Mathieu Melich

Jacques Dupont-Roc

Philippe Jacquier

Efficient atomization of cesium metal in solid helium by low energy (10 µJ) femtosecond pulses

Keywords: 67, 80, B-solid 4 He -61, 72, S-impurities in crystals -06, 60, Jn femtosecond techniques

Metal atoms in solid and liquid helium-4 have attracted some interest either as a way to keep the atoms in a weakly perturbing matrix, or using them as a probe for the helium host medium. Laser sputtering with nanosecond pulsed lasers is the most often used method for atom production, resulting however in a substantial perturbation of the matrix. We show that a much weaker perturbation can be obtained by using femtosecond laser pulses with energy as low as 10 µJ. As an unexpected benefit, the atomic density produced is much higher.

Introduction

Over the past twenty years, atomic and molecular impurities in superfluid and solid helium-4 have been extensively studied by spectroscopic methods either in bulk (for a review (1; 2)) or in clusters (3; 4). Among the motivations of those works, one may cite the investigation of superfluidity at a microscopic level (5; 6), the reactions of atoms, molecules, radicals in the helium matrix (7; 8), investigation of matrix excitations by optical methods (5; 9; 10), measurement of electron EDM (11; 2) or parity violating nuclear anapole moment (12). Several methods (recombination (13), laser sputtering (14; 11), jet (15)) have been developped to introduce atomic impurities into bulk helium. Laser sputtering has been quickly recognized as the most efficient method to introduce various atomic species into liquid (14; 11; 16; 9) and solid helium (17). Atomic density about 10 14 -10 15 m -3 has been reported (14; 18). In this method, atomization proceeds in two steps. In the first step, a metal target situated in condensed helium is sputtered that produces metal grains and clusters embedded in the medium. These grains are then atomized by a second laser and detected by a third one. In superfluid, convection flow induced by the sputtering process carries away the atoms from the detection region in a few milliseconds (14). An improvement was later achieved leading to the detection of atomic Cs in superfluid helium over about 500 ms (19). In solid helium, atoms are more efficiently trapped and can be observed during several hours (18) or even a week (20).

Laser sputtering has some drawbacks however. When YAG second harmonic (532 nm) pulses are used, pulse energies about 1-10 mJ are necessary. This creates transient a Present address : Institut Néel-MCBT, CNRS, Grenoble bubbles in the liquid or melting of the solid matrix over a macroscopic volume. These energetic events are likely to strongly perturb the helium matrix. Indeed evidence for the conservation of the global solid orientation is still lacking (21; 20). A first step may consist in reducing the energy brought by the laser.

In this paper a new method is described making use of amplified femtosecond pulses to atomize cesium grains or clusters. Due to much shorter pulse duration, much lower energies (10 µJ) are used to obtain similar or even greater atomic densities than previous methods. To our knowledge, metal atomization with femtosecond pulses has been reported only once (19), but without details about the atomic densities obtained. We describe first the experimental set-up used and the atomization process of cesium impurities in an initially single helium crystal. Atomic densities obtained are then discussed.

Experimental set-up

A sketch of the experimental arrangement is given in figure 1. A 2 cm wide cell is attached to a helium-4 refrigerator. Its temperature can be regulated between 1 and 1.8 K. To grow a hcp helium crystal, liquid helium is pressurized at constant temperature, typically 1.2 K, up to the solidification pressure (25.4 bar). An electrostatic device (22) nucleates the solid phase as a small single crystal which falls on the bottom of the cell. It is then grown by continuously feeding the cell with helium until the liquid/solid interface reaches the middle of the cell windows. In order not to damage the crystal by the first step of the atomization process, we put the cesium target in the liquid above the solid. Sputtering is produced by second harmonic YAG laser pulses (energy 5 mJ, repetition rate 2 Hz). Sub-millimetric cesium grains, and possibly clusters, fall onto the crystal surface. When their number is sufficient, they are embedded into the crystal by a further growth. They lie then 1 or 2 mm below the solid/liquid interface. The next section explains how they are later atomized by femtosecond laser pulses.

In order to measure the local density of cesium atoms, laser induced fluorescence is used. A Ti:Sa laser ('d' in figure 1) can be used in cw or mode-locked regime. In the cw regime, it excites the fluorescence on the D1 line at 850 nm. The absorption line is shifted with respect to the free atom line due to the interaction of cesium atoms with the helium matrix (23). The fluorescence light is collected at right angle, selected by an interference filter centered at 880 nm and its intensity is measured by a cooled APD (Hamamatsu C4777-01). The use of femtosecond laser pulse for metal sputtering or machining is now well documented (24) and various kinds of amplified sources have been described. In the present case, low average power is desirable in order to keep the low temperature sample with a minimal perturbation. Hence we require a low repetition rate and a pulse energy sufficient to atomize metal grains a focal distance of 0.2 m, comparable with the cryostat radius. Pulse energy on the order of a few microjoules is sufficient. Much shorter focal length would allow to reduce this energy, but would require the focusing lens to be located inside the cryostat, which we wanted to avoid for practical reasons. Microjoule pulse energies are intermediate between the nanojoule energies delivered by Ti:Sa oscillators and millijoules currently reached by the chirped pulse amplifiers. Simple lasers are not available for such pulse energy. Hence we built a simple home made multipass unsaturated amplifier which does not require the 100 femtosecond pulse to be chirped. Non-linear effects in the Ti:Sa crystal are kept below the critical value for self-focusing if pulse energy does not exceed 40 µJ. The Ti:Sa oscillator produces 5 nJ, 200 fs pulses at the rate of 70 MHz. A Pockels cell selects one pulse every 0.1 s. It enters a 4f-cavity where it is amplified 6 times in a 1.5 cm Ti:Sa crystal pumped by two 7 mJ second harmonic Nd-YAG pulses. The pulse energy is then 6±2 µJ. Another opportunity is to let all oscillator pulses go through the amplifier. Then trains of about 12 successive pulses are amplified synchronously with the YAG pump pulses. Other Ti:Sa pulses go through the amplifier unaffected. In the time between successive pulses, atoms and clusters have already been expelled few microns away but have had no time to recombine. Hence clusters produced by one pulse may be further atomized by the next ones before being thermalized and possibly recombine. One expects a more efficient atomization in this multi-pulse regime.

Atomization process inside solid helium

Once cesium grains are embedded 2 mm below the crystal surface, atomization with the Ti:Sa laser begins. The wavelength is tuned to 850 nm so that fluorescence of the atoms will be excited. Monitoring the atomization is done by replacing the APD by a fiber/CCD spectrograph (Ocean Optics 4000). Two detection bands are defined. One from 845 to 855 nm measures the incident light scattered by cesium grains and clusters. The other one measures atomic fluorescence from 870 to 890 nm. This LIF detection is specific to cesium monomers. Dimers and trimers do not fluoresce in this band when excited at 850 nm (25). Larger cesium clusters are not known to fluoresce.

Evolution of both intensities during an atomization process are shown in figure 2. The Ti:Sa laser is modelocked with an averaged intensity 50 mW in the cell, with amplified bursts at a rate of 2 Hz. The burst contribution to the average intensity is negligible. During the sequence shown, the focal point of the laser is moved from time to time to explore the region in which clusters are located. This is indicated by gray areas in figure 2. Intensity of elastically scattered light varies strongly according to the focal point location, probably in relation with the presence of grains. Keeping the laser focus at such place and continuing laser irradiation, one observes a slow decrease of the scattered light intensity, while the atomic fluorescence intensity increases strongly. Note the difference in scale (factor 10) for the two intensities : the atomic fluorescence is much stronger. After 20 minutes at this place, the scattered light has nearly disappeared and the atomic fluorescence does not increase anymore. A straightforward explanation is that successive laser pulses break metal grains into smaller and smaller pieces, and finally into atoms. In some cases, no light is scattered, indicating there are no grains while fluorescence does appear after some time. In these situations, source of atoms are very likely clusters. As we will see now, this atomization process is indeed efficient.

Estimate of the atomic density

Once atomic fluorescence intensity is strong enough, a measurement of the fluorescence intensity is made to provide an estimate of the atomic density. The Ti:Sa laser is switched to its cw mode, while keeping its wavelength at 850 nm. The beam is chopped at 173 Hz and the APD output is measured through a lock-in amplifier. The detected fluorescence intensity I det is proportional to the mean atomic density ρ in the region where the two beams intersect, to the laser intensity I exc and to the absorption cross-section σ for the D1 line. More precisely, ρ is given by ρ

= 1 η σ l det κ 4 π Ω I det I exc ( 1
)
where Ω is the solid angle of the collected light (0.12 sr), κ is the transmission efficiency of the detection beam estimated to be 0.38 at 880 nm, η is the fluorescence efficiency for the D1 line measured to be 0.9 at 25 bar (26). This formula takes into account the fact that the waist of Ti:Sa beam in the cell (0. natural linewidth (FWHM) (Γ/2π = 4.5 MHz) to the linewidth in the helium matrix (∆λ ≃ 10 nm). This gives σ ≃ 1.3 × 10 -19 m 2 .

For a 50 µW excitation intensity, we have measured atomic fluorescence intensities up to 8 × 10 -11 W. According to the formula above, this corresponds to an atomic density about 3.4 × 10 18 m -3 . This is about 4 orders of magnitude higher than what have been reported in solid helium (18). We have obtained repeatedly densities over 10 17 m -3 . As already mentionned the atomic density depends strongly on the number and sizes of the metal grains in the sputtered region. One can get densities varying by several order of magnitude for apparently similar conditions. Note that the atomic density does not vary significantly over the time required for the density measurement. As already reported, at 1.0 K, atomic density decays only over several days (20; 29).

Conclusion

We have shown that femtosecond laser pulses with energy as low as 10 µJ are an efficient tool to atomize metals in solid helium. Such low energy pulses with a repetition rate of a few hertz are suitable for experiments at low temperatures below 1 K where the cooling power of helium refrigerators drops down. These pulses can be produced by simple amplifiers without a stretching/compression device. Substantial atomic densities have been obtained, larger than 10 17 atom/m 3 . However we have no evidence that atomization with such low energy pulses still does not damage the crystal order. In a further step we plan to attempt atomization directly above crystal surface, in the liquid, and to grow the crystal from this 'cesium solution'. This should allow for obtaining good quality doped single crystal.

Fig. 1 .

 1 Fig. 1. Sketch of the experimental arrangement. (a) Cell inside the cryostat containing solid He at the bottom, (b) Solid cesium target immersed into HeII, (c) Sputtering YAG laser, (d) Amplified Ti:Sa laser for atomization (mode-locked) or in cw mode for detection, (e) fluorescence detection, (g) cesium metal grains and clusters.

  3 mm) is smaller than the diameter of the area seen by the APD detector (l det = 1.1 mm). The absorption cross-section σ is the resonant cross-section for the D1 line λ 2 /2π (27; 28), scaled by the ratio of the

Fig. 2 .

 2 Fig. 2. Atomic fluorescence (lower sub-figure) and incident light scattered by cesium grains and clusters (upper sub-figure) during an atomization process at 850 nm. The growth of the atomic fluorescence is correlated with the disappearence of the grains scattering the incident light. Gray areas indicate when the laser focus is moved from one place to a new one, free of pre-existing cesium monomers.

We are indebeted to Béatrice Chatel (LCAR, Toulouse) for the loan of the Ti:Sa laser. This work was supported by the ANR contract META (ANR-05-BLAN-0084-02).


Marco Di Renzo

Alexis I Aravanis

Catching the 6G wave by Using Metamaterials: A Reconfigurable Intelligent Surface Paradigm

Smart radio environments empowered by Reconfigurable Intelligent Surfaces

The ever increasing demand for broadband access has pushed wireless networks away from the archetypal wireless network paradigm, where (mainly) outdoor users were served by centralized network entities. As opposed to this approach, emerging B5G network architectures are expected to employ atomised and softwarized network infrastructures in a dispersed, device-centric manner. Moreover, the unabated increase of indoor traffic [START_REF] Wong | A Vision to Smart Radio Environment: Surface Wave Communication Superhighways[END_REF] is pushing for even more disruptive network designs able to provide high quality service even to indoor users, surrounded by urban blockages. Furthermore, the emphasis of the envisaged 6G networks on high frequency bands (e.g. D-band and THz) makes the adverse effect of blockages more acute [2]. In this setup, a fundamentally distinct wireless ecosystem needs to arise, able -to not only overcome the challenges posed by wireless blockages, but more importantly -to satisfy the need for increased spatial bandwidth, i.e. the need of B5G networks to deliver bits per second per m 3 rather than simply bits per second [2], by exploiting the spatial domain of the wireless environment.

In this course, future networks must challenge the entrenched status where the wireless environment is perceived as an invariable "unintentional adversary", to which the system needs to adapt, and where only the end-points of the communication network can be optimized. This is an extremely inefficient paradigm, where base stations (BSs) transmit radio waves of the order of magnitude of Watts while user equipment detects signals of the order of magnitude of μWatts or even nWatts, with the rest of the energy being dissipated over the wireless environment (i.e. the channel), while creating interference to other network elements. In order to challenge this status, an antipodal approach is required, where the wireless environment (i.e. the channel) needs to dynamically adapt to the wireless network operation, giving rise to what is referred to as a smart radio environment.

A smart radio environment is a controllable wireless environment, where software-defined materials or softwarecontrolled metasurfaces can be overlaid on top of environmental objects or blockages to transform them into controllable network entities, conducive to wireless propagation [START_REF] Renzo | Smart radio environments empowered by reconfigurable AI meta-surfaces: an idea whose time has come[END_REF]. This transformation of the wireless networks into a smart radio environment is made possible by the advancement in the area of electromagnetic (EM) meta-materials [START_REF] Yu | Light propagation with phase discontinuities: generalized laws of reflection and refraction[END_REF], which has given rise to a new technology allowing the control and manipulation of the radio waves traversing through the wireless channels [START_REF] Renzo | Smart radio environments empowered by reconfigurable AI meta-surfaces: an idea whose time has come[END_REF]. This technology has allowed for the design and fabrication of large software controlled meta-surfaces [START_REF] Liu | Intelligent metasurfaces with continuously tunable local surface impedance for multiple reconfigurable functions[END_REF], [START_REF] Kaina | Shaping complex microwave fields in reverberating media with binary tunable metasurfaces[END_REF], [START_REF] Tretyakov | Metasurfaces for general control of reflection and transmission[END_REF], known as Reconfigurable Intelligent Surfaces (RISs) [START_REF] Renzo | Smart radio environments empowered by reconfigurable AI meta-surfaces: an idea whose time has come[END_REF], which are able to recycle radio waves without the need for generating new signals, but rather controlling the radio waves from within the wireless channel.

Reconfigurable Intelligent Surfaces

An RIS is an intelligent surface able to manipulate the impinging radio waves at will. As opposed to a regular surface which reflects impinging waves by adhering to Snell's law of specular reflections, (where the angle of the incident wave is equal to the angle of the reflected wave) an RIS is an "intelligent" surface in the sense that it is able to reflect and transmit electromagnetic waves in a desired direction. This anomalous reflection, also referred to as geometric scattering, is not bound by the rules of reflection or refraction, but guides reflected waves toward directions that can be considered anomalous with respect to Snell's law and this reflection is governed by the so called generalized Snell's law [START_REF] Tretyakov | Metasurfaces for general control of reflection and transmission[END_REF]. The capability of RISs to shape and direct the electromagnetic waves in an intelligent way, gives rise to a number of interesting applications that are expected to play a crucial role in 6G [START_REF] Tariq | A speculative study on 6G[END_REF]. These applications, depicted in Figure 1 [10], include but are not limited to (a) anomalous reflection, (b) beamforming to focal points [START_REF] Qian | Beamforming Through Reconfigurable Intelligent Surfaces in Single-User MIMO Systems: SNR Distribution and Scaling Laws in the Presence of Channel Fading and Phase Noise[END_REF], [START_REF] Di Renzo | Analytical Modeling of the Path-Loss for Reconfigurable Intelligent Surfaces -Anomalous Mirror or Scatterer ?[END_REF], and (c) joint encoding on the RIS reflection pattern [START_REF] Karasik | Beyond Max-SNR: Joint Encoding for Reconfigurable Intelligent Surfaces[END_REF].

RISs are capable of applying the aforementioned customized transformations to the reflected radio waves, by changing the phases of the scattering particles that comprise the RIS [START_REF] Yu | Light propagation with phase discontinuities: generalized laws of reflection and refraction[END_REF], in a way that allows for the constructive interference of all the particle-engendered multipath components at the desired location. These constituent subwavelength scattering particles (a.k.a. unit cells) are dielectric or metallic [START_REF] Liaskos | A new wireless commun. paradigm through software-controlled metasurfaces[END_REF], forming a sub-wavelength array of planar or curved conformation. This malleable conformation of RISs allows for the coating of environmental objects with software-controlled, artificial, thin films of RISs, facilitating the dynamic manipulation of the incident radio waves in a fully reconfigurable manner [START_REF]VISORSURF project, A hardware platform for software-driven functional metasurfaces[END_REF]. This allows the efficient management of the transmitted radio waves, toward (a) improving network coverage, by circumventing physical obstacles [START_REF] Renzo | Smart radio environments empowered by reconfigurable AI meta-surfaces: an idea whose time has come[END_REF], (b) enhancing the signal power at the receiver, exploiting the scaling law of the power reflected from the RIS scattering particles [START_REF] Basar | Wireless Communications Through Reconfigurable Intelligent Surfaces[END_REF], [START_REF] Qian | Beamforming Through Reconfigurable Intelligent Surfaces in Single-User MIMO Systems: SNR Distribution and Scaling Laws in the Presence of Channel Fading and Phase Noise[END_REF], (c) reducing BS power consumption by substituting power-hungry MIMO RF chains with RIS empowered multi-stream transmitters on a single-RF chain (media-based modulation) [START_REF] Basar | Wireless Communications Through Reconfigurable Intelligent Surfaces[END_REF], or (d) cloaking antennas from one another in particular frequency bands allowing for their ultra-tight packing [START_REF] Monti | Mantle cloaking for co-site radio-frequency antennas[END_REF].

Numerous companies are already productizing RIS based solutions, engendering the next generation of RIS empowered wireless networks. In the present chapter we will elaborate on many of those industrial activities, while outlining the state of the art. In this course and in order to visualize the RIS empowered network operation, Figure 2 [18] demonstrates a Metawave implemented solution (Metawave is one of the companies actively involved in the engineering of RIS based solutions [18]) toward improving network coverage by coating building facades, and street furniture with RISs, steering radio waves toward locations of poor coverage. The subsequent interconnection and control of all network RISs (that are used for coating the network environment), through radio access intelligent controllers can indeed transform wireless networks into customizable smart radio environments. In this setup, the spatial domain arises as a fully malleable pillar of flexibility, playing an active role in transferring and processing information [START_REF] Renzo | Smart radio environments empowered by reconfigurable AI meta-surfaces: an idea whose time has come[END_REF].

Types of RISs, advantages and limitations

RISs can be manufactured in practise either as large arrays of inexpensive antennas, usually spaced half of wavelength apart (e.g. Figure 6, Figure 7 of Section 3), or as large metamaterial-based surfaces (i.e. meta-surface based RISs), whose scattering elements have sizes and inter-distances much smaller than the wavelength (e.g. Figure 8, Figure 9 of Section 3). These two approaches, can be effectively viewed as "discrete" and "continuous" implementations of RISs, respectively. In the discrete approach the phases of the antenna elements are optimized individually, whereas in the continuous approach the phases of all scattering particles are optimized collectively. This collective optimization of all scattering particles, in the latter case, is imposed by the very nature of meta-surface based RISs, as will be detailed in the following paragraphs.

To elaborate on meta-surface based RISs, meta-surfaces are electrically thin and electrically large structures, which means that their thickness is considerably smaller and their transverse size is considerably larger than the wavelength. The mode of operation and the reflection properties of these meta-surfaces are defined by the inter-distance and the size of their constituent scattering particles (a.k.a. unit cells). Meta-surface based RISs constitute the third generation of meta- surfaces, coming as the evolution of first generation of uniform meta-surfaces (i.e. surfaces whose unit cells are uniformly distributed), and of the second generation of non-uniform meta-surfaces. This second generation of non-uniform metasurfaces extended the range of applicability of the first generation, by introducing a variability in the spatial domain (over the uniform spatial pattern) to support ultrawideband, beamforming, multibeam and multi frequency operation. The current third generation of meta-surface based RISs introduced an additional variability in the time domain, through the employment of switches, varactors and diodes, to allow for the dynamic reconfiguration of the reflected or refracted waves.

Having outlined the concept of meta-surface based RISs and since the fundamental of antenna arrays are already known to the community, we can proceed we the axiomatic formulation of the aforementioned classification of RISs (described as "discrete" and "continuous"), based on the concept of homogeneity. In particular, RISs can be axiomatically categorised based on the size of their unit cells to homogenizable and inhomogenizable. Homogenizable RISs are surfaces that can be globally or locally described by effective material parameters, like surface impedance, susceptibility and polarizability [START_REF] Wang | Surface-impedance engineering for advanced wave transformations[END_REF]. This means that RISs characterized by homogeneity, can be practically considered continuous and so can be the ensuing analysis on the reflected waves, as opposed to the discrete RISs of inexpensive antennas, mentioned above. Figure 3 [START_REF] Wang | Surface-impedance engineering for advanced wave transformations[END_REF] demonstrates the threshold between homogenizable and inhomogenizable surfaces, with surfaces of unit size (denoted by α) smaller than half a wavelength, like uniform metasurfaces, high impedance surfaces (HDS), or some frequency selective surfaces (FSS) being homogenizable, whereas surfaces of unit size greater than half a wavelength being inhomogenizable. This homogeneity based taxonomy of RISs is further refined in Figure 3, by taking into account not just the unit size, (characterizing the homogeneity of the structure), but also the period of the unit cells, i.e. their inter-distances. In particular, surfaces of unit size smaller than half a wavelength, and of inter-distance (denoted by D) also smaller than half a wavelength, are globally homogenizable, whereas surfaces of unit size smaller than half a wavelength but of inter-distance higher than half a wavelength maintain the homogeneity, but only at a local level. This means that structures such as metasurface-based gratings, which are clustering unit cells in super-cells of varying interdistances, maintain the homogeneity, not at a global, but at a local super-cell level [START_REF] Wang | Surface-impedance engineering for advanced wave transformations[END_REF]. Wang [START_REF] Wang | Surface-impedance engineering for advanced wave transformations[END_REF].

The aforementioned homogeneity of RISs is extremely important to provide properties such as larger angles of reflection, and perfect anomalous reflection or refraction [START_REF] Asadchy | Perfect control of reflection and refraction using spatially dispersive metasurfaces[END_REF], [START_REF] Díaz-Rubio | From the generalized reflection law to the realization of perfect anomalous reflectors[END_REF], [START_REF] Lavigne | Susceptibility derivation and experimental demonstration of refracting meta-surfaces without spurious diffraction[END_REF], as opposed to the imperfect anomalous reflection and refraction of discrete, inhomogenizable structures. In particular, as already mentioned, the unit cells of discrete RISs (that are inhomogenizable due to the half wavelength spacing of the reflect/transmit arrays as shown in Figure 3. Planar structures classified by homogenization property. Here, a is the unit size and D the structure period (inter-distance).) are optimized independently of each other, whereas the unit cells of continuous RISs follow a coupled optimization. These two optimization approaches, described in the literature as local and non-local design respectively, are imposed by the very nature of the two implementations and endow different properties to discrete and continuous RISs.

In the case of the non-local design of continuous RISs, the coupled optimization of unit cells allows the transfer of energy from one unit-cell to another. In particular, energy from an incident wave can be transferred by exciting evanescent superficial (not propagating) waves, travelling on the surface of the RIS [START_REF] Díaz-Rubio | From the generalized reflection law to the realization of perfect anomalous reflectors[END_REF]. Hence, the power received from one unit-cell can be transferred to a different unit-cell, giving rise to a more flexible power budget. To elaborate, the local design of the discrete RISs imposes a standalone power constraint for each unit cell, where the impinging power on each unit cell must be less or equal to the power reflected by the same unit cell, since RISs are in general passive structures. However, the non-local design allows for the transfer of energy between unit cells, giving rise to a globally passive structure that can however be active at a local level. That is, the reflected power by a unit cell can be higher than the power that impinged on the unit cell, due to the amplification achieved by the aggregation of power from the neighbouring unit cells. This gives rise to a flexible power budget of higher power efficiency, that allows continuous RISs to provide larger angles of reflection and perfect anomalous reflection, exploiting the fact that the structures are passive on a global but not on a local level.

At this point it should be noted that even though second generation meta-surfaces are completely passive structures the aforementioned characterization of meta-surface based RISs as globally passive structures is a relatively abusive term, since in reality an RIS is only a nearly-passive structure. That is since, minimal power and digital signal processing capabilities are needed in order for the RIS to interact with the environment and in order for the surface to be re-configured dynamically over time. In this course, RISs are equipped with processing units, micro controllers and radio frequency chains that allow them to either report changes in their environment if they are equipped with appropriate sensing elements, or to receive commands during the control and configuration phase in response to the changing wireless channel. These commands are subsequently implemented by the RIS tuneable elements (i.e. switches, varactors and diodes), resulting in the consumption of power. However, after the control and configuration phase of the RISs is over, no power amplification is used after the RISs enter the normal operation phase. Due to the passive behavior at the normal operation phase and the only minimal power requirements at the control phase, RISs can more accurately be characterized as nearly-passive structures.

Advantages and limitations

Having outlined the types of RISs and their modes of operation we can proceed with the comparison of RISs with other existing technologies to understand the advantages, limitations and trade-offs of this emerging technology. In this direction, an experimental case study is examined as performed by the startup company Pivotal [23], [24], that develops meta-surface based RIS solutions. In this case study, an RIS architecture (developed by the company under the framework of their "holographic beamforming" technology and described in detail in a number of white papers [23],[24]) is compared with the MIMO and Phased Array architectures in terms of cost, size and implementation complexity and is presented in Table 1 [23]. The block diagrams of Table 1 demonstrate that the complexity of the MIMO array is very high, since a high number of antennas is required along with an equal number of RF chains and a complex signal processing unit, while the complexity increases significantly with the number of antenna elements. In the case of the phased array the complexity decreases since instead of an RF chain per antenna element, a phase shifter is employed and the signal processing unit is much less complex. As opposed to these two systems Table 1 demonstrates that the RIS system requires a much higher number of unit cell elements, however, the circuits supporting each element are much less complex and much less expensive. Hence, this gives rise to an implementation related trade-off where the successful application of RISs requires a large number of RIS elements supported however, by circuits characterized by extremely low complexity compared to legacy technologies. This conclusion becomes also evident in Table 2 [24], where an RIS system and a phased array achieving the same quality of service (QoS) are compared. Table 2 demonstrates that the number of RIS elements is much higher than the corresponding elements of the phased array (640 vs 256), however their power consumption is much lower than that of the phased array elements (12.9W vs 39.6W). Evidently, compared with other transmission technologies, e.g., phased arrays, multi-antenna transmitters, and relays, RISs require the highest number of scattering elements, but each of them needs to be backed by the fewest and least costly components, while no dedicated power amplifiers per element is needed. This trade-off between the number of elements and the power, cost and complexity of implementation per element needs to be investigated in detail in future works. However, the aforementioned case study has demonstrated, that RISs arise as prime candidates for realizing what is called a C-SWaP design, i.e. a transmitter design at reduced cost, size, weight, and power [23], through a softwaredefined RIS-enabled architecture. Moreover, such architectures can achieve a sustainable wireless design of low electromagnetic field exposure, by recycling transmitted waves while the transmitter can be manufactured by recyclable materials, that (as will be demonstrated in the following section) can be seamlessly integrated in urban network environments by being physically & aesthetically unobtrusive.

The previous case study has already demonstrated that in order to achieve performance comparable or even superior to that of other technologies a high number of RIS elements is required. Two more key factors determining the performance of RISs that need to be taken into account prior to their productization and their incorporation in wireless networks are the size and transmit distance of the RISs. In particular, it has been demonstrated that for an indicative transmission frequency of f = 28 GHz and an RIS length of 1,5 m = 140 λ (i.e. an electrically large RIS) an RIS can provide a similar performance or even outperform a full duplex (FD) relay without even employing a power amplifier. The data rates achieved by the RIS, the FD relay and a half duplex (HD) relay for different transmission distances are demonstrated in Figure 4 [START_REF] Renzo | Reconfigurable Intelligent Surfaces vs. Relaying: Differences, Similarities, and Performance Comparison[END_REF]. The results obtained in Figure 4 are obtained for inter-distances in the range of λ/5 and a number of unit cells equal to 700 (or λ/2 and 280 respectively). An interesting finding is that for distances up to 25-50 m the RIS behaves as an anomalous mirror (i.e. the transmitter is close enough to the RIS to perceive it as electrically large), whereas for distances greater than 75-100 m the RIS behaves as a local diffuse scatterer (i.e. the transmitter resides that far from the RIS, that in practice sees is as electrically small), while for distances greater than 150 m the RIS exhibits a performance that is inferior to that of the FD relay. This finding demonstrates the importance of the transmit distances and of the size of the RIS, since at higher distances RISs are perceived as electrically small and therefore larger RISs may be required in order to outperform legacy technologies. However, the fact that as already mentioned and as will be demonstrated in the following section modern RISs can be aesthetically unobtrusive and seamlessly integratable on glass building facades, billboards etc. allows for the employment of electrically large structures (depending of course on the operating frequency) giving rise to a performance comparable to this of Figure 4. Moreover, due to the aforementioned C-SWaP design, the use of RISs is expected to be pervasive with ultra-dense deployments of RISs that are expected to minimize transmit distances allowing network operators to effectively manage this trade-off between RIS sizes and transmit distances. This trade-off is also visualized in Figure 5 where the bitrate achieved by the employment of an RIS is compared with the bitrate achieved by an FD and an HD relay for the same setup described above, at 2 different transmit distances of 10 m and 100 m for different RIS lengths. Once again it is demonstrated that for an electrically large RIS the achieved bit rate is higher than that of the FD and HD relay, which motivates the pervasive use of RISs in the network in order to be employed particularly for small transmit distances.

Experimental Activities

Having outlined the key technologies employed for the implementation of RISs as well as the main factors influencing their performance as well as their advantages and limitations, the present section will focus on the practical implementations of RISs and the experimental activities available in the literature. In particular, the potential of the RIS technology toward realizing smart and controllable radio environments for the first time in history has already spurred the practical implementation of RIS prototypes both discrete and continuous, corroborating the theoretical results presented above with respect to the enhancement of received power and capacity, and a brief survey of those prototypes and of their characteristics is performed hereafter.

Large Arrays of inexpensive antennas

RFocus

One of the first prototypes realized based on discrete arrays of inexpensive antennas is the RFocus prototype implemented at the CSAIL lab of MIT [START_REF] Arun | RFocus: Beamforming using thousands of passive antennas[END_REF]. The RFocus prototype, in Fig. 7, employs 3,200 inexpensive antennas distributed over a surface of 6 square-meters and constitutes (to the best of the authors' knowledge, among all published configurations) the configuration comprising the largest number of antennas ever, employed for a single communication link. The prototype constitutes, in reality, a software-controlled surface with thousands of plain switching elements. Each of the switching elements is a two-way RF switch, with two distinct states. Any impinging wave is either reflected or traversing through the element. Moreover, a controller is employed to configure all constituent elements in the way that ensures that any signal impinging upon the RFocus surface from the transmitter will be directed toward the receiver. The controller is agnostic to the location of the transmitter or receiver and just switches between different optimized states to maximize the signal power between the different endpoints of the transmitter and receiver. The RFocus redirected signals are not amplified and the controller can choose between a "mirror" or a "lens" operation, where the endpoints can reside either on the same or on different sides of the surface. The measurements at the premises of the MIT CSAIL laboratory report that the employment of RFocus improved the median signal strength by a factor of 9.5× and the median channel capacity by a factor of 2.0× [START_REF] Arun | RFocus: Beamforming using thousands of passive antennas[END_REF]. At this point however it should be noted that these measurements and gains correspond only to an indoor environment, whereas similar outdoor measurements are required in order to demonstrate the efficiency of the prototype in less controllable environments. In practice RFocus serves as a beamformer, but the beamforming function is now shifted from the radio endpoints to the radio environment itself. This shift of the beamforming functions to the environment allows for the deployment of huge beamforming antenna arrays (of a 6 square-meter area or more) that could not be deployed before, due to the space limitations typically imposed to infrastructure base stations or access points (which are hard to deploy). Thus, allowing for the deployment of massive and potentially multiple beamforming antenna arrays. Moreover, such a beamforming antenna array is not in need of connecting each antenna element to a full-fledged radio transmit/receive circuitry of increased power consumption and cost. However, the deployment of such massive antenna arrays of an excessively high number of antenna elements incurs an optimization overhead cost. In particular, the of all 3200 antenna elements by the controller incurs a significant latency. After collecting TCP throughput data, the latency of the optimization algorithm is equal to 4000 packets. Hence, an interesting trade-off arises between the number of antenna elements and implicitly the level of reflected power, and the incurring latency of the optimization algorithm at the controller. This trade-off needs to be extensively studied and in this direction smaller discrete arrays of reduced latency have also been studied and implemented in practice, like the one mentioned below.

The ScatterMIMO prototype

The ScatterMIMO prototype is another discrete array implementation of an RIS similar to that of RFocus, implemented by the University of California [START_REF] Dunna | ScatterMIMO: Enabling virtual MIMO with smart surfaces[END_REF]. The ScatterMIMO prototype encompasses 48 antenna elements in the form of 3 tiles of 4×4 MIMO antenna arrays forming a virtual access point. This virtual access point complements the active access point by reflecting its signal in a controlled an optimized manner either vertically or horizontally, toward creating additional MIMO streams to double the throughput. Moreover, the location of this small RIS can itself be appropriately optimized in order to ensure that either an LOS link between the transmitter and the receiver is established or that the RIS will reflect the maximum amount of power toward the receiver. In the latter case the RIS needs to be positioned close to the receiver or the transmitter and since the position of the receiver is not fixed the RIS needs to be positioned in the vicinity of the fixed transmitter. Thus, the distance to the receiver or transmitter arises as an additional degree of freedom. By exploiting this degree of freedom and strategically place the RIS at the optimal location the authors of [START_REF] Dunna | ScatterMIMO: Enabling virtual MIMO with smart surfaces[END_REF] have demonstrated that the same QoS can be achieved as that provided by an RIS encompassing more antenna elements but at a suboptimal location. Moreover [START_REF] Dunna | ScatterMIMO: Enabling virtual MIMO with smart surfaces[END_REF] demonstrates that the RIS of 48 antenna element incurs only a minimal optimization-related latency cost which is equal to 3 packets, as opposed to the 4000 packets of RFocus. Hence, the ScatterMIMO approach demonstrates an interplay between the antenna elements and the latency (already demonstrated by the RFocus approach), but also with respect to the distance between the RIS and the receiver or the transmitter respectively. Once again all reported measurement of [START_REF] Dunna | ScatterMIMO: Enabling virtual MIMO with smart surfaces[END_REF] pertain to an indoor environment.

Meta-surface approaches

Further to the discrete array implementation of RISs mentioned above, numerous meta-material based implementations of RISs have also been fabricated, with the majority of those approaches also being tested primarily in indoor and controllable environments. As already mentioned the non-local design of such meta-surfaces (i.e. the coupled optimization of their constituent elements) endows an interesting set of properties such as perfect anomalous reflection at large angles of reflection. One of the first approaches achieving a perfect design of an anomalously reflective surface employing a strongly nonlocal design is that of Aalto university [START_REF] Díaz-Rubio | From the generalized reflection law to the realization of perfect anomalous reflectors[END_REF] with the fabricated metasurface being depicted in Figure 8. The principles of nonlocal design have already been developed in detail in Section 2 and are therefore omitted at this point. However, for the sake of completeness it should be noted that the fabricated meta-surface employs 10 unit cells clustered at a super-cell level with each unit-cell having a width of 3.5 mm (in the x axis) and each super-cell having a width of 40 mm (in the x axis) and a height of 18.75 mm (in the y axis). The overall dimensions of the metasurface are 440mm in the x axis and 262.5 mm in the y axis, which for an operating frequency of f = 8 GHz corresponds to 11.7λ and 7λ respectively. The subwavelength dimensions of the unit cells give rise to a homogenizable metasurface and more importantly pave the way for the advent of homogenizable structures of even smaller granularity (i.e. of even smaller unit cells) that can give rise to structures aesthetically unobtrusive like the one presented below. Such an aesthetically unobtrusive metasurface-based RIS is that fabricated by DOCOMO and depicted in Figure 9 [27]. The DOCOMO prototype employs unit cells of extremely small size, smaller than the 3.5 mm of the Aaltofabricated metasurface or even of the 2 mm size of other contemporary state of the art metasurfaces. These miniscule unit cell sizes and the implicit continuous granularity give rise to a transparent RIS, that can be deployed on glass building facades, vehicles and billboards, as previously visualized in Figure 2. Such transparent RISs do not interfere aesthetically or physically with the surrounding environment, facilitating the proliferation of RISs in wireless networks environments in an unobtrusive manner. Thus, allowing for the transformation of wireless networks into RIS empowered smart radio environments, through the employment of large RISs deployed at small transmit distances, and residing in the vicinity of the receiver or transmitter. In this course, relevant measurements not just in indoor and controllable environments but also in outdoor environments need to be reported and this constitutes one of the key challenges of future research work in the field.

RIS Research Areas and Challenges in the 6G Ecosystem

The previous sections have epigrammatically outlined the potential of RISs, by investigating their potential benefits and limitations, while also comparing them with similar and well established technologies such as conventional relays [START_REF] Renzo | Reconfigurable Intelligent Surfaces vs. Relaying: Differences, Similarities, and Performance Comparison[END_REF], MIMO and phased arrays [23,24]. Moreover, since RISs are a novel paradigm in the context of wireless communications, the realization of proof-of-concept platforms and hardware testbeds is outlined in the previous section [Error! Bookmark not defined., [START_REF] Arun | RFocus: Beamforming using thousands of passive antennas[END_REF][START_REF] Dunna | ScatterMIMO: Enabling virtual MIMO with smart surfaces[END_REF]27] in order to corroborate the theoretical findings and demonstrate the potential b enefits arising from the utilization of RISs by 6G systems. In this course, a multitude of additional experimental activities can also be found in the literature, focusing, for instance, on RIS elements of finer (2-bit) phase resolution [START_REF] Dai | Reconfigurable Intelligent Surface-based Wireless Communication: Antenna Design, Prototyping and Experimental Results[END_REF] or RIS testbeds employed for ambient backscatter communications [START_REF] Fara | Polarization-Based Reconfigurable Tags for Robust Ambient Backscatter Communications[END_REF].

The employment of RISs and their amalgamation with legacy transmission technologies (such as that of [START_REF] Fara | Polarization-Based Reconfigurable Tags for Robust Ambient Backscatter Communications[END_REF]) is also attracting the interest of the wireless community, with RIS being seamlessly conflated with other wireless sections such as: physical layer security [START_REF] Yang | Secrecy Performance Analysis of RIS-Aided Wireless Communication Systems[END_REF][START_REF] Yu | Enabling Secure Wireless Communications via Intelligent Reflecting Surfaces[END_REF][START_REF] Guan | Intelligent Reflecting Surface Assisted Secrecy Communication: Is Artificial Noise Helpful or Not?[END_REF][START_REF] Qiao | Secure Transmission for Intelligent Reflecting Surface-assisted mmWave and Terahertz Systems[END_REF], non-orthogonal multiple access [START_REF] Mu | Exploiting Intelligent Reflecting Surfaces in NOMA Networks: Joint Beamforming Optimization[END_REF][START_REF] Ding | A Simple Design of IRS-NOMA Transmission[END_REF][START_REF] Liu | RIS Enhanced Massive Non-orthogonal Multiple Access Networks: Deployment and Passive Beamforming Design[END_REF], Internet of Things and backscattering communications [START_REF] Zhang | Large Intelligent Surface/antennas (LISA) Assisted Symbiotic Radio for IoT Communications[END_REF], aerial communications [START_REF] Li | Reconfigurable Intelligent Surface Assisted UAV Communication: Joint Trajectory Design and Passive Beamforming[END_REF][START_REF] Yang | On the Performance of RIS-Assisted Dual-Hop UAV Communication Systems[END_REF], wireless power transfer [START_REF] Pan | Intelligent Reflecting Surface Aided MIMO Broadcasting for Simultaneous Wireless Information and Power Transfer[END_REF], multiple-access edge computing [START_REF] Bai | Latency Minimization for Intelligent Reflecting Surface Aided Mobile Edge Computing[END_REF], millimeter-wave, terahertz, and optical wireless communications [START_REF] Zuo | Intelligent Reflecting Surface Enhanced Millimeter-Wave NOMA Systems[END_REF][START_REF] Perovic | Channel Capacity Optimization Using Reconfigurable Intelligent Surfaces in Indoor mmwave Environments[END_REF], as well software defined networking protocols for the control and programmability of the RISs [START_REF] Liaskos | On the Network-layer Modeling and Configuration of Programmable Wireless Environments[END_REF]. For a thorough literature review on the application of RISs on the holistic wireless ecosystem, the reader can also refer to a number of available overviews and tutorials on RISs and the references therein [START_REF] Di Renzo | Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces: How it Works, State of Research, and Road Ahead[END_REF][START_REF] Renzo | Smart radio environments empowered by reconfigurable AI meta-surfaces: an idea whose time has come[END_REF][START_REF] Basar | Wireless Communications Through Reconfigurable Intelligent Surfaces[END_REF][START_REF] Huang | Holographic MIMO Surfaces for 6G Wireless Networks: Opportunities, Challenges, and Trends[END_REF][START_REF] Liu | Reconfigurable Intelligent Surfaces: Principles and Opportunities[END_REF].

Further to the aforementioned cross-sectorial implementation of RISs a number of research challenges have also arisen from the standalone implementation of RISs. In particular, one of the major research challenges pertains to the development of simple but accurate models to account for the power at the receiver, after a transmitter emits radio waves that are reflected from an RIS. Some early research works have already provided models and measurements for this RIS operation [START_REF] Tang | Wireless Communications with Reconfigurable Intelligent Surface: Path-loss Modeling and Experimental Measurement[END_REF][START_REF] Di Renzo | Analytical Modeling of the Path-Loss for Reconfigurable Intelligent Surfaces -Anomalous Mirror or Scatterer ?[END_REF][START_REF] Danufane | On the Path-Loss of Reconfigurable Intelligent Surfaces: An Approach Based on Green's Theorem Applied to Vector Fields[END_REF][START_REF] Gradoni | End-to-End Mutual-Coupling-Aware Communication Model for Reconfigurable Intelligent Surfaces: An Electromagnetic-Compliant Approach Based on Mutual Impedances[END_REF], but additional work is required in order to analyze the performance limits of RISs and optimize their operation. In this direction, some early approximate, and asymptotic analytical frameworks have already been developed, toward quantifying the gains and limitations of RISs in different network scenarios, like in the presence of phase noise, characterizing the distribution and scaling laws of the SNR [START_REF] Qian | Beamforming through Reconfigurable Intelligent Surfaces in Single User MIMO Systems: SNR Distribution and Scaling Laws in the Presence of Channel Fading and Phase Noise[END_REF], or by employing point processes, such as stochastic geometry, and random spatial processes to compute the probability that an RIS coated object in the network acts as a reflector [START_REF] Di Renzo | Reflection Probability in Wireless Networks with Metasurface-coated Environmental Objects: An Approach based on Random Spatial Processes[END_REF].

As already stressed, the next step after the network analysis and performance evaluation in the presence of RISs, is the optimization of the RIS operation. In fact, the resource optimization problem in the presence of RISs (both model-based and data-driven) is one of the most investigated research topics in the context of RIS-empowered networks. The majority of the research activities focus on the problem of active and passive beamforming in MISO systems, i.e., the optimization of transmit (active) beamforming and (passive) RIS phase shifts, with respect to energy and spectral efficiency as well as system rate and optimization-introduced overhead. In general, both analytical techniques [START_REF] Zhou | Spectral and Energy Efficiency of IRS-Assisted MISO Communication with Hardware Impairments[END_REF][START_REF] Han | Intelligent Reflecting Surface Aided Network: Power Control for Physical-layer Broadcasting[END_REF][START_REF] Zhou | Robust Beamforming Design for Intelligent Reflecting Surface Aided MISO Communication Systems[END_REF][START_REF] Zappone | Overhead-aware Design of Reconfigurable Intelligent Surfaces in Smart Radio Environments[END_REF][START_REF] Perović | Achievable Rate Optimization for MIMO Systems with Reconfigurable Intelligent Surfaces[END_REF] such as the alternating maximization (for the non-convex problem) and data-driven, machine learning and artificial intelligence techniques [START_REF] Zappone | Wireless Networks Design in the Era of Deep Learning: Model-based, AI-based, or both?[END_REF][START_REF] Gacanin | Wireless 2.0: Towards an Intelligent Radio Environment Empowered by Reconfigurable Metasurfaces and Artificial Intelligence[END_REF] have been employed. However, the RIS optimization remains an underexplored research challenge, since the problems arising in RIS enabled MIMO systems, or in systems comprising multiple RISs remain yet to be explored, with the complexity increasing with the number of antennas and RISs.

Another open research challenge related to RIS is the channel estimation which accounts for the effect of the RIS on the channel between the transmitter and the receiver. The RIS's transformation of the channel must be either reported by a feedback mechanism to the transmitter or the channel state information (CSI) of the combined channel (transmitter-RSI-receiver) must be estimated by the transmitter as a whole (for all possible RIS states). In general, the nearly-passive operation of RISs and their minimal processing capabilities, impose the investigation of new algorithms and protocols for the channel estimation while avoiding signal processing on-board the RIS to the extent possible. Some research works in this direction, employing neural networks already exist [START_REF] Liu | Deep Denoising Neural Network Assisted Compressive Channel Estimation for mmWave Intelligent Reflecting Surfaces[END_REF], however channel estimation of RIS enabled networks, remains a little explored research avenue.

Last but not least, one of the most promising applications of RISs is the modulation and encoding of data directly on the RIS scattering elements and on the reflected radiation pattern. This is in fact, an RIS enabled variation of the spatial modulation and index modulation concepts [START_REF] Karasik | Beyond Max-SNR: Joint Encoding for Reconfigurable Intelligent Surfaces[END_REF][START_REF] Basar | Wireless Communications Through Reconfigurable Intelligent Surfaces[END_REF][START_REF] Li | Single-RF MIMO: From Spatial Modulation to Metasurface-Based Modulation[END_REF], which, as already explained in detail in Section 2.1, provides a low complexity, power-conscious alternative to massive MIMO chains.

Figure 1 .

 1 Figure 1. Potential applications of "intelligent" reflectors. Source: Di Renzo et al. [10].

Figure 2 .

 2 Figure 2. RIS enhanced network coverageSource: Metawave Corporation.

Figure 3 .

 3 Figure 3. Planar structures classified by homogenization property. Here, a is the unit size and D the structure period (inter-distance). Source:Wang[START_REF] Wang | Surface-impedance engineering for advanced wave transformations[END_REF].

Figure 4 .

 4 Figure 4. Data rate of RISs and relays versus the transmission distance. Source: Di Renzo et al. [10].

Figure 5 .

 5 Figure 5. Data rate of RISs and relays versus the size of the RIS. Source: Di Renzo et al. [10].

Figure 6

 6 Figure6The RFocus prototype surface. Source: Arun[START_REF] Arun | RFocus: Beamforming using thousands of passive antennas[END_REF].

Figure 7

 7 Figure7The ScatterMIMO Hardware prototype. Source:[START_REF] Dunna | ScatterMIMO: Enabling virtual MIMO with smart surfaces[END_REF].

Figure 8

 8 Figure 8 Aalto-fabricated metasurface. Source: [21].

Figure 9

 9 Figure 9 DOCOMO prototype of transparent dynamic metasurface. Source: [27].

Table 1

 1 Summary of key differences among RIS, phased array and MIMO beamformers

	Architecture	Block Diagram	Cost	Size	Challenges
			Super-		Single beam
			sampled,	Thin,	per polarization
	RIS		COTS design,	Conformable	per sub-aperture
			Allows for
			low price

Source: Eric J. Black, PhD, CTO, Pivotal Commware, Holographic Beam Forming and MIMO, 2021.

Table 2

 2 Difference between RIS and Active Phased Array power consumption

		Phased Array	RIS	Unit
	Number of Unit Cells	256	640	#
	Antenna Gain	28	26	dB
	Number of RF chains	256	1	#
	Transmit Power per chain	6.2	2512	mW
	Total RF Transmit Power	1.58	2.51	W
	Power Added Efficiency	4.0%	25.0%	%
	DC Draw for RF	39.6	10.0	W
	RIS Controller	0	2.9	W
	Total DC Power	39.6	12.9	W
	Source: Pivotal Staff, Pivotal Commware, Holographic Beam Forming and Phased Arrays, 2021.


Ali Rahimi Khojasteh
email: ali.rahimi-khojasteh@inrae.fr

Dominique Heitz

Yin Yang

Adjustable interogation window for 2D PIV estimation based on local Lagrangian coherency

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

Introduction

In Particle Image Velocimetry (PIV) algorithms, both correlation-based and local optical flow techniques rely on the interrogation windows. The importance of interrogation window has been studied widely for obtaining effective methods of adapting the window size and shape, which directly impacts the spatial accuracy of velocity estimation [START_REF] Theunissen | Spatially adaptive PIV interrogation based on data ensemble[END_REF][START_REF] Wieneke | Adaptive PIV with variable interrogation window size and shape[END_REF][START_REF] Theunissen | An adaptive sampling and windowing interrogation method in PIV[END_REF]. Since the flow behaviour inside the interrogation window has clusters of small and large scale coherent motions, PIV techniques involve window size reduction to avoid those non-coherent areas and increase the maximum achievable spatial resolution. Generally, the interrogation window size is gradually reduced based on empirical precalculations and tunings, while this empirical approach can be adjusted by temporal and local spatial information. This means flow behaviour in different times and spaces would result in different interrogation window shapes, which is the main objective of this paper. To demonstrate the performance of the proposed method, we integrated the adjustable interrogation window with the local optical flow PIV algorithm. In the local optical flow approach, all pixels inside the window are considered for calculating a single-pixel velocity at the centre of the window. However, to estimate more accurate motions, it is crucial to ignore areas that are non-coherent with the centre pixel. This study seeks to adjust the interrogation window shape in motion estimation by calculating locally coherent and non-coherent areas. We propose performing Lagrangian Coherent Structures (LCS) by looking for the local separatrix ridges that divide the flow field into clusters of coherent regions [START_REF] Haller | Lagrangian coherent structures[END_REF]. The idea of applying LCS in Particle Image Velocimetry (PIV) / Particle Tracking Velocimetry (PTV) algorithms was demonstrated by Khojasteh et al. [START_REF] Rahimi Khojasteh | Lagrangian Coherent Track Initialisation (LCTI)[END_REF]. To this end, all neighbour pixels inside the interrogation window must be classified as coherent or non-coherent with the centre pixel. Similar interrogation window adjustment can be implemented in cross correlation-based PIV techniques.

Local optical flow

Classic optical flow works under the intensity consistency assumption of the acquired images that is inspired by Horn and Schunck [START_REF] Berthold | Determining optical flow[END_REF] formulation. It can be also written in terms of the Optical Flow Constraint Equation (OFCE) as following,

d f dt = + υ.∇ f , (1)
where v is the desired velocity of one time step and f is the image intensity. The operator ∆ denotes gradient over 2D area. On the other hand, we try to minimise the energy function with intensity consistency assumption. However, real PIV images are featured with temporal changes of intensity between consecutive images due to illumination and trigger setup. So this assumption can be violated in PIV applications. Schuster et al. [START_REF] Schuster | Motion Estimation Under Location Uncertainty, Application To Large-Scale Characterization Of A Mixing Layer[END_REF] improved the intensity inconsistency problem by introducing stochastic optical flow formulation. In the stochastic approach, the Eulerian flow velocity field is decomposed into a large-scale smooth component and a small-scale turbulent component. In the present study, we use the same stochastic approach implemented into the Lucas-Kanade optical flow estimator [START_REF] Schuster | Motion Estimation Under Location Uncertainty, Application To Large-Scale Characterization Of A Mixing Layer[END_REF]. In theory, optical flow provides one velocity vector for each pixel of two consecutive images based on spatial and temporal variations of the image intensities. While cross correlation based PIV techniques result in coarse resolution estimation. Therefore, optical flow PIV techniques might provide more details of the flow behaviour in turbulent flows.

Coherent interrogation window

Lagrangian Coherent Structures (LCS) divide the local flow field into regions of coherent motions [START_REF] Haller | Lagrangian coherent structures[END_REF]. LCS is also known as the skeleton of flow that can be utilised as a deterministic criterion to shape the interrogation window. We computed the LCS separatrix ridges using Finite-Time Lyapunov Exponent (FTLE) by employing modified versions of two open-access codes named LCS kit [START_REF] Shadden | Lagrangian analysis of fluid transport in empirical vortex ring flows[END_REF] and LCS tool [START_REF] Onu | LCS Tool: A computational platform for Lagrangian coherent structures[END_REF]. FTLE is a scalar value that measures the amount of spatial stretching over a finite time. In this study, the spatial region is determined by the interrogation window to compute the FTLE value locally. Khojasteh et al. [START_REF] Rahimi Khojasteh | Lagrangian Coherent Track Initialisation[END_REF] showed that using FTLE in the local spatial regions over sparse neighbour particles can reveal signs of local ridges that can be employed in the velocimetry algorithms. FTLE analysis provides spatial and temporal flow field behaviour. We propose to adjust the interrogation window based on separatrix ridges, resulting in different window shapes in space and time. The window shape will not change if the area is entirely coherent. On the other hand, the shape of the interrogation window does not change if all pixels are coherent with the target pixel. The major problem happens when the interrogation window consists of multi-scale dynamics. particles do not cross these lines. Flow motions in between these boundaries have coherent motions. Depending on the centre location, coherent flow motions (in the blue vector field) and regions (in yellow pixels) are on one side of these lines (see Figure 1). Any pixel inside the coherent region is considered for the spatial and temporal gradient of intensity computation. We need to have prior knowledge about the velocity field to compute the FTLE map. The minimisation process in the optical flow is an iterative approach. We found that it is unnecessary to compute the whole iterative process with additional LCS computations since it is costly in time. Therefore, we introduce the LCS computation in the last three iterations of the minimisation process. In this way, we provide near to the final solution vector field for the first Lagrangian separatrices computation.

Results and evaluation 4.1 Synthetic evaluation

We performed synthetic analyses to examine the performance of the proposed technique. The synthetic PIV images were generated from Direct Numerical Simulation (DNS) of a 2D homogeneous isotropic turbulent flow. The boundary condition of each side of the domain was set at periodic. The DNS resolution was 256 × 256 mesh cells. We created the synthetic particle trajectories using linear Euler transport function in time and linear velocity interpolation in space. More details of the DNS simulation can be found in [START_REF] Heitz | Variational fluid flow measurements from image sequences: synopsis and perspectives[END_REF]. We assessed improvements of using coherent interrogation window in velocity estimation results of local optical flow technique. As a result, three terms, including RMS (representing the magnitude of velocity estimation), vorticity, and angular errors, were defined to quantify the local and overall performances of the proposed technique. In an overall view, as shown in Figure 2, we gained around 5% global increase in accuracy of velocity estimation compared with the classic local optical flow. However, it should be noted that the main objective here was to increase the resolution and accuracy around separation and non-coherent areas. Without using adjustable windows, cross-correlation and optical flow techniques would result in up to 50% false estimation at those separation and non-coherent areas. In detail view, Figure 3 shows improvements in three specific flow behaviours, vortex, shear and hyperbolic flows selected locally from 2D synthetic data. These three regions are intentionally picked to illustrate differences in detailed motions. We found that local optical flow with square IW suffers from inaccurate angular estimation compared with the DNS reference in the core vortex regions when the interrogation scale is larger than the vortex scale. Disagreement hits over 7 degrees of angular vector field misestimation, with over 50% angular error. Figure 3 shows significant local improvements in such a region if an adjustment is performed. Similar motion refinements were also observed when high shear or hyperbolic behaviour occurs. We found that coherent optical flow has better velocity estimation in complex local regions. These local improvements impact the overall assessment of the technique in a global view as well.

Experiment case study

We performed a 2D2C PIV experiment of the wake behind a cylinder in the wind tunnel to study the capability of the proposed technique on real experiment images. The Reynolds number corresponding to the cylinder with 12 mm diameter was set at 3900. An sCMOS camera with 2560 × 2160 pixels was employed to acquire images in 49.2 HZ frequency. The measurement plane was illuminated using a 200 mJ laser (EverGreen from Quantel). The disparity of the velocity estimation between optical flow with and without adjustable interrogation window of the current experiment is shown in Figure 4. As mentioned in Section 3, the window shape stays unchanged if the flow motion is coherent inside the interrogation window. This means that disparity should be almost zero in the majority of freestream regions. In agreement with the synthetic analysis, coherent adjustable window only refined velocity estimations of complex motions such as shear, wake, and mixing regions (see Figure 4). We, therefore, compared our proposed technique with the cross-correlation results obtained from Davis software (10.1.2 version). A snapshot of the instantaneous vorticity and vector fields are shown in Figure 5 that is illustrating the existence of complex mixing and vortex generations downstream of the cylinder. The vorticity field shows signs of strong shears in two sidewards of the wake immediately downstream of the cylinder (x/D < 4). These regions are featured by high velocity and acceleration gradients. We compared the cross-correlation results with coherent optical flow, knowing that the synthetic analysis showed significant misestimation in such regions (see Figure 5.a). A 2D sliding average filter was used for both techniques for the image pretreatment. The cross-correlation final spatial resolution was 16 pixels with multi-pass vector calculations starting from 64 × 64 down to 16 × 16 and 75% overlap. As mentioned in Section 2, the resolved resolution of coherent optical flow is the same as the camera resolution. Therefore, the comparison was performed between high resolution coherent optical flow and coarse resolution cross-correlation results. The vector field estimations of coherent optical flow and cross-correlation PIV techniques captured shear with high gradient vector change. In contrast, coherent optical flow estimated detailed vector change in normal to shear direction with smooth change of vectors representing more physics of the flow behaviour. Figure 5.b shows complex vortex and mixing inside the wake region. We found that the centre of the vortex is not aligned in two techniques. There is roughly 3 pixels shift between two estimations. Coherent optical flow maintained smooth rotation with a stretch in diagonal directions. Moreover, the vector field is decreasing gradually toward the vortex centre. However, the cross-correlation technique only captured the large scale motion with a weak signature of stretching in the diagonal direction. The third local comparison is in the formation region with a strong vortex (see Figure 5.c). Similarly, we observed disagreement in the vortex centre estimation between the two techniques while the large scale motions are almost equal. The upper right corner of the vortex is nearby of the large velocity motions (see Figure 5.c). By contrast, the vortex centre is located inside the wake, with drastically lower velocity values. Such a gradient associated with the flow rotation creates a complex local region for PIV estimation. Comparison of two techniques shows that using a coherent adjustable interrogation window resolves more details of the flow field than the classic cross-correlation techniques.

Conclusion

A novel approach to adjust the PIV interrogation windows based on local spatial and temporal coherent motions is proposed. We quantify the coherent and non-content regions using Lagrangian Coherent Structures (LCS) as skeletons of flow. The synthetic analysis showed that coherent optical flow locally improves the velocity estimation accuracy up to 50%. The main advantage of the proposed technique was the improvement in angular estimation in regions with high velocity and acceleration gradients. We also demonstrated our coherent optical flow performance in a real PIV experiment of the wake behind a cylinder at Reynolds number equal to 3900. The experiment case study revealed well-resolved velocity estimations in complex motions such as high shear, wake, and mixing regions.

Figure 2 :

 2 Figure 2: Angular error comparison between local optical flow with and without coherent adjustable window in three scenarios locally selected from 2D homogeneous isotropic turbulence: a), vortex flow; b), shear flow; c), hyperbolic flow. Only high values of angular error are shown.

Figure 3 :

 3 Figure 3: Angular error comparison between local optical flow with and without coherent adjustable window in three scenarios locally selected from 2D isotropic homogeneous turbulence: a), vortex flow; b), shear flow; c), hyperbolic flow. Only high values of angular error are shown.

Figure 4 :

 4 Figure 4: Angular error comparison between local optical flow with and without coherent adjustable window in three scenarios locally selected from 2D isotropic homogeneous turbulence: a), vortex flow; b), shear flow; c) hyperbolic flow. Only high values of angular error are shown.

Figure 5 :

 5 Figure 5: Instantaneous snapshot of vorticity and vector fields obtained from the PIV experiment at a Reynolds number equal to 3900: a), Local view of the vector field estimation comparison between coherent optical flow and Davis cross correlation in high shear region; b), Comparison of vector estimation inside the wake region; c), Comparison of vortex estimation.