Augustin Caillas

Stéphan Suffit

Pascal Filloux

Emmanuel Lhuillier

Aloyse Degiron
email: aloyse.degiron@u-paris.fr

Anomalous Absorption in Arrays of Metallic Nanoparticles: A Powerful Tool for Quantum Dot Optoelectronics

Keywords: Active Metasurfaces, Colloidal Quantum Dots, Local Kirchhoff law, Infrared Waves, Electromagnetically Induced Absorption

MAIN TEXT

In most instances, the optical properties of periodic arrays of noble metal nanoparticles are governed by the plasmonic resonances sustained by each metallic inclusion. The main difference between these resonances and those sustained by isolated nanoparticles is that they are broadened and shifted to longer or smaller wavelengths due to the weak coupling between adjacent unit cells [START_REF] Kelly | The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment[END_REF] . At resonance, the scattering cross-section of the nanoparticles is maximized, resulting in transmission dips that make the structures usable as passive optical absorbers or filters [START_REF] Si | Reflective Plasmonic Color Filters Based on Lithographically Patterned Silver Nanorod Arrays[END_REF][START_REF] Yang | Angle Robust Reflection/Transmission Plasmonic Filters Using Ultrathin Metal Patch Array[END_REF] . Moreover, the high local fields associated with plasmonic arrays have been used to produce strong surface enhanced Raman scattering [START_REF] Grand | Role of Localized Surface Plasmons in Surface-Enhanced Raman Scattering of Shape-Controlled Metallic Particles in Regular Arrays[END_REF] , increase the luminescence output of dipolar media [START_REF] Corrigan | Enhanced Fluorescence from Periodic Arrays of Silver Nanoparticles[END_REF][START_REF] Bakker | Nanoantenna Array-Induced Fluorescence Enhancement and Reduced Lifetimes[END_REF] and endow quantum dot LEDs with advanced functionalities [START_REF] Wang | Electroluminescence of Colloidal Quantum Dots in Electrical Contact with Metallic Nanoparticles[END_REF] .

Conversely, these structures can also enhance the absorption cross-section within solar cells [START_REF] Mandal | Progress in Plasmonic Solar Cell Efficiency Improvement: A Status Review[END_REF] and infrared detectors [START_REF] Yifat | Mid-IR Colloidal Quantum Dot Detectors Enhanced by Optical Nano-Antennas[END_REF][START_REF] Tang | Plasmon Resonance Enhanced Colloidal HgSe Quantum Dot Filterless Narrowband Photodetectors for Mid-Wave Infrared[END_REF][START_REF] Tang | Thermal Imaging with Plasmon Resonance Enhanced HgTe Colloidal Quantum Dot Photovoltaic Devices[END_REF][START_REF] Chu | Near Unity Absorption in Nanocrystal Based Short Wave Infrared Photodetectors Using Guided Mode Resonators[END_REF] , considerably improving the responsivities of the devices.

Interestingly, the properties of periodic plasmonic arrays are known to change dramatically in the special case of nanoparticles plunged in an (almost) symmetric environment and at wavelengths allowing the emergence of non-zeroth diffraction orders. Under these very specific conditions, the coupling to grazing diffraction orders and the plasmonic resonances lead to the formation of lattice surface modes [START_REF] Carron | Resonances of Two-Dimensional Particle Gratings in Surface-Enhanced Raman Scattering[END_REF][START_REF] Zou | Silver Nanoparticle Array Structures That Produce Remarkably Narrow Plasmon Lineshapes[END_REF][START_REF] Auguié | Collective Resonances in Gold Nanoparticle Arrays[END_REF][START_REF] Teperik | Superradiant Optical Emitters Coupled to an Array of Nanosize Metallic Antennas[END_REF] . These dispersive and polarized modes are so narrow (half width at half maximum of a few nanometers) and low-loss that they can dramatically enhance and polarize the luminescence of dipolar media [START_REF] Rodriguez | Quantum Rod Emission Coupled to Plasmonic Lattice Resonances: A Collective Directional Source of Polarized Light[END_REF] and even lead to lasing [START_REF] Guan | Quantum Dot-Plasmon Lasing with Controlled Polarization Patterns[END_REF] and photonic Bose-Einstein condensation in such active layers [START_REF] Hakala | Bose-Einstein Condensation in a Plasmonic Lattice[END_REF] . Here, we show that there exists another interesting special case that emerges when the particle inter-distance is very small, regardless of whether the local environment surrounding the plasmonic nanoparticles is symmetric or not. We start this study with finite element simulations of the periodic array of Au nanoparticles depicted on Figure 1a. The structure is supported by a dielectric substrate with refractive index ng = 1.45 (corresponding to the value of the glass substrates used in our experiments), the nanoparticles are 25 nm thick, they have a square shape of 400 nm by 400 nm and the period is P = 600 nm. The spatial extension of the array is taken as infinite so as to reduce the computational domain to a single periodic unit cell (see simulation details in Section I of the Supporting Information). Figure 2a shows the simulated reflectance spectrum when the structure is illuminated by a plane wave under normal incidence from the air side (dark blue curve). A single peak, corresponding to the excitation of localized plasmon resonances that are considerably broadened due to the closely spaced square nanoparticles 1 , is observed. If one repeats the simulations at an incidence angle of 20°, a more complex spectrum is observed for the TE polarization, with a pronounced dip encroaching on the plasmon resonance at 1280 nm (red curve). The dip occurs for all non-zero incidence angles and is largely dispersionless, as can be appreciated on the dispersion map of Figure 2c where the reflection for TE-polarized waves is plotted as a function of both the photon energy ħω and the in-plane component kx of the incident wavevector. Furthermore, its magnitude evolves from a small dent in the reflectance peak at approximately ħω = 0.97 eV (1280 nm) to a pronounced minimum that shifts to smaller energies (longer wavelengths) as the incidence angle increases.

To gain further insight, we plot the absorption spectra and dispersion relation for the same cases in Figures 2b,2d. A sharp peak, located at the same wavelength as the dip in reflection, emerges on top of the broad plasmonic resonances for all non-zero angles.

These results are unexpected for a simple array of Au nanoparticles because the latter is supposed to exhibit a single reflection maximum caused by the weakly-coupled plasmonic resonances [START_REF] Kelly | The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment[END_REF] . The formation of a narrow reflection dip and an equally sharp absorption peak cannot be attributed to diffraction effects because the onset of non-zeroth diffraction orders, defined by ħω = ±ħkxc/ng ∓ ħ2πc/(ngP) (dashed white lines on Figure 2c), is above the frequency range where it occurs (except at large incidence angles where diffraction renders the dip slightly dispersive). In other words, we operate the nanoparticle array in the subwavelength regime, i.e., as a metasurface. These unusual features disappear when the filling factor of the structure decreases, as shown on Figure S2 for an array with the same period of 600 nm but made of Au nanoparticles with a reduced side of 200 nm. In other words, the reflection dip and absorption peak evidenced on Figures 2a-2d are related to the close proximity between the edges of adjacent metallic patches. This conclusion is supported by an examination of the fields and current density lines around the structure (Supporting Information, Figures S3-S5). The latter reveals that in addition to the plasmonic resonances sustained by the nanoparticles, an array of magnetic LC resonances, characterized by inductive current loops formed by currents i within the metal and pure displacement currents iDisp between the metallic patches, is excited for off-normal incidence angles. Such magnetic resonances occurring in the near-infrared and visible range are well known to the metamaterial community where they play a central role in the realization of a negative effective permeability in coupled nanorods [START_REF] Shalaev | Negative Index of Refraction in Optical Metamaterials[END_REF] and fishnet metamaterials [START_REF] Zhang | Experimental Demonstration of Near-Infrared Negative-Index Metamaterials[END_REF] . Their resonance frequency can be tuned with the inductance (and thus the length of the current loops, defined by the lateral size of the patches and the opening between them) and the capacitance (essentially defined by the opening between the patch). Their magnetic dipole moment 𝑚 ⃗⃗ , oriented perpendicular to the current loops, is normal to the plane of the structure in our case, as sketched on Figure 1b.

We can now understand the results of Figures 2a-2d. The fact that the excitation of the LC resonances creates a sharp dip in the reflectance peak of the surface plasmons indicates that the two sets of modes interfere destructively, reducing the scattering of the structure while increasing its absorbance. In the special case of normal-incidence illumination, the LC resonances cannot be excited because the incident magnetic field is perpendicular to their moment 𝑚 ⃗⃗ . Thus, the spectra computed at 0° in Figures 2a-2b Similar resonances producing sharp absorption peaks have been reported in the past by authors [START_REF] Naweed | Induced Transparency and Absorption in Coupled Whispering-Gallery Microresonators[END_REF][START_REF] Taubert | Classical Analog of Electromagnetically Induced Absorption in Plasmonics[END_REF][START_REF] Taubert | Plasmonic Analog of Electromagnetically Induced Absorption: Simulations, Experiments, and Coupled Oscillator Analysis[END_REF][START_REF] Tassin | Electromagnetically Induced Transparency and Absorption in Metamaterials: The Radiating Two-Oscillator Model and Its Experimental Confirmation[END_REF][START_REF] Song | Integrated Metamaterial with Functionalities of Absorption and Electromagnetically Induced Transparency[END_REF] who sought to demonstrate photonic analogs of electromagnetically induced absorption (EIA)-a narrow absorption resonance of certain atomic systems coherently interacting with pump-probe fields [START_REF] Lezama | Electromagnetically Induced Absorption[END_REF] . A key ingredient for atomistic EIA is either a transfer of coherence from two energy levels or a transfer of population from the ground level to a reservoir [START_REF] Goren | Electromagnetically Induced Absorption Due to Transfer of Coherence and to Transfer of Population[END_REF] . In photonic analogs of EIA, this transfer is played by the interferences between optical modes having different linewidths. More precisely, the few demonstrations of photonic EIA that have been made across the electromagnetic spectrum have relied on pairing one type of optical resonator with another cavity or waveguide that does not directly interact with the incoming radiation [START_REF] Naweed | Induced Transparency and Absorption in Coupled Whispering-Gallery Microresonators[END_REF][START_REF] Taubert | Classical Analog of Electromagnetically Induced Absorption in Plasmonics[END_REF][START_REF] Taubert | Plasmonic Analog of Electromagnetically Induced Absorption: Simulations, Experiments, and Coupled Oscillator Analysis[END_REF][START_REF] Tassin | Electromagnetically Induced Transparency and Absorption in Metamaterials: The Radiating Two-Oscillator Model and Its Experimental Confirmation[END_REF][START_REF] Song | Integrated Metamaterial with Functionalities of Absorption and Electromagnetically Induced Transparency[END_REF] . Here, in contrast, we work with a single class of metallic nanopatches and a photonic analog of EIA appears as a consequence of their mutual coupling in the limit of highly compact structures (see Supporting Information, Section IV and Figure S6 for additional considerations on the design rules and how to obtain the same behavior at other wavelengths).

Moreover, the two resonances involved in the process are both efficiently excited by the incoming radiation. We now confirm these numerical results with experiments that also demonstrate the potential of such metasurfaces for optoelectronics applications. The only differences with the structure studied on Figure 2 We turn to the photoluminescence (PL) properties of the sample (Figure 3b). As shown in a previous article [START_REF] Caillas | Identification of Two Regimes of Carrier Thermalization in PbS Nanocrystal Assemblies[END_REF] , the optoelectronic properties of PbS NCs cross-linked with EDT are governed by their thermalized excitons, implying that the PL intensity I(λ) and the resonant excitonic absorption cross-section ARES(λ) are related by a local Kirchhoff law of the form I(λ)  ARES(λ).W(λ,T), where W(λ,T) = 2hc 2 λ -5 exp[-hc/(λkBT)] is the Wien approximation of Planck's law, h and kB are the Planck and Boltzmann constants, λ is the wavelength and T is the carrier temperature.

Without the metasurface, the PL spectrum of the NC layer on glass features an inhomogeneously-broadened peak in the near-infrared (note that the exact shape and position of the peak depends on the excitation power because the latter determines the carrier temperature, and therefore the Wien term W(λ,T), in the above equation [START_REF] Caillas | Identification of Two Regimes of Carrier Thermalization in PbS Nanocrystal Assemblies[END_REF] ). With the metasurface, a general PL enhancement is observed and a sharp peak appears at the same wavelength as the EIA dip of Figure 2a. This result suggests that the optical analog of EIA has strongly increased the absorption cross-section ARES(λ) of the NCs covering the metasurface, which in turns has led to a sharp enhancement of the PL at the same wavelengths. To confirm this hypothesis, we have measured the dispersion of the emitted PL as a function of ħω and kx and for two orthogonal polarizations (all the relevant experimental details are given in section V of the Supporting Information). When the polarization is perpendicular to kx, corresponding to TE polarized waves in this specific plane of emission, the sharp emission peak is observed and it closely follows the dispersion of the EIA dip in absorption predicted by the model (Figure 3c). For the orthogonal TM polarization, this peak does not appear in the emission spectrum, which is again consistent with the simulated absorption (Figure 3d). These findings do not only provide an experimental confirmation of EIA, but also illustrate its potential for influencing the absorption and luminescence properties of an active dipolar medium. In comparison, the plasmonic resonances alone (i.e. outside the EIA window for the TE polarization and at all angles for the TM polarization) have a weak effect.

Due to the symmetry of the structure, the experimental results plotted on Figures 3c-3d remain true for a 90-degree rotation of the in-plane wavevector, while all other angles are a linear superposition of these two cases. Figure S10 confirms this point by imaging the in-plane wavevector distribution of the PL emitted at 1450 nm (note that Figures 3c,3d and S10 are nothing else than different planes of the kx/k0,ky/k0,ω space). A broad cone is observed, illustrating the emission diagram of the structure caused by EIA at this wavelength. Moreover, since EIA only occurs for TE-polarized waves, the emission beam has an azimuthal electric field distribution, as evidenced on Figure 3e where the same in-plane wavevector distribution of the emitted PL at 1450 nm is imaged through a linear polarizer rotated between 0 and 180 degrees. Such non-trivial polarization features are worth noticing considering that we do not work with laser beams, which can be manipulated at will with optical elements that take advantage of their spatial coherence, but with the spontaneous emission of an assembly of incoherent quantum emitters. Importantly, the PL properties do not depend on the size of the excitation spot: while all the data represented on Figure 3 have been obtained by pumping a tiny fraction of the structure with a diffraction-limited HeNe laser spot, Figure S11 demonstrates that the same results hold true if the 200  200 µm 2 of the sample are illuminated almost in full with visible white light.

Finally, we demonstrate the potential of the metasurface for enhanced photodetection. Since the optoelectronic properties of our layers of PbS NCs are governed by a local Kirchhoff law (see above), the sharp PL peak that occurs at the EIA condition is equivalent to a strong enhancement of their excitonic absorption cross-section ARES at the same wavelength. In other words, by illuminating the sample with oblique TE-polarized waves, the electromagnetic energy is not wasted as heat in the metal but transferred to the NCs-which in turn should enhance their photoconductive properties. To verify this point, we have fabricated a new sample in which the square nanoparticles are now patterned between planar interdigitated Au electrodes. The geometric parameters of the metasurface are the same as before and the sample is also covered with a 15-20 nm thick layer of PbS NCs cross-linked with EDT (see schematic of Figure 1c). Figure 3f shows the spectrum of the photocurrent flowing between the electrodes when the sample is illuminated with an external white light source. The data have been collected with a Fourier transform photocurrent spectroscopy setup described in the Supporting Information, using the same reverse Cassegrain objective as the one used for measuring the reflectance spectrum of Figure 2a. The photocurrent (PC) (yellow curve) exhibits a general enhancement and an additional narrow peak at 1460 nm compared to a control sample without Au nanoparticles (gray curve). We attribute the overall enhancement to an improved bottom reflectivity induced by the metasurface, allowing part of the incident light that has passed through the thin NC layer without being absorbed to contribute to the photocurrent after being backscattered by the Au nanoparticles. As for the new peak, it can be unequivocally attributed to EIA due to its wavelength position and narrow width. To confirm this point, we plot on Figure 3a the ratio between the PC spectra measured with and without metallic nanoparticles.

The curve exhibits a sharp peak at the EIA condition where the enhancement exceeds 10.

Moreover, the peak coincides almost perfectly with the position of the sharp PL maximum of Figure 3b, further demonstrating the equivalence between absorption and emission in our layers of thermalized NCs. In the Supporting Information, we provide another experimental example in which the NC absorption is enhanced at smaller wavelengths using a metasurface with reduced feature sizes (Figure S12).

In conclusion, a structure as simple as an array of square Au nanoparticles can behave as a metasurface with a surprisingly rich and technology-enabling behavior when properly designed at a subwavelength scale. All the effects evidenced in this study are a consequence of the optical analog of EIA that develops within the Au nanoparticle array. Different from earlier demonstrations in the literature, which focused on more complex structures used as passive filters and absorbers that turned photonic analogs of EIA into Joule losses [START_REF] Naweed | Induced Transparency and Absorption in Coupled Whispering-Gallery Microresonators[END_REF][START_REF] Taubert | Classical Analog of Electromagnetically Induced Absorption in Plasmonics[END_REF][START_REF] Taubert | Plasmonic Analog of Electromagnetically Induced Absorption: Simulations, Experiments, and Coupled Oscillator Analysis[END_REF][START_REF] Tassin | Electromagnetically Induced Transparency and Absorption in Metamaterials: The Radiating Two-Oscillator Model and Its Experimental Confirmation[END_REF][START_REF] Song | Integrated Metamaterial with Functionalities of Absorption and Electromagnetically Induced Transparency[END_REF] , we have shown that the absorption can be leveraged to induce dramatic changes in the optoelectronic properties of PbS NC assemblies. As a corollary, the strong enhancements and sharp spectral modifications of the emission, absorption and photocurrent spectra, the demonstration of a directional and azimuthally polarized emission, as well as the direct relationship of all these observations with EIA, demonstrate that the relevant figure of merit to tune the optoelectronic properties of an active medium with thermalized carriers is its absorption cross-section-and not the local density of photonic states as is usually the case for single emitters interacting with nanostructures. In this respect, these results are not restricted to ensemble of PbS NCs and should hold for any active medium with thermalized carriers, including quantum wells, semiconductors, two-dimensional materials and organic layers.

ASSOCIATED CONTENT

Supporting Information.

The following files are available free of charge.

Details on the numerical simulations; Schematic cross-section of the model used to simulate a Au particle array covered with a thin layer of PbS NCs (Figure S1); Dispersion relation of an array with smaller square Au patches (Figure S2); Analysis of the fields supported by the metasurface when EIA occurs (Figure S3); Charge distributions at the EIA wavelength (Figure S4); Current density lines evaluated at the EIA condition and outside the EIA condition (Figure S5); How to design the metasurfaces to operate at other wavelengths (Figure S6

II. Numerical simulations with a much smaller filling factor

In these simulations, the period P= 600 nm is the same as in the main text but the lateral size of the Au particles has been reduced to 200 nm  200 nm (the Au thickness has been kept constant at 25 nm). All other conditions are the same as in Figure 2. Contrarily to the EIA case studied in the main text, there is no dip in the reflectance peak for the TE polarization. Moreover, the absorption maxima are essentially similar to those seen on the reflectance map, which is the standard and expected behavior of a nanoparticle array with optical properties dominated by plasmonic resonances localized on each Au inclusion. Note also that these plasmonic resonances are shifted to higher frequencies due to the smaller size of the Au nanoparticles and that they are strongly modulated by the diffraction orders that arise above the light lines. The associated current distribution are the loops sketched in the main text on Figure 1b. Note that these current loops are formed by real currents flowing on the edges of the Au patches and displacement currents 𝑖 𝐷𝑖𝑠𝑝 ∝ 𝜕𝐷 ⃗ ⃗ 𝜕𝑡 ⁄ within and between the Au patches, as is well documented in the literature for related geometries such as pairs of metallic rods and fishnet metamaterials. [START_REF] Si | Reflective Plasmonic Color Filters Based on Lithographically Patterned Silver Nanorod Arrays[END_REF][START_REF] Yang | Angle Robust Reflection/Transmission Plasmonic Filters Using Ultrathin Metal Patch Array[END_REF] To gain quantitative insight, we plot the actual current density lines predicted by the numerical model on Figure S5. Notice that current loops are only observed when the EIA peak occurs (case B in Figure S5). These loops are resonant because they disappear outside the EIA peak (cases A and C). Each loop has a mirror symmetry with respect to the horizontal x-axis. The loops do not possess a mirror symmetry in the other direction because the plane-of-incidence for oblique illumination is the x-z plane (see notations on Figure 1 in the main text).

IV. How to design the metasurfaces to operate at other wavelengths

To produce a Fano response analogous to EIA, the plasmonic and LC resonances must overlap.

The main geometrical parameter affecting the spectral position of the plasmonic resonance is the side of the Au patches because these plasmons are standing waves across the patches.

However, this geometrical parameter also affects the size of the current loops between adjacent Au patches and thus the inductance of the LC resonances. In contrast, the period P of the system has a relatively small influence on the position of the plasmon resonances (their spectral width, however, is very sensitive to this parameter [START_REF] Grand | Role of Localized Surface Plasmons in Surface-Enhanced Raman Scattering of Shape-Controlled Metallic Particles in Regular Arrays[END_REF] ) but it has a stronger impact on the capacitance of the LC resonance. In the case of an ideal lossless and perfectly conducting LC resonator, its resonance wavelength is proportional to √𝐿𝐶. This result, however, cannot be directly applied to our system due to the strong retardation effects occurring in metals at optical frequencies as well as the complex inhomogeneous environment in which the LC resonances develop. We have heuristically found that an efficient way to shift the EIA peak to smaller (resp. larger)

wavelengths is to reduce (resp. increase) the side of the Au patches and the value of the period simultaneously, but not necessarily with a strict scaling factor, as illustrated on Figure S6.

V. Experimental details Chemicals

Oleylamine (OLA, Acros, 80-90%), %), lead chloride (PbCl2, Afla Aesar, 99%), sulfur powder (S, Afla Aesar, 99.5%), oleic acid (OA, Afla Aesar, 90%), trioctylphosphine (TOP, Afla Aesar, 90%), n-hexane (VWR), Ethanol (VWR, >99.9%), Toluene (Carlo Erba, >99.8%).

PbS nanocrystal synthesis

In a three-neck flask, 300 mg of PbCl2, together with 100 µL of TOP and 7.5 mL of OLA are degassed, first at room temperature and then at 110 °C for 30 min. Meanwhile, 30 mg of S powder is mixed with 7.5 mL of OLA until full dissolution and an orange clear solution is obtained. Then under nitrogen at 80 °C, this solution of S is quickly added to the flask. After 2 minutes, the reaction is quickly quenched by addition of 1 mL of OA and 9 mL of hexane. The nanocrystals are precipitated with ethanol and redispersed in 5 mL of toluene. This washing step is repeated one more time and the pellet is this time dispersed in 10 mL of toluene with a drop of OA. The solution is then centrifugated as is, to remove the unstable phase. The supernatant is precipitated with methanol and redispersed in toluene. Finally, the PbS NC solution in toluene is filtered through a 0.2 µm PTFE filter. The obtained solution is used for further characterization and device fabrication.

Sample fabrication

The array of Au square nanoparticles studied in Figure 3a-3e is defined by electron-beam lithography on a borosilicate glass substrate from Plan Optik coated by a bilayer of CSAR 62 positive resist and Electra 92 conductive coating from Allresist. The conductive coating is applied to avoid a charge accumulation during the writing procedure, the latter being performed with a PIONEER Two Raith system. After deposition of 2 nm of Ti and 25 nm of Au in a Plassys MEB 550S electron beam evaporator, followed by an overnight lift-off in butanone, the resulting Au nanoparticle array occupies an area of 200 × 200 μm 2 . The scanning electron micrograph (SEM) of Figure S7 reveals that the actual size of the square nanoparticles is 415 nm  415 nm instead of the nominal value of 400 nm  400 nm. The measured period is 600 nm, as expected.

The fabrication of the photoconductive detector studied in Figure 3f starts with a first level of optical lithography (using an MJB4 mask aligner and the AZ 5214E photoresist), metal deposition (2 nm of Ti and 70 nm of Au) and lift-off to define interdigitated electrodes. The spacing between two consecutive digits is 10 μm. These 10 μm wide channels are then filled with arrays of Au nanoparticles following the fabrication steps described above in this section.

The total area of the photoconductive device is 870 × 1400 μm 2 .

After defining the periodic arrays with and without interdigitated electrodes, the sample is introduced in a N2-filled glovebox. A 15-20 nm thick layer of NCs is spun onto the sample at 2000 rpm, creating a uniform coating above the metallic patterns. Finally, the sample is dipped into a solution of EDT in ethanol for 60 s followed by a rinse in ethanol to strip the NCs from their native OA ligands and leave them instead cross-linked with shorter molecular chains.

Photoluminescence experiments

All the PL experiments are performed with a customized BX51WI microscope from Olympus.

Except for the results presented on Figure S11, we pump the sample with a continuous HeNe laser at 633 nm that is filtered with a BG40 filter from Thorlabs to remove the parasitic spontaneous emission in the near-infrared. This laser is focused to a micron-size spot using a 50X objective. For Figure S11, we have replaced this localized excitation by a wide field illumination scheme that excites a macroscopic part of the 200 × 200 µm 2 sample. This wide field pumping, covering a circular area with a diameter of 90 µm, is realized with the same objective and the wide field illuminator of our microscope. The light source attached to this illuminator is a tungsten lamp that is filtered to exclude the wavelengths outside the range 400 nm -800 nm.

Our 50X objective (reference LCPLN50XIR) has a numerical aperture of 0.65 and it is also used to collect the infrared PL signal. A dichroic mirror (Thorlabs DMLP950R) is used to separate the IR signal above 950 nm from the visible pump. The remaining visible light that has not been filtered by the dichroic mirror is subsequently blocked with an RG780 longpass filter. The PL is analyzed with an Acton SP2356 imaging spectrograph coupled to a NIRvana InGaAs camera from Princeton Instruments (Figure S8).

-To record a PL spectrum, a 200 µm slit is placed at the spectrograph entrance. Light entering the spectrograph is then dispersed with a 85 groove/mm plane rule reflection grating. The raw spectra are then corrected by taking into account the transfer functions of the 50× objective and the grating.

-To record a dispersion relation, the same configuration is used but an additional Bertrand lens is added in the optical path in a 4f configuration so as to image the back focal plane of the objective. The function of this lens is to Fourier-transform the signal, which is therefore analyzed in the reciprocal space.

-To record a back focal plane image, the reflection grating within the Acton SP2356 spectrograph is replaced by a flat silver mirror.

-For the polarization-resolved experiments, a wire grid polarizer (WP25M-UB from Thorlabs) is inserted in the optical path. We have carefully checked the effect of every optical elements on the polarization state of the PL signal, to make sure that no artifact affects the measurements.

Photocurrent measurements

The interdigitated samples are biased at 7 V and illuminated with a 15X reverse Cassegrain objective using a water-cooled 150 W incandescent tungsten light source passing through a Fourier Transform Infrared (FTIR) spectrometer (Invenio-R from Bruker). The photocurrent that flows between the electrodes is amplified using a Femto DLCPA-200 amplifier, converted into a voltage and plugged back into the FTIR electronics. By normalizing the data with the spectrum measured with a calibrated 818-ST2 Ge photodiode from Newport, one obtains the responsivity of the sample. the same as those obtained with the diffraction-limited laser pumping. In fact, the wide field illumination creates an even nicer set of data because it averages the response of the array over a wide area.

Figure 1 .Figure 3 .

 13 Figure 1. (a) Schematic of the simulated periodic array of square Au nanoparticles. The white arrows represent the wavevector of the incident light (k0) and its projection along the x-axis (kx). (b) Illustration of the currents i and displacement currents iDispl that form a resonant loop associated with a magnetic moment m normal to the surface. Only one current loop is shown for clarity. This pattern repeats itself between all adjacent metallic edges. (c) Simplified view of the photoconductive detector studied on Figure 3. The actual device is made of interdigitated electrodes defining 10 µm wide channels filled with square Au nanoparticles and covered with 2-3 monolayers of PbS NCs (represented as red spheres).

Figure 2 .

 2 Figure 2. Simulated optical properties of the periodic array of square Au nanoparticles. (a) TE-polarized reflectance spectra at normal incidence and for an oblique incidence of 20° degrees. (b) Corresponding absorbance spectra. (c) and (d) TE-polarized reflectance and absorbance spectra plotted as a function of kx/k0 and the photon energy ħω. The white dashed lines are the light lines in the substrate (ng=1.45) and the white dotted lines are the light lines in air. (e) and (f) TM-polarized reflectance and absorbance spectra plotted as a function of kx/k0 and the photon energy ħω.

  only feature the signature of the surface plasmons. Because of the same selectivity rule, the LC resonances do not occur for the TM polarization, a point that can be verified by examining the reflectance and absorption spectra computed for this polarization on Figures2e-2f(the features seen in reflectance closely follow the light lines and are therefore diffractive effects that have little influence on the absorption spectra except at grazing incidence).

Figure 2 .

 2 Figure 2. These spectral features occur at slightly longer wavelengths because the thin layer of

Figure 3 .

 3 Figure 3. (a) Experimental and simulated reflectance spectra of the sample (continuous and dashed purple curves, respectively). (b) PL spectrum of the PbS NCs above and outside the nanoparticle array (yellow and gray curve, respectively). (c) Experimental TE-polarized PL dispersion relation (grayscale colormap in arbitrary units) vs. simulated TE-polarized absorbance dispersion relation (dark blue to yellow colormap). (d) Same as panel (c), but for the TM polarization. The colormap scales are the same as for the TE-polarization. (e) Back focal plane images of the PL at 1450 nm (plotted in the kx/k0,ky/k0 space), taken after inserting a linear polarizer in the beam path. The orientation of its polarization axis is indicated by the double arrows. The outer diameter of the images has a value of 0.65 corresponding to the numerical aperture of our 50X objective. (f) Photocurrent spectra of PbS NC photoconductive detectors with (yellow curve) and without (gray curve) Au nanoparticles patterned between the interdigitated electrodes. The ratio between these two spectra is the red curve of panel (a).

  ); Experimental details (chemicals, PbS NC synthesis, sample fabrication, PL experiments and PC experiments); Scanning electron micrograph of an actual sample (Figure S7); Schematic of the PL experimental setup (Figure S8); Experimental and simulated reflectance spectrum of the sample studied on Figure 2a, plotted over an extended wavelength range (Figure S9); Back focal plane at 1450 nm without polarizer inserted in the beam path (Figure S10); PLexperiments realized with a wide field pumping (FigureS11); Simulated and experimental data (reflectance, photocurrent spectrum) for an array with smaller feature sizes (FigureS12).

Figure S2 .

 S2 Figure S2. Simulated optical properties of the array when the size of the square nanoparticles is reduced to 200 nm  200 nm  25 nm. (a)-(b) Simulated reflectance dispersion relation for the TE and TM polarizations. (c)-(d) Simulated absorbance for the TE and TM polarizations. The dashed and dotted white lines are the light lines in the glass substrate and air, respectively.

Figure S4 .

 S4 Figure S4. Schematic of the charges in the x-y plane.

Figure S5 .

 S5 Figure S5. Current density lines computed for different wavelengths (A: 1120 nm, B and D: 1280 nm, C: 1490 nm) and different incidence angles (A, B & C: illumination at 20° with TE-polarized plane waves, D: illumination at normal incidence). The structure is the array of Au patches examined in Figure 2 in the main text. The absorbance spectra of Figure 2b are reproduced here with gray marks identifying the four cases A, B, C and D.

Figure S6 .

 S6 Figure S6. Numerical simulations of four different arrays of Au patches with different sides S and periods P. Red curve: P = 400 nm and S = 200 nm. Blue curve: P = 500 nm and S = 300 nm. Light blue curve: P = 600 nm and S = 400 nm. Violet curve: P = 700 nm and S = 500 nm. The metal thickness is 25 nm in all cases. All the curves have been computed for the TE polarization and an oblique illumination at 20°.

Figure S7 .

 S7 Figure S7. Scanning electron micrograph of the Au patterns. Scale bar 200 nm.

Figure S8 .

 S8 Figure S8. Schematic of the PL setup.

Figure S11 .

 S11 Figure S11. PL experiments realized with a wide field pumping. The sample is the same as the one studied on Figures 3 and S9-S10, except that the pumping is not realized with a diffraction-limited laser spot but by a white-light illumination scheme covering a macroscopic part of the sample (see page 10 of the present document for experimental details). Panels (a)-(b)-(c) plot the same quantities as those plotted on Figure 3c-3d-3e. Panel (d) plots the same quantity as in Figure S10. The results are essentially

ACKNOWLEDGMENTS

We acknowledge support from the European Research Council grant FORWARD (reference: 771688). This work was supported by French state funds managed by the ANR through grant Copin (ANR-19-CE24-0022).

CORRESPONDING AUTHOR * aloyse.degiron@u-paris.fr

Supporting Information

I. Numerical model

The structures are simulated using the RF module of Comsol Multiphysics, a finite element solver. The model studied in Figure 1 consists of a single unit cell flanked with periodic conditions. The bottom half of the unit cell has a height of 3 µm and is filled with glass with a refractive index ng = 1.45. This index corresponds to the experimental value of our Borofloat glass substrate from Plan Optik, measured by fitting the diffraction orders observed in some of our PL maps with the light lines ω = ±kxc/ng ∓ 2πc/(ngP). The upper half is also 3-µm high and is filled with air (n = 1). At the interface between these two media, the Au antennas are modelled with a permittivity taken from the experimental literature. [START_REF] Kelly | The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment[END_REF] Electromagnetic waves enter and exit the model through ports applied on the top and bottom of the computational domain. The number of ports on each side is chosen so as to take all diffraction orders into account. The port associated with the zeroth diffraction order on the air side is used to launch a TE-or TMpolarized wave at a specified incidence angle.

The simulations presented in Figure 2a utilize a slightly modified version of the model to account for the actual dimensions of the Au squares (415 nm rather than 400 nm, see Figure S7) and for the presence of the PbS nanocrystals (NCs) covering the sample. By systematic comparisons between experiments and simulations, we have noticed that the influence of the PbS NCs on the optical properties of the arrays can be modeled in a satisfying manner by burying the square nanoparticles 10 nm below the surface of the glass substrate (the refractive index is still ng = 1.45 without imaginary part). We have verified that this approximation does not only work for the specific structure studied in the article, but also for other metasurfaces operating at other wavelengths, as can be appreciated for example on Figure S12.

III. Analysis of the fields and associated currents when EIA occurs

Figure S3. Plots of the Ex, Ey and Ez electric field components in the x-z plane (top row) and x-y plane (bottom row) at the wavelength of the EIA resonance (λ=1280 nm). The colors have been saturated to improve the visibility of the field symmetries. The structure shown here is the same as in Figure 2.

The spatial variations of the three components of the instantaneous electric field at the EIA wavelength are plotted in Figure S3 in two orthogonal planes. The positive (resp. negative) values mean that these x, y or z components are oriented along the positive (resp. negative) x-, y-or z-axes. From these maps, it is possible to deduce a snapshot of the charge distribution, based on the consideration that the electric field lines, which are tangential to the electric field vector at all points, always originate from positive charges and terminate at negative charges:

VI. Supplementary experiments

VII. Supplementary references


Jean-Joseph Minviel
email: jean-joseph.minviel@inrae.fr

M 'hand Fares
email: mehand.fares@inrae.fr

Jean-Marc Blazy
email: jean-marc.blazy@inrae.fr

Alban Thomas
email: alban.thomas@inrae.fr.

Technical Efficiency and Complementarity of Agroecological Innovations in French West Indies Banana Production

Keywords: Conditional efficiency, complementarity, agroecological innovations, farm performance. JEL Classification: C14, 033, Q16, Q55

In context of global challenges facing agriculture, our paper addresses the extent to which the synergistic nature of agroecological innovations may reconcile environmental and technical efficiency of farms. We develop an empirical model, namely conditional efficiency framework, which explicitly accounts for contextdependent drivers like synergy and complementarity of innovations. Using a sample of 567 banana farms in the French West Indies, our estimates confirm the complementarity effect since the joint adoption of agroecological innovations increases the technical efficiency scores much more than others drivers and each of the innovations taken in isolation. We also show that advice and extension services as well as human capital variables are key adoption levers for public policy since they reduce the variability of production and thus the risk associated with the joint adoption of the agroecological innovations.

Introduction

Given the challenges of climate change, sustainable food and nutritional security, innovation in the agricultural and food system is a major concern and agro-ecological innovations and bio-based transitions are one of the avenues to be explored in order to meet these multiple challenges (OECD, 2021;WIPO et al., 2017;FAO, 2019). This is particularly true in the French West Indies where the intensive use of chemical inputs in banana monoculture, especially pesticides (chlordecone), has led to soil and ecosystem contamination and human health risks in large areas of the islands [START_REF] Cabidoche | Long-term pollution by chlordecone of tropical volcanic soils in the French West Indies: A simple leaching model accounts for current residue[END_REF]. To mitigate these negative externalities and reduce pesticide use, agroecological innovations have been developed [START_REF] Blazy | BANAD: a farm model for exante assessment of agro-ecological innovations and its applications to banana farms in Guadeloupe[END_REF]. Since agroecological systems are the result of complex interactions at a local level between technologies and biological components of the agroecosystems [START_REF] Duru | Designing agroecological transitions: A review[END_REF], agroecological innovations are then based on a bundle of complementary technologies and practices leading to emergent and synergistic sustainable properties [START_REF] Altieri | Agroecology: the science of natural resource management for poor farmers in marginal environments[END_REF]. The main issue addressed by our paper is whether the adoption of complementary agroecological innovations that increase the environmental performance of the farm may also increase its economic performance [START_REF] Edmeades | Modelling the Crop Variety Demand of Semi-Subsistence Households: Bananas in Uganda[END_REF][START_REF] Lambrecht | Integrated soil fertility manage-ment: From concept to practice in eastern DR Congo[END_REF]. The meta-analysis conducted by [START_REF] Rosenbusch | Is Innovation Always Beneficial? A Meta-Analysis of the Relationship Between Innovation and Performance in SMEs[END_REF] shows that the innovationperformance relationship is context-dependent, and using recent advances in efficiency analysis we suggest the conditional efficiency framework [START_REF] Daraio | Advanced robust and nonparametric methods in efficiency analysis: Methodology and applications[END_REF][START_REF] Daraio | Quality as a latent heterogeneity factor in the efficiency of universities[END_REF] to measure performance (technical efficiency) while explicitly accounting for contextual drivers. The contextual drivers refer to factors which are neither inputs nor outputs, but that form the backdrop of farmer decision-making. Among the relevant contextual drivers, we mainly focus on complementarity between innovations and its impact on technical efficiency since the literature shows that the adoption of complementary innovations improves firm performance [START_REF] Arora | Complementarity and information technology adoption: Local area networks and the Internet[END_REF][START_REF] Fares | Is There Complementarity Between Certified Labels and Brands? Evidence from Small French Cooperatives[END_REF][START_REF] Mohnen | R&D, Innovation and Productivity[END_REF]. Our estimates on a database of 567 banana farms in the West Indies confirm this complementarity effect since the joint adoption of two synergistic agroecological innovations, i.e. Disease Free seedlings (DFS) and Fallow, increases the technical efficiency score much more than each of the innovations taken in isolation. We also show that advice and extension services and other human capital variables are key adoption lever since they reduce the variability of production and thus the risk associated with the joint adoption of the agroecological innovations. The remaining sections are organized as follows. In section 2, we present the empirical model and the context of our farm survey database as well as the the variables of test. Econometric results are presented in section 3 adjoining to discussion and section 4 concludes.

Materials and Methods

Methods

Farmers' production decisions are modeled using the conditional efficiency framework [START_REF] Daraio | Advanced robust and nonparametric methods in efficiency analysis: Methodology and applications[END_REF][START_REF] Daraio | Quality as a latent heterogeneity factor in the efficiency of universities[END_REF][START_REF] Belmonte-Martin | Local tax management in Spain: A study of the conditional efficiency of provincial tax agencies[END_REF], where inputs X ∈ R p + are combined to produce outputs Y ∈ R q + given contextual (conditioning) variables Z ∈ R r + . In this framework, a production process is defined by a production technology ψ Z that describes the set of all technically feasible input-output combinations given the conditioning variables:

ψ Z = {(x, y)|z : x can produce y} (1)
A farm is technically efficient (i.e., located on the boundary of ψ Z ) if it produces the maximum possible level of outputs for a given level of inputs1 . The production process defined in [START_REF] Ainembabazi | The Role of Farming Experience on the Adoption of Agricultural Technologies: Evidence from Smallholder Farmers in Uganda[END_REF] can be fully characterized by the joint-conditional probability:

S (Y |X,Z) (y|x, z)F (X|Z) (x|z)
, where S (Y |X,Z) (y|x, z) denotes the conditional survival function Y , with S Y (y) = P rob(Y ≥ y), and F (X|Z) (x|z) the marginal conditional distribution function of X, with F X (x) = P rob(X x). An output-oriented conditional efficiency score is defined as follows by the upper-boundary

ψ Z of the support of S (Y |X,Z) (y|x, z) : θ(x, y|z) = sup θ|S (Y |X,Z) (θy|x, z) > 0 (2)
To account for outlying observations, we define an order-m frontier that characterizes the expected maximum level of outputs achievable for a subset of m randomly drawn production units with X ≤ x as a yardstick [START_REF] Daraio | Advanced robust and nonparametric methods in efficiency analysis: Methodology and applications[END_REF]. That is, for any value y, there exists θ Z m (x, y) = sup θ|(x, θy) ∈ ψ Z m (x) such that the conditional output-oriented order-m efficiency measure is defined as:

θ m (x, y |z) = E (Y |X,Z) ( θ Z m (x, y) |X ≤ x, Z = z) = ˆ∞ 0 [1 -(1 -S (Y |X,Z) (uy|x, z)) m ]du (3)
The survivor function S (Y |X,Z) (y|x, z) is estimated using the following kernel function:

S (Y |X,Z,n) (y|x, z) = n i=1 I(X i ≤ x, Y i ≥ y)K ĥ(z, z i ) n i=1 I(X i ≤ x)K ĥ(z, z i ) (4)
where

K h (.) = h -1 K((z, z i )h -1
), with ĥ = ( ĥ1 , . . . , ĥr ) a vector of r-estimated bandwidth parameters and I(.) is an indicator function which equals to unity if its argument is true and zero otherwise. Then, the conditional efficiency estimator θm (x, y|z) is given by plugging Ŝ(Y |X,Z,n) (y|x, z) into equation [START_REF] Arora | Complementarity and information technology adoption: Local area networks and the Internet[END_REF] (see for more details Minviel and de Witte, 2017).

To investigate the influence of the contextual drivers on technical efficiency, we use a location-scale nonparametric regression model (Badin et al., 2012):

θ i (x i , y i |z i ) = g(z i ) + σ(z i )ξ i (5)
where ξ i is an error term, g(.

) = E[θ i (x i , y i |z i )] and σ 2 (z i ) = V [θ i (x i , y i |z i )].
The nonparametric functions g(.) and σ 2 (.) are estimated using kernel local linear regression methods. To introduce complementarity effect, we decompose the contextual drivers in two components by rewriting z i = δ 0 s 00 + δ DF S s 10 + δ F s 01 + δs 11 + ζX i , where ζX i represent the other drivers and δ 0 s 00 + δ DF S s 10 + δ F s 01 + δs 11 the four agroecological innovation strategies of the farmer when he can adopt DFS or Fallow innovations. The latter are said to be complements only if the marginal effect of joint adoption is positive (δ > 0) (Fares, 2013).

Materials

To control parasitism and therefore reduce pesticide use in French West Indies banana production, two agroecological innovations have been developed: (i) introducing a fallow period (FP) in rotation with banana; and (ii) using disease-free seedling (DFS) after the fallow period, where seedlings are produced in-vitro (Chabrier and Quenerve, 2003). Although both innovations can be used separately, they are complementary in managing pest pressure since DFS makes it possible to avoid exogenous parasitism after the fallow period. If this synergistic effect may ensure environmental efficiency since it reduces the social cost of having recourse to chemical pesticide, it does necessarily generates incentives to joint adoption by increasing the performance of the farm. To address this issue a survey questionnaire on innovation adoption was administered in Guadeloupe and Martinique between March and June 2008, through one-time faceto-face interviews, to a random sample of 607 banana planters with a sampling rate of about 80% in each island. After eliminating missing values and zero values for input-output vectors, the final dataset used contains 567 observations. To estimate our conditional efficiency model using this dataset, we selected one output, four inputs, and fourteen contextual drivers. The output is measured as the physical value of the banana production in tons. The four inputs include the agricultural area, the labor used, the quantity of chemical fertilizers used, and the quantity of chemical pesticides. Among the relevant contextual drivers, we mainly focus on complementarity between innovations and its impact on technical efficiency (see Table 1).

Results and discussion

The estimates for the effects obtained from the order-m conditional efficiency model are reported in table 2. The average conditional technical efficiency score amount to 0.67, while the unconditional score is only 0.6. This suggests first that farmers in our sample generate 33% less outputs than it is technically feasible. That is, farmers could increase their output by 33% without increasing their input use. Second, in average contextual drivers induces a 7% increase of the efficiency score.

Regarding the average marginal effects of these contextual drivers, our results show that the potential of increase mainly comes from our variable of interest, i.e., complementarity between DFS and Fallow agroecological innovations since marginal effect of joint adoption induces an increase in farmer efficiency of about 20%, while the adoption of DFS alone generates only 15% of increase and Fallow alone has no significant effect. These results highlight that by jointly adopting complementary innovations, farmer becomes more productive (Miravette and Pernias, 2006).

For the other contextual variables, we find that technical assistance and agricultural training significantly increases the conditional efficiency scores since both provide precise information and know-how on agroecological innovations use [START_REF] Xayavong | How training and innovation link to farm performance: a structural equation analysis[END_REF]. Likewise, expectation of increasing selling prices may play as an insurance and incentive to improve farm productivity and this can explain its positive impact on the conditional efficiency score (Karian et al., 2014). For the dispersion effects, the results indicate a positive effect of the DFS/Fallow joint adoption on the variance of the conditional efficiency scores. That is, while synergistic agroecological systems have the advantage of increasing marginal efficiency scores, they also have the disadvantage of increasing their variability, which seems to be a general rule of coupled innovations since intercropping systems (intercropping) also increase the variability. These innovative systems are indeed complex to manage and therefore require high human capital. Our results show that some key variables, such as the existence of technical assistance

Conclusion

This paper uses a context-dependent framework, the nonparametric conditional efficiency model, to examine the innovation-performance nexus in agriculture. Our estimates on a database of 567 banana farms in the West Indies confirm this complementarity effect since the joint adoption of two synergistic agroecological innovations, i.e. Disease Free seedlings (DFS) and Fallow, increases the technical efficiency score much more than each of the innovations taken in isolation. We also show that advice and extension services, as well as well as farmer human capital increase, are key adoption levers for public policy since they reduce the variability of production and thus the risk associated with the joint adoption of the agroecological innovations.

The main limitation of this work is that we analyze the complementarity effect using only two agroecological innovations. It would be interesting in a future research to study the impact and interactions between a large number of agroecological innovations to test the robustness of our complementary result.

Table 1 :

 1 Description of the variables

	Variables	Description	Mean Std	Min Max
	Output
	Banana production	Banana production in tons	464.19	975.53 1	10300
	Inputs
	Land	Area in banana production (ha)	11.31	19.77	0.5	210
	Labor	Labor used in annual working unit	7.46	13.36	0.14	151.42
	Fertilizer	Fertilizers used in tons	23.25	45.24	0.31	453.6
	pesticides	Pesticides used in kg	15.46	33.85	0.05	441
	Contextual drivers
	DFS (Disease Free Seedlings)	1 if farmer has adopted DFS	0.35	0.48	0	1
	Fallow	1 if the system includes fallow	0.39	0.49	0	1
	DFS x Fallow	1 if joint adoption of DFS and Fallow	0.27	0.45	0	1
	Intercropping	1 if the system includes intercropping	0.61	0.49	0	1
	Share of mechanized land	mechanized banana land (%)	4.318	0.483	0	1
	Share of irrigated land	Irrigated banana land (%)	0.31	0.41	0	1
	Guadeloupe	1 for farms located in Guadeloupe	0.26	0.44	0	1
	Farm size	Total Farm area (ha)	16.77	29.95	0.5	262
	Technical Assistance	Number of links with researchers & technicians 31.47	23.41	0	194
	Agricultural training	1 if farmer has training in Agriculture	0.51	0.50	0	1
	Higher education	1 if farmer has made high study	0.07	0.263	0	1
	Social group	1 if Household belongs to a social group	0.37	0.48	0	1
	Older farmer	1 if Age >= 60	0.12	0.32	0	1
	Price Expectation	1 if farmer expects increasing prices	0.20	0.43	0	1

Table 2 :

 2 Conditional Efficiency Estimates

		Marginal effects	Dispersion effects
		Estimate	Bootstrap S.E	Estimate	Bootstrap S.E
	DFS	0.1547**	0.0683	-0.0142	0.0099
	Fallow	-0.0384	0.0564	-0.0129	0.0101
	DFS x Fallow	0.1980**	0.0820	0.0295**	0.0148
	Intercropping	-0.0416	0.0266	0.0122**	0.0059
	Share of mechanized land	0.0051	0.0479	-0.0025	0.0120
	Share of irrigated land	0.1248***	0.0532	-0.0019	0.0104
	Guadeloupe	0.0422	0.0485	-0.0137	0.0087
	Technical assistance	0.0013*	0.0008	-0.0007***	0.0001
	Agricultural training	0.0530*	0.0282	0.0026	0.0066
	Higher education	0.1152	0.0828	-0.0263***	0.0099
	Social group	0.0232	0.0347	-0.0072	0.0064
	Older farmer	0.0364	0.0344	-0.0249***	0.0056
	Price expectations	0.0658**	0.0328	-0.0158**	0.0077
	Mean conditional TE		0.67
	Mean unconditional TE		0.60

In the conventional approach, this set is not conditional to the contextual drivers (Z).