domain: phys phys

text:
Meriem M Karam
email: maha.karam@uphf.fr.

Chrifi Alaoui

Frédéric Jenot

M Baher

Rabih Tauk

Mohammadi Ouaftouh

Jihane Jabbour

Marc Duquennoy

Jamal Assaad

M Chrifi Alaoui

J Jabour

THERMOELASTIC GRATING FOR NON-DESTRUCTIVE TESTING BY LASER ULTRASONICS

Keywords: Laser ultrasonics, Non-Destructive Testing, Rayleigh waves, Flaws

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

INTRODUCTION

Laser ultrasonics is a non-destructive testing method that uses laser to generate and detect ultrasonic waves in metallic and plastic materials [START_REF] Scruby | Laser Ultrasonics Techniques and Applications[END_REF]. Compared to conventional ultrasonic methods, laser ultrasonics provides many advantages such as higher spatial resolution, the ability to test structures with complex geometries and being contactless [START_REF] Perdijon | Le contrôle non destructif par ultrasons[END_REF]. This method has become extensively used in various applications, especially for detecting and characterizing defects in different materials. Over the past decades, lasers have been widely employed as a powerful instrument to generate and detect ultrasound. The Nd:YAG pulsed laser is frequently used to excite these waves either through thermoelastic or ablation mode [START_REF] Scruby | Laser Ultrasonics Techniques and Applications[END_REF][START_REF] Pei | Fully noncontact measurement of inner cracks in thick specimen with fiber-phased-array laser ultrasonic technique[END_REF].

In an isotropic, homogeneous, and semi-infinite solid, a surface acoustic wave, first described by Lord Rayleigh [START_REF] Rayleigh | On waves propagated along the plane surface of an elastic solid[END_REF], can propagate. This Rayleigh wave has an elliptical polarization and propagates with an exponentially decreasing amplitude from the surface to the depth of the solid. In most Laser ultrasounds applications, the Rayleigh wave is generated by a thermoelastic line source for material characterization and defect detection [START_REF] Royer | Experimental and theoretical waveforms of rayleigh waves generated by a thermoelastic laser line source[END_REF]. In this work, we are interested in the simultaneous generation of multiple Rayleigh waves for structures non-destructive testing. An experimental setup for obtaining multiple line sources is implemented. This article focuses on the analysis of the interaction between Rayleigh waves generated by laser ultrasonics and surface defects on an aluminum sample, through both numerical and experimental investigations. In the first part, the propagation velocity and directivity of the Rayleigh wave in aluminum for a line source are determined based on theoretical considerations. The second part describes the generation of Rayleigh waves on the surface of the sample by the Finite Element Method, ex-cited by a grating of thermoelastic line sources, and the resulting outcomes. In the third part, a defect with wellknown characteristics is created on the sample's surface and an experimental study is conducted to measure the Rayleigh wave propagation velocity in the case of both single and multiple line sources. Finally, the approximate position of the defect and certain dimensions of the sample are determined.

CHARACTERISTICS OF RAYLEIGH WAVE

Rayleigh waves are a type of guided waves that propagate along the surface of a material, and they are frequently used for non-destructive testing to detect surface flaws. When a Rayleigh wave interacts with a surface defect, such as a discontinuity or crack, the wave is scattered. This scattering phenomenon provides valuable information about the position and size of the defect, which makes Rayleigh waves an effective tool for detecting surface defects in materials.

Propagation velocity

The propagation velocity of a Rayleigh wave in a homogeneous and isotropic material can be theoretically approximated using the following relation [START_REF] Dieulesaint | Ondes élastiques dans les solides-tome 1: Propagation libre et guidée[END_REF]:

V R = (0, 87 + 1, 12v) (1 + v) .V T (1)
Where: V R : Rayleigh wave velocity, V T : Transverse wave velocity, ν: Poisson's ratio of the material.

For an aluminum sample, the Poisson's ratio is 0.33 [START_REF] Rousseau | Etude d'ondes de type Rayleigh sur des milieux stratifiés[END_REF] and the propagation velocity of the transverse wave is equal to 3130 m/s [START_REF] Beaujard | Métallographie-essais non destructifs[END_REF]. Therefore, Eq. 1 gives a Rayleigh wave propagation velocity in an aluminum sample of approximately 2917 m/s. This theoretical value will be compared to the velocity analysis through the modeling and experimental study.

Directivity

The Rayleigh wave generated by a thermoelastic line source is characterized by its directional aspect. Indeed, this wave mainly propagates in the direction perpendicular to the center of the line [START_REF] Rayleigh | On waves propagated along the plane surface of an elastic solid[END_REF]. Furthermore, the length of the line source has a direct influence on the wave's directivity pattern [START_REF] Faëse | Ondes de rayleigh générées et détectées par laser-applications à la détection de défauts[END_REF]. This one can be graphically represented as a polar plot, which shows the relative amplitude of the waves as a function of the observation angle compared to the line source. The directivity diagram of the Rayleigh wave, assuming a 2 mm-long line source in a thermoelastic regime at a frequency of 6 MHz, is presented in Figure 1.

FINITE ELEMENT METHOD

Many articles in the literature concentrate on modeling the generation of ultrasound by laser and the interaction of these waves with a defect, using the finite element method (FEM) [START_REF] Dai | Finite element modeling of the interaction of laser-generated ultrasound with a surface-breaking notch in an elastic plate[END_REF]. The present study aims to describe the generation of Rayleigh waves on the surface of an aluminum sample with multiple line sources. In order to conduct the analysis, a FEM model is developed. The first part of this section will introduce the modeling parameters used in the analysis. The second part will focus on the meshing technique employed, and the third part will present the results obtained.

Modeling Parameters

To enhance the accuracy of the results and reduce the simulation time, a two-dimensional geometry with a length of 2.5 cm and a thickness of 1 cm is applied in the plane strain structural mechanics model. To characterize the impact of the laser, we implemented the force dipole model, which involves the application of two tangential forces with opposite directions on the surface [START_REF] Achenbach | Laser excitation of surface wave motion[END_REF]. The temporal evolution of the force dipole is expressed by the following Eq. 2, which corresponds to the temporal evolution of the heat source at the surface of the sample [START_REF] Dai | Finite element modeling of the interaction of laser-generated ultrasound with a surface-breaking notch in an elastic plate[END_REF] :

F (t) = t τ 2 exp( -t τ ).H(t) (2)
Where : H(t): Heaviside function, τ : Durée d'impulsion laser.

The two parameters that are involved in this model are the width of the thermoelastic source, and the characteristic laser pulse duration.

Meshing

In order to obtain improved numerical results within a shorter simulation time, specific conditions must be applied to the meshing of the model. Considering f max and λ min the maximum acoustic frequency and the minimum wavelength respectively, the time step ∆t and the size ∆x of a mesh element must satisfy the following two equations in order to ensure the validity of the results obtained [START_REF] Scruby | Laser Ultrasonics Techniques and Applications[END_REF][START_REF] Achenbach | Laser excitation of surface wave motion[END_REF].

Time step :

∆t < 1 20f max (3)
Meshing element size :

∆x < λ min 20 (4)
To satisfy Eq. 3 and Eq. 4, a fixed time step of 2 ns and a maximum element size of ∆x = 8 µm are chosen, assuming a maximum acoustic frequency of approximately 18 MHz. A Perfectly Matched Layer (PML) with a fine mesh is used to effectively absorb both bulk and surface elastic waves, as illustrated in Figure 2.

Results

Experimentally, multiple line sources with different energies is generated on the surface of an aluminum sample using optical devices. To validate the accuracy of the experimental results, a corresponding model is developed. This model consists of three line sources, each with a width of 200 µm and separated by a distance of 3 mm, as shown in Figure 3.

EXPERIMENT

This section begins with a description of the experimental setup used. A comparative study of the effectiveness of using a single source versus multiple sources to measure the propagation velocity is presented. Finally, the sizing of the sample and positioning of the defect are discussed.

Procedure

An aluminum sample with a length of 9.9 cm and a thickness of 4.5 cm having a circular defect of 2.3 mm diameter is studied. A frequency-doubled Nd:YAG laser is employed, which produces a wavelength of 532 nm and emits pulses of approximately 10 nanoseconds. The laser beam passes through a diffraction grating with 600 lines/mm. A cylindrical lens generates multiple thermoelastic line sources at the sample surface. Its normal displacement is detected using a Mach-Zehnder heterodyne interferometer. Figure 8 shows the experimental setup used. In this section, a comparative study between the results obtained using a single and multiple linear sources is presented. In order to obtain the velocity of the Rayleigh wave, the time of flight needs to be measured, for which the propagation distance must be known. To accomplish this, the mirror 2 fixed on a motorized stage is moved in a controlled manner. The signals obtained before and after moving the mirror by a distance of 3 mm are shown in Figure 9. According to the two signals in Figure 9, the time of flight difference is 1.014 µm. This corresponds to a Rayleigh wave velocity of 2958 m/s. This velocity is coherent with both the theoretical velocity calculated in paragraph (2.1) and the velocity obtained through modeling in paragraph (3.3). Having multiple equidistant line sources on the sample enables the generation of multiple Rayleigh waves, which allows the determination of the surface wave propagation velocity through two methods: -The first method consists of considering the distance between sources for calculating the propagation velocity of the Rayleigh wave. It is then no longer necessary to proceed with mirror displacement, which can simplify the experimental setup and improve the measurement accuracy. -The second method consists of performing a displacement to detect a second signal as in the case of a single source. Indeed, obtaining three sources through the diffraction grating allows us to calculate three velocities of Rayleigh wave propagation and improve the measurement reliability. For this purpose, the diffraction grating is placed at a distance of 5.4 cm from the sample. Three line sources spaced of 1.7 cm are obtained. Figure 10 From this signal, the propagation velocity of the Rayleigh wave is calculated using the first method. By knowing the distance between the sources and calculating the difference in time of flight between the obtained echoes, we deduce a propagation velocity of 2890 m/s. The second method of measuring the velocity requires a displacement of mirror 2, which causes a temporal shift in the obtained signal. For a displacement of 3 mm, the difference in time of flight between echoes from the same source is 1.04 µs. The propagation velocity of the Rayleigh wave deduced is equal to 2885 m/s. The propagation velocities obtained for the different configurations are consistent. The multi-sources configuration can therefore be applied to non-destructive testing using surface acoustic waves for various structures.

Sample dimensions

The line sources obtained by the diffraction grating are distributed along the length of the sample. Considering the directivity of the Rayleigh wave associated to each source, it is possible to obtain the sample length and also to detect the defect. To determine the sample length, the sample and optical system are separated by 8.5 cm. The optical system enables the generation of three equidistant sources at the sample surface. Figure 12 shows the respective positions between the sources and the edges of the sample. In order to associate the signal echoes with the line sources, each source is masked. In Table 1, the time of flight and the distance between each source and the detection are provided. The propagation velocity of the considered Rayleigh wave is 2890 m/s, which corresponds to the one previously deduced from multiple sources without miror displacement. 1 shows a good agreement between the calculated inter-source distance and the one measured experimentally, which is approximately 2.7 cm. We notice that the acquired signal contains several echoes associated to the reflections of Rayleigh waves by the edges of the sample. In order to identify the echoes associated to these reflections, masking sources S 1 and S 3 is performed. The masking of source S 1 allows us to deduce the distance between the detection and the left edge of the sample. Figure 14 shows the detected signals with and without source S 1 . We observe that when source S 1 is masked, two echoes are no longer present: -The echo detected at 4.64 µs is related to the path S1detection, -The echo detected at 10.72 µs is related to the reflection This allows us to deduce that the distance between source S 3 and the right edge of the sample is approximately 2.27 cm, and the distance between the detection and the left edge is approximately 0.9 cm. Based on these results, the total length deduce of the sample is approximately 9.9 cm. Note that masking source S 2 also confirms these results. The use of multiple line sources, each generating a Rayleigh wave on both sides of the source, allowed us to determine the length of the sample using the reflections of the different waves on the two edges of the sample. The distribution of several sources on the surface of the sample makes it possible to obtain signals of sufficient amplitude regardless of the chosen detection position.

Defect location

The sample is vertically moved by 1 cm to place sources and the detection at level 0 as shown in Figure 16. By comparing the two signals, it can be observed that:

-For source S 1 , considering the temporal signal up to 12 µs, there is no modification on the series of echoes of signal (a) compared to signal (b). There is therefore no defect on the associated paths.

-For source S 2 , between 12 µs and 21 µs, there is a significant attenuation of the echo located at 14.16 µs and corresponding to the direct path S 2 -detection. The echo corresponding to the wave's reflection on the edge of the sample is almost entirely attenuated. This attenuation is characteristic of the interaction of the Rayleigh wave with the defect on the acoustic propagation path.

-For source S 3 , around 22 µs, we also observe the attenuation of the echo corresponding to the S 3 -detection propagation path. This confirms the presence of the defect in this area of the sample. In addition, a new echo (part circled in signal (a)) is observed. This echo is also clearly representative of the interaction of the Rayleigh wave with the defect. This shows that the waves emitted by each source and traveling through different paths make it possible to obtain significant information of each probed zone of the sample for NDT purpose.

Finally, the experimental results confirm the presence of an echo characterizing the defect as shown in the previously presented modeling in paragraph (3.3), which is clearly visible in Figures 17 and7. However, determining the sample size precisely through modeling is not possible due to the PML layer, which prevents the visualization of reflection echoes on the sample's edges, such as those observed in the experimental results.

CONCLUSION

This study implements an optical device based on a diffraction grating to obtain multiple thermoelastic line sources. These sources allow the simultaneous excitation of Rayleigh waves traveling different paths. The spacing between the sources is determined by precisely positioning the sample surface at a certain distance from the optical system, which enables to obtain the Rayleigh wave velocity. By analyzing the different times of flight obtained for the excited waves, the length of the sample can be determined and a flaw easily detected without moving the sources. Furthermore, finite element modeling is used to predict waves-flaw interaction. The next objective of this study is to characterize the defect, dimensions and shape.

Figure 1 .

 1 Figure 1. Directivity diagram of a Rayleigh wave generated by a line source with a length of 2 mm in aluminum.

Figure 2 .

 2 Figure 2. Meshing of an aluminum structure.

Figure 3 .

 3 Figure 3. Diagram showing the positions of the three sources and the detection point.

Figure 4 (

 4 Figure 4 (a) represents the propagation of multiple types of acoustic waves, such as longitudinal and shear waves, as well as head and Rayleigh waves, generated by linefocused laser pulse on a semi-infinite aluminum sample. The 2-D plot presented in Figure 4 (b) illustrates the results achieved by creating three dipolar sources, similar to those employed in the experimental study.Each of the line sources generates a Rayleigh wave on the surface of the sample with a propagation velocity that depends on the material being considered. The normal displacement at the sample surface is detected and shown in Figure5. From the signal, the propagation velocity of the Rayleigh wave can be calculated.

Figure 4 .

 4 Figure 4. Results of 2-D finite element method for line-source (a) and multiple line sources (b) configurations.

Figure 5 .

 5 Figure 5. Signal representing the normal displacement associated to the Rayleigh waves generated by the three line sources.As part of our modeling study, we incorporated a semi-circular form defect into the sample. The three sources, S 1 , S 2 and S 3 , are positioned on either side of the defect as illustrated in Figure6. The signals in figure7enable a comparison between the cases with and without the presence of a defect on the surface of the sample.

Figure 6 .

 6 Figure 6. Sources, detection and defect configuration.

Figure 7 .

 7 Figure 7. Signals obtained with (a) and without (b) a defect on the surface of the aluminum sample.

Figure 8 .

 8 Figure 8. Experimental setup for generating and detecting surface acoustic waves by laser ultrasonics.

4. 2

 2 Measurement of Rayleigh wave velocity.

Figure 9 .

 9 Figure 9. Signals obtained using a line source for two propagation distances separated by 3 mm.

  represents the signal associated to the Rayleigh waves generated by these three sources.

Figure 10 .

 10 Figure 10. Signal associated to the Rayleigh waves generated by the three line sources.

Figure 11 ,

 11 represents the signals before and after a displacement of 3 mm.

Figure 11 .

 11 Figure 11. Signals obtained with three line sources for two propagation distances separated by 3 mm.

Figure 12 .

 12 Figure 12. Diagram showing the positions of the three sources and the detection point at level 1. The distances on the diagram are in centimeter.

Figure 13 .

 13 Figure13. Signal detected at level 1 without defect.

Figure 14 .

 14 Figure 14. Signals detected with (a) and without (b) S 1 source.

Figure 15 .

 15 Figure 15. Signals detected with (a) and without (b) S 3 source. When source S 3 is masked, three echoes are no longer present: -The echo detected at 23.28 µs corresponds to the S 3detection path, -The echo detected at 29.24 µs corresponds to the reflection of the Rayleigh wave emitted by source S 3 on the left edge of the sample, -The echo detected at 38.96 µs corresponds to the reflection of the Rayleigh wave emitted by source S 3 on the right edge of the sample. This allows us to deduce that the distance between source

Figure 16 .

 16 Figure 16. Diagram showing the positions of the three sources and the detection point at level 0. The distances on the diagram are in centimeter.

Figure 17 .

 17 Figure 17. Signals detected at level 0 (a) and level 1 (b).

Table 1 .

 1 Time of flight and propagation distance associated to the different sources.

	Source Duration (µs) Distance (µm)
	S 1	4.64	1.37
	S 2	14.16	4.09
	S 3	23.28	6.73

Table

Turin, Italy • 11 th -15 th September 2023 • Politecnico di Torino

ACKNOWLEDGEMENTS

The authors would like to thank the Hauts-de-France region for the financial support provided in carrying out this study.


Medhi Cohu

Gaëlle Marinthe

Alice Kasper

Christelle Maisonneuve

MALLEABILITY OF LAÏCITÉ: PEOPLE WITH HIGH SOCIAL DOMINANCE ORIENTATION USE LAÏCITÉ TO LEGITIMIZE PUBLIC PRAYER BY CATHOLICS BUT NOT BY MUSLIMS

The present study examined whether people with high SDO modify their conception of laïcité (French secularism) when judging public expressions of religious beliefs (street prayers) by France's majority (Catholics) or minority (Muslims) religious group. Participants with high SDO saw street prayer as deviating more from French values when the people praying were Muslims but were more likely to view public expressions of religious beliefs as compatible with laïcité when those praying were Catholics. SDO and religion also had indirect effects, via compatibility of public expressions of beliefs with laïcité, on perceptions of deviation from laïcité and normative pressure.

INTRODUCTION

People of Muslim faith accounted for 3.8% of Europe's population in 2010, a figure that had risen to just over 5% in 2018 and that is expected to reach more than 11% by 2050 (Pew Research Center, 2017). Approaches to integrating people from cultural and religious minorities vary across Europe, with each country having a preferred acculturation orientation. France's approach to managing intergroup relations centers round the principle of laïcité, which is subject to frequent societal and political controversies. For example, some people feel that wearing a full veil or praying in the street goes against laïcité, whereas others consider such expressions of faith to be compatible with laïcité (Gorse, 2019). Social psychology research shows that there is no universally accepted conception of laïcité [START_REF] Cohu | Construction et validation de l'échelle de mesure des croyances relatives à la laïcité [Construction and validation of the laïcité belief scale[END_REF]Roebroeck & Guimond, 2016). Rather, laïcité is a malleable concept that people who support social hierarchy (i.e., people with high social dominance orientation, SDO; [START_REF] Nugier | Nouvelle Laïcité" en France et Pression Normative Envers les Minorités Musulmanes [Secularism in France and Normative Pressure Against Muslim Minorities[END_REF][START_REF] Roebroeck | Intergroup threat, social dominance, and the malleability of ideology: The importance of conceptual replication[END_REF][START_REF] Troian | The effect of Social dominance on prejudice towards North-African minorities: Evidence for the role of social representation of Secularism as a legitimizing myth[END_REF] may use to justify prejudice against minority groups. The present study examines the malleability of high SDO individuals' conceptions of laïcité when judging members of a minority (Muslim) versus majority (Catholic) religious group expressing their religion publicly (street prayers). [START_REF] Cohu | Construction et validation de l'échelle de mesure des croyances relatives à la laïcité [Construction and validation of the laïcité belief scale[END_REF] identified four constituent dimensions of laïcité-public expression of religious beliefs, religious neutrality of the State, equality of treatment of different religious beliefs, and protection of religious groups. The two main conceptions of laïcité prevalent in French society, that is historical and new laïcité (Roebroeck & Guimond, 2016;[START_REF] Troian | The effect of Social dominance on prejudice towards North-African minorities: Evidence for the role of social representation of Secularism as a legitimizing myth[END_REF], differ mainly on the public expression dimension [START_REF] Cohu | One Conception of Secularism for All? A Comparison of Conceptions of Laïcité among Nonbelievers, Catholics, and Muslims in France[END_REF]. Historical laïcité places the onus on tolerance and equality between religions and accepts public expressions of religious beliefs, whereas new laïcité extends the State's religious neutrality to the public sphere [START_REF] Adam-Troian | National identification and support for discriminatory policies: The mediating role of beliefs about laïcité in France[END_REF][START_REF] Baubérot | La laïcité falsifiée[END_REF][START_REF] Nugier | Nouvelle Laïcité" en France et Pression Normative Envers les Minorités Musulmanes [Secularism in France and Normative Pressure Against Muslim Minorities[END_REF]Roebroeck & Guimond, 2016). Hence, individuals who embrace new laïcité expect others to express their religious beliefs (e.g., Muslim women wearing the veil) only in the private sphere and exert pressure on them to do so [START_REF] Nugier | Nouvelle Laïcité" en France et Pression Normative Envers les Minorités Musulmanes [Secularism in France and Normative Pressure Against Muslim Minorities[END_REF]. Moreover, new laïcité appears to legitimize prejudice against minority religious groups, because individuals with high levels of prejudice exert greater normative pressure on minority religious groups (e.g., Muslims) than on the majority group (Catholics).

According to social dominance theory, people with high SDO support the idea of a social hierarchy in which higher status groups dominate lower status groups and adhere more easily to inegalitarian ideologies (Sidanius & Pratto, 1999). Thus, people with high SDO might use laïcité to justify treating groups of different status unequally [START_REF] Roebroeck | Intergroup threat, social dominance, and the malleability of ideology: The importance of conceptual replication[END_REF][START_REF] Troian | The effect of Social dominance on prejudice towards North-African minorities: Evidence for the role of social representation of Secularism as a legitimizing myth[END_REF]. For example, [START_REF] Troian | The effect of Social dominance on prejudice towards North-African minorities: Evidence for the role of social representation of Secularism as a legitimizing myth[END_REF] found that people with high SDO use new laïcité to legitimize their prejudice against North Africans, with new laïcité mediating the positive link between SDO and prejudice. In addition, people with high SDO adhered to laïcité when presented with a situational symbolic threat but did not adhere to laïcité in a nonthreatening situation [START_REF] Roebroeck | Intergroup threat, social dominance, and the malleability of ideology: The importance of conceptual replication[END_REF]. Taken together, these results suggest that people with high SDO modify their conception of laïcité toward new laïcité when they feel the need to justify exerting normative pressure on minority groups.

The present study investigated the malleability of conceptions of laïcité in response to street prayers by Muslims or Catholics. More specifically, we focused on the malleability of the public expression dimension of laïcité, as this is the dimension that differs most between historical and new laïcité [START_REF] Cohu | One Conception of Secularism for All? A Comparison of Conceptions of Laïcité among Nonbelievers, Catholics, and Muslims in France[END_REF]. We expected high SDO individuals to be less attached to allowing others to express their religious beliefs in public when the people praying are Muslims than when they are Catholics, in order to justify exerting normative pressure on the minority religious group. We tested three hypotheses: H1: High SDO individuals will exert more normative pressure on people who pray in the street and will view public prayer as less compatible with French values and laïcité when the people praying are Muslims than when they are Catholics. H2: High SDO individuals will view the public expression of religious beliefs dimension as a less important principle of laïcité when considering Muslims praying in the street than when considering Catholics praying in the street.

H3: The effect of H1 will be mediated by the effect of the hypothesized interaction on public expression of religious beliefs.

METHOD Participants

Participants were 103 first-year psychology students (83.5% women), aged between 18 and 28 years (M = 18.62, SD = 1.72), 73.8% of whom declared themselves to be believers (24.3% non-believers, 1.9% did not provide this information). All the participants were of French nationality (three not indicated). Sensitivity analyses showed that this sample allowed us to detect a low to moderate effect size (f² = .08), with an alpha of 0.05% and a power of .80 in a multiple regression testing one predictor among four (G*Power; [START_REF] Faul | G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences[END_REF].

Procedure and Measures

Participants completed two questionnaires, administered one month apart [1]. All answers were provided on scales ranging from 1 = completely disagree to 7 = completely agree. The first questionnaire (pre-induction phase) was a French translation (Duarte et al., 2004) of Sidanius and Pratto's (1999) six-item reduced SDO scale (e.g., "Inferior groups should stay in their place"), Cronbach's alpha = .78, M = 1.89; SD = .81. Participants completed this scale and then provided sociodemographic information (religious beliefs, gender, age, nationality).

In phase two (induction phase), participants were randomly assigned to one of two experimental conditions in which they read a newspaper article describing either Muslims (n = 50) or Catholics (n = 53) praying in the street (see Appendix A). They then completed a beliefs about laïcité measure [2] [START_REF] Cohu | Construction et validation de l'échelle de mesure des croyances relatives à la laïcité [Construction and validation of the laïcité belief scale[END_REF], including the public expression of religious beliefs dimension (e.g., "As a principle of laïcité, everyone should be free to express his or her religious beliefs in private and in public"), Cronbach's alpha = .91, and a five-item normative pressure scale inspired by Nugier et al. (2016) (e.g., "To what extent would you try to change their minds?"), Cronbach's alpha = .82. Finally, they completed a two-item perceived deviation from laïcité measure ("To what extent do these people respect the principle of laïcité?" (reversed), "To what extent do you find the behavior of these people is contrary to the principle of laïcité?"), r = .70, p < .001, and a two-item perceived deviation from French values measure ("To what extent do you think these people respect French values?" (reversed), "To what extent do you think these people's behavior is contrary to French culture"), r = .56, p < .001. Means and standard deviations for each condition and in total, and correlations between all variables are presented in Appendix B.

RESULTS

In all the following analyses we coded religion of the people praying as Muslim = -1 or Catholic = +1, and we standardized the SDO and public expression scores [3]. The main effects of SDO and religion on the dependent and mediating variables that were not directly relevant to the present study are shown in Appendix C.

Effect of SDO x Religion on Perceptions of Deviation and Normative Pressure

We conducted a regression analysis with SDO, religion of the people praying, and the interaction between these two variables as predictors of perceived deviation from French values, deviation from laïcité, and tendency to exert normative pressure. SDO x Religion had an effect on deviation from French values, B = -0.31, SE(B) = 0.15, t99 = -2.09, p = .039, partial eta-squared = .04. In line with H1, SDO predicted perceived deviation from French values when the people praying were Muslims, b = 0.68, se(b) = 0.21, t99 = 3.27, p = .002, partial eta-squared = .098, but not when they were Catholics, b = 0.05, se(b) = 0.22, t99 = 0.25, p = .803, partial eta-squared = .001. Unexpectedly, this model did not reveal any effect of the SDO x Religion interaction on deviation from laïcité or on normative pressure, all |ts| < 1.37, ps > .234, all partial eta-squared < .03.

Effect of SDO x Religion on Public Expression

A regression analysis with SDO and religion as predictors of public expression showed an interaction effect of SDO x Religion, B = 0.23, SE(B) = 0.10, t99 = 2.29, p = .024, partial etasquared = .05. Decomposing this interaction showed that the simple effect of religion on public expression was not significant for high SDO individuals (+1 SD), b = 0.22, se(b) = 0.14, t = 1.60, p = .112, or for low SDO individuals (-1 SD), b = -0.23, se(b) = 0.14, t = -1.65, p = .103. On the other hand, SDO had a marginal effect on associating public expression with the principle of laïcité in the Catholics condition, b = 0.26, se(b) = 0.14, t99 = 1.80, p = .074, partial eta-squared = .032, but not in the Muslims condition, b = -0.01, se(b) = 0.20, t99 = -0.03, p = .976, partial eta-squared < .001.

Tests of Moderated Mediation Models

We tested H3 by using the Monte Carlo method to calculate the overall mediation index (bootstrap 5000). Analyses were conducted using R package JSmediation [START_REF] Yzerbyt | New recommendations for testing indirect effects in mediational models: The need to report and test component paths[END_REF].

Model on Deviation from French Values

As noted above, SDO x Religion had a significant interaction effect on public expression, which then had an effect on deviation from French values, B = -0.81, SE(B) = 0.13, t97 = -6.21, p = .016, partial eta-squared = .28. SDO x Religion also had an indirect effect via public expression on deviation from French values, b = -0.18, 95%CI [-0.37, -0.03]. After controlling for public expression, the direct effect of SDO x Religion was not significant, B = -0.14, SE(B) = 0.13, t97 = -1.08, p = .284, partial eta-squared = .01. Thus, the SDO x Religion interaction had a moderated mediation effect on deviation from French values via the association of public expression with the principle of laïcité (Figure 1).

Model on Deviation From Laïcité

Despite the lack of a total effect of the SDO x Religion interaction on deviation from laïcité, we performed moderated mediation analyses to test for indirect effects (see [START_REF] Hayes | Beyond Baron and Kenny: Statistical mediation analysis in the new millennium[END_REF]. Both components of the moderated mediation model were significant. Indeed, greater association of public expression with the principle of laïcité resulted in lower perceptions of deviation from laïcité, B = -0.91, SE(B) = 0.13, t97 = -7.25, p < .001, partial eta-squared = .35. Analyses confirmed the presence of an indirect effect, b = -0.21, 95%CI [-0.40, -0.03]. The direct effect of SDO x Religion on deviation from laïcité was not significant, B = 0.01, SE(B) = 0.13, t97 = 0.11, p = .912, partial eta-squared < .01.

Model on Normative Pressure

Similarly, despite the absence of a total effect of the SDO x Religion interaction, we tested the model on normative pressure. Both the direct and indirect effects of public expression on normative pressure were significant, B = -0.62, SE(B) = 0.11, t97 = -5 .82, p < .001, partial etasquared = .26 and b = -0.14, 95%CI [-0.28, -0.02], respectively. The direct effect of SDO x Religion on normative pressure was not significant, B = -0.03, SE(B) = 0.11, t97 = -0.25, p = .803, partial eta-squared < .01.

DISCUSSION

The present study investigated whether individuals with high SDO modify their conception of laïcité to justify their differential judgements of Catholics versus Muslims praying in the street. Results partially supported our hypotheses, as the higher a participant's SDO, the more likely they were to feel that Muslims deviate from French values (H1). However, we did not find a link between SDO and deviation from laïcité or intentions to exert normative pressure.

In addition, the higher a participant's SDO, the more likely they were to associate public expression with the principle of laïcité when considering Catholics praying in the street, but not when considering Muslims (H2). These results show an indirect effect of SDO and religion, via the degree to which public expression is considered a principle of laïcité, on judgments of people praying in the street as deviating from French values and laïcité and on the normative pressure exerted on them (H3). However, contrary to our expectations, this effect resulted in Catholics being judged more favorably, rather than in Muslims being judged negatively. Given that people with high SDO believe in a hierarchical society, they may be more inclined to defend the majority religion (Catholicism) compared with a minority religion (Islam).

Note

Because some people consider France to have Christian roots [START_REF] Brubaker | Between nationalism and civilizationism: The European populist moment in comparative perspective[END_REF] and because religion is a criterion that affects perceptions of cultural distance [START_REF] Triandis | Culture and social behavior[END_REF], people with high SDO may perceive themselves as being closer to Catholics and therefore change their conception of laïcité to favor this group. Moreover, debates in France about public expressions of religious beliefs mostly focus on Islam (e.g., wearing the full veil; Gorse, 2019), so people with high SDO may automatically associate such expressions with Islam and therefore weakly associate the public expression dimension with laïcité. However, in situations in which Catholics express their beliefs in public, not according people this right is detrimental to the majority religious group and thus to the maintenance of the social hierarchy that people with high SDO advocate. Consequently, such situations require people with high SDO to re-evaluate their position with respect to public expressions of religion, so they can judge the majority religious group positively.

Our second unexpected result was that religion did not affect the normative pressure expressed by high SDO participants or their perceptions of deviation from laïcité, but it did impact their perceptions of deviation from French values. Although our measures did not allow us to assess which French values participants were thinking about, this result highlights the importance of considering laïcité and French values separately. The lack of a total effect suggests that other factors, not considered here, mitigate negative judgments of Muslims (see [START_REF] Hayes | Beyond Baron and Kenny: Statistical mediation analysis in the new millennium[END_REF]. One such factor may be perceptions of why Muslims pray in the street. For example, reports about Muslims lacking indoor space to practice their religion are quite common: According to [START_REF] Laurent | Combien la France compte-t-elle de mosquées ? Le Monde[END_REF], in 2012 France had only one place of worship for every 1,200 Muslims, compared with one place of worship for every 241 Catholics. This may explain why Muslims praying in the street were not perceived as deviating from the principle of laïcité and why there was no intention to exert normative pressure against them. Because the lack-of-space argument is difficult to apply to Catholics, people with high SDO need to find another way of legitimizing street prayer by Catholics. One way to do this is to more strongly embrace the idea that displaying one's religious beliefs in public is compatible with laïcité. Our results could also be viewed through the lens of Social Identity Theory [START_REF] Tajfel | An integrative theory of intergroup conflict[END_REF]. Indeed, although we considered the measure of deviation from French values as part of the norms and normative pressure field, it might also be a way of reinforcing intergroup distinctiveness. By affirming that Muslims deviate from French values, individuals reinforce the intergroup distinction between Catholics and Muslims in France.

Although our study revealed an important result on the malleability of laïcité, it has limitations. First, all our participants were students. Nevertheless, previous studies of laïcité have reported similar effects for general population and student samples [START_REF] Roebroeck | Intergroup threat, social dominance, and the malleability of ideology: The importance of conceptual replication[END_REF], so there is no reason to suspect that mechanisms should differ between students and the general population. Future studies could check this hypothesis by testing different populations. Second, we did not observe the expected direct interaction effect of SDO and religion (Muslims vs. Catholics) on deviation from laïcité and normative pressure.

In addition to the possible explanations we suggested, this may be due to our sample being slightly too small to detect these interaction effects.

Our study provides further evidence for the ways in which individuals, depending on their level of SDO, use the principle of laïcité to justify their attitudes, in this case, in favor of a majority religious group. In addition to confirming that laïcité is a malleable ideology for people with high SDO [START_REF] Roebroeck | Intergroup threat, social dominance, and the malleability of ideology: The importance of conceptual replication[END_REF], we showed that this malleability encompasses the public expression of religious beliefs dimension when a situation violates a person's position with respect to this dimension. In other words, in situations that would otherwise be considered as deviating from secularist principles, individuals with high SDO adjust their conception of laïcité in order to legitimize the majority group's behavior. Hence, our findings support the idea that although laïcité was conceived as an egalitarian principle, individuals may modify their conception of it in order to justify treating different groups in different ways.

pratiqué leur religion devant celui-ci. Ainsi, différentes personnes se sont installées sur la place, pendant une trentaine de minutes afin de prier. " 1

English Translation

"Prayers in the street on XXX Square. Today, passers-by in XXX were treated to an unusual sight. No fewer than 50 Catholics [Muslims] had gathered in the street to pray. When the service [prayers] was [were] due to begin, the small church [mosque] in XXX Square was particularly crowded with believers. However, some of them decided to stay outside the church and practice their devotions in front of it. Thus, a group of people sat praying in the square for about 30 minutes." 1 Participants were told that the names of the town and the square had been masked to ensure anonymity.

APPENDIX B

Figure

  Figure 1. Moderated Mediation Model Predicting Deviation From French Values

.

  This model shows the effect of SDO x Religion on public expression (a x Mod path), the effect of public expression on deviation from French values (b path), and the total (c x Mod path) and direct (c' x Mod path) effects of SDO x Religion on deviation from French values. * p < .05, *** p < .001

  Means and Standard Deviations for the Full Sample and for Each Condition (-1 = Muslim condition, +1 = Catholic condition) and Correlations Between all the Variables

		Mean (SD)	Mean (SD) -1	Mean (SD) +1	1	2	3	4
	1 SDO	1.89 (.81)	1.77 (.74)	2.20 (.88)	-
	2 Public Expression	3.58 (1.64) 3.58 (1.68) 3.60 (1.60)	.02	-
	3 Normative pressure	3.75 (1.23) 3.70 (1.25) 3.88 (1.22)	.12	-.50***	-
	4 Deviation from laïcité	4.97 (1.55) 5.05 (1.56) 4.79 (1.59)	.03	-.58*** .46***	-
	5 Deviation from French values	3.80 (1.57) 3.70 (1.56) 4.06 (1.65) .24* -.52*** .62*** .53***
	* p < .05, *** p < .001
	APPENDIX C
	Regression of the Dependent and Mediating Variables on Religion, SDO, and their
	Interaction.
	Variable	B	SE(B)	t		p	η²p
		Deviation from French Values
	Religion	0.02	0.15	0.13		.897	.000
	SDO	0.37	0.15	2.45		.016	.057
	Religion x SDO	-0.31	0.15	-2.09		.039	.042
			Deviation from Laïcité
	Religion	0.35	0.15	2.29		.024	.050
	SDO	0.06	0.15	0.41		.682	.002
	Religion x SDO	-0.19	0.15	-1.23		.223	.015

APPENDIX A

Original Newspaper Article "Prières dans la rue sur la place _ Aujourd'hui, c'est une scène particulière qui s'est déroulée devant les passants, dans la ville de _. En effet, pas moins d'une cinquantaine de catholiques [musulmans] se sont retrouvés dans la rue afin de prier. Au moment de la prière, la petite église [mosquée] présente sur la place _ a connu une affluence particulièrement importante de croyants. Une partie d'entre eux a fait le choix de ne pas rentrer dans l'édifice religieux et a Benoit Testé is a full professor of psychology at the University of Rennes 2. His main research interests are the mechanisms and effects of social judgments and behaviors.

Declarations of Interest: None


Peter Sheehan
email: peter.sheehan@dctabudhabi.ae

Malak Mohammed Khalifa

Al Ajou

Nour Al Marzooqi

Maickel Van Bellegem

Anabela Fereira

Jaber Al Merri

Timothee Power

Anne Benoist

Louise Purdue

Anabela Ferreira

Jaber Al

Abu Dhabi

Archaios Maria-Paola Pellegrino

Enrica Tagliamonte

Hélène David- Cuny

The Oman Border Fence Project 2021 -A Journey through the hydraulic, agricultural and funerary

come

INTRODUCTION -THE OMAN BORDER FENCE (OBF) PROJECT, JANUARY-AUGUST 2021

Building on the new insights into the ancient landscape of al-ʿAyn that were gained during work at Al Ain Museum in 2019-2020 [START_REF] Sheehan | Al Ain Museum: an ancient landscape beneath the carpark[END_REF], this paper will present some further observations made during a rather rapid journey through more than eleven kilometers of that landscape in the spring and summer of 2021, during a project by the UAE Armed Forces to renew the border fence between al-ʿAyn and Buraimi. It will introduce the project and the archaeological response, describe the progress of works from south to north highlighting the major archaeological feature groups encountered along the way, offer some preliminary analyses of the associated finds groups and conclude with some brief observations on various aspectshydraulic, agricultural and funeraryrelevant to our understanding of the ancient landscape of al-ʿAyn.

Since 2019 we have recorded more than one hundred separate aflāj locations, of various dates and types, during construction and infrastructure projects in the old shaabiyāt housing areas around Hīlī and Qaṭṭāra oases. It was clear therefore when notification of this project was received in April 2020 that the border fence potentially had important archaeological implications, particularly to the east of the Qaṭṭāra, Jīmī and Hīlī oases, where a number of falaj alignments recorded previously would, if extended eastwards towards their source, cross the line of the border fence. Based on this information it was made a condition of the works that archaeological monitoring would be required from the southern edge of the concerned area, as defined by the Wādī al-Jīmī. From this point the changing alignment of the excavation for the new border fence as it proceeded northwards for 11.5km to the mountain allowed its division into six consecutive zones (Aa, Ab, B, C, D, E), together providing a series of cross-sections through the ancient landscape of al-ʿAyn (Fig. 1).

Fig. 1 -Map showing the different zones Aa-E of the Oman Border Fence project

PROJECT AND ARCHAEOLOGICAL METHODOLOGIES

The scope and rhythm of the construction project determined the excavation and recording methodology employed. The trench was roughly straight-sided, 3.5m wide by 3-4m deep, and the design of the fence and its location predicated from the start that everything along its line would be removed1 . Work entailed machine excavation of more than a million cubic metres, with the spoil temporarily heaped to the external/Oman side of the trench and then used to backfill after the pre-cast fence foundations had been lowered in by crane (Fig. 2). For security reasons excavation was coordinated with the removal and replacement of the existing fence to minimize gaps left open overnight. In general, the archaeological works was not extended beyond the 3.5m width of the trench other than in a few locations of particular archaeological interest discussed below. From our side we approached it as a 'rolling' evaluation trench, proceeding at an average of 80m a day, which we hoped would inform our understanding of the landscape, identify locations for future archaeological work and assist our ongoing efforts to manage and protect the historic environment. Excavation and recording methodologies developed to follow this rhythm. In Zones Ab and B initial excavation after removal of the old fence used a smaller JCB with a ditching bucket and/or a larger excavator with a steel plate fitted over the bucket teeth to remove quite deep and very compact overlying sand deposits to the top of the underlying natural. Each newly revealed area was then carefully cleaned by hand and the limits of individual cut features were recorded by total station and photogrammetry. These cuts were then completely excavated and assigned to feature groups based on typology or function (Fig. 3). Deeper features such as wells were explored to as great a depth as could be safely achieved, and larger cut features which there was no time to fully excavate were explored with sondages. The broad strategy was to assign individual cuts to distinct feature groups (square tree pits, round tree pits, agricultural basins etc.) based on typology or function and then to try to date each of these feature groups, relatively using pottery and other finds and absolutely from any associated C-14/OSL samples. After a second round of photogrammetry of the excavated cuts the machine returned and completed excavation to the full depth of the trench. A third round of photogrammetric recording before the installation of the fence foundations recorded this additional lower part of the sections and deeper cut features like aflāj in plan. In the other zones excavation took place only once and was followed by cleaning and recording of the sections and excavation of any archaeological features noted in plan (Fig. 4). Together these digital photogrammetry sessions created a series of consecutive and overlapping 3D models (more than 200 in all) from which orthophotos in plan and elevation have been produced. Deeper aflāj shafts and tunnels that we were able to enter and explore outside the trench limits were recorded by 3D scanner.

ZONE Aa -AFLAJ AND CHANNELS

Zone Aa comprised the first 500m of the archaeological project and provided a swift introduction to its opportunities and attendant challenges. This first section through the ancient landscape revealed, as expected, mainly linear cut features such as covered aflāj or open channels coming from the southeast and heading towards Jimi Oasis. This type of feature continued into Zone Ab and around the 600m mark included the historic stone-lined Jīmī falaj whose location in plan (but not elevation) was broadly known from Al Ain Municipality mapping and the line of existing covered shafts (thuqbah, pl. thuqb) running towards the oasis. The stone roof of the falaj is intact and the channel consequently a void, which was explored and recorded by 3D scanner to a distance of around 85m to the west and around 10m to the east. Immediately to the north of the Jīmī falaj we recorded what appears to be an Early Islamic brick channel that we have now been able to trace in various locations since 2013 for a total length of more than 1200m. In all these locations it appears to have been a broad straight channel 1m wide and 0.45m deep, carefully built with red brick and lime plaster, open to the air and capable of transporting a significant amount of water, perhaps reflecting a seasonal flow of run-off water from the Wādī al-Jīmī (Sheehan et al., 2022: 362-3).

ZONES Ab and B -IRON AGE CEMETERY, IRON AGE FIELD SYSTEMS, PRE-ISLAMIC RECENT (PIR) TOMBS

Moving north from Zone Aa, Zones Ab and B presented a multi-period funerary, hydraulic and agricultural landscape with a dense array of well-preserved archaeological features and deposits.

Around the 1km mark there are a number of walled modern and pre-modern cemeteries on both the al-ʿAyn and Buraimi sides of the border and at around 1135m a single Late Islamic burial was noted in the trench section. The longevity of this area as a funerary landscape was however soon indicated by three Iron Age graves, partially preserved within the west-facing section, which appear to indicate the southern extent of the Iron Age cemetery discussed below. In form these graves consisted of a narrow access shaft opening into a broader conical burial chamber, with the latter accessed in some cases by a step cut into the natural below the access shaft.

Whilst excavation of these three graves was proceeding, machine excavation was stopped around 70m further north having encountered a group of large, worked stones, which on further cleaning and investigation were shown to be part of the sloping entrance passage to a large stone-built collective tomb (Tomb A). This tomb is at least 25m long (its eastern extent beyond the limits of the border fence trench remains unknown) and 3m wide, with carefully built stone walls lining the side of the cut and remains of a corbelled roof. The overall preserved height of the tomb is around 1m, but the floor appears to have been excavated down below the bottom of the walls, perhaps in a secondary phase. The north side of the portal and entrance passage and the southern jamb (composed of a reused Umm al-Nār ashlar tomb facing) survived. Archaeological investigations here were extended beyond the border fence trench to define the western limits of the structure and establish the sequence of its construction, use and abandonment. This showed it had been disturbed by 2 machine-excavated modern service lines of unknown date 2 , but careful cleaning of the sides of these trenches allowed us to reconstruct this sequence and indicated that the tomb survived largely intact until the Late Islamic period, when a robber trench removed the entire eastern and part of the western wall (ignoring the larger and perhaps therefore less useful stones of the portal) .This apparent focus on the smaller stones from the walls of the tomb may link the robbing to the construction of the nearby Late Islamic Qaṭṭāra falaj. Only 6.3% of the ceramic assemblage from Tomb A can be dated to the Late Bronze Age, with 65% from the Iron Age, the most common shapes being bowls, storage jars, cups and spouted vessels, and 20% dated to the transitional period between the end of the Iron Age and the Late Pre-Islamic Recent (Pre-Islamic Recent or PIR) period.

Fig. 5 -Plan of the prehistoric cemetery between Tomb A and Late Islamic Qaṭṭāra falaj, with orthophotos of the part of Tomb A west of the border fence trench which have been derived from

the photogrammetric model. Note the modern service lines and the robber trench dug to remove the stone from its eastern wall.

Fig. 6 -Table showing the ceramic distribution from the cemetery, divided between Tomb A, the second collective burial and the individual graves.

The northern limit of this prehistoric cemetery is indicated by another similarly aligned and rectangular collective tomb about 120m north of Tomb A. This rectangular cut {069} into the natural is 5m long, 2m wide and 1.4m deep and was originally roofed with stone slabs. Only 3.2% of the assemblage from this tomb can be dated to the Late Bronze Age, with 74% from the early Iron Age and 9% fast wheel-made ware characteristic of the Late Iron Age, suggesting that like Tomb A this tomb continued in use throughout the Iron Age. Excavation of the fill of the collective tomb in six vertical spits indicated some trends which included a higher concentration of Late Iron Age classes in the upper fill and a large amount of pottery imports associated with the Iron Age II (1100-600 BCE) in the lower spits.

Between these two collective tombs we recorded around 35 individual graves within the limits of the trench. Blocking of the burial chamber with stone or gypsum bricks was a feature of a number of the graves, whilst others had narrow slots tunneled into their sides which may have been for burial goods. The individual graves appear to all date to the Early Iron Age/Iron Age II and included a relatively large number of complete or nearly complete vessels. Other finds included gold jewelry, copper arrow heads, beads and shell ornaments.

The cemetery also produced a significant assemblage of softstone vessels, most of them dating to the Iron Age. The assemblage from the project consists of 370 fragments of vessels and lids, the vast majority from the two collective tombs and the Iron Age cemetery at the southern end of Zone Ab. The majority of the fragments from Tomb A and the other collective grave can be dated to the Iron Age, with the most common shapes the conical/closed vessels, open and spouted bowls and beakers. One bowl from the collective grave {cut 069} retains a partial representation of a fish and another is made of a different kind of (mud)stone suggesting a provenance in Mesopotamia or the Levant. Vessels from the individual graves form part of the same Early Iron Age softstone assemblage, although one grave {cut 040} does contain fragments of a calcite vessel, probably a goblet or beaker with a stem, rarely found in Southeast Arabia during the Iron Age. Most of these tree pits were shown to be square cuts carefully excavated into the natural, and the impression that these were intended to function as 'plant pots' is supported by the presence in many of them of a small 'bowl' or depression at the centre, presumably to allow for drainage of excess irrigation water and to prevent waterlogging of the roots (see Fig. 3). There are also some deeper round tree pits (for palms?), also linked by channels, and in several places cutting the earlier square type, perhaps suggesting rather a short interval between different cultivars.

Although cut or overlain by later activity, clear traces of this initial field system continue for at least a further kilometer to the north within Zones Ab and B. Between 1380-1560m in Zone Ab there was also evidence for later land use in the form of deep wells apparently reused as middens and filled with large quantities of PIR pottery, similar to those we had noted in 2019 at Al Ain Museum. (Sheehan et al., 2022: 357-62, Figs. 4-7).

The funerary aspect of the landscape reappears at a slight rise around the 1620m mark, where the dense sand deposits that had accumulated over this earlier Iron Age field system are cut by two masonry-lined subterranean PIR tombs (Tombs B and C). The more southerly of these (Tomb B) is a roughly 2m square masonry-lined cut, while the construction technique of Tomb C appears very similar to that used in the PIR tomb revealed during excavations at Al Ain Museum in 2019 (Sheehan et al., 2022: 362, Fig. 9). A triangular stone squinch at the northwest corner suggests a vaulted or perhaps a corbelled roof like that partially preserved in Tomb B. Lime mortar was used in the construction of the subterranean part of the tomb, with a 330mm thick filling of mortar poured or thrown into the gap between the foundation trench and the 300mm thick facing stones of the burial chamber. Almost all the superstructure of these tombs had vanished, leaving very thin mortar spreads between 50-250mm thick which appear to have been 'blinding' layers of this same lime mortar for the above ground structure. Later robbing of Tomb C for its stone appears to have been interrupted and defeated by a massive Umm al-Nār block that had been used to form most of the east wall of the subterranean chamber. The reverse of the stone is stained by burning and the associated ash appears to represent the fill of a firepit intended to heat and crack it. Distributed, apparently concentrically, around Tomb C are several quite deep (up to 0.85m) rectangular grave cuts, one roofed with stone slabs and more than one containing large bones of ungulates. These appear to represent archaeological evidence for the pre-Islamic balîya practice of slaughtering and/or burying camels around the grave to accompany the high-status occupant in death (Jasim 1999:69-101;King 2009: 81-93).

The lower fill of Tomb C contained numerous fragments of iron weapons and other grave goods.

In relation to the iron material it was already apparent in situ that there was a mixture of arrow heads and larger sword (single edge) or spear heads. It was also clear that some of this material had mineral preserved structure of wood grain, likely from the scabbard of the sword, on the surface. This material is most often described as Mineral Preserved Organics (MPO), and can be observed when while being in the ground, the metal ions diffuse into the organic materials adjacent to a metal part and crystallize while the organic material degrades. The organic material is mostly no longer present but the physical features can still be seen in the shape of the corrosion products.

There were also around 200 ferrous arrow heads/small spears, most of which show the presence of mineral preserved wood on the tangs. Amongst the larger blades, either swords or spear heads, there appear to be about 15 tips and 4 pieces with the interface of blade and tang. There are blade fragments with a number of profiles, both single and double edged, or with a groove and ridge along the middle of the blade. There are also remains of scabbard and sword handles, including MPO such as wood, textile and skin product, as well as likely scabbard fittings, staples and rivets and two possible pommels. Much of the material shows brittle fractures, indicating that it broke after it was already entirely corroded and suggesting that the tomb may have remained undisturbed for a considerable time.

A typology of PIR ceramics had previously been developed during the Al Ain Museum project and was used as the basis for the study of the PIR assemblage from the border fence [START_REF] Power | A First Ceramic Chronology for the Late Islamic Arabian Gulf[END_REF][START_REF] Power | An Iron Age Ceramic Sequence from the Bayt Bin Ati, al-Ain, UAE[END_REF]Sheehan et al., 2022: 361-62, Figs. 5-7). A chronological framework was provided by the presence or absence of type fossils documented at key regional sites, especially Mleiha and ed-Dur [START_REF] Mouton | La Péninsule d'Oman de la fin de l'Âge du fer au début de la période Sassanide[END_REF][START_REF] De Paepe | A Petrographic, chemical and phytolith analysis of late pre-Islamic Ceramics from ed-Dur (Umm al-Qaiwain, UAE)[END_REF][START_REF] Haerinck | Mleiha (Sharjah, UAE): The 2009 & 2012 Belgian Excavations of Mound AI -pottery and chronology[END_REF]. The PIR funerary assemblage comes from Tombs B and C and from a large ashy dump about 50m to the north, which we have interpreted as evidence for ritual feasting contemporary with Tomb C and associated with funerary rites or visitation. This material comprises almost half (47.20%) of the total PIR assemblage from the project and includes a greater portion of prestige imports, particularly wine jars and serving bowls, deposited as grave goods. Initial analysis of the ceramics has suggested that the tombs may belong to different phases of activity within the PIR.

To the north of the PIR tombs the Iron Age agricultural landscape continues, now however with evidence for two distinct phases. Here surviving 'islands' of bedrock preserving the earlier arrangement of tree pits and channels alternate with deeper and apparently roughly rectangular basins cut through this bedrock that are watered, and perhaps linked by, deeper V-shaped channels at one end of each basin. What seems to be a broadly similar orientation of the basins to that of the earlier irrigation channels might suggest a degree of continuity. There is however a distinct character to the fill of the basins, with darker silty deposits containing copper fragments suggestive of a manuring layer reusing domestic refuse.

The ceramic assemblages from both agricultural phases are dominated by Iron Age common wares, with only a single sherd from each of fast wheel-made ware which is considered the main chronological marker for the Late Iron Age. The development of organic wares and some differences between the shapes of bowls found in the tree pits and the later basins points to a discrete evolution, but overall the similarity between the assemblages means that dating these different phases and understanding the reasons for the change for now remains a work in progress.

The relative paucity of Late Islamic ceramics was a feature of the whole length of the border fence trench. Traces of the field wall system known from historic archive photographs were noted at either end of Zone Ab, very close to modern ground level and lying above the thick layer of compact windblown sand that seals the Iron Age agricultural landscape. One activity that does seem to date to the Late Islamic period based on the ceramics is an area in Zone Ab between the 1845 and 1950m marks containing a dense series of intercutting pits, apparently for the mining of green clay deposits in this area. These clay mining pits clearly cut through and post-date the earlier array of tree pits, a few truncated examples of which survive in section or between adjacent claypits.

ZONES C-E

The eastward extent of the Iron Age basins in Zone B lies around the 2600m mark of the border fence trench. Beyond this, natural deposits come gradually closer to the modern surface and a large section of Zone C produced no archaeological material until around the 4.8km mark, where a pair of very large and deep thuqb filled with loose sand form part of a falaj that was clearly known into modern times, as part of it appears on the municipality mapping. Around 100m further north a quite different falaj was noted, consisting of three rectangular thuqb, 5m deep and with a gravel layer in the side of the falaj collecting and directing water into the rock-cut channel below. This type of relatively shallow falaj tapping subsurface flows appears to be the earliest typology we have encountered in various locations in in al-ʿAyn over the last couple of years.

Zone D presented a 4km long section through the landscape as it approaches the rocky hills north and east of the archaeological site of Hīlī. Here, where ancient ground levels are sealed by increasingly thick layers of colluvium and deep deposits of windblown sand, we recorded the upstream sections of more than thirty aflāj of various typologies and depths, with similar typologies broadly arranged in groups, most running southwest towards Hīlī but at least three actually heading northwest in the direction of al-Fû'ah. Zone E lies north of a buried spur of the adjacent hills cut through by the border fence trench.

Here we noted three more aflāj but perhaps the most notable features of the landscape in this section are the dark silty deposits overlying a layer of greenish clay, a product of oxido-reduction indicating ancient groundwater levels. These silt deposits occur from around the 10.5km mark and perhaps extend westward from the mountains to form the agricultural hinterland north of the Bronze Age and Iron Age settlements of Hīlī.

THE HYDRAULIC LANDSCAPE

The primary evidence for the transport of water within the landscape is the 50+ aflāj of various dates and techniques of construction recorded during the project. Although most of these linear features were noted in the harder natural deposits of Zones C-E, aflāj were found in every zone.

Other important evidence was recorded in the form of natural channels and watercourses (Arabic wudyān, sing. wādī) that appear to have strongly influenced the overall direction and functioning of the aflāj, and on the micro level by the regular network of minor distribution channels or rills within the agricultural areas. There are few finds from the aflāj, but a number of distinct typologies can be identified, including relative shallow (up to 5m) tunnels with closely spaced rectangular access shafts, extremely deep circular shafts with winding tunnels, and broad open ghayli channels, in addition to the Early Islamic brick falaj and the stone lined aflāj of the Late Islamic and early modern period.

For the Iron Age there are clearly a large number of aflāj, including broad open ghayli channels directing surface flow from the nearby mountains and tunnels with rectangular shafts collecting shallow subsurface flow from the natural gravels. Whether there is a development from one type to the other in response to changing technology or groundwater levels remains to be clarified by ongoing investigations. Most of these Iron Age aflāj are found in Zones C-D, coming from the northeast and heading towards Hīlī and Rumaila. Some can be tentatively linked from their alignment and level to locations that we have recorded during stormwater works in the old shaabiyāt, including one that can probably by identified as the upstream part of Hīlī 15 (al-Tikriti, 2002).

For the Pre-Islamic Recent period perhaps the most interesting question is whether the origin of the deep circular shafts and tunnels noted in Zones C & D can be linked to the creation of the northern oasis cores in the PIR, as we have previously suggested may have been the case for al-ʿAyn Oasis (Sheehan et al., 2022: 367). There is now evidence that wells formed a significant element of the PIR agricultural landscape from both the border fence and Al Ain Museum, but at the museum site we also dated the large rock cut Falaj 1 and the associated cut for a large bustan palm grove to the creation of the oasis core in the PIR, with both the falaj and the oasis landscape subsequently repaired and revitalized in the Early Islamic period. Ongoing monitoring of infrastructure work in the Kuwaitāt area of downtown al-ʿAyn to the east of the Al Ain Museum site (notable for graves containing PIR weaponry found in 1984 and again in 2022) is providing additional evidence for more PIR aflāj, with large circular shafts and tunnels at an intermediate depth between the extremely deep ones (15m) of the Late Islamic period and the shallower rectangular shafts of the Iron Age.

For the Early Islamic period we recorded a number of relatively shallow aflāj in Zone Aa and the beginning of Zone Ab, including the brick channel discussed earlier. These do not extend much beyond the 650m mark and appear to be largely heading towards the southeastern end of Jīmī Oasis which may represent its core. In Zones C-E the border fence trench produced no direct evidence for Early Islamic aflāj but in 2020 in the Hīlī Misbah area northeast of Hīlī Oasis we were able to trace 55m of a falaj that is likely to have been the westward continuation of one of the Iron Age aflāj recorded in Zone D that was re-excavated and given a vaulted roof with fired gypsum bricks in the Early Islamic period. For the Late Islamic period we have the two stonelined and roofed historic Jīmī and Qaṭṭāra aflāj, both apparently built with reused stone from nearby prehistoric tombs.

THE AGRICULTURAL LANDSCAPE

For the Iron Age agricultural landscape the most striking evidence relates to its scale, its regular layout and orientation and the existence of at least two distinct phases of activity. The orientation of the border fence trench and the alignment of features noted within it in Zones Ab and B allows us to estimate an irrigated cultivated area of at least 100 hectares. However the similarity of these features to those revealed in earlier works like the 2009-11 excavations at the Bayt Bin Ati House in Qaṭṭāra Oasis and during geophysical survey in Buraimi in 2014, and more recently the monitoring of infrastructure and housing projects in Hīlī and Qaṭṭāra oases, indicates that the maximum extent of the area under cultivation during the Iron Age was probably closer to 500 hectares [START_REF] Power | An Iron Age Ceramic Sequence from the Bayt Bin Ati, al-Ain, UAE[END_REF][START_REF] Power | First preliminary report on the Buraimi Oasis Landscape Archaeology Project[END_REF]. This agricultural landscape extends from the present Sa'āra Oasis in the east to the western edge of Qaṭṭāra Oasis. To the south it is delimited by the Iron Age cemetery, whilst to the north its extent is suggested by the junction of irrigated fields with the numerous aflāj passing through and south of the present Hīlī Oasis towards Rumaila. The second striking aspect is the orientation and regular layout of this field system, which runs broadly southeast to northwest, following the direction of its associated irrigation network, and appears to be reflected in the similar alignments of the tree pits and basins within the border fence trench to those indicated by geophysics carried out in Buraimi in 2014.

There is clear stratigraphic evidence in a number of locations that this Iron Age agricultural activity can be divided into two major phases, with surviving 'islands' of bedrock preserving the earlier and shallower arrangement of rows of tree pits and channels, alternating with a series of deeper and apparently rectangular basins that have cut through this bedrock to a lower level. This sequence is broadly supported by the initial pottery and finds analysis but the similar orientation of features from both phases might suggest a relatively narrow timescale, a point which we hope will be addressed by forthcoming C-14 analysis from the different phases. The earlier of these phases extends perhaps 200m further to the south, where it is apparently delimited by the contemporary cemetery. The southern extent of the second (basin) phase is sealed by a thick layer of hard compacted windblown sand and ends just north of the PIR tombs described earlier, which are located at a slightly higher level than the first phase of Iron Age fields to the south. If, as we have suggested was the case for Al Ain Museum, there is a PIR proto-oasis centred around the southern end of the present Jīmī and Qaṭṭāra oases, the deep wells we noted in Zone Ab may lie within the classic middle zone of fields and villages of Wilkinson's oasis schema, with tombs on a slight eminence above them (Wilkinson 1977: 68). In the Early Islamic period the revitalization of the agricultural landscape appears confined to the area of this proto-oasis, with little activity in the earlier Iron Age fields. This appears to have changed in the Late Islamic period when previous archaeological work in Buraimi and the evidence of historic photographs showing an expansion into this area is supported by the deflated field walls which were noted at both ends of Zone Ab, close to the surface and high above the earlier Iron Age fields. The same historic photographs show that this Late Islamic landscape was itself clearly in retreat by early modern times.

THE FUNERARY LANDSCAPE

There is now a third major prehistoric cemetery to add to those of Hīlī and Hafīt, with the difference that this funerary landscape has continued in use from the Late Bronze Age to the present day, shifting at times in relation to the agricultural landscape and reusing or fetishizing elements from earlier periods. The modern walled cemeteries on both sides of the border are attempts to delimit and manage a huge area of Late Islamic and pre-modern burials which have continued to use this ancient burial ground. Clearly the location of the Iron Age cemetery at the southern edge of the earliest phase of the contemporary field system is significant, as too the relationship between the collective tombs and the satellite individual graves. The relationship between the funerary and agricultural landscapes extends to the famous Qaṭṭāra Tomb , excavated in the 1970s. Bedrock here is close to the modern ground surface, suggesting that it was located on another slight rise, whilst the absence of any Iron Age tree pits or features for about 50m in the section of the trench as it passes the tomb indicates that at this time it was probably covered still by a mound and formed a marker in the landscape which for reasons of cult or convenience remained undisturbed.

The 2019 discovery at Al Ain Museum of the first monumental PIR tomb to be found in al-ʿAyn has now been followed by others, located on a slight rise marking the southern edge of the second phase of Iron Age agricultural landscape and, as with the museum site, in relative proximity to a putative Jīmī /Qaṭṭāra proto-oasis. Can we see in both cases the choice of prominent locations acting as territorial markers in the oasis landscape similar to the towers and forts of the Late Islamic period?

CONCLUSION

The border fence project has peeled off a long and revealing strip through the heart of the complex and shifting palimpsest of land use that is the cultural landscape of al-ʿAyn. In doing so it has shown once again that although the advent of the bulldozer and rapid urbanisation from the 1970s onwards truncated the ancient landscape, it did not destroy it. This paper has aimed to give a necessarily broad overview of the project, essentially a very long evaluation trench, and to highlight the nature and extent of the new information it has provided. Further progress towards what this means for our understanding of the landscape will be provided by the ongoing work on the finds assemblages briefly presented here, as well others including the human bone from the tombs and in particular the extensive geoarchaeological samples taken during the project. Along with informing targeted future archaeological work or remote sensing in areas adjacent to the border or along the line of falaj alignments, these new insights into landscape archaeology in al-ʿAyn can now inform some of our earlier observations, which began with excavations at the Bayt Bin Ati in 2009 [START_REF] Power | The Bayt Bin 'Ãti in Qaṭṭāra oasis: a prehistoric industrial site and the formation of the oasis landscape of al-'Ayn (UAE)[END_REF][START_REF] Power | The origin and development of the oasis landscape of al-'Ayn (UAE)[END_REF]) and included a season on the other side of the fence in Buraimi in 2014, as well as those made during work in progress on ongoing construction or infrastructure projects like the Al Ain Museum and the installation of new stormwater networks in the old shaabiyāt. Like these projects, the OBF has demonstrated once again the extent to which evidence for previous episodes of site formation survives, and how the ongoing process of urban transformation and the archaeological response to it will doubtless continue to transform too our understanding of the origins and development of the oasis landscape of al-ʿAyn.

Fig. 2 -

 2 Fig. 2 -View looking south along the border fence in Zone Ab showing the sequence of works, with archaeological investigations and recording of a falaj in the foreground and in the distance backfilling around the fence foundations

Fig. 3 -

 3 Fig. 3 -Plan of parts of Zones Ab and B, with detail of plan sheet 22 showing survey and orthophotos of tree pits and other cut features during different stages of excavation

Fig. 7 -

 7 Fig. 7 -Examples of softstone vessels from the collective burials and individual graves in theIron Age cemetery in Zone Ab.

Fig. 8 -

 8 Fig. 8 -Tomb C after excavation, with insets showing the numerous fragments of iron weaponry in situ and during conservation.

Fig. 9 -

 9 Fig. 9 -Excavation was extended to the east in Zone D to establish the direction of a falaj encountered in the border fence trench and explore a pair of 12m deep thuqb and the connecting tunnel.

Fig. 10 -

 10 Fig. 10 -Plan showing the likely extent of the Iron Age field systems based on recent observations, with inset a sample of magnetometry survey in adjacent areas of Buraimi showing similar features to those revealed during excavation of the border fence trench

An exception to this was made for the PIR tombs in Zone Ab discussed below, where the foundation design of a section of the trench was modified to allow these important structures to be preserved in situ beneath the fence.

SHEEHAN et Al PSAS 52 (2023), pp 323-337

The Oman Fence Border . a journey through the hydraulic, agricultural and funerary landscape of al-'Ayn.

FIGURES


teaching and research institutions in France or abroad, or from public or private research centers.

Urban metabolism:

Jean-Baptiste Bahers CNRS researcher, UMR ESO (Spaces and societies), Nantes university Urban metabolism Industrial ecology: the material and energetic functioning of cities. This research aims to quantify the metabolic inputs (e.g. biomass, minerals, food, and fuel) and outputs (e.g. waste, atmospheric emissions) (from Wolman 1965), optimise flows and improve their environmental performance.

Urban political ecology: the socio-technical transformation of matter generated by urban capitalism and uneven processes, through the metabolic rift (from Marx 1894). The aim is to explore both how nature is transformed and inscribed in the political and socio-economic practices that shape the urban form and its hinterland, and how flows are entangled in relations of domination and power.

Ecological economics: the long-term socio-ecological process by which material, energy and water flows are consumed, transformed and discharged in different forms by cities. This research aims to understand the urban implications of sociometabolic regime transitions.

Related terms (separated by commas)

Industrial ecology, political ecology, sociometabolism research Further reading (Key books, articles, papers utilizing the term. Use citation format, e.g. Jones, 2012;Rashid, 1985). Wolman, 1965;Clift, Druckman, 2016;Marx, 1894;Ernstson, Swyngedouw, 2018;Haberl, Fischer-Kowalski, Krausmann, Winiwarter, 2016.


Political-industrial ecology

Political-industrial ecology: a recent approach developed by geographers and political ecologists that "entails an importing of method and an exporting of spatial sensitivity and critical political economy" (from Newell, Cousins, 2015). The aim is to use quantitative methods from industrial ecology and social ecology to inform a radical critique of metabolic processes in terms of urban political ecology. The understanding of the urban metabolism of industrial-political ecology reaches this stage by combining an extensive Marxist apparatus, which combines socio-political dynamics with largely qualitative and spatialized methodological approaches by revealing the 'hidden' flows of material and energy consumption. It is therefore a question of territorialising urban metabolism, in order, for example, to show the impact relationships in terms of environmental and social injustice. Newell, J.P., Cousins, J.J. 2015. The boundaries of urban metabolism: Towards a political-industrial ecology. Progress in Human Geography, 39:702-728. Pincetl, S., Newell, J.P., 2017. Why data for a political-industrial ecology of cities? Geoforum 85: 381-391.

See also: Urban metabolism


domain: spi phys

text:
J Haumant
email: julien.haumant@elliptika.com

P Massaloux

D Diedhiou

A Manchec

R Allanic

C Quendo

C Person

R-M Sauvage

Ultralight Wideband Open Boundary Quad-Ridged Antenna Manufactured Using 3D Printing Technology

Keywords: dielectric slots, lightweight, open boundary quad-ridged, ultrawideband antenna, 3D printing. I

In this paper, authors propose to manufacture an ultra-wideband open boundary quad-ridged antenna using a 3D printing manufacturing method followed by a chemical metallization process. The lowest operating frequency has been decreased from 550 MHz to 300 MHz using dielectric slots. Furthermore, the structure of the antenna is optimized in term of weight and reached only 1100 g for an overall size of 442x442x442 mm 3 . Finally, measurements show good performances over the frequency band from 300 MHz to 6 GHz.

INTRODUCTION

The huge expansion of wideband applications in military, wireless communication or biomedical domains, show that wideband antennas have become essential components in radiofrequency applications. Since the early of 1960's, the challenges associated to ultra-wideband antennas such as the radiation performances over the bandwidth, weight, compacity or cost have been widely studied [START_REF] Chatterjee | Compact design of an UWB dual ridged horn antenna[END_REF]- [START_REF] Chang | [END_REF]. Among all types of wideband antennas, the dual-ridged [START_REF] Chatterjee | Compact design of an UWB dual ridged horn antenna[END_REF] and quadridged [START_REF] Wenliang | Quad-ridge dual polarized horn antenna design and optimization[END_REF] antennas are commonly used and generally allow to achieve bandwidth up to 20:1.

The multiplication of wideband applications coupled with a need of higher performances seems to lead toward an increased complexity of RF structures. Consequently, new shapes of antennas are studied, conducting to longer development time, heavier devices, and thus higher cost.

This last decade, the emergence of plastic additive manufacturing techniques has carried out an important number of researches in radiofrequency devices: lens [START_REF] Zhang | A K-Band 3-D Printed Focal-Shifted Two-Dimensional Beam-Scanning Lens Antenna With Nonuniform Feed[END_REF], waveguide slotted antenna [START_REF] Zhao | 3D-Printed Frequency Scanning Slotted Waveguide Array with Wide Band Power Divider[END_REF], orthomode transducer [START_REF] García-Vigueras | Mm-wave antennas and components: Profiting from 3D-printing[END_REF] or front end device [START_REF] Borgne | An Integrated Monobloc 3D Printed Front-end in Kuband[END_REF]. The wide accessibility of these rapid prototyping methods makes them an interesting alternative to conventional manufacturing techniques. Unlike conventional machining, 3D printing allows to manufacture extremely complex shapes with a minimum of constraints and development time.

The new degrees of freedom thus unlocked can be exploited to optimize the weight of structures without affecting radiofrequency performances as reported in [START_REF] Huang | Lightweight Perforated Waveguide Structure Realized by 3-D Printing for RF Applications[END_REF] and [START_REF] Haumant | Ultralight Wide-band Double Ridged Horn Antenna Using AdditiveTechnologies[END_REF]. In these articles, a waveguide and then a dual ridged horn antenna are completely perforated with electrically small holes which allowing to decrease drastically the global weight of the structure. Moreover, the usage of low volume density plastic materials in [START_REF] Haumant | Ultralight Wide-band Double Ridged Horn Antenna Using AdditiveTechnologies[END_REF] minimizes the weight of radiofrequency devices.

In this paper, an open boundary quad-ridged antenna is first designed with conventional parameters. Then, dielectric slots are added on the flares and allow to increase the electrical length of the antenna, thus to decrease the lowest operating frequency. Finally, the shape of the antenna is optimized and perforated with electrically small holes to remove the maximum amount of material without affecting the mechanical integrity and the performances of the antenna.

II. ANTENNA CONCEPTION

A. Reference antenna

The reference antenna is designed according to conventional open boundary quad-ridged antennas which allow to achieve ultra-wideband performances from 550 MHz to 6 GHz. The exponential taper has proved its interests in wideband solutions for antennas [START_REF] Wenliang | Quad-ridge dual polarized horn antenna design and optimization[END_REF], [START_REF] Perdana | Design of Vivaldi Microstrip Antenna for Ultra-Wideband Radar Applications[END_REF] and has been consequently chosen for the geometry of each flares. Regarding the considered manufacturing technique, the back cavity is circular which avoids any cantilevers surfaces as well as keeping the wideband matching of the antenna. The antenna is fed using two coaxial probes separated by a few millimeters to isolate the two orthogonal polarizations. The height, width and length of the body are equal to 442 mm. The design of the reference antenna and the feeding probes coaxial RG402 cables are shown in Fig. 1. The inner and the outer profiles of the ridges are terminated with a circularly shape. The profiles follow the values given in Tab. 1.

The antenna is simulated using the full-wave simulator HFSS™ and shows good matching results over the frequency band from 550 MHz to 6 GHz as presented in Fig. 2. However, the matching level under 700 MHz reaches -7 dB.

B. Bandwidth enhancement using dielectric slots

In this section, authors propose to increase the electrical length of the antenna by adding dielectric slots on each of flares. This technique [START_REF] Perdana | Design of Vivaldi Microstrip Antenna for Ultra-Wideband Radar Applications[END_REF] applied on a planar Vivaldi antenna shows a reduction of the antenna size regarding to its lowest operating frequency. First, to keep mechanically strong structure and an easy printability, the slots height and width are respectively chosen to 𝐻 ,-./ = 10 𝑚𝑚 and 𝑊 ,-./ = 20 𝑚𝑚. The electrical properties of the dielectric material are fixed to 𝜀 8 = 2.87 and tan 𝛿 = 0.027 which correspond to the measured properties in S band (2.2 GHz -3.3 GHz) of the used resin. The slots will resonate at the frequency where their lengths are equal to a quarter of the guided wavelength. Since the local structure is in a mixed medium, the challenge is to determine the effective permittivity seen by the wave inside the slots in order to calculate its length. As an approach to get an initial value for the electromagnetic optimization, the problem is solved as a microstrip transmission line as shown in Fig. 3. The slots inserted inside the two ridges can be seen as a substrate where two opposed and thick microstrip lines are separated by a perfect electrical conductor (PEC). The effective permittivity can be calculated using the transmission line impedance tool LineCalc (ADS). The thickness of the line is restricted to 4.99 mm due to the model limitation (𝑇 < 𝑊 = 5 𝑚𝑚) but it should be sufficient to get an approximate value of the effective permittivity. The effective permittivity calculated on LineCalc (𝜀 8 = 2.87 ; 𝐻 = 5𝑚𝑚 ; 𝑊 = 5 𝑚𝑚 ; 𝑇 = 4.99 𝑚𝑚) is equal to 𝜀 8FGG = 2.01 and leads to the following slots length 𝑙 ,-./ :

𝑙 ,-./ = 𝑐 4𝑓 K 𝜀 8FGG = 176 𝑚𝑚
Where 𝑐, the speed of light in vacuum and 𝑓 the desired resonant frequency (300 𝑀𝐻𝑧).

The length of the slots after optimization are changed to 180 mm which gives better results. The slots have been placed at 𝐻1 = 322 𝑚𝑚 height from the bottom of the antenna and tilted by 𝜃 = 20 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 (They cannot be place horizontally due to insufficient space). The design of the antenna with the slots is shown in Fig. 4. The simulated scattering parameters response is shown in Fig. 5. The results show that dielectric slots have induced a new resonance and allow the antenna to operate from 300 MHz.

C. Weight optimisation and mechanical considerations

The low volume density of most plastic materials is commonly used to decrease the global weight of a structure. As an example, the resin used to print the structure is around 1.1 g/cm 3 against 2.7 g/cm 3 for aluminum. Most of all, the flexibility of 3D printing allows to modify the structure easily in order to remove a huge amount of materials without disrupting antenna performances and maintaining a strong mechanical structure.

The weight of the proposed antenna is drastically decreased by perforating the structure with multiple holes of different sizes. The small holes are designed to have a neglectable impact at the shortest wavelength at 6 GHz. The diameter of these holes is equal to 5 mm which correspond to 0.1 𝜆 at 6 GHz. Then bigger holes (30 mm to 60 mm of diameter) are added in order to remove a higher volume of material. They are placed in the center of each ridge where the current density is lower than on their sides. In this way, it should have lower impact on the response. The volume of material for the final antenna shown in Fig. 6 is around 430 cm 3 against 895 cm 3 for the reference antenna.

The simulated realized gain as a function of the frequency is presented in Fig. 7 for the antenna without holes, the antenna with the small holes, and the antenna with the small and big holes. The small holes reduce the realized gain at high frequencies above 5.5 GHz and the big ones above 1 GHz where it is slightly lower in the privilege radiation direction. The final realized gain varies from 1.5 dBi at 300 MHz to a maximum of 11 dBi. The low mechanical properties of the plastic, compared to aluminum ones, can cause deformations at different steps of the manufacturing process due to the large dimensions of the antenna. Thus, several non-metallized structures are added as shown in green color in Fig. 6 and allow to keep the flares at a good distance from each other. These non-metallized structures are placed in order to limit the radiation perturbations and have not shown any noticeable impact on the scattering parameters response.

III. MANUFACTURING DETAILS

The antenna is manufactured in one piece using an SLA printer. The electrical properties of the resin are unknown, nevertheless, this resin has been used for purely mechanical purposes by being fully metallized.

The slots are also manufactured with an SLA printer, therefore, the complex permittivity of the resin has been measured in S-band (2.2 GHz -3.3 GHz) with a transmission line waveguide method and is equal to 𝜀 8 = 2.87 and tan 𝛿 = 0.027. The printed antenna and slots are shown in Fig. 8.

The antenna is then metallized using the conventional chemical deposition reported in [START_REF] Haumant | Ultra Wideband Transition From Coaxial Line to Two Parallel Lines Manufactured Using Additive Manufacturing Technology[END_REF] on a slotted coaxial line: (i) surface roughness enhancement by dry sandblasting, (ii) palladium catalysis, (iii) 3 µm chemical copper deposition, (iv) 10 µm electrolytic copper deposition and (v) 10 µm electrolytic tin deposition. The significant thickness of the tin deposition is not mandatory, especially because the conductivity of tin is lower than the copper one. However, the large scale of the antenna makes an inhomogeneous thickness of deposition. The time in the electrolytic bath are thus increased and ensure a minimal thickness of tin on all surfaces. The selective metallization is done using pieces of tape. The final body is shown in Fig. 9 (a). However, due to the temperature of the metallization bathes (≈ 40 °𝐶 -50 °𝐶), the flares of the antenna undergo deformations, especially on the slots and the base of the antenna where the feeders are placed. In order to rectify the structure, several non-metallized small pieces are added as shown in Fig. 9 (b). The final body measured weight comprising all slots and mechanical parts is equal to 1100 g which is light compared to the size of the antenna.

IV. MEASUREMENTS

The scattering parameters of the manufactured antenna are shown in Fig. 10. The two polarizations are matched under -10 dB on the most part of the frequency band, however, few peaks reached -7 dB in the lowest frequencies' region. The coupling between the two polarizations varies from -24 dB to -40 dB over whole the bandwidth.

V. CONCLUSION An ultra-wideband quad-ridged antenna in the frequency band from 300 MHz to 6 GHz is manufactured using a stereolithography printing method followed by a selective metallization process. Four 3D printing dielectric slots have been added and allow to reduce the size of the antenna compared to its lowest operating frequency. The final body' volume is 442x442x442 mm 3 and the optimization of the structure maintains the weight lower than 1100 g. Finally, measurements are in good agreement with the simulations and present a global matching level lower than -10 dB with some regions at -7 dB at the lowest frequencies.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Design and parameter given in mm of the reference antenna

Fig. 3 .

 3 Fig. 3. Model of the microstrip line approach for the determination of the effective permittivity

Fig. 5 .

 5 Fig. 5. Simulated scattering parameters of the antenna with the dielectric slots

Fig. 7 .Fig. 8 .

 78 Fig. 7. Simulated realized gain of the final antenna

Fig. 9 .

 9 Fig. 9. Photographs of the (a) printed antenna after the metallization process; (b) mechanical structures to rectify the deformations