domain: spi phys

text:
Maxime Pinaud

Georges Humbert

Sebastian Engelbrecht

Lionel Merlat

Bernd M Fischer

Aurelian Crunteanu
email: aurelian.crunteanu@xlim.fr

Terahertz Devices Using the Optical Activation of GeTe Phase Change Materials: Towards Fully Reconfigurable Functionalities

Keywords: phase-change materials, optical activation, reconfigurable terahertz metamaterials, polarizer

Multifunctional terahertz (THz) devices are crucial for the development of practical applications such as high-speed communications, spectroscopy and imaging, but their expansion is still requiring efficient agility functions operating in the THz domain.

Chalcogenide phase change materials (PCMs) with broadband responses, non-volatile and reversible transitions between a dielectric and metal-like phases, were successfully investigated as agile elements in photonics or electronics applications but their potential for controlling the THz waves is still under evaluation. We are demonstrating the optical control of specific states of the germanium telluride (GeTe) PCM and its integration as control element for enabling future optically-reconfigurable THz devices. The excellent contrast of material's THz properties in the two dissimilar states were used for optical-induced modulation of THz resonances of a metamaterial based on split-ring-resonator metallic structures integrating GeTe patterns. We experimentally confirm for the first time the feasibility of all dielectric GeTebased THz polarizers presenting broadband responses, high extinction ratios when the GeTe is in the metal-like phase and almost transparent when is amorphous. This highly functional approach based on optically-controlled multi-operational THz devices integrating PCMs, is extremely stimulating for generating future disruptive developments (field-programmable metasurfaces, dielectric coding metamaterials) with multifunctional capabilities for THz waves manipulation.

Introduction

Terahertz (THz) waves hold very promising applications such as high-speed wireless communication, security screening, chemical identification and non-destructive sensing. [START_REF] Tonouchi | Cutting-edge terahertz technology[END_REF] A prerequisite to the extensive development of these domains at THz frequencies is the development of reconfigurable devices (filters, spatial light modulators, lenses, frequency selective surfaces,…), which allow controlling the properties of electromagnetic waves such as their amplitude, phase, polarization and/ or spatiotemporal distribution of their wave fronts [START_REF] He | Metasurfaces for Terahertz Wavefront Modulation: a Review[END_REF] .

Reconfigurable devices are essential in reducing the cost, complexity and overall dimensions of THz systems. Reconfiguration strategies and the associated technologies already employed in the optical and microwaves domains are difficult or ineffective to transpose to THz frequencies [START_REF] Dragoman | Terahertz fields and applications[END_REF] . Current approaches for manipulating THz radiation are based on artificially engineered metasurfaces or metamaterials consisting of two-dimensional arrays of subwavelength metallic resonators [START_REF] He | Metasurfaces for Terahertz Wavefront Modulation: a Review[END_REF] . The topology or the electromagnetic properties of these individual building blocks can be modified by the integration in their design of different agility functions such as semiconductors, [START_REF] Kleine-Ostmann | Spatially resolved measurements of depletion properties of large gate two-dimensional electron gas semiconductor terahertz modulators[END_REF][START_REF] Chen | Active terahertz metamaterial devices[END_REF] liquid crystals, [START_REF] Savo | Liquid Crystal Metamaterial Absorber Spatial Light Modulator for THz Applications[END_REF][START_REF] Wang | Tunable optical negative-index metamaterials employing anisotropic liquid crystals[END_REF][START_REF] Zografopoulos | Tunable terahertz fishnet metamaterials based on thin nematic liquid crystal layers for fast switching[END_REF] MEMS devices, [START_REF] Zhengli | Tunable Terahertz Filter and Modulator Based on Electrostatic MEMS Reconfigurable SRR Array[END_REF] phase transition materials (VO2) [START_REF] Han | Broadband modulation of terahertz waves through electrically driven hybrid bowtie antenna-VO2 devices[END_REF][START_REF] Wang | Hybrid Resonators and Highly Tunable Terahertz Metamaterials Enabled by Vanadium Dioxide (VO2)[END_REF] or graphene [START_REF] Lee | Switching terahertz waves with gate-controlled active graphene metamaterials[END_REF][START_REF] Zhang | Tunable terahertz absorption in graphene-based metamaterial[END_REF] which has been proven as effective means to control the properties of THz waves.

In particular, vanadium dioxide (VO2) material has lately triggered a broad interest as active element in reconfigurable THz devices due to its ability to perform an insulator-to-metal phase transition at relatively low temperature (68°C) and under different applied stimuli (electrical or optical) [START_REF] Jeong | Dynamic Terahertz Plasmonics Enabled by Phase-Change Materials[END_REF][START_REF] Seo | Active Terahertz Nanoantennas Based on VO2 Phase Transition[END_REF] . Still, the low transition temperature of VO2, associated with the volatile phase transition (the material becomes insulator after removing the specific stimulus needed for the phase transition to the metallic state), although very practical for demonstration of specific functionalities, is inducing large non-linearity in material's properties and is limiting its operation at moderate temperatures.

In a similar way, most of the agile elements cited above have volatile-type responses requiring permanent optical or electrical bias, and complex integration technology with electrical/ optical control schemes over large areas. At the same time, they have to be integrated within the fixed topology of metadevices's for active manipulation of THz waves.

Chalcogenide phase change materials (PCMs) such as GeTe (germanium telluride) or Ge2Sb2Te5-GST (germanium antimony telluride) have been successfully integrated for realizing reconfigurable electrical or optical devices. The reconfiguration capability is based on the unique properties of PCMs undergoing a non-volatile phase transition on nanoseconds timescales from an amorphous (insulating) state to a crystalline (metallic), drastically changing their electrical and optical properties upon application of thermal, electrical or optical stimuli. [16-19] These PCM capabilities have been exploited over the years for realizing non-volatile memories by stacking the material between two electrodes and changing its state using pulsed current-Joule heating [START_REF] Ovshinsky | Reversible Electrical Switching Phenomena in Disordered Structures[END_REF][START_REF] Raoux | Phase change materials and phase change memory[END_REF] . More recently, GeTe and GST compositions have shown their ability to be used as high performance, bi-stable switching devices in the microwaves/ millimeter waves domains, holding high-promises for future multi-reconfigurable telecommunication systems [22,[START_REF] El-Hinnawy | A Four-Terminal, Inline, Chalcogenide Phase-Change RF Switch Using an Independent Resistive Heater for Thermal Actuation[END_REF] . Their implementation requires a planar electrodes indirect heating scheme using short voltage/ current pulses applied on a thin-film heater isolated through a dielectric film underneath the PCM films [22][START_REF] El-Hinnawy | A Four-Terminal, Inline, Chalcogenide Phase-Change RF Switch Using an Independent Resistive Heater for Thermal Actuation[END_REF][START_REF] Mennai | Bistable RF Switches Using Ge2Sb2Te5 Phase Change Material[END_REF] .

Compact optical metadevices based on PCMs, such as flat optics-like switchable/ tunable filters, multi-focus Fresnel zone plates, super-oscillatory lenses with subwavelength focus, and optical holograms have also been demonstrated [START_REF] Ohta | Overwritable phase-change optical disk recording[END_REF][START_REF] Dong | In PCRAMsim: System-level performance, energy, and area modeling for Phase-Change RAM[END_REF][START_REF] Karvounis | All-dielectric phasechange reconfigurable metasurface[END_REF][START_REF] Wang | Optically reconfigurable metasurfaces and photonic devices based on phase change materials[END_REF][START_REF] Singh | Characterization, Optimization, and Fabrication of Phase Change Material Germanium Telluride Based Miniaturized DC-67 GHz RF Switches[END_REF][START_REF] Gholipour | An all-optical, non-volatile, bidirectional, phase-change meta-switch[END_REF] . Furthermore, optical activation of PCMs between the two states has been widely used for rewritable optical disks storage memories [START_REF] Yamada | High-speed overwritable phase-change optical disk material[END_REF][START_REF] Chen | Compound materials for reversible, phase-change optical-data storage[END_REF] . Nevertheless, the large area capabilities of this technology are based on the association of mechanical movement of the storage medium and activation regions of PCMs limited by the laser beam size.

Most recently, it has been proven that PCMs can be used to realize all-dielectric, metal-free agile functions in the optical domain using optical control of GST-based metadevices. [START_REF] Karvounis | All-dielectric phasechange reconfigurable metasurface[END_REF][START_REF] Gholipour | Reconfigurable Ultraviolet and High-Energy Visible Dielectric Metamaterials[END_REF] Unlike electrical-based control schemes [START_REF] Ovshinsky | Reversible Electrical Switching Phenomena in Disordered Structures[END_REF][START_REF] Raoux | Phase change materials and phase change memory[END_REF][22][START_REF] El-Hinnawy | A Four-Terminal, Inline, Chalcogenide Phase-Change RF Switch Using an Independent Resistive Heater for Thermal Actuation[END_REF] , fast optical activation using femtosecond and nanosecond lasers of PCMs allows a more accurate control of the specific thermal diffusion effects associated with the crystallization and amorphization processes during the phase change mechanisms of the materials. [START_REF] Makino | Ultrafast optical manipulation of atomic arrangements in chalcogenide alloy memory materials[END_REF][START_REF] Liu | Crystallization of Ge2Sb2Te5 films by amplified femtosecond optical pulses[END_REF][START_REF] Lei | Refractive index modulation of Sb70Te30 phase-change thin films by multiple femtosecond laser pulses[END_REF] From the electrical point of view, in the amorphous state at low temperatures, GeTe is behaving like a disordered bandgap semiconductor with two main defect-induced band traps within the bandgap, located at ~0.26 eV and ~0.57 eV from the valence band edge 37 . It was previously shown that the electronic properties of amorphous GeTe are temperature-dependent, with nonlinear current-voltage behavior which can be modeled by space charge limited transport with uniform trap bands 37 . With increasing temperature and its transformation to the crystalline state, the material behave as a degenerate p-type semiconductor, with mobility and hole concentrations values up to 11 cm 2 /Vs and 8.8x 10 20 cm 3 , respectively, at 375K 37 . The THz conductivity of charge carriers in amorphous and crystalline phase change materials exhibits also a complex behavior, with a Lorentz-type resonance attributed to a phonon mode (grain boundaries tunneling) and losses due to free carriers (Drude relaxation conductivity term) 38 .

In the THz domain, the potential of PCMs as agile elements for controlling the properties of THz waves is still under evaluation. The few published studies report on their THz properties [38] , and on the possibility to integrate GeTe and GST stripes within THz metadevices which can adapt their response using thermal or electrical stimulus to change PCM's state only from amorphous to crystalline. [START_REF] Kodama | Tunable split-ring resonators using germanium telluride[END_REF] Recently, a THz metadevice based on 2x2 panels of metallic asymmetric split ring resonators (A-SRR) with dissimilar dimensions fabricated on a GST film has been reported to present multilevel states at THz frequencies using the electrical control (through a direct Joule heating scheme) of the crystallinity degree (and thus of the conductivity) of the GST material. [START_REF] Pitchappa | Chalcogenide Phase Change Material for Active Terahertz Photonics[END_REF] While the electrically induced nonvolatile and multi-state modulation of the THz transmission of the devices at multiple frequencies was validated for the amorphous-to-crystalline state of the GST material, the reverse operation of the system corresponding to the crystalline-to-amorphous state change of GST is yet to be proven. Electrical activation has obvious and numerous advantages for individual devices. However, the amorphization/ crystallization processes requires extremely localized areas of PCMs inserted between the command electrodes making it hardly compatible with design constraints of metadevices at THz frequencies.

In addition, the use of subwavelength metallic resonators as elementary building blocks of THz metadevices strongly limits the possibility to achieve large reconfiguration functionalities since the integration in their topology of active reconfigurable elements over wide areas (and associated electrical control) remain complex.

Although PCM-only metadevices made on GeTe-based split ring resonator arrays have been proposed in the past, they show very weak changes in their specific response at THz frequencies during GeTe phase transition from amorphous to the crystalline phase. [START_REF] Kodama | Tunable split-ring resonators using germanium telluride[END_REF] Nevertheless, THz devices fabricated with PCM active layers that are compatible with an optical activation between their dissimilar states, would lead to improved performances, simplicity of integration and may attain multiple reconfiguration functions [START_REF] Choi | Nanopattern enabled terahertz alloptical switching on vanadium dioxide thin film[END_REF] .

Here, we demonstrate for the first time to our knowledge an implementation scheme of PCMs and their associated optical control, foreshadowing the development of PCM-only THz devices with nonvolatile and reversible reconfiguration capabilities.

We validated the fabrication of GeTe phase change films with high contrast of their THz properties between amorphous and crystalline states allowing the first developments of all-PCM THz components. Furthermore, we experimentally show that these PCM films can be successively optically switched on large areas between their amorphous and crystalline phases using nanosecond laser pulses, while keeping an excellent contrast of their THz properties in the two dissimilar states. These performances were further used for demonstrating optical-induced THz response of a hybrid THz metadevice based of arrays of split ring resonator metallic structures integrating GeTe patterns. The significant amplitude contrast of the THz transmission between the two states of the GeTe film was finally exploited for developing all-PCM THz components by experimentally demonstrating optically activated GeTe-only THz polarizer devices with compelling performances to incident THz waves. This proof of principle based on the GeTe building elements and their associated activation method holds high-promises for future THz devices with fully reconfigurable transfer functions.

Thermal and optical activation of GeTe phase change material and its electrical performances at THz frequencies

We investigated the modification of electrical properties of GeTe films obtained on c-cut sapphire substrates, at DC and THz frequencies, for both direct plate heating or optical activation of phase changes (Figure 1a) (see also experimental section for details). As fabricated, the 500-nm thick GeTe film is amorphous with high DC resistivity of 800 Ω•cm. In the case of direct heating, the film's two-point resistance is gradually reducing with the temperature until ~175°C, when it is abruptly decreasing and stabilizes to the crystalline state resistance, as illustrated in Figure1b. The material retains its conductive state crystalline state with a resistivity value of 12x 10 -5 •Ω•cm, upon further annealing up to 300°C and subsequent cooling at ambient temperature, confirming its non-volatile electrical transition.

The GeTe phase change through thermal heating is inducing a large modification of the The thicknesses of investigated GeTe films are much smaller compared to the THz wavelengths and, taking also into account that the GeTe in the amorphous phase is almost transparent to the THz waves, it is very difficult to evaluate the complex permittivity of the 500 nm-thick GeTe films prepared in the two states, within acceptable errors. [START_REF] Withayachumnankul | Limitation in thin-film sensing with transmission-mode terahertz time-domain spectroscopy[END_REF] Still, the analysis of similar THz-TDS experimental data obtained for 1-µm thick GeTe films on sapphire substrates (supplementary material, Figure S1) allowed us to extract conductivity values of 1000 ±20% S/m for GeTe in the amorphous phase and (2.2 ±10%) x10 5 S/m for GeTe in the crystalline phase in the 0.2-1 THz frequency domain. These values are consistent with previous reported data on different phase change material compositions [38] . showing the spatial modulation of the THz transmission (the spectral profile of a section of the 2D image on the right-hand side panel).

An alternative and suitable method to achieve the amorphous -to-crystalline phase change in PCMs is their optical irradiation using nanosecond laser pulses (Figure 1a) [START_REF] Wang | Optically reconfigurable metasurfaces and photonic devices based on phase change materials[END_REF][START_REF] Yamada | High-speed overwritable phase-change optical disk material[END_REF][START_REF] Chen | Compound materials for reversible, phase-change optical-data storage[END_REF][START_REF] Makino | Ultrafast optical manipulation of atomic arrangements in chalcogenide alloy memory materials[END_REF] .

Compared to the plate heating method for which is extremely difficult to cycle in a reversible way the material between its dissimilar phases, the laser-induced phase change in PCMs has proven to be a method with fast switching capabilities, allowing the repetitive and sequential preparation of the material in a specific, desired state [START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF] .

Our approach for optically switching the GeTe layers between the two states is employing the direct irradiation of the films using 35-ns long UV pulses from an excimer KrF laser operating at 248 nm (Figure 1a) [START_REF] Valdes | A Polarization Reconfigurable Patch Antenna in the Millimeter-Waves Domain Using Optical Control of Phase Change Materials[END_REF] . The normalized THz transmission of the optically-crystallized GeTe shows performances identical to those of the crystalline GeTe films prepared by the plate heating method (Figure 1e). The employment of the KrF excimer source for laser-induced phase change in GeTe has a major advantage: the convenient way of preparing a specific state of the material in a recurrent and reproducible manner over large areas (the imprint -beam dimensions on the irradiated surface-of the laser beam covering a surface as large as 1.5x 0.5 mm 2 ) by simple direct irradiation or using raster scanning. Alternatively, specific crystalline GeTe patterns can be prepared by laser irradiation of the layer through contact masks carrying a particular design. The specific THz transmission response of the GeTe film in the two dissimilar states was further confirmed by the THz 2D spatial mapping of the interface between the amorphous and crystalline phases after laser irradiation of the amorphous GeTe material (Figure 1f). Although THz imaging has much lower resolution than the optical microscopy, the THz image allow evaluating the spatial interface between the two GeTe regions with dissimilar properties, as perceived by the THz waves. The associated THz transmission at 1 THz (righthand side panel in Figure 1f, presenting the spectral profile of a section of the 2D image) shows that the optically transformed crystalline GeTe is highly blocking the THz waves propagation while the amorphous GeTe is transparent to the incident waves.

Thus, to crystallize an initially amorphous GeTe 500-nm thick layer, an UV laser pulse with a power density of 1.1 x 10 17 W/m 3 (peak power volume density) is required to heat the material above its crystallization temperature, TC (Figure 2a). For bringing back the crystalline GeTe film to its amorphous phase, a higher power laser pulse should be employed, with power densities around 8.4 x 10 17 W/m 3 , in order to rapidly heat the material above its melting temperature TM and quench it in a disordered (amorphous) phase (Figure 2b). This meltquenching step is essential for reversible change of PCMs between their two states and requires intense and fast thermal pulses (electrical or optical induced) which can be difficult to implement using usual thermal heating approaches involving heating plates or ovens [START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF] .

The mechanism of the crystalline-to amorphous phase change is particularly complex, in which the temperature of the material above the melting temperature needs to drop down quickly, with cooling rates higher than 10 9 K/s, i.e. the fast quench should occur faster than the timescale for thermal diffusion from cell to neighboring cell, preventing reorganization into a crystalline structure [START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF] . It is then possible to define a critical quench time (CQT) of PCM materials, defined as the longest thermal time constant (i.e. the slowest cooling) that still results in an amorphous PCM material after the layer has been melted. The material undergoing the cooling process will be recrystallized if the quench time is longer than CQT, its estimation is therefore very important for defining the design, power budget and thermal response constraints for a given device configuration. For a specific PCM composition, the CQT is both device geometry and stimulus dependent, but it is possible to evaluate it experimentally or by multi physics simulations. Although several reports found that optical-based melt-quenching can be performed at times shorter than 1 ns (with recrystallization times of about 13 ns on optimized multilayer structures), common values for CQT range from tens to hundreds of nanoseconds [START_REF] Yamada | High-speed overwritable phase-change optical disk material[END_REF][START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF] .

In The evolution of the sheet resistance of the film following the sequential transformation from amorphous to crystalline states shows that crystallization and melt-quenched processes are reproducible and that the resistance values in each of the states are stable after more than 20 laser pulses. The initial, as-obtained, amorphous sheet resistance value of the film is higher than the values of the melt-quenched process which can be explained by the laser irradiation process performed in ambient atmosphere, without any capping or protective layer.

Indeed, additional capping layers placed on top of the PCM films will prevent the long-term degradation of the material during the melt-quench process. The atmosphere exposure may thus modify the composition of the film through oxidation, inter diffusion with adjacent materials or segregation or loss of tellurium from the alloy (for the materials lying on the (GeTe)/ (Sb2Te3) pseudo binary line), which affect its electrical performances. Potential capping layers like ZnS, ZnS:SiO2, silicon nitride-Si3N4 or alumina-Al2O3 films have proven to be highly effective for increasing the reliability of the optical switching of PCMs in optical data storage devices, providing an additional control of the thermal responses of the stacked layers within the devices [START_REF] Yamada | High-speed overwritable phase-change optical disk material[END_REF][START_REF] Njoroge | Influence of dielectric capping layers on the crystallization kinetics of Ag5In6Sb59Te30 films[END_REF] . Additionally, they may also act as anti-reflection coatings for a more efficient lasermatter interaction. Although for THz applications, some of the materials cited above may introduce additional adsorption losses, their influence can be minimized by the use of compositions that are quasi-transparent in the THz domain (e.g. Al2O3, SiO2).

Nevertheless, in our experiments, even without the use of a capping layer, the electrical contrast between the resistances values of the crystallized and melt-quenched GeTe phases is still higher than 10 5 , resulting in a high THz transmission ratio between the two phases (Figure 2d). Thus, at 1 THz, the mean normalized transmission of the optically crystallized GeTe layer is 1.5% and of 83% for the optically melt-quenched, amorphous phase.

The response times of the GeTe material upon laser irradiation were recorded by performing optical pump-electrical conductivity probe measurements. We used a simple electrical circuit in which the GeTe layer was connected using planar electrodes with a constant voltage source and a series resistance of fixed value. The conductivity variation of the GeTe layer subsequent to laser irradiation will largely modify the current circulating in the circuit and, consequently, will modify the voltage drop on the series resistance. The real-time recording of this voltage give useful insights on the dynamics of the material phase change. Thus, the measured response times following laser irradiation with 35-ns long laser pulses, for both amorphous-to-crystalline and crystalline-to amorphous phase changes, lie in the 45-50 ns range. Although these short switching times offer a preliminary indication on the temporal responses and electrical conductivity modification of the GeTe layer, further investigations are planned for evaluating the direct THz response timescales.

In the following sections, we will experimentally demonstrate that this optically-prepared high transmission ratio between the two dissimilar states of the GeTe film may be employed for recurrent non-volatile switching of THz waves. In addition, the presented technique shows high capabilities for the design of essential THz devices with high compatibility to reconfigurable functionalities for which the integration of active GeTe material is straightforward.

Integration of GeTe in hybrid reconfigurable metamaterial THz device

We exploit the optical activation and the high contrast of THz transmission between amorphous and crystalline phases of GeTe to demonstrate optical activation of a hybrid metamaterial acting as a notch filter in the THz frequency domain. The design of the device is based on a periodic collection of metallic square-shape split-ring resonators (SRR) for which the gap is closed by a GeTe pattern (Figure 3 a,b). Such metamaterial SRR-based topologies had proven their capacity to effectively manipulate the THz waves [START_REF] Crunteanu | Tunable THz metamaterials based on phase-changed materials (VO2) triggered by thermal and electrical stimuli[END_REF][START_REF] Al-Naib | Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials[END_REF] , having sharp LC-type resonances for which the frequency and resonance amplitude can be conveniently adjusted by varying their dimensions, shape or and the dielectric environment in the gap of the structure [START_REF] Withayachumnankul | Metamaterials in the Terahertz Regime[END_REF][START_REF] Chen | Manipulation of terahertz radiation using metamaterials[END_REF] .

The simulated response of the proposed device based on a network of SRR unit cells (Figure 3b) spaced by 20 µm in both directions in the plane of the overall structure is shown on Figure (Figure 3d) and its performances were evaluated using the THz-TDS measurement technique in both configurations (GeTe patterns in the amorphous states and in the optically-crystallized one, respectively). For crystallizing the GeTe integrated in the SRR unit cells, the entire metamaterial structure was irradiated using a single laser pulse, as mentioned before.

The measured normalized THz transmissions of the fabricated metamaterial device are represented in Figure 3e for both amorphous and crystalline GeTe in the gap of the SRR structures and they are corresponding very well to the theoretical performances. Although some differences between the simulated and experimental results are still occurring, they can be explained by the imprecision in evaluating the exact electrical and optical properties of such very thin GeTe films and the slight dimension differences occurring in the microfabrication process between the simulated structure and the fabricated device. The performances of the fabricated device can be also evaluated in terms of the quality factor of each of the resonance peaks, defined as Q = f0/Δf, where f0 is the resonance frequency and Δf is its bandwidth at half minimum. When the GeTe is amorphous, Q= 9.36 (LC resonance at Amorphous GeTe Crystalline GeTe Measures 0.26 THz), while Q = 15.8 when the GeTe is transformed to its crystalline state (resonance occurring at 0.58 THz). These quality factors are similar to the ones corresponding to metalliconly SRR planar devices (replacing with air the amorphous GeTe and with pure gold patterns the crystalline GeTe in the corresponding designs). Although these figures are also designdependent, the introduction of GeTe material within the SRR unit structure does not alter their values, implying that the losses induced by the integration of GeTe in the amorphous state or the lower conductivity of crystalline GeTe (worst case scenario when compared to a pure metal conductivity) may be alleviated in such metamaterial hybrid implementations.

The same analysis was performed on identical devices fabricated on silica (SiO2) substrates (see supplementary Figure S7) and shows comparable performances, although the specific resonances of the device are appearing at different frequencies, given the different substrate permittivity.

We obtained quasi-identical responses for similar devices integrating GeTe patterns which were prepared to the crystalline state using direct thermal activation on a heating plate (as indicated on supplementary Figure S8) which is clearly indicating that the optical-induced phase change of GeTe within the metamaterial structure is a highly effective and much more appropriate method in modifying, on-demand, the THz response of such devices.

The strong variation of the transmission at 0.58 THz (higher than 35dB) of the GeTe implemented SRR device between the optically-induced two dissimilar phases is a strong representation of the capabilities of these type of materials and associated switching technique in the development of low consumption, highly integrated THz devices relevant for switching functions, filters etc. with a plethora of applications in telecommunication and imaging [START_REF] Cui | Coding metamaterials, digital metamaterials and programmable metamaterials[END_REF] .

All-dielectric reconfigurable THz polarizer based on GeTe phase change material

The strong contrast in THz amplitude signals transmitted through the GeTe films optically prepared in the two different states suggests that simple structures made only in GeTe (without additional metallic structures) could be feasible, offering interesting and promising opportunities for developing active THz reconfigurable devices. In particular, THz polarizers are essential devices, with critical roles in imaging and wireless communication applications [START_REF] Lu | A high extinction ratio THz polarizer fabricated by double-bilayer wire grid structure[END_REF][START_REF] Watanabe | Terahertz Polarization Imaging and Its Applications[END_REF][START_REF] Huang | High extinction ratio and low transmission loss thin-film terahertz polarizer with a tunable bilayer metal wire-grid structure[END_REF][START_REF] Wong | Active meta polarizer for terahertz frequencies[END_REF][START_REF] Yamada | Terahertz wire-grid polarizers with micrometer-pitch Al gratings[END_REF][START_REF] Deng | Extremely high extinction ratio terahertz broadband polarizer using bilayer subwavelength metal wire-grid structure[END_REF] . For demonstrating the potential capabilities of the GeTe material for these applications,

we develop what we believe being the first all-PCM THz polarizer, i.e. the first device using the metallic/ crystalline state of GeTe to produce the selection of the polarization state of a transmitted THz wave.

The design of the proposed polarization device is based on GeTe wire-grid parallel structures on a sapphire substrate and have reconfiguration capabilities (turning on or off its polarization behavior) brought by the optically-active GeTe material (Figure 4).

We designed three different polarizers with dissimilar wire widths (w) and periods (P) which were fabricated by patterning a 500-nm thick GeTe layer on a sapphire c-cut substrate (Figure 4b). The polarizer P1 was made with a period P = 10 µm and a wire width w = 3 µm (P1(10/3

on Figure 4b). The P2 device was realized with a smaller period P = 6 µm and the same wire width w = 3 µm while for the third design, the width of the wires was reduced to w = 2 µm and the period was fixed to P = 9 µm (denoted as P2(6/3) and P3 (9/2), respectively, on Figure 4b).

A fourth polarizer structure was realized using gold instead of GeTe to serve as a reference, with P = 6 µm and w = 3 µm(P4(6/3) on Figure 4c).

When the GeTe is amorphous, the wire-grid structures act as a transparent dielectric material, allowing TM and TE THz waves to be transmitted with identical results (see supplementary

Figure S5

). However, when the GeTe is brought to its crystalline, metal-like state using UV laser pulses, it induces a wire-grid polarizer effect, blocking a significant part of the TE-polarized waves [START_REF] Withayachumnankul | Metamaterials in the Terahertz Regime[END_REF] . This behavior is clearly visible on the simulated and measured performances of the GeTe-based devices shown on Figure 4c. Usually, the TE transmission of wire-grid polarizers is increasing with frequency and, while the TM transmission is roughly constant, this will results in a small extinction ratios at higher THz frequencies [START_REF] Yamada | Terahertz wire-grid polarizers with micrometer-pitch Al gratings[END_REF][START_REF] Deng | Extremely high extinction ratio terahertz broadband polarizer using bilayer subwavelength metal wire-grid structure[END_REF] (see supplementary material information Figure S9). Although the measurement results of the gold-based polarizer shown on Figure 4c are only roughly consistent with this behaviour, the difference can be explained by the poor signal to noise ratio of our THz-TDS measurement system, less adapted to the evaluation of high extinction polarizers. In addition, in the case of the GeTe-based polarizers, the rather constant evolutions with frequency of the TE transmissions can be also explained by the difference in conductivity between metallic gold and crystalline GeTe. Indeed, compared to gold, crystalline GeTe has metal-like properties with much lower conductivity (≈ 220 kS.m -1 ) than metallic gold (47000 kS.m -1 ).

When comparing the results for the P1 and P3 polarizers we may notice that a decrease of the fill factor (defined as the ratio of the width of a single GeTe line to the period of the wire grid) from 0.3 (P1) to 0.2 (P3) for a fixed period (P= 10 µm) is decreasing the attenuation of the TE mode from -13.04 dB to -10.9 dB while the TM transmission is slightly improving from -0.26 dB for the P1 device to -0.22 dB for the P3 polarizer. The best performances were obtained for the P2 device (having a fill factor of 0.5 and a smaller period value, of P= 6 µm), showing an experimentally-recorded contrast of 16.5 dB between TE and TM polarizations. This behavior is consistent with previous studies on THz polarizers showing that fill factors over 0.5 should be preferred for achieving high extinction ratios between the TE and TM modes in the THz domain [START_REF] Yamada | Terahertz wire-grid polarizers with micrometer-pitch Al gratings[END_REF][START_REF] Deng | Extremely high extinction ratio terahertz broadband polarizer using bilayer subwavelength metal wire-grid structure[END_REF] . The polarization performances of the GeTe-based devices induced by laser irradiation are similar with those of identical devices in which the GeTe was prepared to the crystalline phase by direct thermal heating (supplementary material Figure S10).

By comparing the performance of the GeTe-based P2 polarizer to the device having the same design but fabricated with gold instead of crystalline GeTe, we clearly notice the better performance of the latter (P4 on Figure 4c) which is expected, taking into account the lower conductivity of the crystalline GeTe compared to that of Au. Nevertheless, a gold-based structure is a fixed and passive structure whereas the GeTe structure can be tuned between its amorphous and crystalline states by optical stimuli while showing very good polarization performances of the THz waves. Thus, we have demonstrated the feasibility to develop all dielectric (metal free) THz polarizers using solely chalcogenide phase change materials which presents a broadband response, a high extinction ratio when in metal-like phase (up to 16.5 dB) and almost transparent in the amorphous phase, using an optically-induced non-volatile transition.

To our knowledge, this is the first experimental demonstration of such broadband devices based on GeTe PCM in the THz domain. As the overall performances of such THz devices can be further improved through design adjustments, the presented approach is highly functional, technological disruptive and extremely stimulating for fast THz waves control and manipulation using reconfigurable or switchable THz devices such as frequency-selective surfaces, polarizers, lenses and waveplates, spatial modulators, power limiters etc. [START_REF] Cui | Coding metamaterials, digital metamaterials and programmable metamaterials[END_REF]

Conclusion

In conclusion, we have demonstrated hybrid and all-dielectric THz devices based on GeTe phase change material integration, which can be optically switched between its two different amorphous and crystalline phases, in a reversible way and with zero-power holding capabilities by using nanosecond UV laser pulses. We experimentally realized optically-induced nonvolatile resonance switching by hybrid integration of GeTe with metallic elements within the unit cell of a metamaterial device. The good contrast of GeTe THz properties between the amorphous and the crystalline state, allowed us to design and prove for the first time the possibility to realize an all-dielectric reconfigurable THz devices based solely on GeTe which can achieve a strong modification of the polarization of incident THz waves (extinction ratios of 16.5 dB). The approach offers a great reconfiguration flexibility for multifunctional manipulation of THz waves, and can be easily adopted for implementing optical reconfiguration techniques capable to activate PCM structures within a particular THz device on large areas or on specific regions (through raster scanning or optical excitation of precise elements within the device) in order to program precise, on-demand functionalities of THz waves (arbitrary spatial profile of intensity, phase, and/or polarization distribution). This highly versatile approach that we are proposing, based on non-volatile optically controlled multi-operational THz devices integrating PCMs, will, most certainly, generate stimulating, disruptive developments in the THz domain like field-programmable metasurfaces, all-dielectric coding metamaterials with multifunctional capabilities for THz field manipulation.

EXPERIMENTAL AND METHODS

The THz hybrid metamaterial was fabricated in a cleanroom environment by standard photolithography and deposition procedures using a two-mask levels process. Firstly, a 500-nm thick GeTe layer have been obtained on a 500-µm thick c-cut sapphire substrate using DC magnetron sputtering from a GeTe (50-50 stoichiometry) target in an argon atmosphere. The GeTe elements were patterned using a lithographically-defined photo-resist mask and a wet etching process. The subsequently deposited metallic patterns (20/500-nm thick Ti/Au bilayers) defining the SRR structure were obtained by electron-beam evaporation of the respective metallic elements and an optical lithography step using the lift-off method. The GeTe-based THz polarizer was obtained by patterning a GeTe film using a one-mask lithographically step defining a photo-resist mask and a subsequent dry etching process while the metallic gold-based polarizer was fabricated in a similar matter from a Ti/Au (20-500 nm) film obtained by electronbeam evaporation.

For the optical reversible switching of the GeTe film between the two amorphous and crystalline states we employed the direct irradiation of the obtained GeTe films using pulses from an excimer KrF laser with a wavelength of 248 nm and a pulse duration of 35 ns. Laser pulses with energy densities ~90 mJ/cm 2 where employed for transforming the GeTe from the amorphous to the crystalline state while the reverse transition requires energy densities in the range 185-190 mJ/cm 2 . The conductivities of the GeTe films were measured using a four probes set-up.

The full-wave simulations of the THz devices were performed using the commercially available Ansys HFSS software package. For the GeTe materials parameters, we used the dc conductivities layer extracted in the two states by the four-probe method, while for the permittivity of the amorphous GeTe we used a value of 20. Similar permittivity values were reported previously for different PCM compositions [38] .

The THz characterization of the bare GeTe films and of the different fabricated THz devices was realized using a homemade THz time domain spectroscopy (THz-TDS) system.

Notes

The authors declare no competing financial interest and no conflict of interest.

Supporting Information

  material's THz properties. The transmitted temporal signals for both amorphous and crystalline 500-nm thick GeTe film recorded by terahertz time domain spectroscopy (THz-TDS) measurements are represented on Figure 1c. The corresponding Fast Fourier Transform (FFT)calculated frequency domain of THz transmission of the GeTe film in amorphous and crystalline states (spectra normalized by the substrate THz transmission) show normalized transmissions around 90% for the amorphous phase and of 1.7% for the crystalline state, with relatively constant values over the entire measured domain (Figure 1d). The metallic behavior of the crystalline phase of GeTe is manifested by a strong reflection of the incident THz radiation and therefore a drastically decrease of the amplitude of the transmitted THz pulse.

Figure 1 .crystalline

 1 Figure 1. (a) Amorphous-to-crystalline phase change of a 500-nm thick GeTe (initially amorphous) film obtained on a sapphire substrate (20x 20 mm 2 overall dimensions) using either

  our experiments, the finite elements multiphysics simulations indicate that the temperatures rise within the GeTe layers subsequent to the application of the two energy-dissimilar laser pulses (black curves in Figures2a and band temperature distribution over the entire laser pulse area on supplementary FigureS2) makes possible the reversible change of the GeTe film between the amorphous and crystalline phases. As the optical control of a specific phase of the GeTe material on a large area is critical for the realization of reconfigurable THz devices, we experimentally validated for the first time the reversible amorphous-to-crystalline phase changes of a GeTe layer obtained initially in the amorphous state on a sapphire substrate by recording its two-probe sheet resistance change subsequent to the application of alternating UV laser pulses with distinctive energies (Figure2c).

Figure 2 .

 2 Figure 2. a and b. Finite element simulations of temperature rise within a 500-nm thick GeTe

3c.

  When the GeTe pattern within the SRR gap is amorphous, it is almost transparent to the THz waves and the normal LC resonance of the SRR structure occurs at around 0.26 THz accompanied by higher order resonances at 0.73 and around 1.1 THz (red curve on Figure 3c). When the GeTe is crystalline, it electrically closes the gap of the SRRs and the LC resonance vanished, and different resonance appears at 0.58 THz, corresponding to the mutual coupling between each of the thus modified SRR structures. The electric field distributions of the SRR unit cell for both amorphous and crystalline states of the GeTe material, allowing identifying the origin of a specific resonance are displayed and extensively explained in the supplementary material associated with Figure S5 and Figure S6. The SRR metamaterial based on the hybrid integration of GeTe-metallic structures was further fabricated on a c-cut sapphire substrate

Figure 3 .

 3 Figure 3. (a) Schematic of the THz set-up for evaluating the performances of a metallic split-

Figure 4 .

 4 Figure 4. (a) Measurement scheme of the GeTe-only THz polarizer (b) Close-up optical images

Available: 1 .

 1 GeTe thin film conductivity extraction at THz frequencies 2. Multi physics simulation of thermal distribution within the GeTe film upon laser irradiation 3. Representation of the THz transmission curves of the GeTe material in logarithmic scale 4. Study of the SRR unit cell electromagnetic responses of the GeTe based metamaterial at different resonant frequencies 5. Comparison of thermal and optical activation performances of reconfigurable GeTe-based THz metamaterials on SiO2 substrates 6. Electromagnetic simulation of a gold-based polarizer structure 7. Performance analysis of thermal and optical activation of GeTe-based THz polarizers This material is available free of charge from the ACS Publications website and from the authors.

Acknowledgement

This work was partially supported by the France's Centre national de la recherche scientifique (CNRS), under the PEPS INSIS/DGA project AROMe. M.P. is kindly acknowledging the partial funding of his PhD grant from the French-German Research Institute of Saint-Louis (ISL).

For Table of Contents


Keywords: Simulation, Biosourced material, Solar energy, Solar evaporation, Porous media, Heat and mass transfers

A two-dimensional axisymmetric finite element model of a solar evaporator based on a tannin foam has been developed using COMSOL Multiphysics. This model includes a set of boundary conditions and mass transfer within the porous structure. Experiments were conducted to validate the model as the parameters changed over time. Using the model, the effects of light absorption at the surface, water diffusion inside the material, and the thickness of the material and the insulating wall were investigated. We showed that a 38% decrease in evaporation rate was observed when water diffusion does not allow sufficient transport of water to the surface. In addition, an increase in light absorption from 0.8 to 0.9 increases the evaporation performance by 12% and insulation of the exterior does not yield significant changes. A final section of the article focuses on the temporal evolution of water evaporation in several locations around the world. We concluded that hot and dry climates have the highest evaporation potential. Among the cities studied, the highest theoretical evaporation for this biosourced foam was predicted for Dubai, 5342 kg.m -2 , followed by Cairo, 4723 kg.m -2 .

Nomenclature a

[-] Water activity cp [J K -1 kg -1 ] Heat capacity D [m 2 s -1 ] Coefficient of diffusion of water inside the material E

[-] Emissivity of the material and of the side of the beaker hc [W m -2 K -1 ] Heat transfer coefficients hv [kJ.kg -1 ] Enthalpy of vaporisation HR [-] Relative humidity k [m.s -1 ] Convective mass exchange coefficient M [kg mol -1 ] Molar mass of water P

[Pa] Pressure Ps,0 [W.m -2 ] Average solar illumination R [J mol -1 K -1 ] Universal gas constant T

[K] Temperature Tref [K] Reference temperature

Special characters ε [-] Volume fraction λ [W m -1 K -1 ] Thermal conductivity ᵠ [-] Porosity ρ [kg m -3 ] Density η [-] Efficiency σ [W m -2 K -4 ]
Stefan-Boltzmann constant o [-] Tortuosity

INTRODUCTION

Due to global warming, increasing world population and river pollution, drinking water resources will become scarcer in the coming years. By 2050, 3.9 billion people, or more than 40% of the world's population, will be living in watersheds under severe water stress [START_REF] Chen | Challenges and Opportunities for Solar Evaporation[END_REF]. To solve this problem, in addition to reducing consumption, several complementary approaches could be developed, including storage and/or recovery and treatment of water unsuitable for consumption.

One of the water purification strategies is direct evaporation by a passive evaporation system, using solar energy to recover salty and/or polluted water. Indeed, some materials called photothermal, once placed on the surface of water, have the ability to absorb solar energy and accelerate its evaporation, thus transforming between 80 % and 90 % of the solar energy received into water vapour [START_REF] Zhang | Direct solar steam generation system for clean water production[END_REF]. Water evaporation systems improve evaporation compared to a system without materials and therefore have attracted much attention and a wide variety of materials have been developed [START_REF] Zhao | Materials for solar-powered water evaporation[END_REF].

Heat transfer is the driving force of the evaporation phenomenon and its study is the key to optimize performance of the evaporation process [START_REF] Meng | Interfacial Radiation-Absorbing Hydrogel Film for Efficient Thermal Utilization on Solar Evaporator Surfaces[END_REF][START_REF]Hierarchically structured evaporator with integrated water supply and evaporation layers to retard salt accumulation -ScienceDirect[END_REF][START_REF] Md | Waste Egg Tray and Toner-Derived Highly Efficient 3D Solar Evaporator for Freshwater Generation[END_REF]. A water evaporation system consists of a material that has high absorption of light radiation to allow maximum utilisation of the incoming energy. In the literature, three configurations have been proposed. The first configuration consists of an absorbing material placed at the bottom of the water [START_REF] Dwivedi | Experimental validation of thermal model of a double slope active solar still under natural circulation mode[END_REF][START_REF] Mahdi | An experimental wick-type solar still system: Design and construction[END_REF]. In the second configuration, the material is dispersed in the water as a powder, giving a black tint to the bulk water [START_REF] Zhang | Direct solar steam generation system for clean water production[END_REF][START_REF] Hota | Activated carbon dispersion as absorber for solar water evaporation: A parametric analysis[END_REF]. In the last and most efficient configuration, the material is placed on top of the bulk water. In this case, after absorption of sunlight, the heat must remain at the top of the material, where evaporation occurs, to increase the surface temperature and thus the vapour pressure. To keep the heat at the evaporative surface, thermal insulation is placed between the bulk water and the evaporative material [START_REF] Li | Harvesting conductive heat loss of interfacial solar evaporator for thermoelectric power generation[END_REF]. In this case, thin materials such as cotton or other water transport media can be used to transfer the bulk water to the evaporation interface [START_REF] Liao | Lotus leaf as solar water evaporation devices[END_REF]. Therefore, the thin material is placed on an insulating layer to allow it to float and increase the evaporation rate [START_REF] Xu | Mushrooms as Efficient Solar Steam-Generation Devices[END_REF][START_REF] Li | Graphene oxide-based efficient and scalable solar desalination under one sun with a confined 2D water path[END_REF]. Alternatively, some materials such as wood show good insulating and water transport properties, and they can be placed in direct contact with bulk water. By using India ink to enhance the sunlight absorption of basswood, a production of 1.6 kg.m -2 .h -1 under 1 sun illumination was achieved [START_REF] Zhang | Chinese ink enabled wood evaporator for continuous water desalination[END_REF]. Another example achieved 1.5 kg.m - 2 .h -1 under 1 sun illumination with a flame-treated coconut [START_REF] Li | Evaporation efficiency monitoring device based on biomass photothermal material for saltresistant solar-driven interfacial evaporation[END_REF]. 3D structures have also been used

to increase the exchange area with reported values higher than 10 kg.m -2 .h -1 [START_REF] Finnerty | Interfacial Solar Evaporation by a 3D Graphene Oxide Stalk for Highly Concentrated Brine Treatment[END_REF][START_REF] Xu | All-in-one polymer sponge composite 3D evaporators for simultaneous high-flux solar-thermal desalination and electricity generation[END_REF]. Although numerical simulations have been implemented for solar evaporation systems [START_REF] Wang | Enhancing solar steam generation using a highly thermally conductive evaporator support[END_REF][START_REF] Zhao | Highly efficient solar vapour generation via hierarchically nanostructured gels[END_REF][START_REF] Menon | Enhanced solar evaporation using a photo-thermal umbrella for wastewater management[END_REF], they have been limited to verifying certain aspects of their design, such as temperature distribution, airflow velocity, water diffusion or geometry.

Most of the studies reported in the open literature focus on the development of materials from a chemical or structural point of view without addressing the impact of material properties on the overall performance. In order to understand the phenomena undergone and to optimise these systems, a two-dimensional axisymmetric model of a tannin-based foam solar evaporator was developed in a previous study [START_REF] Fillet | Modelling heat and mass transfer in solar evaporation systems[END_REF], including a set of boundary conditions and water transport in the porous medium. The latter study helped to validate the previously recommended conditions for measuring evaporation performance [START_REF] Li | Measuring Conversion Efficiency of Solar Vapor Generation[END_REF], namely an air temperature of about 25 °C and a relative humidity of less than 60 %.

The present study utilises the previously used tannin foam with an optimised configuration. In our previous study [START_REF] Fillet | Modelling heat and mass transfer in solar evaporation systems[END_REF], the foam was placed directly on top of liquid water, whereas here the foam is placed on top of an insulator to limit the downward heat loss and increase the surface temperature of the foam. The previous model has been modified accordingly and is used to study specific material properties, such as sunlight absorption, water transport and thickness of the porous structure and the insulating wall. In a first step, the validation of the model against the experimental data is performed with a cyclic evolution of lighting conditions to simulate the day and night phases and, in a second step, a parametric study is performed on the material properties and the geometry of the system. Finally, a temporal study of evaporation during a summer day for the city of Paris is performed. This is followed by the determination of water evaporation over a full year and the study of the impact of latitude, temperature and relative humidity for several cities around the world using our tannin-derived foam.

MATERIALS AND METHODS

EVAPORATION MATERIAL

The tannin used to produce the foam was extracted from the bark of the mimosa tree (Acacia Mearnsii) using an industrial process, and the synthesis of the foam from this tannin is described elsewhere [START_REF] Tondi | Tannin-based carbon foams[END_REF][START_REF] Marie | First approach for modelling the physical foaming of tannin-based thermoset foams[END_REF]. The foam was then cut to the appropriate size (58 mm diameter and 2 mm thick)

and can be seen in Figure 1.

Figure 1. Experimental setup with a photo of the tannin foam in the upper right frame.

EXPERIMENTAL PROTOCOL AND MEASUREMENT METHODS

The experiments were conducted using a solar light simulator (SOLAR LIGHT LS-1000) to illuminate a beaker (60 mm diameter) filled with distilled water: see Figure 1. The tannin foam was on a cotton layer wrapped around a polystyrene foam for insulation between the evaporation and water surfaces. The system was placed on a Sartorius ENTRIS balance accurate to the milligram to monitor the overall mass of the system and thus the evaporation rate. In addition, a thermal camera (OPTRIS PI) pointing to the top of the beaker was used to measure the surface temperature. Ambient temperature and humidity conditions were also monitored during the experiment using a sensor placed in the room. The solar simulator was first calibrated to deliver 1000 W.m -2 of solar light and the beaker was wrapped with the insulation layer and filled with water and, the evaporation system was placed on its surface. It was then positioned on the balance to record the evolution of the water mass over two six-hour cycles (Figure 2a), during which the sunlight was switched on for the first three hours and off for the last three hours. The evolution of the mass over time was used to calculate the evaporation rate and to compare the experimental results to those predicted by the numerical model. The evolution of heat and mass could thus be followed with the variation of the solar concentration. The overall system efficiency was calculated using Eq.1.

𝛈 = 𝐦̇[𝐡 𝐯 𝐜 𝐩,𝐯 (𝐓 𝐓 𝐫𝐞𝐟 )] 𝐏 𝐬

Eq. 1

with ℎ the vaporisation enthalpy (kJ.kg -1 ), 𝑐 , the thermal capacity of water vapour (J.kg -1 .K - 1 ), 𝑇 the reference temperature (273.15 K), 𝑃 (W.m -2 ) the sunlight power on earth per unit area and 𝑚̇ (kg.m -2 .h -1 ) the evaporation rate, calculated as follows :

𝐦̇= 𝟏 𝐒 𝐢 ∫ 𝐅 𝐦 𝐝𝐒 𝐒 𝐞 𝟎 Eq. 2
with 𝑆 (m 2 ) the projected area that is irradiated by sunlight, 𝑆 (m 2 ) the evaporation surface and 𝐹 the boundary mass flux calculated later in Eq.10.

In the literature, a typical result is an evaporation rate coupled with an efficiency, for a given solar energy concentration. Theoretically, an efficiency of 100 %, knowing that the enthalpy of evaporation of water is 2450 kJ.kg -1 (at standard temperature and pressure), gives an evaporation rate 𝑚̇ of 1.47 kg.m -2 .h -1 for a received solar energy of 1 sun. This represents the theoretical evaporation limit for these conditions, if the material were perfect. It should be noted, however, that this does not take into account the thermal exchanges with the exterior.

PHYSICAL AND NUMERICAL MODEL

COMSOL 6.0 was used to build a 2D axisymmetric model of the system. Rectangles were used to model the bulk material and water (red and blue in Figure 2, respectively). Heat transfers occur in the overall geometry while mass transfers occur only in evaporative material. Boundary conditions at the surface include solar illumination, air convection and water evaporation. Air convection occurs at the sides and conduction occurs at the bottom. All input parameters used for the system simulation are gathered in Table 1.

General equations for the evaporative material

The mass transfer was described by the diffusion of water into the material. A transient equation was used to allow the material to dry out and thus reduce surface evaporation when it is no longer saturated. This equation was obtained by maintaining liquid water inside the material (Eq. 3).

𝛒 𝐰 𝛛𝛆 𝐥 𝛛𝐭 + 𝛁 ⃗ . 𝐦̇𝐰 ⃗ + 𝐦̇𝐯 ⃗ = - 𝛛 𝛆 𝐠 𝛒 𝐯 𝛛𝐭 Eq. 3
where 𝜀 is the liquid volume fraction, 𝜀 is the gas fraction, 𝜌 is the density of liquid water (kg.m - ³), 𝜌 is the density of vapour (kg.m -³) and 𝑚̇ and 𝑚̇ are the mass fluxes of water and vapour (kg.m -2 .s -1 ), such as :

𝐦̇𝐰 ⃗ = -𝛒 𝐰 𝐃 𝐰 𝛁 ⃗ 𝛆 𝐥 Eq. 4 𝐦̇𝐯 ⃗ = -𝛒 𝐠 𝐃 𝐯 𝛆 𝐠 𝝉 𝒐 𝝋 𝛁 ⃗ 𝛒 𝐯 𝛒 𝐠 Eq. 5
where 𝜌 is the density of gas defined as a mixing of dry air and vapour at atmospheric pressure (kg.m -³), 𝐷 (m².s -1 ) is the diffusion coefficient of water in the material, 𝐷 (m².s -1 ) is the diffusion coefficient of vapour in the air, 𝜑 (dimensionless) is the porosity of the material and o (dimensionless) the tortuosity of the material.

The heat and mass transfer that occurs during the evaporation process was simulated using two state variables, the temperature, T, and the volume fraction of liquid in the pores, εl, with the energy and mass conservation equations (Eq. 3 and Eq. 6, respectively). The energy associated with mass transfer was assumed to be negligible due to the very slow kinetics of this phenomenon.

𝛒 𝒎 𝐜 𝐩,𝐦 𝛛𝐓 𝛛𝐭 + 𝛁 ⃗ . -𝛌 𝐦 𝛁 ⃗ 𝐓 + 𝐦̇𝐰 ⃗ 𝐜 𝐩,𝐰 (𝐓 -𝐓 𝐫𝐞𝐟 ) + 𝐦̇𝐯 ⃗ 𝐜 𝐩,𝐯 (𝐓 -𝐓 𝐫𝐞𝐟 ) + 𝐡 𝐯 = - 𝛛 𝛆 𝐠 𝛒 𝐯 𝛛𝐭 𝐡 𝐯 Eq. 6
where 𝜌 is the density of the material (kg.m -³), 𝑐 , is the thermal capacity of the material (J.kg - 1 .K -1 ), 𝜆 is the thermal conductivity of the material (W.m -1 .K -1 ), 𝑐 , is the thermal capacity of water (J.kg -1 .K -1 ), 𝑇 is the reference temperature (273.15 K), 𝑐 , is the thermal capacity of the vapour (J.kg -1 .K -1 ), ℎ is the vaporisation enthalpy (kJ.kg -1 ) and 𝜌 is the density of the vapour (kg.m -³)

General equations for bulk water, beaker and insulation

In the other parts of the system, the beaker, the bulk water and the outer insulation as well as the insulation between the water and the material, there is only heat transfer:

𝛒 𝒊 𝐜 𝐢 𝛛𝐓 𝛛𝐭 + 𝛁 ⃗ . -𝛌 𝐢 𝛁 ⃗ 𝐓 = 𝟎 Eq. 7
where 𝜌 is the density (kg.m -³), 𝑐 . is the thermal capacity (J.kg -1 .K -1 ) and 𝜆 is the thermal conductivity (W.m -1 .K -1 ) of the component i (water, beaker or insulation).

Boundary conditions

At the surface boundary (Eq. 8), the heat exchange takes into account air convection, sunlight radiation and heat loss due to water evaporation. The latter involves the energy required for evaporation (enthalpy of vaporisation of water, ℎ in J.kg -1 ) multiplied by the evaporation rate 𝑚̇ in kg.m -2 .h -1 .

-𝐧 ⃗. -𝛌 𝐦 𝛁 ⃗ 𝐓 = 𝐡 𝐜 (𝐓 𝐚 -𝐓) + 𝐅 𝐦 [𝐜 𝐩,𝐯 (𝐓 -𝐓 𝐫𝐞𝐟 ) + 𝐡 𝐯 ] + 𝐏 𝐬 + 𝐄 𝐦 𝛔 𝐓 𝐚 𝟒 -𝐓 𝟒 Eq. 8

with 𝜆 (W.m -1 .K -1 ) the thermal conductivity of the material, ℎ (W.m -2 .K -1 ) the convection coefficient at the surface, 𝑇 (K) the air temperature , 𝐸 (dimensionless) the emissivity of the material and 𝜎 (5.67 ×10 -8 W.m -2 .K -4 ) the Stefan-Boltzmann constant. -𝑛 ⃗ represents the unit vector normal to the boundary.

At the upper surface, water evaporation was described by the following equation:

-𝐧 ⃗. 𝐦̇𝐰 ⃗ + 𝐦̇𝐯 ⃗ = 𝐅 𝐦 Eq. 9

Finally, 𝐹 was deduced from the difference between the water concentration at the material surface and the air and was calculated as follows [START_REF] Nicolas | Modeling bread baking with focus on overall deformation and local porosity evolution[END_REF]:

𝐅 𝐦 = -𝐤 𝐦 𝐌 𝐑 𝐏 𝐰 𝐯,𝐬𝐚𝐭 𝐓 𝐚 𝐰 -𝐇 𝐑 𝐏 𝐚 𝐯,𝐬𝐚𝐭 𝐓 𝐚
Eq. 10

where 𝑀 (18 × 10 -3 kg.mol -1 ) is the molar mass of water, 𝑅 (8.314 J.mol -1 .K -1 ) is the universal gas constant, 𝑃 , (Pa) and 𝑃 , (Pa) are the water vapour pressures at the local temperature, 𝑇 (K), and at the air temperature, 𝑇 (K), respectively, 𝑎 (dimensionless) is the water activity, 𝐻 (%) is the relative humidity and 𝑘 (m.s -1 ) is the convective mass exchange coefficient, calculated using the Colburn analogy [START_REF] Cengel | Heat Transfer a practical approach[END_REF]:

𝐤 𝐦 = 𝐡 𝐜 𝟏𝟎𝟎𝟎 Eq. 11
Besides, 𝑃 , and 𝑃 , were calculated from the Clapeyron formula as follows:

𝐏 𝐱 𝐯,𝐬𝐚𝐭 = 𝐏 𝟎 𝐞𝐱𝐩 𝐡 𝐯 𝐑 𝐌 𝟏 𝐓 𝟎 - 𝟏 𝐓 Eq. 12
where 𝑃 is the reference pressure, 1 atm, and 𝑇 is the boiling point of water, 373.15 K.

The heat exchange between the air and the insulation takes place by convection and radiation:

-𝐧 ⃗. -𝛌 𝐢 𝛁 ⃗ 𝐓 = 𝐡 𝐜,𝐬 (𝐓 𝐚 -𝐓) + 𝐄 𝐬 𝛔 𝐓 𝐚 𝟒 -𝐓 𝟒 Eq. 13

where 𝜆 is either 𝜆 , 𝜆 or 𝜆 depending on the location, ℎ , (W.m -2 .K -1 ) is the convection coefficient on the side and 𝐸 (dimensionless) is the emissivity of the beaker side.

At the interface between the balance and the bottom of the insulation, only a convective heat flow was assumed:

-𝐧 ⃗. -𝛌 𝐛 𝛁 ⃗ 𝐓 = 𝐡 𝐜,𝐛 (𝐓 𝐚 -𝐓) Eq. 14

where ℎ , (W.m -2 .K -1 ) is the convection coefficient at the bottom of the beaker.

At the interface between the water and the material, as the material was considered saturated, the liquid fraction was set equal to the porosity, and thermal continuity was assumed.

𝛆 𝐥 = 𝛗 Eq. 15

where 𝜑 is the porosity of the material.

The calculated variables, T and 𝜀 , were obtained by using the commercial software COMSOL Multiphysics 6.0. A mesh consisting of 1517 elements was used (Figure 2b) to model the entire system (beaker, insulation foams, water and evaporation material). The evaporating surface area was divided into smaller elements to have a better accuracy, and 59 elements were used for this purpose. The rest of the mesh was created automatically by the software, depending on the physics

involved. An internal parametric study on the number of mesh elements was performed. The mesh presented here offers the most interesting compromise between simulation time and calculation accuracy. Using a desktop computer with two Xeon Silver 4214R CPUs (24 cores) combined with 256 GB of RAM, the model was computed in 48 seconds.

RESULTS AND DISCUSSION

MODEL VALIDATION

In order to validate the model, experiments were conducted and the ambient conditions of these experiments (𝑇 and 𝐻 ) were set as parameters in the simulation. Figure 3 shows the simulated and experimental results of the temperature, measured at the evaporation surface, as well as the simulated and experimental evolution of the water mass of over time.

During the first phase of illumination, the evaporation rate is 1.17 kg.m -2 .h -1 and the average surface temperature reaches 35°C after the three-hour period. During the second period, when the sunlight is switched off, the evaporation rate is 0.34 kg.m -2 .h -1 and the average surface temperature after three hours is about 18°C. Overall, the cycles are well visible and the simulation fits for the evolution of the water mass well. The calculated surface temperature shows a slight difference, which is due to temperature variations. We can therefore validate the model and conclude that it can be used to simulate the behaviour of the evaporation system over time. 3.2 PARAMETRIC STUDY

Solar flux absorption coefficient

One parameter that can vary depending on the type of material is the absorption of sunlight by its surface. Typically, materials achieve absorption values above 95% for maximum solar energy utilisation [START_REF] Zhang | Direct solar steam generation system for clean water production[END_REF][START_REF] Du | A floating vapor condensation structure in a heat-localized solar evaporation system for facile solar desalination[END_REF][START_REF]Biomimetic Hybridization of Janus-like Graphene Oxide into Hierarchical Porous Hydrogels for Improved Mechanical Properties and Efficient Solar Desalination Devices[END_REF]. A parametric study was conducted to investigate the impact of this parameter on performance.

Figure 4a shows the evaporation rate and efficiency as a function of surface absorption of sunlight.

A gain of 0.1 in sunlight absorption results directly in a gain of 0.1 kg.m -2 .h -1 in evaporation rate and 5% in efficiency. This represents a loss of evaporation performance of 11%, which means that the improvement in surface absorption makes sense.

Thickness of the porous structure

Some types of materials allow for different thicknesses to be chosen during manufacture. Wood, for instance, can be set to a certain thickness [START_REF] Yu | Enhancing efficiency of carbonized wood based solar steam generator for wastewater treatment by optimizing the thickness[END_REF], while a lotus leaf has a fixed thickness [START_REF] Liao | Lotus leaf as solar water evaporation devices[END_REF][START_REF] Fang | Hierarchical Porous Carbonized Lotus Seedpods for Highly Efficient Solar Steam Generation[END_REF].

For a material with a controlled thickness (wood, foam etc.), there is an optimal value for its use as an evaporation material. Figure 4b shows the simulated evaporation rate and efficiency as a function of thickness, from half a centimetre to several centimetres. Overall, the evaporation rate increases with the material thickness, but a local maximum can be seen at 3 cm. This is due to the fact that, with increasing material height, water transport starts to be a limiting factor. In addition, the thicker the foam, the higher the evaporation area. Thus, until water transport becomes a limiting factor, the evaporation rate increases. For thicknesses greater than 3 cm, water transport is limited, so that only lateral evaporation increases until a maximum is reached and water can no longer progress through the foam. However, this does not increase the overall evaporation rate since the evaporation rate at the surface decreases with thickness This is clearly visible in Figure 4c for the 6 cm and 10 cm cases. The water activity at the surface is low, meaning that the surface is dry. For 3 cm, the water activity is still close to 1, so evaporation is still possible. The increase in evaporation with thickness up to a certain point correlates with recent studies that have been conducted to harness the maximum transportability of water [START_REF] Finnerty | Interfacial Solar Evaporation by a 3D Graphene Oxide Stalk for Highly Concentrated Brine Treatment[END_REF].

Diffusion coefficient of liquid water

Diffusion within the evaporative material is essential, because even if energy management at the surface is effective, insufficient water will prevent evaporation from occurring, as it has been shown in 3.2.2. To simulate the unavailability of water at the surface, a parametric study of the water diffusion coefficient within the porous structure was conducted.

Figure 5a shows the results of the evaporation rate and efficiency as a function of the diffusion coefficient. Little change is visible when water transport is sufficient (above 10 -9 m.s -1 ). However, below this value of diffusion coefficient, the evaporation rate is strongly impacted by the limited water transport, decreasing from 1.0 kg.m -2 .h -1 to 0.6 kg.m -2 .h -1 for a diffusion coefficient of 10 -9 m.s -1 and 10 -10 m.s -1 , respectively. This phenomenon can be explained by the fact that, with a low diffusion coefficient, the water does not reach the surface (Figure 5d), resulting in a decrease in evaporated flux (Figure 5b) and an increase in surface temperature (Figure 5c). After 2 hours, the surface of the foam is completely dry for a diffusion coefficient of less than 10 -9 m.s -1 , while the water uptake stabilises at 86%, which still allows water to reach the surface, for a coefficient of 10 - 9 m.s -1 .

Thickness of the insulating wall

Since external conditions affect evaporation performance [START_REF] Fillet | Modelling heat and mass transfer in solar evaporation systems[END_REF], it may be worthwhile to add a layer of insulating foam to focus on studying the performance of the material at the surface where evaporation occurs. Figure 6a shows the performance of the system as a function of the thickness of the insulating foam, with a thermal conductivity of 0.043 W.m -1 .K -1 , around the beaker. The evaporation rate increases until it stabilises at about 1.04 kg.m -2 .h -1 , which represents a 4% increase compared to the system without thermal insulation. This is due to the fact that energy is no longer lost through the sides of the material, which increases the surface temperature and thus the evaporation rate (Figure 6b). However the increase is minimal compared to a previous study [START_REF] Fillet | Modelling heat and mass transfer in solar evaporation systems[END_REF],

because an additional insulating layer is used between the water and the evaporating material.

Exchanges through the side of the beaker are carried out with already insulated bulk water.

Water evaporation potential

In the literature, experimental measurements are performed in a controlled environment with constant simulated solar radiation, or outdoors in a chamber (or under a bell jar or in a solar still)

subjected to solar radiation that varies throughout the day. This section proposes to simulate the behaviour of the evaporator illuminated by real solar radiation and to estimate the potential water evaporation of this system if it were located in large cities in the northern hemisphere.

Temporal evolution in Paris

Figure 7 shows the evolution of solar radiation, efficiency, surface temperature and evaporation rate for four 21 st of the month, from winter to summer solstice. Sunshine data from Paris (France -Latitude 48°51′12″) were used [START_REF] Honsberg | Photovoltaics Education Website[END_REF] as well as air temperature and humidity data throughout 2021 [START_REF]MERRA-2 tavg1_2d_slv_Nx: 2d,1-Hourly,Time-Averaged,Single-Level,Assimilation[END_REF]. As expected, the evaporation rate increases with solar radiation. It should be noted that a phase shift is observed between the solar radiation and the evaporated flux. Indeed, the maximum evaporation does not occur at the time when the solar flux is the most important, the maximum is at 13h for evaporation while the solar flux is maximum at 12h. It should be noted that solar time is considered here, i.e., for which the sun is at its zenith at noon. Considering the calculation of the efficiency (Eq. 1), the value calculated at the beginning and end of the day is inconsistent because it implies a sunshine close to 0. Nevertheless, an overall increase in efficiency is observable during the day and is maximal in the afternoon (Figure 7b). The increase in efficiency at the beginning and end of the day can be explained by Eq. 1, which shows a decreasing illumination until it reaches zero, thus mathematically increasing the efficiency value. This phenomenon and the observed phase shift are due to the temperature at the evaporation surface increasing with the concentration of solar radiation (Figure 7a) and the thermal energy stored in the material (Figure 7c), which enhances evaporation (Eq. 10 and Eq. 12). The total potential evaporation on a summer day (21 st June) is 12 L per m 2 of the present tannin foam.

Annual potential water evaporation for different locations on earth

Figure 8 shows the annual and monthly evaporation per unit area simulated for different locations on the planet. In these calculations, direct radiation is changed as well as local air temperature and humidity, taken throughout the year [START_REF]MERRA-2 tavg1_2d_slv_Nx: 2d,1-Hourly,Time-Averaged,Single-Level,Assimilation[END_REF]. The monthly calculation was made for a typical day corresponding to the 21 st of the month in order to take into account the summer and winter solstices.

The annual calculation was performed by summing the evaporated quantities of all months of the year, the monthly value being considered constant. The monthly results show significant variations with the latitude of the city studied. Indeed, cities located near the poles show almost no evaporation during winter and evaporation close to other latitudes during the summer, since the sun shines almost all day in Reykjavik in summer time, for example (Figure 9a). On the contrary, cities located near the equator offer similar evaporation performance all year round, about 8.5 kg.m - 2 for Quito from December to June, which is due to the constant illumination throughout the year (Figure 9g). Indeed, between the northernmost capital city, Reykjavík, and a city located on the equator, Quito, there is a 76% increase in annual evaporation. However, evaporation is not only related to latitude, as local ambient conditions, relative humidity and temperature also have a significant impact on evaporation, as has been shown previously [START_REF] Fillet | Modelling heat and mass transfer in solar evaporation systems[END_REF]. Dubai, for instance, is located 25° north of Quito and has a 72% higher annual evaporation, which is due to the fact that the local air is much drier and the average temperature is higher throughout the year, as shown in Figure 9e and Figure 9h.

In Figure 8b, we can observe that the simulated annual freshwater production increases at low latitudes with an arid climate, with the highest theoretical evaporation located in Dubai with 5342 kg.m -2 , followed by Cairo with 4723 kg.m -2 . For the other cities selected, Beijing, Paris or Moscow, evaporation decreases with latitude. Figure 8d shows that the annual amount of water produced is not directly linear with latitude, as warmer climates have higher evaporation values compared to the trend observed for other cities as a function of latitude. This Figure shows that there can be a dispersion in the amount of water recovered for the same latitude. Figure 8e shows that the main factor impacting on the amount of water produced is temperature with a linear trend with the annual average temperature and therefore with the climate. Climate, all others ○ (colours as in a); and of (e) the average air temperature the for the cities studied. Using a two-dimensional axisymmetric model that was validated for temperature and water mass changes as a function of time, several phenomena were explored. These included the effect of three material properties: water diffusion coefficient, material thickness and surface light absorption coefficient. Foam thickness, diffusion coefficient and light absorption have been shown to be key factors. By increasing the area available for evaporation, thickness directly increases the performance until the material can no longer diffuse water. The diffusion coefficient allows for the presence of liquid water, because if it is too low, not enough water can be transported to the surface, and light absorption improves energy consumption and therefore performance. The study of the thickness of insulation around the measuring system shows that evaporation is no longer improved above a certain thickness and that the presence of insulation between the bulk water and the evaporation surface decreases the usefulness of the added insulating layer around the beaker.

A typical summer day in Paris was also evaluated, and we show that the theoretical potential amount of water evaporated would be 12 L per m 2 of foam area, using the (non-optimised) rigid foam used here to validate the model. The simulated evolution of the evaporation rate at different locations of the planet shows that latitude has a significant impact on the performance in winter.

Ambient temperature and humidity conditions also play a major role in evaporation performance.

Dubai, for instance, is located 25° north of Quito and has 72% higher annual evaporation, which is due to the fact that the local air is much drier and the average temperature is higher throughout the year.

Figure 2 .

 2 Figure 2. a) Types of heat exchange at the boundaries of the water evaporation system and b)

Figure 3 .

 3 Figure 3. (a) Experimental (red dots) and simulated (blue line) mass changes, and (b)

Figure 4 .

 4 Figure 4. (a) Simulated evaporation rate and efficiency for different solar flux absorption

Figure 5 .

 5 Figure 5. (a) Simulated evaporation rate and efficiency for different values of water diffusion

Figure 6 .

 6 Figure 6. (a) Evaporation rate and efficiency; and (b) surface temperature as a function of the

Figure 7 .

 7 Figure 7. (a) Simulated hourly evolution of solar radiation; (b) efficiency; (c) surface temperature

Figure 8 .

 8 Figure 8. (a) Map [33] of locations used to estimate simulated (b) yearly and (c) monthly

Figure 9 .

 9 Figure 9. Simulated evolution of: (a), (d) and (g) solar radiation; (b), (e) and (h) surface

Table 1 .

 1 Input parameters used in the simulation.

	Symbols	Definitions	Units	Values
	𝜆 , 𝜆 , 𝜆 ,	Thermal conductivities of water, skeleton of the	W m -1 K -1	0.6, 0.32,
	𝜆 , 𝜆	evaporation material, air, insulating material and		0.0262, 0.043,
		beaker		1.38
	𝜑	Porosity of the evaporation material	-	0.955
	𝑐 , , 𝑐 , , 𝑐 , ,	Heat capacities of water, vapour, evaporation	J K -1 kg -1	4180, 1890,
	𝑐 , , 𝑐 ,	material, insulating material and beaker		1800, 871, 703
	Dw	Coefficient of diffusion of water inside the	m 2 s -1	10 -8
		material
	Dv	Coefficient of diffusion of vapour in the air	m 2 s -1	2.82 × 10 -5
	𝜌 , 𝜌 , 𝜌	Density of water, skeleton density of the	kg m -3	1000, 1550, 30
		evaporation material and bulk density of the
		insulating material
	𝜎	Stefan-Boltzmann constant	W m -2 K -4	5.67 × 10 -8

ACKNOWLEDGEMENT

This work was partially supported by the French Ministry of the Armed Forces -Defence Innovation Agency and the TALiSMAN2 project (ERDF-LO0022687). This study was presented and published in the proceedings of the 15 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT2021), online, 26 -28 July 2021.


Rachid Ridouane¹
email: rachid.ridouane@univ-paris3.fr

Phil Hoole²
email: hoole@phonetik.uni-muenchen.de

Susanne Fuchs³
email: fuchs@zas.gwz-berlin.de

LARYNGEAL BEHAVIOR IN VOICELESS WORDS AND SENTENCES: A PHOTOELECTROGLOTTOGRAPHIC STUDY

Keywords: (gestural aggregation, laryngeal gestures, voiceless words) f s f s

An important challenge in the study of speech production is to gain theoretical understanding of how laryngeal and supralaryngeal movements are coordinated, and to determine which factors influence this coordination. This study investigates how these movements are coordinated during the production of completely voiceless words and sentences in Tashlhiyt Berber. Results show that the glottis does not simply remain open but that glottal aperture is continuously modulated in a manner that can be related quite systematically to the phonetic nature of the segments present in the sequence.

INTRODUCTION

This study investigates the nature of laryngeal and supralaryngeal adjustments during the production of Tashlhiyt Berber words and sentences composed of voiceless obstruents only. An important challenge in the study of speech production is to gain theoretical understanding of how supralaryngeal and laryngeal movements are coordinated, and to determine which factors influence this coordination. Understanding this is of special interest in creating models of speech production as well as in uncovering the relations between phonetic and phonological specifications. Voiceless consonant sequences are of special importance in handling this issue since the production of such clusters requires specific coordinated activities of the laryngeal and supralaryngeal articulatory movements.

Numerous studies have shown that the coordination between laryngeal and supralaryngeal events plays a major role in accomplishing the phonemic distinction of voicing and aspiration in several languages. In addition to the study of single phoneme combinations, other studies, though less numerous, have also focused on finding out how voiceless consonant clusters are organized at the level of the glottis. Germanic languages (English, German, Icelandic, and Swedish) are by far the most studied languages. Pétursson [START_REF] Pétursson | Timing of glottal events in the production of aspiration after [s][END_REF], Löfqvist and Yoshioka [START_REF] Löfqvist | Laryngeal activity in Swedish obstruent clusters[END_REF], Yoshioka et al. [START_REF] Yoshioka | Laryngeal adjustments in the production of consonant clusters and geminates in American English[END_REF], and Jessen [START_REF] Jessen | Redundant aspiration in German is primarily controlled by closure duration[END_REF], for example, observed glottal adjustment and the number of glottal abduction gestures in fricative-stop clusters separated by word boundaries. A comparable study has also been conducted on similar data drawn from Tashlhiyt Berber [START_REF] Ridouane | Laryngeal adjustments in the production of voiceless obstruent clusters in Berber[END_REF]. One major generalization that came out from this study was that sequences produced with n fricatives are most often produced with n peak glottal openings; these peak glottal openings are located during the production of these fricatives. These results are in general agreement with those obtained from some of the Germanic languages mentioned above. We thus have additional evidence from different unrelated languages that laryngeal activity during the production of voiceless obstruent clusters is organized in several glottal-opening peaks and that the manner of articulation of obstruents and their position in the cluster play an important role in determining both the number and the location of these peaks (in addition to speech style, etc.).

This study follows up on the examination of how laryngeal and supralaryngeal adjustments are coordinated during unvoiced clusters. We will focus on much more complex clusters, since the data examined include completely voiceless words and sentences. How are such words organized at the glottal level? Knowing that these items are produced with no vocal folds vibration, one may expect that the "devoicing gesture" may be considered by the speakers as superfluous and simply eliminated, leaving the glottis in constant opening degree. If, on the other hand, the glottal aperture is rather continuously modulated, it will be important to determine the nature of these modulations and the mechanisms that govern them. This study may thus provide important insight into coarticulatory phenomena at the level of laryngeal adjustments and provide evidence for the interpretation that a static glottal opening position of the glottis is unlikely to occur (e.g. Munhall & Löfqvist [START_REF] Munhall | Gestural aggregation in speech: laryngeal gestures[END_REF], Yoshioka et al. [START_REF] Yoshioka | Laryngeal adjustments in the production of consonant clusters and geminates in American English[END_REF]), since we included combinations of up to 15 voiceless consonants in our data.

METHOD AND PROCEDURE

Two male native speakers of Tashlhiyt Berber (RR and RF) were recorded by means of simultaneous transillumination, fiberoptic filming, and acoustic recordings. Acoustic and transillumination data have a sampling frequency of 24 kHz, transillumination data were further downsampled to 200 Hz, and the fiberoptic data have the standard video format of 25 i/s. An example of our data is presented in Figure 1. The top panel shows the acoustic waveform of the form [ftWt] "roll it" (embedded in a carrier sentence). The second panel shows the glottographic pattern, which indicates the duration, degree, and number of glottal-opening peaks. The vertical axis shows the amount of light in arbitrary unit. In this figure, we can see that two glottal-opening peaks were produced, being located during the production of the fricatives /f/, and /W/. The third panel indicates the velocity of glottalopening and -closing gestures (i.e. the derivative of the transillumination data). The number of glottal-opening peaks in voiceless words was calculated algorithmically as the number of (negative) zero crossings in the velocity signal. The number of peaks averaged over all repetitions is indicated in the following figures with ensemble-averaged data (voiceless sentences were not averaged). To obtain some further basic information on the shape of the glottal movements, we also counted the number of positive velocity peaks during opening movements and the number of negative velocity peaks in closing movements. The simplest movements are those in which each glottal-opening peak is associated with exactly one positive and one negative velocity peak. The speech material consisted of 17 voiceless words and 3 voiceless sentences, embedded in a carrier sentence "inna … jat twalt" (he said … once). The whole data consisted of 208 tokens. 3. Rtf "crush" (7,5)

6. tkkststt "you took it off" (7, 5) 3. fkt "give it" (7, 5) 6. tssftWt "you made him roll" (5, 4) 3. kst "feed it on" (7, 5) 6. tsskRft "you dried" (6, 4) 3. tks "she feeds on" (7, 3) 7. tftWtstt "you rolled it" (7, 5) 4. ftWt "roll it" (7, 5) 7. tftktstt "you sprained it" (7, -) 4. tRtf "she crushed" (8, 2) 8. tssftktstt "you made him sprain it" (7, -) 4. tkst "you feed it on" (-, 2) 8. tssftWtstt "you made him roll" (9, -) 5. tRtft "you crushed" (6, 8) 8. tsskRftstt "you dried it" (7, 6) 6. tfktstt "you gave it" (7, 4) 13. tftktstt tfktstt "you sprained it and you gave it" (7, 5) 14. tsskRftstt tfktstt "you dried it and gave it" (7, 5) 15. tsskRftstt tftWtstt "you dried it and rolled it" (7, 5)

RESULTS

Can the glottis maintain a static open position in speech? Data from Tashlhiyt Berber clearly shows that this is not the case, since glottal area is continuously changing even in completely voiceless sentences (see figure 2 below). We thus have important evidence that the glottis is unlikely to keep a constant opening degree, showing that glottal articulation is "cyclical" in nature. A biomechanical interpretation of this fact has been suggested by Yoshioka et al. [START_REF] Yoshioka | Laryngeal adjustments in the production of consonant clusters and geminates in American English[END_REF].

f t W t

According to them, there is an upper and lower limit on the velocity of glottal opening and closing gestures during speech, and the lower limit implies that a static open position of the glottis is unlikely to occur or at least difficult to maintain, and the glottal aperture is thus continuously modulated. Voiceless words and sentences are produced with multiple glottal opening and closing gestures. These typical continuous gestures are not strictly related to the number of consonants each form contains. As shown in figure [START_REF] Löfqvist | Laryngeal activity in Swedish obstruent clusters[END_REF], the number of glottal opening peaks does not systematically increase as the number of consonants increases (though some trend in this direction is clearly visible). For example, a form composed of four consonants (e.g. [ftWt], see figure 1) may be produced with the same number of glottal opening peaks as a form composed of 7 or 8 consonants (e.g. [tftktstt] see figure 6). Notice also that there are often different numbers of peaks for the same number of segments (compare [ftWt] and [tkst]). Notice that the data discussed so far include only sequences where a fricative is surrounded by stops. In case a sequence contains two adjacent fricatives, these fricatives are often produced with only one peak glottal opening located during the leftmost fricative. This is for instance the case of the form [tsskRftstt] "you dried it", as shown in figure 7. The labial fricative /f/ is produced within the closing phase of the glottal gesture for the preceding fricative and within the opening phase for the following /s/ segment. The general pattern observed in voiceless words may also account for the laryngealsupralaryngeal adjustments observed in voiceless sentences. The form [tftktstt tfktstt], for example, contains four fricatives and is often produced with four glottal opening peaks located during these fricatives. This pattern is illustrated in figure 8 (see also figure 2 for the sentence [tsskRftstt tftWtstt] which contains six non-adjacent fricatives and is produced with six peaks located during these fricatives).

Number of consonants Number of peaks

CONCLUSION

The first important result of this study is that the glottis, even in completely voiceless words and sentences, does not simply remain open, but rather that the glottal aperture is continuously modulated. The second important result is that this laryngeal modulation is quite systematically related to the phonetic nature of the individual segments present in the sequence: segments produced with a high rate of oral airflow are produced with a separate laryngeal-opening gesture. This result is in general agreement with those obtained from some Germanic languages (e.g. [START_REF] Löfqvist | Laryngeal activity in Swedish obstruent clusters[END_REF], [START_REF] Munhall | Gestural aggregation in speech: laryngeal gestures[END_REF]). From these previous investigations, it is clear that the continuous change in glottal opening is actively controlled by muscular activity. This active laryngeal modulation with respect to supralaryngeal events even in clusters up to 15 voiceless obstruents suggests that the larynx and the oral articulators are functionally coupled as a unit during speech. This provides a compelling demonstration of how intimately laryngeal and oral articulations are linked.

Figure 1 :

 1 Figure 1: Acoustic waveform and glottal abduction pattern for [ftWt] as realized by RR.

Figure 2 :

 2 Figure 2: Acoustic waveform and glottal abduction pattern for [tsskRftstt tftWtstt] as realized by RF.

Figure 3 :

 3 Figure 3: The number of glottal opening peaks produced during the production of the 17 voiceless words. Words are arranged following the same order as in table 1.

Figure 4 :

 4 Figure 4: Averaged glottal abduction pattern for the forms [kst] (left) and [tks] (right) as realized by RR. Each figure displays the number of amplitude peaks as well as the number of abduction and adduction velocity peaks. The number of repetitions of each sequence is indicated between parentheses. The dashed lines delimit the onset and offset of each segment.

Figure 5 :

 5 Figure 5: Averaged glottal abduction pattern for the form [tkkststt] as realized by RF. Symbols as in Figure 4.

Figure 6 :

 6 Figure 6: Averaged glottal abduction pattern for the form [tftktstt] as realized by RR. Symbols as in Figure 4.

Figure 7 :

 7 Figure 7: Averaged glottal abduction pattern for the form [tsskRftstt] as realized by RF. Symbols as in Figure 4. The label 'c' stands for the alveopalatal /R/.

Figure 8 :

 8 Figure 8: Acoustic waveform and glottal abduction pattern for [tftktstt tfktstt] as realized by RR.

Table 1 .

 1 Linguistic material. Number of consonants in bold. Numbers within parentheses indicate the number of repetitions, first value for RR and second value for RF.