D Hissel
email: daniel.hissel@univ-fcomte.fr

Ongoing research on fuel cell powertrains

Keywords: components, energy management, diagnostic, prognostic, durability

Continuous depletion of the crude oil and gradual increase in the oil price have emphasized the need of a suitable alternative to our century-old oil-based economy. A clean and efficient power supply device based on a renewable energy source has to be available to face this issue. Among the different technological alternatives, fuel cell power generation becomes a more and more interesting and promising solution for both automotive industry and stationary power plants. However, many technological hurdles have still to be overcome before seeing the development of industrial and competitive products in these fields.

Among them and focusing on automotive applications, different issues must be solved regarding development of specific components (e.g. air compressors, high efficient power electronics, …), new on-line energy management strategies for fuel cell hybridized systems, efficient diagnostic and stateof-health estimation methodologies, able also to operate in real-time and with limited number of additional physical sensors. Moreover, regarding the increase of the durability and of the reliability of those powertrains, prognostic algorithms able to estimate the remaining useful lifetime of the fuel cell system under actual operating conditions are requested. The proposed presentation will provide a state-of-art on these different items.

Fig. 1 :

 1 Fig. 1: Mobypost vehicles -First fleet of FCV in France (FC powertrain integrated @ FCLAB / UTBM)


Yan-Feng Wang
email: wangyanfeng@bjtu.edu.cn

Vincent Laude
email: vincent.laude@femto-st.fr

Longitudinal Near-Field Coupling between Acoustic Resonators Grafted onto a Waveguide

Keywords: near-field coupling, acoustic resonator, Fabry-Perot interferometer

We investigate longitudinal near-field coupling between acoustic resonators grafted along a waveguide. Experiments are performed in the audible range with a simple acoustic system composed of a finite aperiodic sequence of air resonators. Transmission typically shows a zero around a resonance frequency of a single resonator, as is well known. When two identical resonators are brought in close proximity, however, we observe that longitudinal near-field coupling strongly influences the acoustic transmission. When the separation between resonators is increased so that they can be considered in the far field of one another, we further observe the appearance of Fano-like transmission profiles. We explain this observation by the formation of locally resonant Fabry-Perot interferometers from every pair of resonators. All experimental results are compared to three-dimensional finite element analysis of the acoustic system.

Introduction

Control of acoustic/elastic wave propagation with small-size structures and in the low-frequency range is currently becoming an urgent demand, for applications to filters, waveguides, noise insulators, or energy harvesting [START_REF] Deymier | Acoustic Metamaterials and Phononic Crystals[END_REF][START_REF] Hussein | Dynamics of phononic material and structures: Historical origins, recent progess, and future outlook[END_REF][START_REF] Popa | Non-reciprocal and highly nonlinear active acoustic metamaterials[END_REF][START_REF]Phononic Crystals[END_REF]. In 2000, Liu et al. proposed that a sonic crystal exhibiting band gaps though the lattice constant is two orders of magnitude smaller than the relevant sonic wavelength [START_REF] Liu | Locally resonant sonic materials[END_REF]. Those band gaps are generated owing to local resonances, with little dependence on periodicity. It was further shown that locally resonant structures can also present negative effective properties at frequencies associated with the local resonance [START_REF] Lai | Hybrid elastic solids[END_REF][START_REF] Zhu | Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial[END_REF]. The use of local resonance for band gap engineering and the achievement of other intriguing properties have indeed paved new paths for the control of wave propagation.

Numerous works have been devoted to the design of resonant acoustic elements. Various configurations have been proposed, including systems with cross-like holes in a solid medium [START_REF] Wang | Large bandgaps of two-dimensional phononic crystals with cross-like holes[END_REF], very soft inclusions in a binary system [START_REF] Wang | Two-dimensional locally resonant phononic crystals with binary structures[END_REF], split rings inside water [START_REF] Elford | Matryoshka locally resonant sonic crystal[END_REF], inertial amplifiers [START_REF] Yilmaz | Phononic band gaps induced by inertial amplification in periodic media[END_REF], lattice structures with suspended masses [START_REF] Ma | Three-dimensional dielectric phoxonic crystals with network topology[END_REF], plates or surfaces with pillars [START_REF] Pennec | Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate[END_REF][START_REF] Achaoui | Experimental observation of locally-resonant and Bragg band gaps for surface guided waves in a phononic crystal of pillars[END_REF], or Helmholtz resonators [START_REF] Fang | Ultrasonic metamaterials with negative modulus[END_REF][START_REF] Lemoult | Acoustic resonators for far-field control of sound on a subwavelength scale[END_REF]. The corresponding line of research has broad scientific and practical implications into harnessing the propagation of acoustic and elastic waves [START_REF] Hussein | Dynamics of phononic material and structures: Historical origins, recent progess, and future outlook[END_REF]. In particular, elastic wave power can be transferred between small transducers coupled by their near-field radiation patterns [START_REF] Feng | Design of a CMOS system-on-chip for passive, near-field ultrasonic energy harvesting and back-telemetry[END_REF][START_REF] Mehdizadeh | Chip-Scale Near-Field Resonant Power Transfer via Elastic Waves[END_REF].

When resonators are brought at a close distance, typically smaller than the operating wavelength, near-field coupling between them may occur. In addition to transverse coupling [START_REF] Fu | A Micromachined reconfigurable metamaterial via reconfiguration of asymmetric split-Ring resonators[END_REF], longitudinal near-field coupling, i.e., coupling between adjacent units in the direction of wave propagation, is, for instance, employed to tune the response of photonic crystals [20,[START_REF] Powell | Near-field interaction of twisted split-ring resonators[END_REF]. In the context of locally resonant phononic or sonic crystals, longitudinal coupling has been shown to introduce deviations from simple models that neglect it [START_REF] Wang | Coupling of evanescent and propagating guided modes in locally resonant phononic crystals[END_REF]. In this paper, we investigate longitudinal near-field coupling between acoustic resonators. We specifically consider a very simple and inexpensive system composed of a finite sequence of air resonators grafted onto a waveguide. Measurements are performed in the audible range. It is found that longitudinal near-field coupling has very significant effects on the transmission through the waveguide. Furthermore, as we increase the separation between two identical resonators, spanning the range from the near to the far field, we observe a transition from a collective response of the near-field coupled resonators to a Fano-like transmission profile arising from pairs of resonators forming Fabry-Perot (FP) interferometers.

The paper is organized as follows. Experimental design and numerical methods used to obtain transmission spectra are described in Section 2. Evanescent waves of the acoustic waveguide and their appearance at the grafting point are discussed in Section 3. In Section 4, we turn our attention to aperiodic sequences with increasing separation between resonators. Finally, our results are summarized in Section 5.

Experimental and Numerical Methods

For the purpose of demonstration, we consider possibly one of the simplest resonant systems: a one-dimensional sequence of air tubes grafted onto a waveguide [START_REF] Fang | Ultrasonic metamaterials with negative modulus[END_REF][START_REF] Wang | Coupling of evanescent and propagating guided modes in locally resonant phononic crystals[END_REF]. The principle of the experiment and some samples are shown in Figure 1. We use inexpensive cylindrical polyvinyl chloride (PVC) cylinders for both the waveguide and the resonators. The waveguide supports only one propagating acoustic mode in air for frequencies under 2009 Hz; all experiments and computations are performed well below this cut-off frequency. The dispersion relation of guided waves in a waveguide is specifically discussed in Section 3.1.

Resonators are chosen between tubes of two different lengths, either long (h 1 = 24 cm) or short (h 2 = 4 cm). Such cylindrical tubes have a series of natural resonances that depend both on their length and on the boundary conditions at their ends. With one end closed and the other opening inside a waveguide, natural resonances of a tube are up-shifted in frequency compared to the same tube closed at both ends; the frequency shift can be related to the appearance of evanescent waves at the grafting location [START_REF] Wang | Coupling of evanescent and propagating guided modes in locally resonant phononic crystals[END_REF]. The fundamental resonance of the grafted short tube is at 1456 Hz; the third resonance of the grafted long tube is at 1642 Hz. By choosing close but different resonance frequencies, we wish to differentiate the strong coupling between tubes of equal length from the comparatively weaker coupling between tubes of unequal lengths (see the specific discussion in Section 3.2). We consider aperiodic sequences of five grafted tubes that are either short (0) or long [START_REF] Deymier | Acoustic Metamaterials and Phononic Crystals[END_REF]. The distance between two adjacent tubes is set to a = 8 cm, or about one third of the wavelength in air for all considered frequencies. Transmission spectra are considered around the fundamental resonance frequency of the short tube, with sequences [00111], [01011] and [01110], i.e., for a progressive increase of the separation l between short tubes. For comparison, we consider also transmission spectra around the third resonance frequency of the long tube, with sequences [11000], [10100] and [10001].

Measurements were conducted using a sound card connected to a personal computer to generate Gaussian pulses with adjustable central frequency and bandwidth. The pulses were played with a loudspeaker placed at one end of the waveguide. The same sound card was used to sample the signals recorded with a microphone at the other end of the waveguide. The sampling rate was chosen to be 384 kHz, which is amply sufficient to capture the relevant spectra. The acquisition duration was also chosen long enough to capture all signals exiting the waveguide with delay. All experimental measurements are normalized against the measurement for a bare waveguide, i.e., with no resonator present, obtained with exactly the same Gaussian pulse. Such a normalization procedure is used to smooth Fabry-Perot oscillations that appear from reflections at the ends of the 2-m-long waveguide. Though these oscillations are not completely canceled and can still appear in the normalized experimental transmission spectra, they have a negligible influence on the experimental results reported in Section 3. It is also noted that acoustic nonlinearities were verified to be negligible with our samples. We checked this point by repeating our experiments at different signal levels. Further details on the experimental measurement of isolated resonators and periodic sequences can be found in [START_REF] Wang | Coupling of evanescent and propagating guided modes in locally resonant phononic crystals[END_REF]. In order to evaluate numerically transmission through the samples, we used a three-dimensional time-harmonic finite element model of pressure wave propagation. Examples of such simulations are shown in Figure 1. Numerical implementation was performed using the Acoustics module of the commercial software Comsol Multiphysics 3.5a. The partial differential equation solved is the linear acoustics equation with pressure as the independent variable. Material parameters used here are the mass density, ρ = 1.2041 kg•m -3 , and the speed of sound, c = 342 m•s -1 . Moreover, sound attenuation is introduced in the calculation. In the frequency range from 1360 Hz to 1720 Hz, the sound attenuation parameter is supposed to be proportional to frequency. In comparison to the value for open air, the attenuation parameter we used is three times larger for a better match to experimental results. This larger attenuation in our experiments may be due not only to additional losses arising from imperfections of the samples, but also to the interactions at the interface between air and wall, which are not explicitly captured in the acoustic model. Continuity boundary conditions for pressure are imposed on all internal boundaries. A radiation boundary condition including an incident harmonic plane wave with unit pressure (p 0 = 1 Pa) is imposed on the left entrance boundary (denoted as σ 1 ), and a radiation boundary condition canceling incoming waves is applied on the right exit boundary (denoted as σ 2 ). All other external boundaries are set to the "wall" boundary condition, meaning that the normal velocity is zero on them, or, equivalently, that the normal derivative of pressure vanishes. With this setting, we avoid reflections at the ends of the waveguide and the appearance of spurious FP oscillations in the simulated spectra. Integration of the pressure field over the entrance and exit boundaries allows us to estimate the reflection and the transmission coefficients. More precisely, the transmission coefficient, t, and the reflection coefficient, r, are evaluated as

t = σ 2 pdV Ap 0 , (1)
r = σ 1 pdV Ap 0 -1, ( 2
)
where p is the pressure inside the waveguide and A = πd 2 1 /4 is the surface area of the boundaries. We let the angular frequency ω sweep the frequency range of interest in order to obtain spectra. Note that these formulas work if there is only one propagating guided mode and if boundaries σ 1 and σ 2 are in the far field of the resonators, so that evanescent waves can be assumed to have decayed sufficiently to be unnoticeable at those boundaries.

Evanescent Waves Originating from a Grafting Point

Guided Evanescent Waves

The dispersion relation of guided waves in a homogeneous acoustic waveguide are obtained by solving the acoustic wave equation

∂ 2 p ∂x 2 1 + ∂ 2 p ∂x 2 2 + ∂ 2 p ∂x 2 3 = - ω 2 c 2 p (3)
under the assumption that guided waves can be expressed as

p = ψ(x 1 , x 2 ) exp(-ıkx 3 ), ( 4
)
where ψ is the transverse modal distribution. Substituting Equation (4) into Equation (3), we get

∂ 2 ψ ∂x 2 1 + ∂ 2 ψ ∂x 2 2 + ω 2 c 2 ψ = k 2 ψ, ( 5
)
where k is the wavenumber of the guided waves. The complex dispersion relation of guided waves shown in Figure 2 is obtained by sweeping the frequency f = ω/(2π) in the range of interest and obtaining k 2 as the eigenvalue and ψ as the eigenvector in Equation [START_REF] Liu | Locally resonant sonic materials[END_REF]. At a given frequency, the wavenumber is either real or pure imaginary, corresponding to either propagating or evanescent guided modes. The fundamental resonance frequency of the short grafted tube and the third resonance frequency of the grafted long tube are indicated in Figure 2 by the two horizontal black lines. Around these frequencies, only the fundamental guided mode can propagate in the waveguide and all other modes are evanescent. The fundamental guided mode is non-dispersive and propagates at celerity c. For a homogeneous waveguide, the transverse modal function ψ 0 (x 1 , x 2 ) is simply a constant. All other higher-order guided modes are evanescent and dispersive: their wavenumbers are imaginary-valued functions of frequency and their amplitude decreases exponentially along the propagation direction. Owing to the symmetry of the waveguide, the first evanescent dispersion branch supports two independent and frequency-degenerate modes, as shown in Figure 2. These modes ψ 1a and ψ 1b are mutually orthogonal. Their transverse pressure distributions are typically representative of half-wavelength standing wave patterns.

Single Grafted Tube

Considered separately, a single grafted tube mostly acts as a localized and strongly dispersive mirror having a reflection coefficient peaking almost at unity at the resonance frequency. Actually, unit reflection would be obtained in the absence of loss. Figure 3a shows the computed reflection coefficient for a single short or long tube in the frequency range of interest. At the fundamental resonance ( f = 1456 Hz) of the short tube, the reflection coefficient of the long tube is quite small (|r| ≈ 0.1). This implies that the long tube has a small impact on transmission at the fundamental resonance of the short tube. In contrast, at the third resonance ( f = 1642 Hz) of the long tube, the reflection coefficient on the short tube retains a significant value (|r| ≈ 0.3). Similarly, this implies that the short tube could have a noticeable impact on transmission at the resonance of the long tube. Thus, when one type of tube is at resonance, the other type is not, but its presence still cannot be completely neglected.

Figure 3b,d present experimental measurements and numerical simulations for the single short or long tubes grafted onto a waveguide. A transmission dip following the standard Lorentzian profile is introduced at the resonance frequency, as should be expected [START_REF] Wang | Coupling of evanescent and propagating guided modes in locally resonant phononic crystals[END_REF] (see also Reference [START_REF] Wang | Coupling of evanescent and propagating guided modes in locally resonant phononic crystals[END_REF] for measurements of the other resonances of the long tube). The pressure distributions at resonance are shown for the single short tube in Figure 3c and for the single long tube in Figure 3e. Both show that a standing wave is formed to the left of the tube due to the interference of the incident propagating guided wave and the reflected propagating guided wave. Evanescent guided waves are clearly formed at the grafting points. They appear because the translational symmetry of the waveguide is broken at the grafting position, and they ensure the continuity of pressure before and after it.

Considering only the fundamental propagating guided mode and the first evanescent guided mode, the total pressure field inside the waveguide can be expressed as p = ψ 0 e -ıkx 3 + rψ 0 e ıkx 3 + sψ 1b e αx 3 if x 3 < 0, tψ 0 e -ıkx 3 + sψ 1b e -αx 3 if

x 3 > 0, (6)
where k = ω/c, α = | (k 1 (ω))| is the modulus of the imaginary part of the wavenumber for the first evanescent guided mode, and s is the evanescence coefficient [START_REF] Wang | Coupling of evanescent and propagating guided modes in locally resonant phononic crystals[END_REF]. Of the first two evanescent guided modes, only ψ 1b is excited because of the position of the grafting point on the waveguide. At a resonance frequency, the reflection and transmission coefficients are |r| ≈ 1 and |t| ≈ 0, respectively. Then, Equation ( 6) can be rewritten as

p ≈ ψ 0 (e -ıkx 3 + re ıkx 3 ) + sψ 1b e αx 3 if x 3 < 0, sψ 1b e -αx 3 if x 3 > 0. (7)
Since the amplitude of the transmitted guided wave is almost zero, the extent of evanescent waves along the direction of propagation can be visualized clearly on the right side of the grafting point. Moreover, the evanescent contribution in Equation ( 7) decreases rapidly to zero with increasing distance from the grafting point (see Table 1). Therefore, the standing wave pattern formed on the left side of the resonator as well as the canceling of transmission on its right side can be clearly observed in the far field of the pressure distributions of Figure 3c,e. [START_REF] Deymier | Acoustic Metamaterials and Phononic Crystals[END_REF]. Normalized pressure distributions at the remarkable frequencies are shown on the right-hand side. For simplicity, we only display vertical cross-sections going through the symmetry axis of the waveguide. In each case, the frequency of the incident harmonic guided waves is shown on top. The color scale is for pressure normalized with respect to the maximum pressure (Max).

( ) a2
( ) a3
( ) b2
( ) b3
( ) c2
( ) c3

Near-Field Coupling Regime

Let us first consider the case of sequence [00111] with two adjacent resonant short tubes (case l = a in Figure 4a). Amazingly, the transmission dip disappears almost completely and transmission to the propagating guided wave is close to unity for all frequencies. This fact does not mean, however, that the two short tubes are out of resonance, as can be checked from the pressure distributions at frequencies S 1 0 and S 1 1 in Figure 4a. Instead, each resonator strongly feels the evanescent waves attached to the other resonator and a strong near-field coupling results. Furthermore, it was checked by reproducing the numerical simulation without the long tubes that their presence almost does not change the transmission. This fact is consistent with the result in Figure 3 that the long tube has a small reflection coefficient around the fundamental resonance of the short tube. Interchanging the role of short and long tubes with sequence [11000] in Figure 5a, we note that the general trends remain the same.

When the separation between the two short tubes is enlarged to l = 2a with sequence [01011], a system of two transmission dips results in Figure 4b. Observing the pressure distributions at frequencies S 2 01 and S 2 02 , however, the first short tube is more strongly excited and plays a dominant role in the cancellation of transmission. The difference between both states seems to be that pressure in the second short tube oscillates with the same or the reverse phase compared to the first. In the case of the [10100] sequence around the resonance of the long tube in Figure 5b, there is only a single transmission dip. It was checked numerically that the presence or absence of the off-resonance short tubes leads to a single dip or a system of two dips in the transmission spectrum, respectively. This fact is consistent with the result in Figure 3 that the short tube has a relatively significant reflection coefficient around the third resonance of the long tube. These observations are a strong indication that a small perturbation in the environment of the long tubes, through weak near-field coupling, can anyway lead to significant changes in the transmission.

In case the separation between two resonant tubes remains small, l ≤ 2a, it appears from the previous discussion that the short tubes have a stronger influence on transmission at the resonance frequency of the long tubes than in the reciprocal situation. This can be explained by the difference in quality factors at resonance. Indeed, the long tubes have higher mechanical quality factors than the short tubes [START_REF] Wang | Coupling of evanescent and propagating guided modes in locally resonant phononic crystals[END_REF]. The value of the quality factor dictates the value of the reflection coefficient on a tube away from its resonance, as Figure 1a shows. Furthermore, at frequencies for which the reflection coefficient is close to zero, it is as if the off-resonance tubes were not present and could be replaced by the bare waveguide from the point of view of transmission.

Locally-Resonant Fabry-Perot Interferometers

When considering a larger separation (l ≥ 4a) between short tubes, such as for sequence [01110], it is expected that the near-field coupling that is due to evanescent waves gets smaller and eventually vanishes exponentially, in accordance with Table 1. The transmission spectra in Figure 4c start to assume an asymmetric Fano-like shape [START_REF] Goffaux | Evidence of fano-like interference phenomena in locally resonant materials[END_REF][START_REF] Miroshnichenko | Fano resonances in nanoscale structures[END_REF] instead of the simpler Lorentzian shape observed for smaller separations. More precisely, this shape is characterized by the simultaneous presence of a transmission dip centered near the resonance frequency of the single tube and of one or more transmission units. At the transmission dip S 4 0 , it can be observed in Figure 4(c2) that acoustic waves localize on the first tube while the second tube remains almost idle. This property was checked to remain true for larger separations. At the transmission unit S 4 1 , both short tubes are rather strongly excited in Figure 4(c3) and a standing wave establishes between them. Similar observations can be made regarding the transmission spectrum, the transmission dip L 4 0 , and the transmission unit L 4 1 in Figure 5c.

We interpret transmission units as caused by locally resonant FP interferometers formed by localized reflections on the resonators. Indeed, since the resonating tubes reflect efficiently propagating guided waves, a system of standing waves can be formed between two successive resonant tubes. According to this picture, the number of transmission units must increase proportionally to the separation between the two resonating tubes. Their frequencies are given by the condition that the effective round-trip FP cavity length is an integral number n of wavelengths, leading to the equation

l = Na = n λ 2 + 2η = n c 2 f + 2η, ( 8
)
where η is an effective distance accounting for the fact that reflection does not occur exactly at the center of the tubes because of the excitation of evanescent waves. This effective distance is a frequency-dependent quantity related to the details of the grafting geometry and is only obtained numerically in this work, as illustrated in Figure 6.

According to Equation ( 8), the resonances of locally resonant FP interferometers are given by parameters n and η, for a given separation l = Na. For instance, the parameters defining the frequencies of FP resonances in Figure 6b are n = 3 and η = -0.13a; parameters defining the frequencies of FP resonances in Figure 6c are n = 3 and η = 0.04a.

The influence on transmission units of off-resonance tubes present inside a locally resonant FP interferometer depends on the type of the additional tubes. For resonating short tubes, the presence or absence of off-resonance long tubes do not significantly affect the transmission: in Figure 4c, the frequency of the transmission unit is almost the same as the frequency in Figure 6b. Conversely, for resonating long tubes, the presence or absence of off-resonance short tubes affects the transmission: in Figure 5c, the frequency of the transmission unit moves to the other side of the transmission dip compared to Figure 6c. In a practical system based on resonators grafted on a waveguide, the transmission could thus be tuned efficiently by adjusting the properties of additional off-resonance resonators within a locally resonant FP interferometer.

Two Identical Resonators Grafted onto the Waveguide with a Large Separation

According to the analysis in the previous section, two identical tubes grafted at an arbitrary distance l along a waveguide create a locally resonant FP interferometer. The validity of this concept can be checked numerically for a rather large separation of the tubes. In this case, n in Equation ( 8) is large and we expect that the sequence of FP resonances will be given by the approximate formula

f n ≈ n c 2l , (9)
or a sequence of harmonics of a fundamental frequency. Figure 7 shows transmission spectra in the case that l = 30a. This distance is l = 2.4 m, about 10 times larger than the wavelength (λ ≈ 0.23 m). In this case, the two resonators could naively be supposed to be insensitive to one another. In fact, coupling of their evanescent fields can safely be ignored, but interference of reflected guided waves can still occur. Figure 7a shows transmission spectra for pairs of short or long tubes. The series of transmission units is seen to be given with a good approximation by formula [START_REF] Wang | Two-dimensional locally resonant phononic crystals with binary structures[END_REF]. The sequence of states S 30 11 to S 30 16 are actually associated with the values n = 19 to 24. The sequence of states L 30 11 to L 30 13 also correspond to n = 22 to 24. The pressure distributions for all these states are plotted in Figure 7b. FP oscillations with enhanced amplitude can clearly be seen to extend between the two resonating tubes.

As a note, a coefficient of finesse indicative of the width of the transmission peaks can be defined as

F = 4|r 0 | 2 (1 -|r 0 | 2 ) 2 , ( 10
)
where r 0 is the reflection coefficient on one resonator at the considered frequency. From this expression, it is clearly seen that high finesse can only be obtained as |r 0 | tends to unity. Locally-resonant FP interferometers can thus be made highly selective in frequency as a result of the strong dependence of the reflection coefficient with frequency. It should be noted, however, that if the separation

Conclusions

We have observed that longitudinal coupling between resonant elements grafted along an acoustic waveguide can be very strong in the near-field regime and can be exploited to tune the transmission. We have formed experimentally sequences of grafted resonators chosen among tubes of two different lengths. The sequences show either almost no attenuation or strong attenuation over a rather wide frequency bandwidth, simply by changing the separation between resonators. We have observed strong coupling between resonators having the same resonance frequency and weak coupling between resonators having different-but close-resonance frequencies. Moreover, when the separation between two identical resonators was larger than about half a wavelength, we observed the additional appearance of transmission units arising from the formation of locally resonant Fabry-Perot interferometers.

The acoustic system we have considered is one-dimensional and is easily reconfigurable [START_REF] Driscoll | Memory metamaterials[END_REF][START_REF] Tao | Reconfigurable terahertz metamaterials[END_REF][START_REF] Ou | Reconfigurable photonic metamaterials[END_REF][START_REF] Caleap | Acoustically trapped colloidal crystals that are reconfigurable in real time[END_REF] just by adjusting the length of the resonators and the order of their sequence. Longitudinal near-field coupling should be observable in two-and three-dimensional acoustic systems as well, since waves that are evanescent in the direction of propagation must also appear at the grafting positions of the resonators. Beyond acoustic waves, the same considerations extend naturally to elastic waves, though their vector character clearly would need to be taken into account.

1 Figure 1 .

 11 Figure 1. An acoustic system composed of a sequence of five short or long tubes grafted onto a waveguide. The displayed sequences are denoted by (a) [01110] and (b) [10001], where 0 or 1 represent either a short or a long tube. The distance between adjacent tubes is a. Photographs of the actual samples are shown as insets. Numerical simulations illustrating transmission cancellation are shown at the resonance frequency of (a) the short tube ( f = 1456 Hz) and (b) the long tube ( f = 1638 Hz). The color-bar indicates the amplitude of the pressure field normalized to the maximum pressure (Max). λ is the wavelength at the considered frequency. Dimensions in the experiment are L = 2 m, a = 8 cm, d 1 = 10 cm, d 2 = 5 cm, h 1 = 24 cm, and h 2 = 4 cm.

Figure 2 .

 2 Figure 2. Dispersion relation of the guided modes of an acoustic waveguide of diameter d 1 , obtained by solving for the square of the wavenumber, k 2 , as a function of frequency. Both real (propagating, blue color) and imaginary (evanescent, red color) branches of the dispersion relation are shown. Note that the branches with opposite sign of k exist as well. The cut-off frequency of the first guided mode is 2009 Hz. The two black lines mark the two resonances considered in this work. Pressure distributions for the two degenerate modes at the marked point on the first imaginary branch are shown on the right side.

Figure 3 .

 3 Figure 3. (a) numerical reflection coefficients for the single short (blue line) or the single long (red line) tube grafted onto a waveguide; (b) experimental and numerical transmission spectra for the single short tube grafted onto a waveguide; (c) pressure distribution field at the resonant frequency for the short tube; The color bar represents the normalized pressure with respect to the maximum pressure (Max) at the corresponding frequency; (d) experimental and numerical transmission spectra for the single long tube grafted onto a waveguide; (e) pressure distribution field at the resonant frequency for the long tube.

Figure 5 .

 5 Figure 5. Transmission through a sequence of five short or long tubes grafted onto a waveguide with increasing separation between long tubes for (a) l = a; (b) l = 2a; and (c) l = 4a. Other dimensions are defined in Figure 1. Experimental (thick black line) and computed (thin red line) transmission spectra around the third resonance frequency of the long tube are shown on the left-hand side. Remarkable frequencies are labeled L α β , with α = l/a indicating the normalized separation between the two long tubes and β indicating either a transmission dip (0) or unit[START_REF] Deymier | Acoustic Metamaterials and Phononic Crystals[END_REF]. Normalized pressure distributions at the remarkable frequencies are shown on the right-hand side. For simplicity, we only display vertical cross-sections going through the symmetry axis of the waveguide. In each case, the frequency of the incident harmonic guided waves is shown on top. The color scale is for pressure normalized with respect to the maximum pressure (Max).

Figure 6 .

 6 Figure 6. (a) schematic of a locally resonant Fabry-Perot interferometer formed by localized reflections. Reflections on the resonators are effectively shifted by distance η from the grafting center. Fabry-Perot resonances are formed when the separation l between resonators is the sum of an integer number of half-wavelengths plus twice distance η; (b,c) normalized pressure distributions at resonance for locally resonant Fabry-Perot interferometers in case of short or long tubes, for l = 4a. The color scale is for pressure normalized with respect to the maximum pressure (Max).

Figure 7 .

 7 Figure 7. Case of two resonators grafted onto a waveguide at distance l = 30a (l∼10 λ). (a) transmission spectra are shown for two short tubes (solid blue line) or two long tubes (solid red line); (b) normalized pressure distributions are shown at the remarkable frequencies indicated in (a). The color scale is for pressure normalized with respect to the maximum pressure (Max).

Table 1 .

 1 Amplitude decay of evanescent guided waves exp(-αna) as a function of the imaginary part of the wavenumber (α) and of the propagation distance na.

	α (m -1 )		n
		0	1	2	4
	21.1 @ 1456 Hz	1	0.18	0.034	0.0012
	25.3 @ 1642 Hz	1	0.13	0.017	0.0003

Acknowledgments: We thank Sarah Benchabane and Yue-Sheng Wang for fruitful discussions. Photographs of samples are courtesy of Rémi Meyer. Financial support by the Labex ACTION program (Contract No. ANR-11-LABX-0001-01) and the National Natural Science Foundation of China (grant No. 11642023) is gratefully acknowledged.

Aperiodic Sequences of Resonators

From this point on, we discuss measurements and numerical simulations for sequences of five grafted tubes. Figure 4 reports the transmission spectra in the frequency range of the fundamental resonance of the short tube, considering aperiodic sequences [00111], [01011] and [01110]; it also shows the pressure distribution at remarkable frequencies for which transmission minima and maxima are observed. Those remarkable frequencies are labeled S α βγ , with "S" referring to the short tube and with α = l/a indicating the normalized separation between the two short tubes and β indicating either a transmission dip (0) or unit [START_REF] Deymier | Acoustic Metamaterials and Phononic Crystals[END_REF]. [0111 ] 0 Remarkable frequencies are labeled S α βγ , with α = l/a indicating the normalized separation between the two long tubes and β indicating either a transmission dip (0) or unit [START_REF] Deymier | Acoustic Metamaterials and Phononic Crystals[END_REF]. If there are two transmission dips, they are identified using γ = 1, 2. Normalized pressure distributions at the remarkable frequencies are shown on the right-hand side. For simplicity, we only display vertical cross-sections going through the symmetry axis of the waveguide. In each case, the frequency of the incident harmonic guided waves is shown on top. The color scale is for pressure normalized with respect to the maximum pressure (Max).

Author Contributions: Both authors contributed equally to this research, discussed the results, and wrote the manuscript.

Conflicts of Interest:

The authors declare no conflict of interest.


Maroua Allani

H Nehari

K Cabane

Lebbou

M Alani

N Batis

T Laroche

A Nehari Ct

H Cabane

K Lebbou

J J Boy

Influence of the growth and annealing atmosphere on the electrical conductivity of LTG crystals

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Introduction

Owing to its high acoustic quality, its high piezoelectric coefficients and thermal stability, La 3 Ga 55 Ta 0. s0 14 (LGT) Langatate is a promising piezoelectric crystal for acoustic devices developed in the time and frequency domain and particularly for ultra-stable resonators (Bulk Acoustic Waves resonators) and high temperature wireless sensors. However, these applications requir homogenous material with reproducible and performed properties.

In ac . during the growth b Czochralski process and postgrowth heat treatment defects are created in LGT crystal, which limits its potential use. Poin defects, arising of the growth and post-growth conditions, can react as ionic and electronic charge carriers and generate conductive tosses particularly at high temperatures.

The presence of point defects significantly affects the physical and chemical properties. They can be revealed by chemical. optical and/or electrical analytical methods. In this paper, we present the characterization of the point defects and the electrical resistivity measurement of LGT crystals.

• Corresponding author. E-mail address: kheirreddine.lebbou@univ-lyonl.fr (K. Lebbou). hllp://dx.doi.org/ 10. 101 G/j.optmat.201 G.09.072 0925-3467/

Experimental

The samples

As presented previously [1.2], we have selected different LGT ingots grown under different conditions. For comparison, we selected LGS sample as standard. Details of the growth conditions, thermal annealing treatment and color are indicated in Table 1 which concerns 3 different sources: Cl (France), CK (USA) and FO (Russia).

Chemical analysis of LGT crystals

Electron Probe Micro-Analysis EPMA: major contents analysis

We have analyzed LGT samples by Electron Probe Micro-Analysis (EPMA) and we determined their atomic compositions. This microanalysis is performed on small polished samples (a few hundred square microns) having a thickness of about fifty microns. They are then bonded on resin or metal support. Each measurement corresponds to the average of a few tens of scans.

Femtosecond laser ablation !CP-MS (analysis of traces and ultra-traces of impurities)

Ail measurements were carried out on a DRC2 quadrupole ICPMS (Perkin Elmer) instrument coupled to an Alfamet Please cite this article in press as: M. Alani, et al., Influence of the growth and annealing atmosphere on the electrical conductivity of LTG crystals, Optical Materials (2016), http://dx.doi.org/10.1016/j.optmat.2016.09.072

HAL

  is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come    Influence of the growth and annealing atmosphere on the electrical conductivity of LTG crystals Maroua Allani, N Batis, Thierry Laroche, A Nehari, H Cabane, K Lebbou, Jean Boy To cite this version: Maroua Allani, N Batis, Thierry Laroche, A Nehari, H Cabane, et al.. Influence of the growth and annealing atmosphere on the electrical conductivity of LTG crystals. Optical Materials, 2017, 65, pp.99 -102. hal-02392622


Passive cooperative targets for subsurface physical and chemical measurements: a systems perspective

Jean-Michel Friedt

Abstract-We investigate the use of a commercially available Ground Penetrating RADAR (GPR) for probing the response of sub-surface sensors designed as passive cooperative targets. Such sensors must meet two design criteria: introduce a signature unique to the sensor which will hence be differentiated from clutter, and introduce in this signature a response characteristic allowing for recovering the physical quantity under investigation. Using piezoelectric substrates for converting the incoming electromagnetic pulse to an acoustic wave confined to the sensor surface (Surface Acoustic Wave transducer -SAW) allows for shrinking the sensor dimensions while providing sensing capability through the piezoelectric substrate acoustic wave velocity dependence with the physical quantity under investigation. Two broad ranges of sensing mechanisms are discussed: intrinsic piezoelectric substrate velocity dependence with a quantityrestricted to the measurement of temperature or strain and hence torque or pressure -and extrinsic load dependence on the sensor, allowing for the measurement of variable capacitive or resistive loads. In all cases the delay introduced by the physical quantity variation induces a phase rotation of the returned signal of a few periods at most, to be measured with a resolution of a fraction of a period: the GPR receiver sampling time reference must exhibit a long term stability at least as good as the targeted phase measurement needed to recover the physical quantity. We show that the commercial GPR exhibits excessive time-base drift, yielding a loss in the sensing capability, while a quartz-oscillator based alternative implementation of the classical stroboscopic sampling receiver compensates for such a drawback. Index Terms-surface acoustic wave, passive, wireless, sensor, ground penetrating radar, stability

I. INTRODUCTION

G ROUND Penetrating RADAR (GPR) cooperative targets [START_REF] Allen | The use of ground-penetrating radar with a cooperative target[END_REF] acting as passive sensors of sub-surface properties offer a complementary approach to mapping sub-surface dielectric and conductivity interfaces. In the cooperative target approach, the incoming electromagnetic pulse is delayed beyond clutter (Fig. 1), in our prefered implementation by converting the electromagnetic pulse to a 10 5 times slower acoustic wave [START_REF] Pohl | A review of wireless saw sensors[END_REF], and the returned signal delay is processed to recover the physical quantity. Clutter response, whose envelope including all returned signals from targets located at various distances from the emitter, is illustrated as the red envelope in Fig. 1: its power decays following the RADAR equation of Free Space Propagation Loss (FSPL) in which the emitted wave spreads energy on the surface of the propagating wavefront as 1/d 2 , meets a point-like target acting itselft as the source of the spherical wave, resulting in the classical 1/d 4 power decay with distance d. Because the acoustic wave,

FSPL clutter

Fig. 1. Time dependence of the various backscattered signal, allowing for time-division multiple access to the radiofrequency channel: a short time window includes the envelope of echoes returned by all the buried interface reflections (green), while the sensor response is delayed beyond clutter in a longer time-window. In a resonator configuration, either a strongly coupled but lower Q device (red) or a poorly coupled but high Q (blue) allows for delaying the response above clutter at a time beyond 0.6 µs. Between 0.6 and 1 µs, the strongly coupled material provides a better link budget, above 1 µs the weakly coupled material provides the best solution. The assumptions in drawing this chart is that the operating frequency is f = 100 MHz so that the link budget at 300 ns (d = 100 m in air) is 20 log 10 (f d/c) = 60 dB, the clutter RADAR cross section is 1 m 2 , and the resonator coupling coefficient and quality factor are K 2 0.03% ⇒ 20 log 10 (3 • 10 -4 ) = -70 dB and Q = 2200, or K 2 1% ⇒ 20 log 10 (1 • 10 -2 ) = -40 dB and Q 220 -the larger the coupling coefficient the lower the quality factor [START_REF] Wang | High kt2q, multi-frequency lithium niobate resonators[END_REF].

propagating at the air-piezoelectric substrate interface to meet boundary conditions of the acoustic field, exhibits a velocity dependence on such quantities as temperature [START_REF] Reindl | Theory and application of passive saw radio transponders as sensors[END_REF], stress [START_REF] Stoney | Characterization of differentially measured strain using passive wireless surface acoustic wave (saw) strain sensors[END_REF] or mass-loading [START_REF] Oh | The development of a wireless love wave biosensor on 41 • YX LiNbO 3[END_REF], the returned signal delay will be dependent on those quantities, with the sensor design stage aiming at selecting a piezoelectric substrate orientation and packaging emphasizing one of these quantities.

The delay between the incoming radiofrequency pulse and returned signal is either generated by loading energy in a cavity which only slowly unloads once the excitation is completed -a property of resonators with a power release time constant of τ = Q/(π •f ) with Q the quality factor and f the resonance frequency [START_REF] Reindl | Saw devices as wireless passive sensors[END_REF], or by patterning mirrors on the surface of a piezoelectric transducer propagating the pulse converted from electromagnetic to acoustic [START_REF] Bulst | State of the art in wireless sensing with surface acoustic waves[END_REF]. The former approach is poorly suited to the broadband GPR which records hardly enough periods of the (exponentially decaying) returned signal to accurately identify f [START_REF] Friedt | High-overtone bulk acoustic resonator as passive ground penetrating RADAR cooperative targets[END_REF], and the latter delay line method appears best suited when designing a GPR cooperative target. By using a differential approach, with two echoes returned by the sensor, the time of flight from the GPR unit to the buried sensor is eliminated, and an accurate estimate of the acoustic velocity is achieved by comparing the time of arrival of one echo with respect to the other. Such a comparison is classically performed by cross-correlation [START_REF] Howland | Fm radio based bistatic radar[END_REF], in this example by crosscorrelating the two time-windows including each one of the two echoes returned by the cooperative target.

The core assumption in extracting a precise acoustic velocity estimate from the echo delays is that the sampling rate is constant. Indeed, typical acoustic transducer velocity dependence with temperature are at most in the 100 ppm/K: assuming a 100 MHz transducer delaying the echo by 1 to 1.5 µs -enough to get rid of clutter and yet prevent excessive acoustic losses while propagating on the substrate surface [START_REF] Morgan | Surface acoustic wave filters: With applications to electronic communications and signal processing[END_REF] -then the time difference of 1.5 -1.0 = 0.5 µs is associated with 0.5 µs/0.01 µs= 50 complete phase rotations. Since the phase ϕ and velocity v variations are related by dϕ ϕ = dv v , then a numerical application with the given values of dv v 100 ppm/K and ϕ 50 × 2 • π yields dϕ 0.03 rad/K= 1.8 • /K. This targeted accuracy of 1/200th of a period for 1 K resolution requires that the sampling rate varies by no more than this targeted resolution, otherwise echo analysis cannot differentiate between time of flight variations (observed as phase shift) or sampling rate variations. This topic is addressed here when using a Commercial, Off The Shelf (COTS) RADAR system for probing acoustic transducers acting as cooperative targets. The experiments reported throughout this paper have been acquired with a Malå ProEx unit running either the proprietary software provided by the manufacturer (Groundvision) or custom software specifically designed for sensing applications [12].

II. ACOUSTIC TRANSDUCERS AS GPR COOPERATIVE TARGETS FOR PASSIVE SENSING

Two approaches for using acoustic transducers as passive cooperative targets for remote sensing use either intrinsic material property dependence with the environment of the sensor -temperature or stress dependence of the electromechanical coefficients [START_REF] Bechmann | Higher-order temperature coefficients of the elastic stiffinesses and compliances of alpha-quartz[END_REF] combined with dilatation and deformation of the substrate subject to such effects -or connect an external load to the acoustic mirrors [START_REF] Laroche | A coupled-mode filter structure for wireless transceiver-sensors using reactive loads[END_REF]. Such an external load impedance variation with a quantity -e.g. capacitance variation with moisture [START_REF] Reindl | Radio-requestable passive SAW water-content sensor[END_REF] when considering a capacitance architecture -induces a phase and amplitude variation on the reflected signal, readily detected on the echoes returned by the sensor. The challenging aspect of designing an external load is that matching impedance conditions must not prevent the incoming acoustic wave from being reflected: most demonstrations in the literature [START_REF] Reindl | Radio-requestable passive SAW water-content sensor[END_REF], [START_REF] Lee | Wireless hydrogen smart sensor based on Pt/graphene-immobilized radio-frequency identification tag[END_REF] introduce such large amplitude variations of the returned signal that the interrogation range becomes strongly degraded.

In addition to the development of dedicated transducer for sensing purposes as discussed previously [START_REF] Friedt | Surface acoustic wave devices as passive buried sensors[END_REF], we have considered commercially radiofrequency band-pass filters as suitable to this task [START_REF] Friedt | Passive cooperative targets for subsurface physical and chemical measurements[END_REF]: indeed, very high frequency (VHF) filters are compact thanks to the conversion of the electromagnetic wave to an acoustic wave using a piezoelectric substratemost commonly quartz, lithium niobate or lithium tantalate -and hence exhibit suitable properties. Such VHF filters are traditionally characterized in transmission mode (S 21 ) but are here considered as reflective transducers (S 11 ) with either a fixed impedance on the second port inducing a strong reflected signal due to impedance mismatch, with a delay dependent on the acoustic velocity and hence the physical environment of the transducer, or a variable impedance inducing a phase rotation on the returned echo. The constraint on selecting the appropriate transducer are on the one hand in the frequency domain -the filter central frequency must match the GPR pulse characteristics but more significantly the inverse of the filter bandwidth must match the GPR pulse duration for efficient coupling -and in the time domain the group delay of the filter must be within acceptable measurement durations for a GPR, ideally in the 1 to 2 µs range, but being twice the tabulated group delay given in transmission mode in the manufacturer's datasheet, practically closer to the 2 to 4 µs range when the filter is used in reflection mode . As an example of such an application, the TDK/Epcos B3607 (Fig. 2) filter exhibits an appropriate response: its center frequency of 140 MHz is compatible with a Malå 200 MHz unshielded dipole antenna located on a concrete slab, and its 6 MHz bandwidth induces a 150 ns returned echo duration, compatible with typical GPR measurement time windows. Fig. 3 demonstrates the measurement of a capacitive load, which was selected to demonstrate a load variation representative of classical Time Domain Reflectometry (TDR) moisture level measurement conditions. In this demonstration, the load circuit is tuned through an inductor selected to be resonant at 140 MHz with the capacitance. Recovering the capacitance value is demonstrated through the filter reflection coefficient: on top of Fig. 3, the amplitude is hardly affected by the load variation with the returned echo delayed by 2.7 µs, while the phase (bottom graph) rotates by 120 • a 14 to 63 pF load capacitance variation. In this example simulating a moisture detector in which soil permittivity is assumed to evolve from ε r 5 when dry to ε r 22 when wet or a 4.5-fold relative permittivity rise, measuring the returned echo phase with sub-30 • accuracy is again mandatory.

Fine time delay analysis is best performed as a crosscorrelation between adjacent echoes. Since a cross-correlation of a periodically varying signal is itself varying with the same period, the technique is sensitive to 2π phase rotation uncertainties. Furthermore, while cross-correlation in the time domain is an algorithm whose complexity rises as the square of the number of samples, the classical implementation is to reach the Fourier domain in which the cross-correlation becomes the dot product of the Fourier transforms, an algorithm requiring only a N • log(N ) complexity thanks to the Fast Fourier Transform (FFT). Hence, analyzing the difference of the phase of the Fourier transform at its maximum power provides a fine estimate of the lag between adjacent echoes [START_REF] Oppenheim | The importance of phase in signals[END_REF] and, considering the fixed geometrical path over which the acoustic wave propagates, a fine measurement of the acoustic velocity. Such a fine analysis will however emphasize the poor stability of GPR receiver time base with respect to current frequency references.

III. COMMERCIAL GPR MEASUREMENT OF ACOUSTIC

TRANSDUCERS

Experimental measurements have been performed as follows: a set of 250 MHz shielded Malå antennas were elevated about 10 cm above concrete using two wooden blocks in order to locate an acoustic transducer connected to a dipole antenna with a polarization parallel to the GPR antennas (Fig. 4). In order to optimize the transducer signal when illuminated by the GPR, the transducer is no longer a commercial filter diverted from its original purpose but a custom delay line made of lithium niobate YXl/128 • , a crystalline orientation well known for propagating a Rayleigh wave exhibiting strong coupling and high temperature sensitivity (70 ppm/K), two properties suitable for a cooperative target for measuring sub-surface temperature. The design of this transducer was described in detail in [START_REF] Friedt | Surface acoustic wave devices as passive buried sensors[END_REF] and will be used to gather the data shown in Figs. 5 to 8.

The GPR unit is switched on, and measurements start right after the software configuration setup is complete, requiring at most a few minutes. While we are well aware of the electronic unit warming up during the initial minutes, Figs. 5 exhibit slow drift for well above an hour, a significant hindrance when measuring on the field with a unit running on batteries. Figs. 5 and6 (bottom right) exhibit the difference of the phases of the Fourier transform at its maximum amplitude, a fine measurement of the lag between the two echoes returned by the sensor. We have verified that a second-order polynomial fit on the cross-correlation magnitude of the two real signals, or the phase of the Fourier transform at the bin at which maximum power is measured (in the frequency domain) yield consistent results. In the time domain, a cross correlation on samples acquired with sampling step t s yields a time resolution on the echo position delay of t s , which is then oversampled by using a parabolic fit on the cross-correlation magnitude. Such an oversampling strategy allows for reducing the delay uncertainty to a fraction of t s dependent on the signal to noise ratio. In the charts shown in Figs. Reaching a stable asymptotic condition, three current pulses power a 5 Ω power resistor to heat the sensor to 80 • C as observed on the Pt100 probe. Having reached this temperature, the sensor is let to cool back to room temperature before the next heating step starts (Fig. 5). The experiment is repeated (Fig. 6) after the GPR unit has stabilized after more than 2 hours of operation: here no significant drift of the baseline is observed and the two heating steps to 80 • C are readily identified.

Rather than focus on the processed data, the raw RADARgram already exhibits such a drift: Fig. 7 focuses on the emitted pulse (top) and the returned echo (bottom). Because the acoustic delay line transducer is made of an optimum number of electrode pairs of 20 (equal to the inverse of the electromechanical coupling coefficient [START_REF] Morgan | Surface acoustic wave filters: With applications to electronic communications and signal processing[END_REF]), a single incoming echo induces 20 periods in the returned echo, as seen on Fig. 7 (bottom). The initial drift between traces 0 and 1000, followed by the slow stabilization prior to the three heating steps (traces 2500, 3000 and 4000), is well visible while the emitted pulse position remains stable throughout the experiment.

IV. DISCUSSION

The excessive time-base drift requires either to increase the sensor sensitivity, or to improve the time base stability. The former approach requires for example to increase the time delay between the reflected echoes, with the drawback of additional acoustic losses (which remains hardly an issue at sub-GHz frequencies) and increased sensor dimensions. Most dramatic though is the physical limitation in some measurement strategies which prevent high sensitivity: in the case of gravimetric measurements for detecting chemical compounds in sub-surface environments, typical gravimetric sensitivities S relating the relative velocity shift to the mass ∆m adsorbed per unit area A are S = dv v • A ∆m 200 cm 2 /g at most, so that a detection limit given by ∆m A = ∆ϕ ϕ • 1 S = 25 µg/cm 2 , well above the targeted detection limit of a few tens of nanograms par square centimeters in most applications.

Despite being well suited to sensor probing thanks to the ability to define the time-offset of various time-windows, either for sub-surface interface probing or sensor interrogation, stroboscopy must not degrade the sampling rate stability. Although the detailed implementation by Malå of their stroboscopic receiver is described in [START_REF] Johansson | Ground penetrating radar array and timing circuit[END_REF], we base our analysis on our own implementation attempt [START_REF] Chrétien | A stroboscopic approach to surface acoustic wave delay line interrogation[END_REF] in which the variable delay is coarsely set by an FPGA and finely tuned by a programmable delay line, in our case Maxim DS1023. Since this particular component stability with environment, and most significantly temperature, is not characterized by the manufacturer, we consider the information provided by Data Delay Devices Inc. in their 3D3418 series programmable delay lines in which a ±3% stability is given over the 0 --70 • temperature range. Such a percent range stability, or 10000 ppm if 1% is considered, is well below expected stabilities for high quality acquisition systems, with quartz oscillators commonly exhibiting stability in the few tens of ppm, or a thousand fold stability improvement. Hence, the alternative is to replace the poor sampling rate stability generated by the programmable delay lines with a quartz-stabilized sampling rate. Such a solution was proposed in [START_REF] Minary | Note: A dualchip stroboscopic pulsed radar for probing passive sensors[END_REF], and indeed yields acceptable sensor resolution with, for example, a gravimetric detection limit lowered to a few tens of nanograms per square centimeter, consistent with classical biosensor detection limits.

In addition to these considerations focusing on the receiver stage, another cause of concern is on the emitter: the avalanche transistor [START_REF] Williams | High speed amplifier techniques[END_REF] feeding the antenna with a single powerful pulse in the pulsed RADAR approach introduces a possible variability on the emitted spectrum (Fig. 8). Indeed, while the pulse duration is determined by the high-voltage capacitance accumulating charges on the collector of the avalanche transistor before the next pulse is triggered by polarizing the base, the antenna connected to the transistor emitted through a balun acts as a filter of the broadband pulse. The transfer function of the antenna is strongly dependent on the permittivity of its environment [START_REF] Balanis | Antenna theory -analysis and design[END_REF]: even shielded antennas are in close contact with the soil and permittivity variations will introduce variations in the emitted pulse spectrum. However because the acoustic wave propagation introduces a phase given by the acoustic path length to the wavelength ratio, varying the pulse spectrum will vary the phase rotation introduced by a given path length and assuming a constant acoustic velocity. Because wet to dry soil will induce drastic permittivity changes, the loaded dipole central frequency can vary by up to 50% and so will the emitted pulse spectrum. Such effects are readily observed when performing GPR measurements on wet snow, where permittivity strongly varies from rock to ice to snow to water soaked snow.

V. CONCLUSION

We have addressed the issue of stability of the receiver stage of stroboscopic sampler of a commercial Ground Penetrating RADAR (GPR) when probing the response of a cooperative target acting as a passive wireless sensor whose output information lies in the returned echo phase. While the echo delay is representative of the physical quantity under investigation, the phase variation associated with typical temperature, stress or mass loading variations is in the fraction of period range, while the sampling rate drift after the receiver is switched on is in the multiple period range. Since the sensor sensitivity is limited by the physics of acoustic wave propagation, the sensor response being delayed beyond clutter in a compact package by converting the electromagnetic to an acoustic wave through the polarization of a single crystal piezoelectric substrate, the solution lies in providing a stable receiver time-base. By using a stroboscopic approach clocked by a quartz stabilized timebase, sufficient stability is reached for probing passive wireless sensors by a GPR instrument.

Jean-Michel Friedt obtained his PhD in 2000 after working on biosensors and scanning probe microscopy. He became involved in the use of acoustic transducers as passive wireless sensors when he joined the company SENSeOR as a systems engineer in 2006, and with GPR as a tool for mapping a polar glacier thickness and subsurface features in Spitsbergen. Both topics appeared perfectly matched, becoming a core research activity since he joined the Franche-Comté University in Besanc ¸on, France, in 2014 as assistant professor.

  J.-M. Friedt is assistant professor at Franche-Comté University with his research activities hosted by the Time & Frequency department of the FEMTO-ST Institute in Besanc ¸on, France. E-mail: jmfriedt@femto-st.fr.

Fig. 2 .

 2 Fig. 2. Pictures of the closed (top) and opened (bottom) SAW filter: despite some scratches made on the electrodes while removing the polymer seal over the electrode area, the general structure of the filter with the input and output interdigitated transducer electrodes is visible.

Fig. 3 .

 3 Fig.3. Magnitude (top) and phase (bottom) of the time-domain response of the filter used in reflection mode and loaded with a variable capacitance in parallel to a fixed 10 pF capacitance. The sum of the capacitances is given in the legend on the top left of the top graph, the color coding scheme being also valid for the bottom graph and the inset. Inset: zoom on the magnitude of the first echo, emphasizing the losses confined to the 19 to 24 dB range over the whole capacitance range.

Fig. 4 .

 4 Fig. 4. Experimental setup including a sensor connected to a dipole antenna operating in the 250 MHz range, and the Maå ProEx GPR unit fitted with shielded 250 MHz antennas.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Left: low sampling rate of the whole GPR trace (top left) and zoom on the echo returned by the sensor (bottom left), acquired using the proprietary Malå Groundvision software. Right: window centered on the two echoes returned by the sensor, recorded with the custom ProexGPRcontrol software (right), and phase difference extracted as the cross-correlation maximum position.

Fig. 7 .

 7 Fig. 7. Two time windows of the acquisition emphasizing the lack of drift on the position of the emitted pulse (top), and the sampling rate associated drift in the returned signal position after 1.33 µs.

  5 and 6 (bottom right), the sampling rate being 6834 MHz, the phase lag given as an ordinate scale is converted to a time lag by selecting t s = 1/6834 µs=146 ps and 15 sampling interval lags last 2.2 ns or about half a period of a 250 MHz signal. Hence, the drift during warm up observed in Fig. 6 of 30 sampling time intervals is equal to 4.4 ns or one full period of the 250 MHz signal. While these measurements are performed, a Pt100 probe glued to the sensor is used to check that the room temperature does not vary by more than 1 • C during this time interval. One full phase rotation would have needed, on our sensor with 70 ppm/K sensitivity, a temperature variation of dϕ/ϕ = 70 • 10 -6 × 1/dT ⇒ dT = (1/325) • (1/70 • 10 -6 ) = 44 • C since the phase rotation of a 1.3 µs echo delay on a 250 MHz delay line is 1.3 × 250 = 325 periods.

Fig. 8 .

 8 Fig.8. Emitted spectra recorded over 35 minutes (green region of the time domain inset curve), and spectrum of the signal returned (red region of the time domain inset curve) by the sensor in a constant environment: no visible evolution of the emitted or returned signal is visible over this time span, confirming the cause of the phase drift as being due to the stroboscopic receiver timebase.

ACKNOWLEDGMENT

The Malå ProEx GPR control unit acquisition was funded by a grant from the Franche-Comté district. Part of these investigations were motivated by the CITEPH SMASH project.


C Fluhr

B Dubois

V Soumann

G Le Tetû

V Giordano

S Grop

J Paris

A Low Power Cryogenic Sapphire Oscillator with better than 10 -15 short term frequency stability

In the field of Time and Frequency metrology, the most stable frequency source is based on a microwave whispering gallery mode sapphire resonator cooled near 6 K. Provided the resonator environment is sufficiently free of vibration and temperature fluctuation, the Cryogenic Sapphire Oscillator (CSO) presents a short term fractional frequency stability of better than 1 × 10 -15 . The recent demonstration of a low maintenance CSO based on a pulse-tube cryocooler paves the way for its deployment in real field applications. The main drawback which limits the deployment of the CSO technology is the large electrical consumption (three-phase 8 kW peak / 6 kW stable operation) of the current system.

In this paper, we describe an optimized cryostat designed to operate with a low consumption cryocooler requiring only 3 kW single phase of input power to cool down to 4 K a sapphire resonator. We demonstrate that the proposed design is compatible with reaching a state-of-the-art frequency stability.

I. INTRODUCTION

The Cryogenic Sapphire Oscillator (CSO) is the microwave oscillator which features the highest short-term frequency stability [START_REF] Giordano | The autonomous cryocooled sapphire oscillator: A reference for frequency stability and phase noise measurements[END_REF]. With the advent of low maintenance CSO based on a closed cycle cryocooler, 1 × 10 -15 fractional frequency stability is now avaible for real field applications. The autonomous CSO enables the operation of laser-cooled microwave clocks at the quantum limit [START_REF] Santarelli | Quantum projection noise in an atomic fountain: A high stability cesium frequency standard[END_REF], [START_REF] Abgrall | High-stability comparison of atomic fountains using two different cryogenic oscillators[END_REF], the improvement of the resolution in Very Long Baseline Interferometry (VLBI) and in the deep-space netwoks for space-vehicle ranging and Doppler tracking [START_REF] Dick | Temperature compensated sapphire resonator for ultra-stable oscillator capability at temperatures above 77K[END_REF]- [START_REF] Rioja | The impact of frequency standards on coherence in VLBI at the highest frequencies[END_REF]. It can enhance the calibration capability of Metrological Institutes, and help for the qualification of high performances clocks and oscillators [START_REF] Dolgovskiy | Ultra-stable microwave generation with a diode-pumped solid-state laser in the 1.5-µm range[END_REF], [START_REF] Giordano | New generation of cryogenic sapphire microwave oscillator for space, metrology and scientific applications[END_REF]. Nevertheless, the large electrical consumption (three-phase 8 kW peak/6 kW stable operation) of the current system is the main obstacle to the deployment of the CSO technology. This paper describes an optimized cryostat designed to operate with a low consumption cryocooler requiring only 3 kW single phase of input power to cool down to 4 K a sapphire resonator. The proposed design is compatible with reaching a state-of-the-art frequency stability.

II. HIGH PERFORMANCES CSOS OF THE OSCILLATOR-IMP PROJECT

The Oscillator IMP project targets at being a facility dedicated to the measurement of noise and short-term stability of oscillators and devices in the whole radio spectrum (from MHz to THz), including microwave photonics. A set of three CSOs constitutes one of the reference of the Oscillator IMP metrological platform [START_REF] Giordano | The autonomous cryocooled sapphire oscillator: A reference for frequency stability and phase noise measurements[END_REF]. The figure 1 shows these three instruments that have been successively assembled since 2012. They are in principle equivalent, but differ from several details. Two of them (CSO-1 and CSO-2) are equiped with a PT-405 cryocooler from Cryomech requiring a 6 kW compressor. The last one incorpores a PT-410 and a 8 kW compressor. The three-cornered-hat method has been used to extract the individual fractional frequency stability of each CSO. The three oscillators present a stability better than 1 × 10 -15 between 1 s and 10,000 s (see Fig. 2) [START_REF] Fluhr | Characterization of the individual short-term frequency stability of cryogenic sapphire oscillators at the 10 -16 level[END_REF].

III. THE ULISS PROJECT

One of these CSOs, codenamed ULISS, can be transported with a small truck. In two years ULISS visited several European sites, traveling more than 10,000 km [START_REF] Giordano | New generation of cryogenic sapphire microwave oscillator for space, metrology and scientific applications[END_REF]. Measuring ULISS before and after traveling, we can validate stability and spectral purity at destination. It has been used for example to check on the stability of a laser stabilized on a ULE cavity, and to run with a cold atom fountain at SYRTE (see Fig. 3). The ULISS Odissey was the opportunity to demonstrate the potentiality and the reliability of our technology. It was also pointed out that the electrical consumption and the heat released by the compressor could turn out to hinder the deployment of this technology. The project ULISS-2G was launched to solve this technological difficulty with the aim to divide by two the electrical consumption.

IV. NEW CRYOSTAT DESIGN OVERVIEW

Our design is based on a 3 kW PT-403 cryocooler from Cryomech delivering typically 0.25 W at 4 K. For this cryocooler the frequency of the thermodynamical cycle is about 1.4 Hz. The levels of mechanical displacement of the 2 nd stage cold plate induced by the gas flow inside the Pulse-Tube are 25 µm peak-to-peak in the vertical direction and 12 µm peak-to-peak in the horizontal one [START_REF] Wang | Development of 4 K pulse tube cryorefrigerators at cryomech[END_REF]. The temperature variation on the PT 2 nd stage is typically 100 mK rms. Our main objective is to develop a cryostat as simple as possible avoiding a high cost and a complex optimisation. Thus we choose a simple passive filtering inspired from Tomaru et al. [START_REF] Tomaru | Cryocoolers 13, ch. Vibration-Free Pulse Tube Cryocooler System for Gravitational Wave Detectors, Part I: Vibration-Reduction Method and Measurement[END_REF]. Fig. 4 shows an overview of the CSO cryostat. The microwave resonator is rigidly attached to the top flange of the cryostat whose external surrounding walls are made as rigid as possible keeping reasonable mass and space. The rotary valve unit, which could generate large vibrations, is separated from the cold-head. The cold-head itself still remains an important source of vibrations. Thus it is supported by a set of 8 springs providing the vibration insulation. A bellows makes the connection with the vacuum can. The remaining vibrations come from the pressure oscillation in the pulse tube and regenerator transmitted to the cold-stage through thermal links. The vibration reduction is obtained by using flexible metal heat links (copper braids). The temperature variations are passively filtered by the thermal ballast constituted by the stainless steel top flange of the 2 nd stage thermal shield. Associated with the thermal resistance of the flexible thermal link it is equivalent to a first order filter. The cavity is attached to the thermal ballast. A thermal sensor and a 25 Ω resistive heater are anchored in the cavity foot. They allow the control of the resonator temperature. Four microwave UT-085 semirigid Be/Cu cables link the resonator assembly to the external circuits. These cables are thermalized on each stage.

To optimize this design with regard to the CSO performance, trade-offs have been made between the vibration attenuation, the thermal conductance of the links and the ballast thermal mass [START_REF] Fluhr | A low power cryocooled autonomous ultra-stable oscillator[END_REF].

The figure 5 shows a 3D-view of the cryostats internal part and a picture of the 2 nd stage suspension. The V-shaped suspension rods enable to stiffen the suspension in the transverse direction. To limit the thermal conduction these suspensions are made in Mylar and simply realized using a 3D-printer.

V. EXPERIMENTAL VALIDATION

A resonator was assembled and mounted inside the cryostat. The sapphire resonator is made from a Kyropoulos monocrystal [START_REF] Giordano | Tests of sapphire crystals manufactured with different growth processes for ultra-stable microwave oscillators[END_REF]. The temperatures evolution during the cool down is shown in Fig. 6 The resonator temperature is stabilized using a commercial temperature controller. By changing the temperature set-point step-by-step we obtain the resonator frequency evolution (see Fig. 8). The resonator presents a turnover temperature equals to 5.24 K. Stabilized at this point, its frequency is no longer ν-ν (Hz) sensitive to the temperature fluctuations and a high frequency stability can be obtained. This resonator has been inserted in an oscillator loop complemented with a Pound servo and a power stabilization. The oscillator delivers 10 dBm at ν 0 = 10.02 GHz.

In a first step, the close-to-carrier phase noise of the prototype has been evaluated. Its 10 GHz output signal is mixed with those delivered by one of the ultra-stable 6 kW CSO. The obtained 26 MHz beatnote is sent to a Symmetricom 5125A phase noise test set. The observed phase noise is shown in the Fig. 9. The upper curve was recorded when the springs supporting the PT cold-head were intentionally blocked: the bolt getting through every spring was tightened. In this case the vibration of the cold-head are almost integrally transferred to the cryostat. The spectrum shows a large line at 1.47 Hz and its harmonics, which are the signature of the cold-head vibration. The other smaller line at 1.41 Hz comes from the 6 kW CSO. When the springs are released (see Fig. 9 lower curve), the 1.47 Hz line almost completely disappears and its harmonics are also strongly attenuated. From this second spectrum, the resonator displacement is estimated to be less than 0.1 µm.

To evaluate the frequency performance of the prototype, it has been simultaneously compared to two high stability 6 kW CSOs. The three-cornered-hat method [START_REF] Fluhr | Characterization of the individual short-term frequency stability of cryogenic sapphire oscillators at the 10 -16 level[END_REF], [START_REF] Gray | A method for estimating the freqeuncy stability of an individual oscillator[END_REF] has been used to extract the prototype fractional frequency stability. 10. Fractional frequency stability of the 3 kW prototype evaluated using the three-cornered-hat-method with two ultra-stable 6 kW CSOs used as references [START_REF] Fluhr | Characterization of the individual short-term frequency stability of cryogenic sapphire oscillators at the 10 -16 level[END_REF]. presents a fractional short term frequency stability below 1 × 10 -15 . At long integration time the fractional frequency stability is degraded proportionnaly to τ . The observed drift (approximately 3 × 10 -14 /day) could result from the large temperature variations inside the laboratory. The three reference CSOs have recently been moved in a temperature stabilized room at 22 • C ±0.5 • C. The new prototype stays in another experimental room equipped only with the standard air-conditioning system of the flat. Depending on the sunlight the temperature near the cryostat can vary of several degrees during the day.

VI. CONCLUSION

A new cryostat has been designed to cool-down a sapphire microwave resonator intented to serve as the frequency reference of an ultra-stable oscillator. This new cryostat is equipped with a 3 kW PT cryocooler sufficient to reach a temperature of 4.1 K. A specially designed suspension permits to filter the 1.4 Hz vibration generated by the pulse-tube. A preliminary performance evaluation shows a short term fractional frequency stability below 1 × 10 -15 for 1 s≤ τ ≤ 2000 s.

Fig. 1 .

 1 Fig. 1. The three CSOs of the OSCILLATOR-IMP platform.

Fig. 2 .

 2 Fig. 2. The three individual ADEV obtained from the 3-cornered-hat method.

Fig. 3 .

 3 Fig. 3. ULISS in SYRTE, where it was used as flywheel oscillator to run the fountain atomic clock.

Fig. 4 .

 4 Fig. 4. CSO cryostat: design overview (left), picture of the prototype (right). The rotary valve is located remotely from the cryostat.

Fig. 5 .

 5 Fig. 5. Internal 3D view of the cryostat and picture of the 2 nd stage suspension.

  :

Fig. 6 .

 6 Fig.6. Temperatures evolution during cool-down. Resonator temperature (bold line), 2 nd -stage shield temperature (dotted line), 1 st stage shield temperature (dashed line).

Fig. 7

 7 Fig. 7 shows the modulus of the resonator response around the whispering gallery mode at ν 0 ∼ 10 GHz measured at the minimum achievable resonator temperature, i.e. 4.1 K. The bandwidth is 7.2 Hz equivalent to a loaded Q-factor Q L ∼ 1.4 × 10 9 .The resonator temperature is stabilized using a commercial temperature controller. By changing the temperature set-point step-by-step we obtain the resonator frequency evolution (see Fig.8). The resonator presents a turnover temperature equals to 5.24 K. Stabilized at this point, its frequency is no longer

Fig. 7 .Fig. 8 .

 78 Fig. 7. Transmissiom resonator response around the resonance frequency ν 0 ≈ 10 GHz.

φFig. 9 .

 9 Fig. 9. Upper curve: Phase noise when the bellows springs are blocked. Lower curve: bellows springs realesed.

ACKNOWLEDGMENT

This work has been realized in the frame of the ANR projects: Equipex Oscillator-Imp and Emergence ULISS-2G. The authors would like to thank the Council of the Région de Franche-Comté for its support to the Projets d'Investissements d'Avenir and the FEDER (Fonds Européen de Développement Economique et Régional) for funding one CSO.