Oumar Ba

Mihaela Chis

Christophe Cassagne

Georges Boudebs
email: georges.boudebs@univ-angers.fr

Phase shift imaging in thin films using CW Z-scan based technique

Keywords: Thermo-optical heating, thermal lens, phase shift, Z-scan, linear absorption

INTRODUCTION

Historically, images of objects invisible to the naked eye were necessary in several fields including material science engineering. Particularly, the technique of phase contrast in microscopy has found many applications thanks to its propriety of revealing objects that are transparent. High power laser beam induces temporary phase shifts due to thermal effect in quasi transparent material [1,[START_REF] Khurgin | Ultrafast thermal nonlinearity[END_REF]. Indeed, in high repetition rate laser systems, the responses observed in different materials are highly dependent on cumulative heat in the sample. If the repetition rate is such that the sample does not have time to cool down between two shots the cumulative effect may induce nonlinear (NL) phase shift due to increase in local temperature and can be damaging the tested medium. The dependence of the thermal response of the material is not simple and many studies try to simplify the problem considering only few parameters. Thermal lens effect has been reported in the literature since 1964 [1]. Several studies followed to improve the model, most of which considered the beam as gaussian [START_REF] Hu | New thermooptical measurement method and a comparison with other methods[END_REF][START_REF] Whinnery | Laser measurement of optical absorption in liquids[END_REF][START_REF] Carman | Time dependence in the thermal blooming of laser beams[END_REF]. Besides, with much higher intensities it is possible to induce phase shifts through the third order NL optical susceptibility. To characterize this phenomenon, the Z-scan technique was first proposed by Sheik-Bahae et al. [START_REF] Sheik-Bahae | Sensitive measurement of optical nonlinearities using a single beam[END_REF] where the far field diffraction method of the laser beam interacting with the induced phase shift has been simplified. Here the sample is moved with a focused laser beam through its focal region. Information on the magnitude of twophoton absorption and Kerr effect is acquired by analysing the normalized transmission of the sample as a function of its position. It is one of the most popular methods used for the determination of third order and higher NL optical properties due to its simplicity and high sensitivity. Later, the dependence of the far-field intensity on sample position due to intensity-dependent optical nonlinearities has been analysed on the basis of the thermallens model of Gordon et al. [START_REF] Gordon | Long-transient effects in lasers with inserted liquid samples[END_REF] and the Gaussian decomposition analysis of Sheik-Bahae et al. [START_REF] Cuppo | Thermal-lens model compared with the Sheik-Bahae formalism in interpreting Z-scan experiments on lyotropic liquid crystals[END_REF]. The beam waist relative variation (BWRV) method [START_REF] Boudebs | Nonlinear characterization of materials using the D4σ method inside a Z-scan 4f-system[END_REF] which will be used in this paper is a Z-scan based technique. It has been already successfully applied to measure the Kerr effect using picosecond pulsed laser [START_REF] Boudebs | Nonlinear characterization of materials using the D4σ method inside a Z-scan 4f-system[END_REF][START_REF] Araújo | Techniques for nonlinear optical characterization of materials: a review[END_REF][START_REF] Wang | Picosecond cubic and quintic nonlinearity of lithium niobate at 532 nm[END_REF][START_REF] Derkowska-Zielinska | Nonlinear optical study of Schiff bases using Z-scan technique[END_REF][START_REF] Boudebs | Influence of strong light beams on the nonlinear refraction and absorption coefficients of transparent materials[END_REF].

The parameters to be measured here in low power CW regime are not due to the Kerr effect but to thermal ones. Indeed, moving the sample around the focal point of the beam will induce a change in the incident intensity and therefore a change in the refractive index of the sample due to increasing thermal effect. This can be exploited to obtain images showing different absorbent objects as chemical species in microbiological samples [START_REF] Uchiyama | Thermal lens microscope[END_REF] or in semiconductor optoelectronic components especially when high output power is required [START_REF] Mansanares | Temperature field determination of InGaAsP/InP lasers by photothermal microscopy: Evidence for weak nonradiative processes at the facets[END_REF]...Laser photothermal microscope with coaxial excitation and probe beams was proposed in [START_REF] Uchiyama | Thermal lens microscope[END_REF] and application for absolute temperature determination in semiconductor laser diode was performed in [START_REF] Mansanares | Temperature field determination of InGaAsP/InP lasers by photothermal microscopy: Evidence for weak nonradiative processes at the facets[END_REF].

This work begins with a rapid presentation of the BWRV method. We demonstrate its feasibility to characterize the thermal effects induced by a CW beam of a few mW at 532 nm. The contribution of the absorption in a liquid and the linearity of the signal with the power of the incident beam will be investigated using some classical solvents. Then, the method will be extended to transversally scan the sample in the focal region. We demonstrate that this new single beam technique (XYZ-scan) allows to extract an image of the phase shift induced by the local thermal heating. It will be applied to map an inhomogeneous thin film doped with different concentrations of silver nanoparticles.

THEORY

Thermal effect

Following reference [START_REF] Sheldon | Laser-induced thermal lens effect: a new theoretical model[END_REF] in which some assumptions were considered: dimensions of the cell are large compared with the diameter of the beam, heat conduction through the ends can be neglected, and thus the temperature variation can be taken as purely radial. The following symbols will be used: α absorbance in m -1 ; ρ density in Kg/m 3 ; Ι beam intensity; thickness of the medium (cell) in m; Ρ beam power in W; specific heat in J/Kg/K; beam radius in ; ∆Τ temperature variation in °K; thermal conductivity in J/s/m/K; λ wavelength in m.

Starting from the heat equation in transient mode, assuming an incident Gaussian beam and taking into account the aberrant nature of the thermal lens [START_REF] Sheldon | Laser-induced thermal lens effect: a new theoretical model[END_REF], the variation in temperature in the medium is given by:

∆ , = ⁄ " # exp ( ) ⁄ * ⁄ " + ′, (1)
where = -4 ⁄ . This temperature variation induces a change in the linear index according to the following relationship:

Δ0 , = 12 13 Δ , , (2)
with +0 + ⁄ denoting the thermo-optical coefficient. The induced phase shift is related to Δ0 as usual using 45 = 2740 8 ⁄ .

Characterization method

The next step is to determine what effect this refractive-index distribution has on the beam intensity at the output of a 4f imaging system. The experimental setup used to implement the BWRV is presented in Fig. 1. We recall here briefly the method; more experimental details can be found in [START_REF] Boudebs | Nonlinear characterization of materials using the D4σ method inside a Z-scan 4f-system[END_REF][START_REF] Araújo | Techniques for nonlinear optical characterization of materials: a review[END_REF][START_REF] Wang | Picosecond cubic and quintic nonlinearity of lithium niobate at 532 nm[END_REF]. This setup is composed of an afocal imaging system (9 = 10 ; 9 = 20 ) so that the magnification is equal to 2. The sample under investigations is moved along the beam direction in the focus region. An image of the output beam, transmitted by the sample, is then recorded by a CCD camera. It has been shown in [START_REF] Boudebs | Nonlinear characterization of materials using the D4σ method inside a Z-scan 4f-system[END_REF][START_REF] Araújo | Techniques for nonlinear optical characterization of materials: a review[END_REF] that the signal, 4 ;< which is the difference between the peak and the valley (see Fig. 2-a) is a linear function of the peak induced effective phase shift ∆5 # (defined at the center of the beam) and at the focus (= = 0) (Δω ?@ = 0.3∆φ # ). The laser is a CW Nd:YAG type emitting at 532 nm. At the laser output, a polarizing system (λ/2 + GLAN) (not visible in Fig. 1) allows the incident power to be varied from 0 to ≈ 15 E. Then, a spatial filter

RESULTS AND DISCUSSIONS

Checking the linearity of the signal

In the first place, the feasibility of the experiment has been achieved with the study of a basic solvent (methanol) to which we have progressively added Indian ink as absorbing pigment at different concentrations under different incident laser beam power. In Fig. 2(a), we show two BWRV profiles corresponding to pure methanol and to a few drops of ink dissolved in methanol characterized by an absorption coefficient: H = 5.2 × 10 (J ( . The signal ∆ ;< is the difference between the maximum and the minimum of the profile.

Fig. 2. (a) BWRV profiles of pure methanol (blue circles) and methanol with ink (black squares) for the same beam power (K L = 700 µW, L= 2 mm); the vertical arrow shows the signal: Δ pv. (b) Evolution of the signal as a function of the laser beam power for a fixed concentration in ethanol. (c) Evolution of Δ pv versus H, the linear absorption characterizing different concentrations of ink diluted in methanol (red circles) and ink diluted in water (blue squares) for a fixed input power (2 mW). Solid lines in (b) and (c) are the linear regression lines.

It is well known that the thermal effect contributes to a negative phase shift related to a negative variation of the refractive index. This change is due to a decrease in density with the increase of temperature. In contrary to classical open aperture Z-scan, the signature of the BWRV showing a minimum followed by a maximum is typical of a negative Δ0. Comparing the two profiles, notice the 30 times higher response of methanol with ink inducing higher 4 ;< which indicates a larger variation in the refractive index due to a higher absorption inside the liquid. The question that remains is whether our signal 4 ;< is linear as a function of the input power for a given concentration. In Fig. 2 (b), we highlight the evolution of this response showing the predicted linearity on a large scale using ethanol as a solvent. To show the effect of the concentration and the solvent thermo-optical characteristics on the signal, measurements were taken using two solutions: ink with distilled water and ink with methanol at different concentrations. We gradually diluted the solutions and reported in Fig. 2 (c) the measured 4ω ;< corresponding to each absorption value α, with an incident power Pe of 2 E and a cell of 1 Beam Waist Relative Variation thickness. Of course, we notice the linear response as a function of the absorption, which is in accordance with the theoretical equations developed in [START_REF] Gordon | Long-transient effects in lasers with inserted liquid samples[END_REF]. Note the difference in the slope of the solid regression lines when the solvent changes, due to the different thermo-optical coefficients. Indeed, for the same ink concentration the solvent induces different index variations (different 4ω ;< according to its different thermal parameters such as the specific heat, the thermal conductivity and the density.

Transversal sample mapping

We have described the BWRV method which makes it possible to obtain the induced phase from a Z-scan over one point of a sample. This phase shift 45 # allows us to find the refractive index 40. After this, a scanning system is added in the focal plane orthogonal to the optical axis z over which the scan is made. Three translation plate were separately motorized covering xyz axes and controlled by three controllers (Fig. 3 (a)). These plates allow 30 translation for each axis with a step (resolution) of 1.25 µ . Connected to the computer, the the same for all the acquisitions over all the considered points, one can check that the higher variation of 40 is related to the higher concentration of doping metallic Ag nanoparticles in the film.

According to reference [START_REF] Uchiyama | Thermal lens microscope[END_REF] using coaxial excitation and probe beams, the spatial resolution of the thermal lens microscope is determined by the spot size of the excitation beam and was less susceptive to the thermal diffusion length. In fact, the probe beam in [START_REF] Uchiyama | Thermal lens microscope[END_REF] had approximately the same spatial extension as the excitation one. Thus, in theory, when dealing with single-beam techniques, the final image can have a spatial resolution of the same order of magnitude as conventional linear imaging systems, since the variation in index is related to the variation in intensity profile in the focal plane, which in the best case has a dimension close to the micrometer. Here the excitation beam ( = 18 μ is far from that ideal case using high numerical aperture microscope objective but the purpose of the paper is to demonstrate the feasibility of extracting this phase shift image with only one beam.

Evidently, the spatial resolution will also depend on the time it takes to obtain the final image which is related to the number of dots per millimeter square to be measured, the power of the computer, the efficiency of the CONCLUSION

Fig. 1 .

 1 Fig. 1. Experimental setup. The sample (NLM) is scanned along the beam direction around the focal plane (z=0). The labels refer to: lenses (L1 and L2) and Camera (CCD).

  is placed to clean and to expand the beam. The output beam irradiates the object plane at the input of the afocal imaging system. The first lens (L1) focuses the light on the sample (NLM) with a beam waist approximately equal to 18 µm. The NLM can move around the common focal plane of both lenses L1 and L2. Then, the image of the output beam is formed on the CCD sensor thanks to L2. The dimensional variation in the transmitted beam profiles are directly related to the induced phase-shifts in the NLM. The evolution of the BWRV, calculated using the first and second moment of the recorded spatial beam intensity distribution, is then calculated versus the position z of the sample. Two sets of acquisitions are performed for each measurement. The first set is done in the high-power regime and the second in the low-power one; this is necessary to remove from the measurements the diffraction, diffusion and/or imperfection due to the inhomogeneity of the sample. For all subsequent acquisitions, 0.465 mm pitch is used on the z axis, for a total displacement of 28.365 mm. This gives 61 images per scan and 122 images for a complete acquisition (low and high power). The exposure times range from 100 F to 2 F. Taking into account the characteristic time ( ) of our samples it is considered that the acquisitions are carried out in the stationary regime. Indeed, the CCD camera has a relatively long response time and does not allow to study time dependence for rapid transient regimes. Moreover, a minimum delay time of 0.5 F between each acquisition is necessary to move the motor and to dampen the generated mechanical vibrations. Tests were performed at different integration times of the CCD (0.25F, 0.5F, 0.75F and 1F) and the that the generated signals were very close validating the steady state induced phase shift measurements.

  translation system is driven by a LABVIEW program. A Z-scan is made for each coordinate point N O , P O to find the index variation of the material at that point. A restitution of all these measurements would give a thermo-optical image of the solid thin film sample. This process is called XYZ-scan, it is very useful for studying inhomogeneous materials in terms of density, absorption...

Fig. 3 : 5 .

 35 Fig. 3: (a) The thin film on the tri-axis translation plate. (b) image of the thin film 1.6µm thick (SiO2-TiO2 + Ag) shown in (a); (c) cartography of the thermal effects and the measured ∆n (-8x10 -3 < ∆n < -3x10 -3 ) for Pe = 7.5 mW. Acquisition and processing time 20 0 for 64 measurement points.. To validate our method, the studied sample was an inhomogeneous thin sol-gel film of QRS RS T UV (10 (W X) (Fig.3(b)) with a thickness of 1.6 μ deposited on a microscope glass slide. The film was exposed to a 7.5 E continuous laser beam. 64 measurement points (Fig.3(c)) were carried out over an area covering 5 ×5. This area was divided into 8x8 equidistant squares on the edge of the film where the inhomogeneity

  software and the smallest step of the motor used for transverse-scanning… Concerning the contrast, it is related to the evolution of the BWRV response showing the predicted linear relation with the induced phase shift. Fig.2(b) shows an example of how large the scale of the response could be. We estimated to a maximum of 100% (BWRV=1) the relative variation of the beam dimension where the signal remains linear with the absorption. This value corresponds to a phase shit of ∆5 Z = π. Tests have been done to estimate the minimum detectable signal to be around 3x10 -3 , which corresponds to ∆5 [ = 10\+. The contrast of the images should then be ] = ∆5 Z -∆5 [ ∆5 Z T ∆5 [ ⁄ ≈ 0.99 which is theoretically very close to the maximum value that one can obtain in imaging systems.

Acknowledgements

The authors would like to acknowledge the financial support from the NNN-TELECOM Program, Région des Pays de la Loire, contract n°: 2015 09036.

impurities in transparent thin films irradiated with a low power CW laser beam using a single beam technique.

The beam waist relative variation (BWRV) method at the output of an imaging system has been successfully applied to demonstrate the feasibility of quantifying the measurable coefficients that allow for retrieving these images. For this purpose, we have experimentally demonstrated the linearity between the measured signal and the incident laser power as well as the concentration in some weakly absorbing solutions. The obtained steady signals with a CCD are not sensitive to the characteristic time for the transient induced nonlinear index variation.

Otherwise, this paper also aims to draw attention to the possible confusions that some researchers may have by associating the relatively slow thermal responses obtained with a low power continuous mode laser generating induced phase shifts due to absorption with that of instantaneous Kerr induced phase shifts using high intensity pulsed lasers.


domain: sde chim

text:
Pascal Thiébeau

Cyril Girardin

Sylvie Recous
email: sylvie.recous@inrae.fr

Water interception and release of soluble carbon by mulches of plant residues under contrasting rain intensities

Keywords: carbon, crop residue, no-till, rain regime

Soluble C leaching

Introduction

The development of no-till agricultural systems modifies the way crop residues are incorporated back into the soil compared to conventional systems with ploughing. These residues form a layer, or mulch, on the soil surface in no-till systems or are partially incorporated into the first few centimetres of soil with reduced tillage. The presence of crop residues on the soil surface has very significant consequences on water and heat flows between the atmosphere, mulch and soil, as well as on the regulation and stratification of biological activity and organic matter in soil and mulch [START_REF] Bussière | Modification of the soil temperature and water content regimes by a crop residue mulch: experiment and modeling[END_REF][START_REF] Baumhardt | Residue management and tillage effects on soil-water storage and grain yield of dryland wheat and sorghum for a clay loam in Texas[END_REF][START_REF] Fuentès | Conservation agriculture, increased organic carbon in the top-soil macroaggregates and reduced soil CO2 emissions[END_REF][START_REF] Dietrich | Gradient of decomposition in sugarcane mulches of various thicknesses[END_REF]. However, the determinants of water retention by crop residues and the consequences of rainfall on the transport of soluble elements, particularly soluble carbon (C), are much less known, despite their importance for C and nutrient cycling in soils [START_REF] Lee | Soil moisture and soil-litter mixing effects on surface litter decomposition: a controlled environment assessment[END_REF][START_REF] Iqbal | Rain regime and soil type affect the C and N dynamics in soil columns that are covered with mixed-species mulches[END_REF]. In particular, it has been shown that plant litter-derived soluble C may constitute a significant pathway of C stabilization in soil [START_REF] Cotrufo | The Microbial Efficiency-Matrix Stabilization (MEMS) framework integrates plant litter decomposition with soil organic matter stabilization: do labile plant inputs form stable soil organic matter?[END_REF]. Soluble C can account for an important fraction of C in crop residues, varying from approximately 10 to 80 g 100 g -1 total C for main crops and cover crops depending on the degree of maturity and part of the considered plant [START_REF] Trinsoutrot | Relationships between biochemical quality of crop residues and C and N mineralisation kinetics under nonlimiting N conditions[END_REF][START_REF] Redin | How the chemical composition and heterogeneity of crop residue mixtures decomposing at the soil surface affects C and N mineralization[END_REF].

Although the amount of rainwater that can be intercepted and retained by mulches has received little study, we know that this interception depends mainly on the amount and nature of crop residues (Tuckey, 1970). Previous studies have shown that the maximum water content of these mulches can be modulated according to the crop residue characteristics [START_REF] Quemada | Characteristic moisture curves and maximum water content of two crop residues[END_REF][START_REF] Iqbal | Tissue density determines the water storage characteristics of crop residues[END_REF] and their morphological, anatomical and chemical traits [START_REF] Garnier | Leaf anatomy, specific mass and water content in congeneric annual and perennial grass species[END_REF]. [START_REF] Iqbal | Tissue density determines the water storage characteristics of crop residues[END_REF] showed for stems of different annual species that the main explanatory characteristic of their maximal ability to retain water was the density of the tissues of the stems (or its inverse, i.e., porosity), whereas chemical characteristics were not directly related to water retention properties. A number of studies have compared the effects of rainfall intensity on the water retention capacity of mulch on the soil surface, mostly on forest systems with leaf litters (e.g., [START_REF] Sato | Experimental analysis of moisture dynamics of litter layers-the effects of rainfall conditions and leaf shapes[END_REF][START_REF] Schrumpf | TOC, TON, TOS and TOP in rainfall, throughfall, litter percolate and soil solution of a montane rainforest succession at Mt. Kilimanjaro, Tanzania[END_REF][START_REF] Dunkerley | Percolation through leaf litter: What happens during rainfall events of varying intensity?[END_REF]. More recently, the fact that residue mulch constitutes a "hot spot" of biological activity and denitrification has led to interest in the water retention capacity of mulches [START_REF] Kravchenko | Hotspots of soil N2O emission enhanced through water absorption by plant residue[END_REF] but such study is still rare. To our knowledge, the transport of soluble C or nutrients under the influence of rainfall carried out in an agricultural context are rare [START_REF] Halvis | Nutrient leaching from field-decomposed corn and soybean residue under simulated rainfall[END_REF][START_REF] Schreiber | Leaching of nitrogen, phosphorus, and organic carbon from wheat straw residues: II. Loading rate[END_REF]Schreiber and McDowell, 1985;[START_REF] Schreiber | Nutrient leaching from corn residues under simulated rainfall[END_REF] despite the experimental observation of residue-derived soluble C transport into soil [START_REF] Coppens | Soil moisture, carbon and nitrogen dynamics following incorporation and surface application of labelled residues in soil columns[END_REF][START_REF] Lee | Soil moisture and soil-litter mixing effects on surface litter decomposition: a controlled environment assessment[END_REF][START_REF] Iqbal | Rain regime and soil type affect the C and N dynamics in soil columns that are covered with mixed-species mulches[END_REF].

The objective of this work was to understand the relationships among the rain regime (varying by the intensity and amount of water applied), water retention by mulch and soluble C loss from mulch under the influence of rain. Experimentally, mulch residues from four different crops were placed under simulated rains of realistic and contrasting intensities representing the conditions in temperate to tropical climates. We measured the dynamics of water interception by mulches and the leaching of soluble C from the mulch. To facilitate the dynamic and quantitative monitoring of soluble C extracted from the mulch by the rains, we did not place soil under the mulch.

Materials and methods

Crop residues

Maize (Zea mays L.), rice (Oriza sativa L.), and soybean (Glycine max L.) were harvested at the mature stage, while pea (Pisum sativum L.) was harvested at flowering so that its residues represented those of a cover crop. The crop residues were collected in the field in three areas, namely, an area of intensive agriculture in northern France, a family farm in Cerados (Brazil) and upland rice cropping systems in the Central highlands of Madagascar. We used all organs to compose the residues, except for the grains and roots. Samples were dried at 40°C until they reached a constant weight and then were stored in paper pockets. The chemical characteristics of the selected residues were determined prior to the rainfall experiment and are given in Table 1. Briefly a sub-sample of each residue was ground and analysed to determine the chemical and biochemical characteristics via a proximal analysis, thus providing the relative proportion of the so-called "van Soest" fractions of the residue dry matter.

The soluble fraction was determined by extraction in hot water (100 °C) for 30 min followed by extraction with a neutral detergent (100 °C) for 60 min. The hemicellulose, cellulose and lignin fractions were subsequently determined via a proximate analysis [START_REF] Goering | Forage Fiber Analysis (apparatus, reagents, procedures and some applications)[END_REF]. The cold water-soluble fraction of the residues was determined by extraction in deionised water over 30 min at 20 °C (plant material/water ratio 1/100). The total C and N contents of the plant residues were determined via total combustion using an elemental analyser (NA 2000, Fisons Instruments, Milan, Italy). Physical characteristics were also determined. Residue-particle bulk density was calculated using the immersion method in water [START_REF] Iqbal | Tissue density determines the water storage characteristics of crop residues[END_REF]. Mulch thickness was measured for 4 replicates per residue type, with 7 measures per replicate [START_REF] Thiébeau | Measuring the thickness of crop residues on the soil surface to estimate their biomass[END_REF]. The bulk density of the mulch layers was calculated from the thickness of the layers and the added mass of the residues for each residue type.

Insert Figure 1 Insert Table 1 2.2 Simulated rainfall experiments A similar residue quantity was used for the 4 types of crops to facilitate the comparison of results, with 12.4 g of dry residue, which is equivalent to 0.75 kg dry matter m -2 of residue, placed as a litter layer (mulch) on a 1 mm nylon mesh in a PVC cylinder that was 14.5 cm in diameter (165 cm 2 ) and four cm in height. This amount of residue corresponded to the usual residue biomass in fields for the main crops [START_REF] Thiébeau | A method to quantify crop residue biomass left on soil surface after harvesting[END_REF][START_REF] Thiébeau | Measuring the thickness of crop residues on the soil surface to estimate their biomass[END_REF]. The crop residue samples were cut into fragments of two centimetres in length (Fig. 1) to reduce the heterogeneity of composition of the mulches between replicates for each crop species. Indeed, the inherent biological variability in the composition and morphology of plant organs for a given species prevent the replication of 12.4 g of mulches on a 165 cm 2 surface and do not allow the results to be related to an initial residue composition; thus, the particle size had to be reduced. Thus, the potential natural differences between species were eliminated to some extent. Depending on the residue morphological characteristics and density, the particles formed a layer with an initial thickness of 9.3 ± 0.8 mm for rice, 8.6 ± 1.3 mm for maize, 12.8 ± 1.5 mm for pea and 6.7 ± 1.0 mm for soybean. Therefore, the mulch layers had initial bulk densities of 81 ± 6.4 (rice), 87 ± 11.4 (maize), 59 ± 6.2 (pea) and 112 ± 14.5 kg m -3 (soybean). intensity (n=3). Drainage buckets were placed under each cylinder to collect the percolated water and were weighed and sampled periodically to characterize the drained water under the litter layer. The experiment was run under controlled temperature conditions at 20 ± 1 °C.

The drop-forming rainfall simulator, described earlier by [START_REF] Iqbal | Rain regime and soil type affect the C and N dynamics in soil columns that are covered with mixed-species mulches[END_REF], consisted of capillary tubes (inner diameter of 0.5 mm) that were equally distributed over the surface (186 cm 2 ) using 72 needles (0.3 mm diameter x 13 mm long; "BD Microlance 3"; Becton Dickinson, Fraga, Spain) separated from each other by 16 mm; the simulator released 3906 drops per m² (Fig. 2). The rainfall simulator was fed with a flow of deionized water controlled by a Gamma L electromagnetic pump (ProMinent, Heidelberg, Germany). Flow rates were adjusted to predetermined intensity profiles and maintained at a constant value to achieve a constant rainfall intensity. Three rainfall intensities were chosen to simulate different climatic scenarios consistent with the field conditions of the studied crops: i) a low regular rainfall intensity of 4 to 5 mm h -1 representative of temperate climates; ii) an intermediate rainfall intensity of 11 to 12 mm h -1; and iii) a strong rain intensity at 24 to 25 mm h -1 , representative of the intensity that occurs frequently in tropical conditions.

Insert Figure 2

Experimental protocol

The rain experiment was run for 24 hours. First, the rain simulations started one hour before the positioning of the cylinders; then, each cylinder with a mulch layer was placed under one simulator for 23 hours. During the first 7 hours of rain, mulch layers and buckets were quickly removed every hour and placed into a pre-weighed tray to record the weight of the water held in the litters and the percolates in the buckets. These data were used to calculate the water interception by the litter and the amount of leached water. Each sieve was immediately returned under the rain simulator until the next measurement. After the homogenization of the bucket water content, an aliquot of water was sampled and frozen until the determination of dissolved organic carbon (DOC). After 22 and 23 hours of continuous rain, sieves and buckets were weighed again, and sub-samples of water were collected.

Notably, under the simulated rainfall intensity of 24 mm h -1 , a large volume of water had leached through the samples between hour 7 and hour 22 and could not be quantitatively stored, so the above measurement was not conducted.

Analysis

At the end of experimentation (23 hours), the moist residues were first weighed, and then samples were dried at 40 °C until they reached a constant weight, and the loss of mass was calculated.

The maximum water storage capacity (MaxWC) was calculated for each residue type and each rain intensity as the difference in weight between the wet mulch and the mulch dried at 40°C, expressed per g of residue dry matter (DM) at 40 °C. The residues were then dried at 120 °C until constant weight. Minimum water storage capacity (MinWC) was calculated as the difference in weight between the mulch dried at 120 °C and at 40 °C, expressed per g of residue DM at 40 °C [START_REF] Iqbal | Tissue density determines the water storage characteristics of crop residues[END_REF]. A subsample of each crop residue was ground to a particle size of 80 microns, and the total C and N contents were determined by total combustion using the elemental analyser NA 2000 (Fisons Instruments, Milan, Italy). The DOC in the leached water was measured with a total organic carbon (TOC) analyser (Shimadzu TOC-5050A, Shimadzu SAS, Marne la Vallée, France).

Calculations and statistical analysis

The characteristics of the interception storage capacity of the different residues as a function of the total rain were calculated using a non-linear equation with two parameters [START_REF] Iqbal | Tissue density determines the water storage characteristics of crop residues[END_REF]:

ƒ = a. X b (1)
where "a" is the water absorbed by the first mm of rain per g of residue and "b" is the propensity of the residue to retain an additional mm of water until reaching the maximum retention value.

Statistical analysis was carried out with the Sigma-Plot 12 Statistics programme (Systat Software, USA). The significance level chosen in our study was p < 0.05. Means were classified in a homogenous group according to the results of ANOVA and the Newman-Keuls test. The statistical model evaluation criteria were the root mean square error (RMSE) and coefficient of determination (R²) values.

Results

Rainfall assessment

The rainfall balance according to rain intensity and residue species showed that the objective of using the three rain intensities was achieved (Supplementary material SM1), with no statistically significant difference between crop treatments for each rain intensity. The cumulative amounts of water provided by the three rainfall regimes during the experiment were 105 ± 1 mm, 266 ± 7 mm and 560 ± 3 mm. The water flow, calculated from the bucket weight at each hour, showed the establishment of a regular flow of 72 mL h -1 for 4 mm h -1 , 190 mL h -1 for 11 mm h -1 and 400 mL h -1

for 24 mm h -1 after 4 to 5 hours of rain (Supplementary material SM2).

Water interception by crop residues

From the evolution of the weight of mulches throughout the experiment, we inferred the dynamics of water uptake by the four residues under three rainfall intensities (Fig. 3). However, these uptake values were only "apparent" because the loss of crop residue matter under the rainfall was not determined, except for at the end of the experiment using destructive sampling of the residue layers.

Insert Figure 3

During the first 7 hours of rain, water uptake kinetics were fast for all residues. The kinetics of the 4 mm h -1 rain intensity were markedly lower than those of the 11 and 24 mm h -1 rain intensities, which did not differ from each other; this was true for all four types of residues. At the end of the experiment (measurements at +22 and +23 h of continuous rain), the water uptake values under the three rain intensities differentiated from each other for almost all residues, and the residues under the most intense rainfall absorbed the most water (24 mm h -1 > 11 mm h -1 > 4 mm h -1 ).

The water storage of residue particles measured at the end of the experiment for each residue type and each rain treatment varied depending on the residue type and the cumulative quantity of water received (itself resulting from the rain intensity applied) (Fig. 4A). The rice and maize mulches behaved very similarly, with high water retention under 100 mm of water. The soybean mulch retained much less water than the rice and maize mulches. The pea mulch demonstrated intermediate water retention, with a relatively low but continuous increase in water retention with increasing amounts of rain. The relationships between MaxWC and cumulative rain were well fitted by the non-linear equation with two parameters (Table 2). The water absorbed by the first mm of rain ("a" coefficient) varied from 0.3 to 1.5 g H2O g -1 DM, with the lowest value for pea residues. Furthermore, the "b" coefficient, which is the propensity of the residue to retain an additional mm of water until reaching the maximum retention value, was quite constant (approximately 0.22) for the soybean, maize and rice residues and was 0.46 for the pea residues. The modelled MaxWC confirmed that pea, maize and rice residues contained large amounts of water, with values that were not significantly different from each other (5.9 to 6.6 g H2O g -1 DM), while soybean retained much less water, with a value of 3.5 g H2O g -1 DM (Table 2). Conversely, the measured MinWC was higher for pea residues (0.06 g H2O g -1 DM) than for the three other residues.

Insert Table 2

Insert Figure 4 3

.3 Loss of mulch DM under rain

Pea residues lost much more DM than the three other residues, losing 28.4% of their initial weight under the highest intensity/highest cumulative rain. In contrast, the soybean, maize and rice residues behaved similarly, losing 9.4, 10.7 and 8.3% of their initial weight under the highest rain intensity, respectively, which were not significantly different. (Fig. 4B, supplementary material SM3).

This mass loss represented 16.7, 20.5, 31.9 and 29.5% of the initial mass of the "van Soest" soluble fraction for pea, soybean, maize and rice, respectively. The mass loss increased with increasing rain intensity, particularly for pea residues. The N concentration and C:N ratio of the remaining residues measured at the end of the experiment (Supplementary material SM4) showed that leaching affected the residue soluble N as expected. The initial and final C:N ratios did not change significantly for the pea and soybean residues, indicating that the C:N ratio of the residue fraction leached was similar to the C:N of the whole residue, except soybean at 24 mm h -1 intensity. For maize, the final C:N ratio increased significantly for the three rain regimes compared to the initial C:N, thus indicating a larger loss of soluble residue-N compared to residue-C. Conversely, the C:N ratio slightly decreased for rice residue but the difference was not significant.

Dynamics of soluble C release

The soluble C concentration of the leached water varied according to residue type, with pea >> soybean > rice > maize, and varied greatly according to rain intensity (Fig. 5). The 11 mm h -1 rain intensity resulted in high soluble C concentrations beginning in the first hour, while the 4 mm h -1 led to concentrations in the same range with a delay in the extraction of soluble C. This delay manifested in an offset concentration peak at hours 3 to 6, except for in rice. For all residues, the soluble C leaching was markedly lower under the 24 mm h -1 regime than under the other two regimes, which suggests that the leaching of soluble C by percolating water was not proportional to the rain intensity.

In all cases, except for the case of maize, the concentration of soluble C in the leached water decreased over time and became similar under all treatments and rain intensities during the last time interval (22h -23 h).

Insert Figure 5

The cumulative soluble C leached, calculated from the volume of recovered leached water and its soluble C concentration at each sampling point of the experiment, showed an almost linear increase during the first 7 hours for all residues and rain intensities (Fig. 6). Strikingly, for all residues except for pea, similar amounts of soluble C were removed under the 24 mm h -1 and 11 mm h -1 intensities until hour 7, with different values at 22 h and 23 h, while the 4 mm h -1 intensity removed markedly less soluble C from residues. In terms of the total amount of C released, the residue treatments were ranked as follows: pea > rice = soybean > maize (Fig. 6). However, when the soluble C leached by rain was expressed as a function of the initial water-soluble C (20°C), the ranking of the crop residues was different (Fig. 4C). While approximately 40% of the soluble C was removed by the 4 mm h -1 intensity over 23 h for rice, maize and soybean, only 18% of the soluble C was lost from the pea residues. The loss of soluble C increased to 90% for maize and rice at the maximal rate, while it was 53% of the initial water-soluble C for pea and soybean. A comparison of the soluble C losses under the same total amount of water at the three rain intensities (Table 3) can clearly show the effect of rain intensity on C transport. Under a total application of 500 mL of water, the soluble C loss was identical at 4 and 11 mm h -1 (P = 0.940) and significantly lower for the 24 mm h -1 intensity relative to 4 mm h -1

(P = 0.007) and 11 mm h -1 (P = 0.005).

Insert Figure 6

Insert Table 3 4

. Discussion

The objective of this study was to quantify the extent of soluble C leaching from crop residues depending on the nature of the residues and rainfall regime. The four types of residues were chosen because of their agricultural importance and the diversity among their chemical compositions. Pea plants sampled in the vegetative stage as a cover crop had a large soluble fraction compared to rice and maize sampled at maturity, while soybean had intermediate values. Soybean had a high lignin content compared to the other three crops due to the pods in the soybean residue mass [START_REF] Liu | The utilization of soybean straw. I. Fiber morphology and chemical characteristics[END_REF]. We acknowledge that the differences in the physical characteristics of the litter layers were partially erased by standardizing the average particle size by hand cutting but this reduction in particle length was crucial for reducing the compositional variability of the mulch replicates, which is inherent to the variability in composition of plant debris. However, the residue particles were not ground but hand cut; therefore, the morphological integrity of the residue particles was not altered.

The experimental litter mulches used here fell within the lower ranges of bulk density and thickness described under natural conditions, particularly in conservation agriculture systems [START_REF] Thiébeau | Measuring the thickness of crop residues on the soil surface to estimate their biomass[END_REF] and natural forest systems (e.g., [START_REF] Dunkerley | Percolation through leaf litter: What happens during rainfall events of varying intensity?[END_REF]. The different mulch thicknesses measured in farmer plots by [START_REF] Thiébeau | Measuring the thickness of crop residues on the soil surface to estimate their biomass[END_REF] varied from 5 mm to 26 mm for residue masses ranging from 0.2 to 1.3 kg DM m -2 . [START_REF] Dietrich | Gradient of decomposition in sugarcane mulches of various thicknesses[END_REF] measured sugarcane mulch thicknesses varying from 19 mm to 47 mm for residue masses ranging from 0.4 to 1.2 kg DM m -2 . [START_REF] Sato | Experimental analysis of moisture dynamics of litter layers-the effects of rainfall conditions and leaf shapes[END_REF], using leaves of Lithocarpus edulis, an evergreen stand coppice, obtained a similar mulch thickness range (10-20 mm) for applications of 0.5 to 1 kg DM m -2 . Nevertheless, data on the thickness of mulches in agrosystems is still very rare, even in investigations of residue masses that were increased to 5 to 15

Mg maize residue ha -1 [START_REF] Schreiber | Nutrient leaching from corn residues under simulated rainfall[END_REF].

Since the experimental duration was identical for all treatments, treatments with a high rain intensity also corresponded to increased amounts of rain, and the two factors could not be fully distinguished except by comparing treatments with the same amount of water received. In the literature, available studies with simulated rainfall fall within the precipitation intensity range of our study (e.g., 3.6 to 24.2 mm h -1 , Sato et al., 2004; 25 mm h -1 , Schreiber, 1985). For agricultural situations, the range investigated by [START_REF] Schreiber | Nutrient leaching from corn residues under simulated rainfall[END_REF] was larger (6 to 99 mm h -1 ) as it aimed at including the simulation of storm events.

Water dynamics under simulated rains

Mulches of all four types of crop residues intercepted water, and the interception of water (manifested by the weight gain of the moist mulches) depended on the rainfall regime. The 4 mm h -1 rainfall accumulated water more slowly, while the 11 and 24 mm treatments behaved similarly. At the end of the experiment, the MaxWC values (5.9 to 6.6 g H2O g -1 dry residue) obtained for pea, maize and rice were significantly higher than the range (1 to 3 g H2O g -1 dry residue) previously reported by several authors [START_REF] Kreye | Toward a mechanism for Eastern North American forest mesophication: differential litter drying across 17 species[END_REF][START_REF] Dunkerley | Percolation through leaf litter: What happens during rainfall events of varying intensity?[END_REF][START_REF] Talhelm | Litter moisture adsorption is tied to tissue structure, chemistry, and energy concentration[END_REF]. Soybean mulches retained less water, even at high cumulative rain amounts, than the other three residues, which cannot be explained by the initial differences in the bulk density of these mulches, and we hypothesize that this is due to the high proportion of high-density soybean material and low water retention of soybean pods. Conversely, water interception by the pea mulches showed a very different response to increasing rainfall application compared to that of rice, maize and soybean mulches and exhibited low initial absorption (a parameter of the model) and high b values, thus reflecting the continual increase in water interception as the amount of water received increased. This response is almost parallel to the observed loss of mass of pea mulches with increasing amounts of water. We assume that the porosity of pea residue tissues, which contain a very high proportion of leachable soluble compounds, increased as the amount of rain received increased, thus promoting increased water retention by the tissues. [START_REF] Iqbal | Tissue density determines the water storage characteristics of crop residues[END_REF] observed an increase in tissue porosity of maize stems with decomposition in soil, and this finding was translated to an increased MaxWC of these stems. [START_REF] Dunkerley | Percolation through leaf litter: What happens during rainfall events of varying intensity?[END_REF] highlighted the high porosity of mulch, which represented 75% to 95% of the total volume and resulted in the high capacity of the litter layer to intercept and store rainwater. In the present study, pea mulches had lower density than the three other mulch types, thus allowing for higher retention by the mulch itself.

In terms of rain interception, the amount of water intercepted by the mulches after 7 hours represented 2 to 4 mm of rain and increased with rain intensity (Supplementary material SM5), confirming findings from [START_REF] Sato | Experimental analysis of moisture dynamics of litter layers-the effects of rainfall conditions and leaf shapes[END_REF], who obtained a comparable range (0.8 to 3 mm rain intercepted), as well as results reported by [START_REF] Dunkerley | Percolation through leaf litter: What happens during rainfall events of varying intensity?[END_REF], while [START_REF] Schreiber | Nutrient leaching from corn residues under simulated rainfall[END_REF] did not find any significant differences between different rain intensities, with 0.7 to 0.9 mm rain intercepted by maize mulches under his experimental conditions.

Last, the excess water percolated under the mulch was directly influenced by the rainfall regime (24 mm h -1 > 11 mm h -1 > 4 mm h -1 ), and this percolate flow stabilized at the 2nd hour of rain. [START_REF] Walsh | Vegetation litter: an underestimated variable in hydrology and geomorphology[END_REF] studied the percolation flows under simulated rain every 30 seconds and found that, at the fine temporal scale, the percolate flow under a fixed rain intensity was not steady, revealing the filling and emptying processes of litter porosity. At our time scale, this was obvious only at the onset of the experiment where the percolate flow increased during the 0-2 h interval and then stabilized.

Therefore, the crop residue mulches behaved in a similar manner as forest litter mulches, showing a high water retention capacity varying with crop species, with kinetics and maximum values that depended on the intensity and duration of rainfall. These layers of litter, although intercepting rain, quickly allowed the passage of a flow of solutes, even under the lowest rain duration and intensity tested (e.g., 1 hour at 4 mm h -1 ).

Effect of rain on residue C leaching

Along with water, soluble C was washed away for all residues and at all rainfall regimes as expected. The loss of mass and C could only be attributed to the effect of rain because the loss of mass by microbial decomposition can be considered negligible within one day [START_REF] Trinsoutrot | Relationships between biochemical quality of crop residues and C and N mineralisation kinetics under nonlimiting N conditions[END_REF].

After 23 hours, the measured DM loss under rain varied significantly with residue type and was much higher for the pea residue than for the other residues, which can be explained by the higher initial size of the soluble fraction of pea residue (representing 55% of the initial DM). However, expressed as a proportion of the initial soluble fraction, pea residues lost only 16% of the mass of the soluble pool, while maize and rice lost approximately 30% of their soluble pool, suggesting that the soluble compounds were less accessible to water leaching in the pea residue than in the other residues. Few data are available on the transport of soluble fractions under the influence of rainfall. [START_REF] Uselman | Quality of soluble organic C, N, and P produced by different types and species of litter:root litter versus leaf litter[END_REF] showed the high variability of the quantities involved from forest litter (leaves, branches, roots).

Coppens et al. ( 2006) measured a very transient peak of soluble C accumulation in the soil solution after rain applied to mulch.

Expressed as a function of the initial water-soluble C pool, the cumulative loss of soluble C, at t = 7 h, represented 9.2 to 23.7 % (4 mm h -1 ) and 19.3 to 55.2 % soluble C (24 mm h -1 ). After 23 hours, the loss of soluble C represented 15.2-36.0 % (4 mm h -1 ) to 52.6-97.9% (24 mm h -1 ) of the initial water-soluble C. This finding indicates that although the cumulative quantities of water received in 23 h were unrealistic at high intensities (totalling more than 550 mm), there was a near-complete soluble C leaching potential, which can occur in the context of very heavy rainfall events and/or with successive but frequent rainfall over time. [START_REF] Schreiber | Nutrient leaching from corn residues under simulated rainfall[END_REF] investigated maize residues placed under simulated rain and observed that 0.5 to 1% of the total soluble C was leached with 25 mm of rain applied at different intensities, i.e., in the range of values obtained in the early phase of our study. The differences in the loss of DM and water-soluble C resulted from other nutrients (as suggested by the final C:N ratio of leached residues in the present study), particularly soluble organic and inorganic N, being leached down with water, and this was most likely the case for pea residues rich in nitrogen, thus explaining the large difference observed between % soluble DM and % soluble C lost under rain.

The hourly monitoring of the C concentration of the leached water revealed that the 24 mm h -1 intensity had a higher water flow but a much lower C concentration than the 11 mm h -1 intensity, which is indicative of a higher soluble C dilution. This is also highlighted by the amounts of leached soluble C collected, which were almost identical for the two highest intensities throughout the kinetics of all residue types except for soybean. The dilution of leachates under a higher rain intensity was previously shown by [START_REF] Schreiber | Nutrient leaching from corn residues under simulated rainfall[END_REF] in the range 6 to 99 mm h -1 rain applied to 10 Mg ha -1 of maize residues. Thus, at high rain intensities, not all the rain efficiently leached down the soluble fraction of the residue; therefore, there is a rain intensity threshold below which soluble C is not completely entrained and beyond which water can pass through the mulch without entraining more soluble compounds. This hypothesis is also supported by the observed increase in the C concentration of the leached water during the 0-4 h period (for all residues except rice), which then decreased slightly, under the 4 mm h -1 rainfall intensity. This finding suggests that at a low rain intensity, a longer contact time between the rainfall and the residue before the beginning of leaching allowed for the displacement of soluble C, as observed by [START_REF] Schreiber | Nutrient leaching from corn residues under simulated rainfall[END_REF].

Conclusions

Rainfall washed away significant quantities of soluble C from plant residue mulches, and the results depended on the nature of the residues and the duration of the rainfall and its intensity. As expected, the soluble pool and soluble C leaching was increased for pea residues, which have a high initial proportion of soluble compounds, because they were collected in the vegetative stage to mimic cover crop residue. C leaching also increased with increasing rainfall intensity from 4 to 11 mm h -1

and then decreased at 24 mm h -1 , suggesting a maximum intensity threshold, after which the water would percolate through the mulch without leaching more soluble C. The magnitude of the observed fluxes suggests that crop-soil models should incorporate soluble C transport from mulches to soils by rainfall, which is not, to our knowledge, rarely the case. This work was performed using a single standardized particle size and a single mass for each species; however, the effect of rain on C loss for mulches of residues of different particle sizes or different masses should be better understood because these factors can be modified by management. Lastly, this study emphasized the importance of better characterizing the physical properties (thickness, density, and water properties) of mulches and residue particles in the future to better understand their interactions with water dynamics, which is a key factor of mulch decomposition and the environmental impacts of residue management.

Figure captions

Figure 1 :

 1 Figure 1: Mulches composed of pea, soybean, maize and rice residue particles

Figure 2 :Figure 3 :

 23 Figure 2: Rain simulator and leachate collection experimental design

Figure 4 :

 4 Figure 4: Mulch water content (A), weight loss (B) and leached soluble C (C) of pea, soybean, maize

Figure 5

 5 Figure 5 Soluble C concentration of the leached water under different rain intensities (4, 11 and 24 mm h -1 ) for the 4 crop residues. Values are the means of 3 replicates per treatment and per date (±

Figure 6 :

 6 Figure 6: Cumulative soluble C in the leached water (mg/sample) as a function of rain intensity (4, 11 and 24 mm h -1 ) for the 4 crop residues. Values are the means of 3 replicates (± standard error).

  Figure 1

Acknowledgements

This work was supported by INRAE (French National Research Institute for Agriculture, Food and Environment) and ANR (National Research Agency), the PEPITES project (ANR-08-STRA-10). We thank Olivier Delfosse and Gonzague Alavoine for their technical assistance with crop residue chemical characterization; Dr S. J. Giacomini and Dr B. Chabbert for their helpful comments on an earlier version of this manuscript; and two anonymous referees for their comments that contributed to improving this work.

Data availability statement

The data that support the findings of this study are available at Data INRAE, https://doi.org/10.15454/KQS5EK

Conflict of Interest Statement

The authors have no conflict of interest to declare

Authorship

Study concept and design: SR and PT; Acquisition and statistical analysis of the data: PT and CG;

Writing of the manuscript: PT, CG, and SR. Obtained funding and performed study supervision: SR Values are the mean of 3 replicates with their standard error. The exact duration of rain application (in minutes) needed to reach 500 mL cumulated rain was calculated by intrapolation between two sampling dates for each rain intensity and residue type.

Rain intensity