the electronic systems, i.e. bandwidth and resolution. In our experiments we used an electronic card from National Instrument (NI PCIe-7841R).

In the case where no driven electric field is applied, and taking into account the background pressure, the motion of the trapped particle can be predicted by solving the Mathieu equations [27]:

d 2 u dy 2 + µ du dy + (a u -2q u cos 2y)u = 0, (1)
where u denotes either the z or the r coordinate of the trapped particle. The dimensionless parameters a u , q u and µ are defined as follows:

a u = 16 Q M V DC Ω 2 f (r, z), q u = 8 Q M V AC Ω 2 f (r, z), µ = 36 η ρd 2 Ω . (2)
. The dimensionless parameter y is related to time by y = Ωt/2, where Ω is the frequency of the electrical field. By solving numerically Eq.1 for each direction of space, i.e. r and z, we can obtain the solutions depending on the dimensionless parameters a u and q u leading to a stable trap. A stable 3D trapping occurs when the different solutions in r and z overlap.

The function f (r, z) depends on the geometry of the electrodes, d is the diameter of the particle, ρ is the density of the material and η the viscosity of the medium. We can remark that both parameters a u and b u depend on the charge-to-mass ratio Q/M and that a u depends on a static voltage applied on the electrode. Particles are commonly trapped with a pure oscillating field, V a c, without any static field V d c, meaning that a u = 0. a u and q u depend on the spatial parameter u = r, z but due to the symmetry of the electrode, a z and a r are linked via the relation a z = -2a r . The same relation occurs for the q u parameters, q z = -2q r . Solving Eq.1 provides the r or z coordinates leading to a stable position of the particle in the trap. For that purpose, a second-order Runge-Kutta method is implemented. This allows us to plot the stability diagram of the PPT as a function of the dimensionless parameters a u , q u for a given µ. µ is taken equal to 30 in air and equal to 0 in vacuum. We consider the case of an AC voltage with 1kHz frequency, 70 V amplitude and a 100 nm diameter gold particle (typical value used in the experiment). The solutions r and z are calculated with respect to a u , q u and the resulting stable 3D trapping solutions are plotted in Fig. 2(a) as functions of a and q. We can clearly see that the domain of stabil-Fig. 2. Stability Diagram. Calculated stability diagram for a charged particle in an oscillating electrical field under vacuum (orange area) and in air (blue area) conditions. a and q are the solutions of the equation of motion of the particle. For this calculation we use a particle of 100 nm diameter of gold placed in air and vacuum conditions. ity is much larger in air (in blue) than under vacuum (in orange). This result highlights the interest of electrostatic traps to operate in ambient conditions. We can observe in Fig. 2 a large range of stable solutions for a wide range of a and q values, i.e. for a wide range of object sizes with different charge-to-mass ratio Q/m, for the same field applied. This also means that RF traps can operate for an even wider range of object sizes by tuning the voltage amplitude and frequency. This numerical study allows to find the voltage parameters that lead to an efficient trap of the gold nanoparticles. It was shown in [28] that an additional DC voltage in the radial or axial direction shifts the node of the potential in the radial or axial direction. This property shall be used to shift the position of the node in the radial direction r above the planar electrodes. For that purpose, we use additional DC voltages applied to compensation electrodes. The position of the node in the axial direction can be tuned thanks to the AC voltage. For the radial displacement, the x and y coordinates have first to be discriminated. 4 DC electrodes are placed in the (0, x, y) cartesian coordinates, 2 along the Ox axis at (-X, 0) and (+X, 0), and 2 along the Oy axis at (0, -Y) and (0, +Y) (see Fig. 3a). Before manipulating the particles, we study with finite elements method (COMSOL Multiphysics) the possibility to tailor the position of the node of the electric field with voltages, without displacing the electrode. We start with the classical configuration used to trap individual particles above the planar electrode with AC voltage applied to the outer circular electrode (70V, 1kHz). We clearly observe the node of the electric field 0.5mm above the circular electrode, centered on the z axis (Fig. 3b,c). On a second step, an additional DC voltage of 10V is applied on a DC electrode along the Ox axis and we can see that the node is displaced along the Ox axis by around 100µm (the scale is in mm) (fgr:fig3d). The height of the node is very slightly increased to 0.6 mm while the distribution of the electric field in the YoZ plane is slightly modified (fgr:fig3e). These simulations confirm the possibility to tailor position of the trap with additional DC voltages without modifying the position of the electrode.

This electronic system allows for a 3D positioning of the particle with a nanometer precision. Our system provides maximum modulation frequencies up to 180 kHz meaning that the time separating two successive points can be as short as 5.5 µsec. We first generate trajectory with a maximum of 4000 points that will behave as pixels of the graphics. The frequency of 100 kHz Fig. 4. Free space graphics. Mosaic of images showing the performances of the nanotrap display. On the left side, the image describes the motion of the particle and on the right side the applied trajectory design: (a) heart, (b) pentagon, (c) star and (d) butterfly. We have illuminated the area with a green laser under a diascopic dark-field configuration. The scale bar is 10µm. All the trajectories have been generated under the same conditions: V AC =70 V, f trapping =4 kHz, V DC = 9 V, f sampling =100kHz. f trapping is the frequency of the applied electrical field while f sampling is the frequency used to scan the points of the particle trajectory. All the images are captured by a coupled objective lens 50× and a CMOS camera set in POV conditions (50 ms integration time). allows for a scanning of the 4000 pixels of the trajectory in less than 40 milliseconds, i.e. in a time much shorter than the POV (roughly around 100 milliseconds). Trajectories of the particle in the (Oxy) plane above the planar electrodes are implemented point by point. For that purpose, we used a computing software (Matlab) and the (x, y) coordinates of the contour plot are extracted directly from a black and white image. This list of the (x, y) pixel coordinates are then converted in polar coordinates (r, θ) and ranked with respect to increasing θ. The ranked coordinates are then converted into voltage values and directly applied to the different electrodes by digital-to-analogue outputs. An example of the treated result with the different directions is presented in Fig. 4(a). Each x and y coordinate corresponds to a voltage applied to a pair of electrodes of a given quadrant.

This method is followed to generate different images such as stars, hearts, rectangles, hexagons,... Each trajectory contains 4000 pixels square and is scanned in 40 milliseconds by a single 100 nm gold particle. The particle is illuminated by a collimated green laser beam and the scattered light is collected (i) directly by a webcam (logitech C920) and (ii) by a microscope objective (Nikon CFI60 TU plan EPI ELWD 50×, NA=0.6) and imaged onto the CMOS camera. The different images generated with the electrically driven levitated plasmonic particle are displayed in Fig. 4 (b-f). The results show the versatility of this electrical approach to tailor the motion of 3D nano-objects at high frequency and accuracy. The technique is also assessed by writing Greek letters. We generated all letters of the Greek alphabet. In a sake of illustration, we assembled different images of letters to form the word FRESNEL (see Fig. 5).

Fig. 5.

Letters of the Latin alphabet can be obtained with electrically driven plasmonic nanoscatterers. To display the word FRESNEL, each letter is first obtained individually before assembling the 7 images to form the word.

CONCLUSION

In conclusion, we showed the ability of planar RF traps manipulate nanoparticles at high frequency and high precision. The position of the particle can be controlled by tuning the applied DC voltage on the four compensation electrodes. The motion dynamics is imposed by the modulation frequency of the electronic card connected to the electrodes (150 kHz). The high frequency allows for driving the particle to 4000 different coordinates in less than 40 milliseconds, a time shorter than the POV. Free-space graphics can therefore be encoded in the trajectory of the particle. The ability of this technique to draw free-space graphics was evidenced by plotting a wide variety of contour plots. Our work shows the proof-of-concept of electrical levitation applied to free-space graphics imaging. The volume of the image depends on the typical size of the electrodes and we anticipate that much larger images could be easily achieved (i) by increasing the size of the electrodes from the millimeter range to the centimeter size and (ii) by using higher voltage amplifiers than the electronic card to the 4 compensation electrodes that will increase significantly the displacement. Planar RF traps are very stable and can trap a wide range of particle sizes, meaning that this technology has a strong potential to yield large size images entirely driven with electrical voltages.

FUNDING INFORMATION

H2020-MSCA-IF-2015-705616-SMART-LANLIGHT

Fig. 1 .

 1 Fig. 1. Planar Paul traps. (a) Photography of a surface electrode trap used in this study. It is composed of different electrodes: inner electrode, RF electrode and 4 compensation DC electrodes. (b) Photography of a 100nm gold particle put in levitation with the PPT presented in (a). (c) Schematic illustration of the electrically driven motion of the particles. Each compensation electrode is used to control a -Ox, +Ox, -Oy, +Oy direction. The displacement value is related to the amplitude of the applied electric field. The trajectory along the z axis is controlled with the inner electrode. Insert on the right is a free-space 2D image of a star obtained with our PPT.

Fig. 3 .

 3 Fig. 3. Electric field maps above the PPT electrode and influence of the DC compensation electrodes. a) Schematic view of the trapping geometry and the different electrodes with the 3 axis definition. b-e) 2D cross sections in the plane XoZ (left row) and YoZ (right row) of the simulated electric field map for 3 different voltage conditions applied on the different electrodes of the PPT :(b,c) RF voltage only, (d,e) RF voltage and one DC electrode at 10V.

ACKNOWLEDGMENTS

J.B. is supported by H2020 Marie Skłodowska-Curie Actions fellowship of the European Commission. The authors thank the Fresnel Institute for its financial support through the "Fond pour la Science". The authors thank Jérôme Wenger, Laurent Gallais and Guillaume Baffou for fruitful discussions.