Joelle Youssef

Shaodi Zhu

Aurelia Cruntean

Jean-Christophe Orlianges

Ho-Pui Ho

Renaud Bachelot

Shuwen Zeng
email: shuwen.zeng@cnrs.fr

Highly Sensitive Plasmonic Biosensors with Precise Phase Singularity Coupling on the Metastructures

Keywords: surface plasmons, phase-change material, vanadium dioxide, phase detection, Goos-Hänchen shift, Goos-Hänchen sensitivity, cancer biomarkers

In this paper, we demonstrated the ability of a plasmonic metasensor to detect ultra-low refractive index changes (in the order of ∆n = 10 -10 RIU), using an innovative phase-change material, vanadium dioxide (VO 2 ), as the sensing layer. Different from current cumbersome plasmonic biosensing setups based on optical-phase-singularity measurement, our phase signal detection is based on the direct measurement of the phase-related lateral position shift (Goos-Hänchen) at the sensing interface. The high sensitivity (1.393 × 10 8 µm/RIU for ∆n = 10 -10 RIU), based on the Goos-Hänchen lateral shift of the reflected wave, becomes significant when the sensor is excited at resonance, due to the near-zero reflectivity dip, which corresponds to the absolute dark point (lower than 10 -6 ). GH shifts in the order of 2.997 × 10 3 µm were obtained using the optimal metasurface configuration. The surface plasmon resonance (SPR) curves (reflectivity, phase, GH) and electromagnetic simulations were derived using the MATLAB programming algorithm (by the transfer matrix method) and Comsol modeling (by finite element analysis), respectively. These results will provide a feasible way for the detection of cancer biomarkers.

Introduction

For nearly a decade, the world has been witnessing innovative medical advances, more recently the various COVID-19 vaccines, which tend to increase the lifespan of humanity. Consequently, an augmented percentage of people diagnosed with cancerous diseases is being recorded due to the expanding number of people in old age. Cancer is one of the leading death-causing diseases according to the World Health Organization [1]. Statistics by an international agency for research on cancer show that by 2040, cancer cases are expected to increase (to 29.5 million), along with a rise in the number of deaths (to 16.4 million) worldwide [2]. This, instantly, puts urgency on the development of early diagnosis procedures, since cancer treatments are shown to be highly effective in early stages of detection. Current diagnosis methods include laboratory tests, such as the enzymelinked immunosorbent assay (ELISA) that detects some antibodies in blood [START_REF] Wang | Targeted Sub-Attomole Cancer Biomarker Detection Based on Phase Singularity 2D Nanomaterial-Enhanced Plasmonic Biosensor[END_REF], the complete blood count (CBC) test that measures the different types of blood tests (red and white cells, platelets), cytogenetic analysis that evaluates any change in the number of chromosomes in white cells, and some imaging techniques such as computerized tomography (CT) scanning and magnetic resonance imaging (MRI) [START_REF]Understanding Laboratory Tests Fact Sheet-NCI[END_REF]. These approaches are time-consuming and expensive, requiring complex equipment, and some of them cannot detect cancer in its earliest stages. MRI, for example, cannot detect cancerous cells below the size of 1 cm [START_REF] Mousa | Biosensors: The new wave in cancer diagnosis[END_REF]. Accordingly, alternatives known as 'plasmonic biosensors' have been suggested as substitute tools.

Plasmonic biosensors are used to detect the presence of specific biomarkers (DNA, RNA, protein) in blood, serum, or urine and test the efficacy of chemotherapy treatments. They are known for their high sensibility, fast and early detection ability, accuracy, flexibility, easy access (point-of-care testing), and cheapness [START_REF] Mousa | Biosensors: The new wave in cancer diagnosis[END_REF]. They rely, principally, on the excitation of 'surface plasmon polaritons'-collective oscillations of free electrons-excited at the interface between a metal and a dielectric. Plasmons have a specific momentum, which depends on the nature of the metal-dielectric employed and the surrounding medium [START_REF] Kooyman | Chapter 2. Physics of Surface Plasmon Resonance[END_REF]. A resonance occurs when the momentum of incident light (defined by its wavelength and incident angle) matches that of the plasmons; in this case, nearly all of the incident energy is transferred to the surface plasmons and, as a direct result, a dark band is observed in the reflected spectrum. A microfluidic channel is, afterward, installed, through which deionized water is initially flown, followed by the sample solution; the presence of cancerous biomarkers is distinguished according to the modification in the refractive index they introduce. This change can be tracked through several schemes: change in resonance angle, minimum reflectivity, and wavelength [START_REF] Zeng | Graphene-Gold Metasurface Architectures for Ultrasensitive Plasmonic Biosensing[END_REF][START_REF] Zeng | Plasmonic Metasensors Based on 2D Hybrid Atomically Thin Perovskite Nanomaterials[END_REF][START_REF] Mondal | Recent Advances in Surface Plasmon Resonance for Biosensing Applications and Future Prospects[END_REF][START_REF] Lv | Transition Metal Dichalcogenides and Beyond: Synthesis, Properties, and Applications of Single-and Few-Layer Nanosheets[END_REF]. These practices have shown poor performances, especially when subjected to extremely small refractive index modifications (in the order of 10 -6 ) and, therefore, cannot detect cancer in its early stages (supporting information Tables S2-S5). Instead, the latest research has started considering phase measurements that take advantage of the singular behavior of the phase when excited at the resonance angle [START_REF] Zeng | Graphene-Gold Metasurface Architectures for Ultrasensitive Plasmonic Biosensing[END_REF][START_REF] Zeng | Plasmonic Metasensors Based on 2D Hybrid Atomically Thin Perovskite Nanomaterials[END_REF][START_REF] Kravets | Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection[END_REF]. However, the detection of phase changes requires interferometry schemes with complex experimental setups [START_REF] Zeng | Plasmonic Metasensors Based on 2D Hybrid Atomically Thin Perovskite Nanomaterials[END_REF].

A more significant order of the phase, known as the Goos-Hänchen (GH) shift, can be more pronounced and easily detected; it is a lateral shift of the reflected beam, when totally internally reflected at the boundary between two materials of distinct refractive indexes [START_REF] Yin | Goos-Hänchen shift surface plasmon resonance sensor[END_REF][START_REF] Jiang | Multifunctional Hyperbolic Nanogroove Metasurface for Submolecular Detection[END_REF]. Theoretical approaches have been developed to characterize this shift and quantify it in terms of mathematical formulations. Two key opposing points of view are cited: conservation of energy (or the energy flux method) and the stationary phase method for a finite wave packet [START_REF] Yasumoto | A new evaluation of the Goos-Hänchen shift and associated time delay[END_REF]. The second approach has been proven to yield better approximations, in comparison to the experimental models. Academic studies have reported the inclusion of additional layers to enhance the GH shift and sensitivity: perovskite [START_REF] Zeng | Plasmonic Metasensors Based on 2D Hybrid Atomically Thin Perovskite Nanomaterials[END_REF], graphene [START_REF] Zeng | Graphene-Gold Metasurface Architectures for Ultrasensitive Plasmonic Biosensing[END_REF][START_REF] Zeng | Graphene-MoS 2 hybrid nanostructures enhanced surface plasmon resonance biosensors[END_REF], transition metal dichalcogenides (TMDs) such as MoS 2 and WS 2 , hybrid structures such as silicon-graphene, and/or gold nanoparticles and metasurfaces [START_REF] Lv | Transition Metal Dichalcogenides and Beyond: Synthesis, Properties, and Applications of Single-and Few-Layer Nanosheets[END_REF][START_REF] Zeng | Graphene-MoS 2 hybrid nanostructures enhanced surface plasmon resonance biosensors[END_REF]. These configurations have proven good efficiencies for detecting low refractive index changes ~10 -9 , as they promote an effective charge transfer and, hence, an enhanced electromagnetic field at the sensing layer. Although these materials have reported high theoretical GH sensitivities at low refractive index changes (1.5458 × 10 9 µm/RIU for perovskite [START_REF] Zeng | Plasmonic Metasensors Based on 2D Hybrid Atomically Thin Perovskite Nanomaterials[END_REF]), they still lag experimentally due to their non-negligible surface roughness at the nanoscale and the impossibility to achieve thickness accuracies at the angstrom scale [START_REF] Berguiga | Ultimate phase sensitivity in surface plasmon resonance sensors by tuning critical coupling with phase change materials[END_REF]. As a direct result, the predicted theoretical values are hardly reachable. Recently, phase-change materials have started gaining popularity due to their distinctive nature, which allows them to alter the physical properties of nanostructures; this is the result of a fast modification in their structure caused by an external thermal, electrical, or optical stimulus. Physically, the change in the crystallography of the material is observed via a notable variation in the dielectric function [START_REF] Cueff | 2 nanophotonics[END_REF].

SPR detection, based on phase-change materials, is expected to yield better experimental GH sensitivities due to their high absorption coefficients in the visible and infrared, at low thicknesses. Moreover, the dielectric function can be easily readjusted when it seems to be deviated from its optimal value, by regulating the crystallization conditions [START_REF] Cueff | 2 nanophotonics[END_REF][START_REF] Lei | Optically-Triggered Nanoscale Memory Effect in a Hybrid Plasmonic-Phase Changing Nanostructure[END_REF]. SPR sensors based on GeSbTe (germanium-antimony-tellurium) [START_REF] Sreekanth | Electrically Tunable Singular Phase and Goos-Hänchen Shifts in Phase-Change-Material-Based Thin-Film Coatings as Optical Absorbers[END_REF] and Sb 2 S 3 (antimony trisulfide) [START_REF] Sreekanth | Phase-Change-Material-Based Low-Loss Visible-Frequency Hyperbolic Metamaterials for Ultrasensitive Label-Free Biosensing[END_REF] as phase-change materials have been already theoretically modeled but yielded poor results (GH shifts in the order of a few tens of micrometers for Sb 2 S 3 ). This report concentrates on another type of phase-change material, known as vanadium dioxide (VO 2 ). Experimental studies indicate high absorption coefficients in the visible-infrared region at high temperatures, so, a deep reflection and large GH shift can be anticipated. The insulator-to-metal behavior was first discovered by Morin in 1959, during their studies on the relation between temperature and electrical conductivity; then, a few years after, the same laboratory (Bell Labs) issued the first experimental datasheet describing the optical properties of VO 2 [START_REF] Cueff | 2 nanophotonics[END_REF]. VO 2 undergoes a reversible structural transition from insulator (monoclinic phase) to absorbing metal (tetragonal phase), when heated at 68 • C, which is known as the metal-insulator-transition temperature (MIT). This effect has been largely exploited in optical and optoelectronic instruments such as optical data storage devices, plasmonic modulators, and hybrid tunable VO 2 waveguides, due to their capability to retain and 'memorize' the state when the trigger is removed [START_REF] Cueff | 2 nanophotonics[END_REF][START_REF] Lei | Optically-Triggered Nanoscale Memory Effect in a Hybrid Plasmonic-Phase Changing Nanostructure[END_REF][START_REF] Orlianges | Electrical and Optical Properties of Vanadium Dioxide Containing Gold Nanoparticles Deposited by Pulsed Laser Deposition[END_REF]. Recently, biosensors based on vanadium dioxide are starting to attract attention due to their ability to detect glucose in blood. The surface of the phase-change material was properly functionalized to detect the presence of the target molecule. Glucose oxydase (GOx) enzyme, dissolved in PBS buffer solutions (1.5 mg/L) along with 5% of glutaraldehyde solution, was injected on the VO 2 surface for 1 min and then left to dry for 24 h. The efficiency of the immobilization of the enzyme by covalent cross-linking was, subsequently, tested as a function of glucose concentration and yielded promising results. This will pave the way for the development of highly sensitive plasmon sensors to be used for more advanced medical applications [START_REF] Vieira | Development of amperometric biosensors using VO 2 /GOx films for detection of glucose[END_REF].

Materials and Methods

The excitation of the surface plasmon polaritons is usually performed through various methods: prism-coupled SPR, SPR waveguide, and diffraction-grating-coupling-based SPR sensing. The well-known Kretschmann configuration, based on a prism coupling of incident light into a metal-dielectric substrate, is presented here. The model depicted in Figure 1, consists of an SF11 prism, a BK7 glass substrate with a fixed thickness of 100 nm, gold film (with or without metasurface), vanadium dioxide (VO 2 ) as the sensing layer, and water as a calibration/testing medium. The variables used for evaluating the performance of the sensor include minimum reflectivity, GH shift, and GH sensitivity, with respect to a refractive index change.

modeled but yielded poor results (GH shifts in the order of a few tens of micrometers for Sb2S3). This report concentrates on another type of phase-change material, known as vanadium dioxide (VO2). Experimental studies indicate high absorption coefficients in the visible-infrared region at high temperatures, so, a deep reflection and large GH shift can be anticipated. The insulator-to-metal behavior was first discovered by Morin in 1959, during their studies on the relation between temperature and electrical conductivity; then, a few years after, the same laboratory (Bell Labs) issued the first experimental datasheet describing the optical properties of VO2 [START_REF] Cueff | 2 nanophotonics[END_REF]. VO2 undergoes a reversible structural transition from insulator (monoclinic phase) to absorbing metal (tetragonal phase), when heated at 68 ℃, which is known as the metal-insulator-transition temperature (MIT). This effect has been largely exploited in optical and optoelectronic instruments such as optical data storage devices, plasmonic modulators, and hybrid tunable VO2 waveguides, due to their capability to retain and 'memorize' the state when the trigger is removed [START_REF] Cueff | 2 nanophotonics[END_REF][START_REF] Lei | Optically-Triggered Nanoscale Memory Effect in a Hybrid Plasmonic-Phase Changing Nanostructure[END_REF][START_REF] Orlianges | Electrical and Optical Properties of Vanadium Dioxide Containing Gold Nanoparticles Deposited by Pulsed Laser Deposition[END_REF]. Recently, biosensors based on vanadium dioxide are starting to attract attention due to their ability to detect glucose in blood. The surface of the phase-change material was properly functionalized to detect the presence of the target molecule. Glucose oxydase (GOx) enzyme, dissolved in PBS buffer solutions (1.5 mg/L) along with 5% of glutaraldehyde solution, was injected on the VO2 surface for 1 min and then left to dry for 24 h. The efficiency of the immobilization of the enzyme by covalent cross-linking was, subsequently, tested as a function of glucose concentration and yielded promising results. This will pave the way for the development of highly sensitive plasmon sensors to be used for more advanced medical applications [START_REF] Vieira | Development of amperometric biosensors using VO 2 /GOx films for detection of glucose[END_REF].

Materials and Methods

The excitation of the surface plasmon polaritons is usually performed through various methods: prism-coupled SPR, SPR waveguide, and diffraction-grating-couplingbased SPR sensing. The well-known Kretschmann configuration, based on a prism coupling of incident light into a metal-dielectric substrate, is presented here. The model depicted in Figure 1, consists of an SF11 prism, a BK7 glass substrate with a fixed thickness of 100 nm, gold film (with or without metasurface), vanadium dioxide (VO2) as the sensing layer, and water as a calibration/testing medium. The variables used for evaluating the performance of the sensor include minimum reflectivity, GH shift, and GH sensitivity, with respect to a refractive index change. The dispersion relation of gold was obtained from the Lorentz-Drude model and that of VO2 from experimental data. The refractive index of the prism and glass substrate are obtained using equations described in supporting information. The transition temperature of VO2 is theoretically set at 68 °C [START_REF] Lei | Optically-Triggered Nanoscale Memory Effect in a Hybrid Plasmonic-Phase Changing Nanostructure[END_REF][START_REF] Orlianges | Electrical and Optical Properties of Vanadium Dioxide Containing Gold Nanoparticles Deposited by Pulsed Laser Deposition[END_REF]; thus, the two chosen temperatures represent both the insulating and conducting states of the phase-change material. Simulations were performed using MATLAB as the programming algorithm and the transfer matrix The dispersion relation of gold was obtained from the Lorentz-Drude model and that of VO 2 from experimental data. The refractive index of the prism and glass substrate are obtained using equations described in supporting information. The transition temperature of VO 2 is theoretically set at 68 • C [START_REF] Lei | Optically-Triggered Nanoscale Memory Effect in a Hybrid Plasmonic-Phase Changing Nanostructure[END_REF][START_REF] Orlianges | Electrical and Optical Properties of Vanadium Dioxide Containing Gold Nanoparticles Deposited by Pulsed Laser Deposition[END_REF]; thus, the two chosen temperatures represent both the insulating and conducting states of the phase-change material. Simulations were performed using MATLAB as the programming algorithm and the transfer matrix method (TMM) (Section 1: Methods and Theoretical Modeling) for obtaining the SPR curves (reflectivity, phase, GH) and COMSOL Multiphysics 6.0 for evaluating the electric field inside the structure.

Results

The GH shift is expected to increase with the addition of VO 2 as a sensing layer due to the magnification of the electric field within the structure. In this section, the performance of the sensor is deeply analyzed according to certain parameters such as minimum reflectivity, GH shift, and sensitivity. However, beforehand, a general presentation of the physical and optical properties of this material is required.

At 95 • C (see above, the metal-insulator temperature of VO 2 is ~68 • C [START_REF] Cueff | 2 nanophotonics[END_REF][START_REF] Lei | Optically-Triggered Nanoscale Memory Effect in a Hybrid Plasmonic-Phase Changing Nanostructure[END_REF]), the real component of the permittivity of VO 2 , as shown in Figure 2a, goes through a linear decrease after 400 nm and reaches negative values (0 at approximately 985 nm). On the other hand, the imaginary component, Figure 2b, in the range of 400-700 nm, experiences a reduction and then rises again for longer wavelengths. As for 20 • C, no significant modifications of either the real or the imaginary components of the phase-change material in the UV-visible-IR region is shown. The metallic behavior can then be summarized at 95 • C, for excitations approximately greater than 985 nm, which is the starting point at which the real part of the dielectric function begins to switch to negative values, and the imaginary part of the refractive index (n = √ ε = n r + ki) describing the absorption of the metal increases. method (TMM) (Section 1: Methods and Theoretical Modeling) for obtaining the SPR curves (reflectivity, phase, GH) and COMSOL Multiphysics 6.0 for evaluating the electric field inside the structure.

Results

The GH shift is expected to increase with the addition of VO2 as a sensing layer due to the magnification of the electric field within the structure. In this section, the performance of the sensor is deeply analyzed according to certain parameters such as minimum reflectivity, GH shift, and sensitivity. However, beforehand, a general presentation of the physical and optical properties of this material is required.

At 95 °C (see above, the metal-insulator temperature of VO2 is ~68 °C [START_REF] Cueff | 2 nanophotonics[END_REF][START_REF] Lei | Optically-Triggered Nanoscale Memory Effect in a Hybrid Plasmonic-Phase Changing Nanostructure[END_REF]), the real component of the permittivity of VO2, as shown in Figure 2a, goes through a linear decrease after 400 nm and reaches negative values (0 at approximately 985 nm). On the other hand, the imaginary component, Figure 2b, in the range of 400-700 nm, experiences a reduction and then rises again for longer wavelengths. As for 20 °C, no significant modifications of either the real or the imaginary components of the phase-change material in the UV-visible-IR region is shown. The metallic behavior can then be summarized at 95 °C, for excitations approximately greater than 985 nm, which is the starting point at which the real part of the dielectric function begins to switch to negative values, and the imaginary part of the refractive index (n = √ε=nr + ki) describing the absorption of the metal increases.

Continuous Gold Model

Taking advantage of the singular behavior displayed at the resonance angle, detection based on phase is reported here [START_REF] Zeng | Graphene-Gold Metasurface Architectures for Ultrasensitive Plasmonic Biosensing[END_REF][START_REF] Zeng | Plasmonic Metasensors Based on 2D Hybrid Atomically Thin Perovskite Nanomaterials[END_REF][START_REF] Kravets | Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection[END_REF].The Goos-Hänchen shift, which is related to the phase delay of the reflected wave upon resonance, is employed for evaluating the sensitivity of the SPR device [START_REF] Yin | Goos-Hänchen shift surface plasmon resonance sensor[END_REF][START_REF] Jiang | Multifunctional Hyperbolic Nanogroove Metasurface for Submolecular Detection[END_REF]. Due to its absorbing properties, the phase-change material is responsible for lowering the reflected signal, improving the GH shift and enhancing the electric field at the sensing layer. Figures 3 and4 illustrate and compare the effects of wavelength (630 and 785 nm), temperature (20 and 95 °C), and VO2 thickness (0 to 4 nm) on the minimum reflectivity, phase, and GH shift at fixed gold thickness (46 nm). Furthermore, Figure 5 depicts the enhancement effect introduced at the surface of the sensing layer.

Continuous Gold Model

Taking advantage of the singular behavior displayed at the resonance angle, detection based on phase is reported here [START_REF] Zeng | Graphene-Gold Metasurface Architectures for Ultrasensitive Plasmonic Biosensing[END_REF][START_REF] Zeng | Plasmonic Metasensors Based on 2D Hybrid Atomically Thin Perovskite Nanomaterials[END_REF][START_REF] Kravets | Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection[END_REF]. The Goos-Hänchen shift, which is related to the phase delay of the reflected wave upon resonance, is employed for evaluating the sensitivity of the SPR device [START_REF] Yin | Goos-Hänchen shift surface plasmon resonance sensor[END_REF][START_REF] Jiang | Multifunctional Hyperbolic Nanogroove Metasurface for Submolecular Detection[END_REF]. Due to its absorbing properties, the phase-change material is responsible for lowering the reflected signal, improving the GH shift and enhancing the electric field at the sensing layer. Figures 3 and4 illustrate and compare the effects of wavelength (630 and 785 nm), temperature (20 and 95 • C), and VO 2 thickness (0 to 4 nm) on the minimum reflectivity, phase, and GH shift at fixed gold thickness (46 nm). Furthermore, Figure 5 depicts the enhancement effect introduced at the surface of the sensing layer. According to Figure 3a-f, for a 630 nm excitation, the lowest reflectivity of ~3.075 × 10 -6 is set at 3 nm for a temperature of 95 °C; the maximum GH shift of ~264 μm is higher than that at 20 °C (69 μm), along with a more confined GH curve profile. Since this study is mainly based on the evaluation of the GH shift, a confined GH curve is needed for a fine angular tuning of the sensor. For a higher excitation wavelength of 785 nm, Figure 4a-f, the lowest reflectivity, at 20 and 95 °C, is comparable in value (8.239 × 10 -5 and 4.481

Design with Metasurface

The GH shift can be further improved by replacing the continuous gold film with a metasurface based on a nanogroove configuration. The depth of the continuous film is chosen to be 30 nm, while that of the nanostructures is 20 nm (check Table S7 in supporting information). The width and periodicity of the grooves are the key variables of this setup and are optimized to yield the best results according to minimum reflectivity and GH shift.

Heating the phase-change material to 95 °C does not necessarily result in lower reflectivity and GH shift, even though the phase-change material has a higher absorption coefficient at higher temperature (S8 in supporting information). Designing a metasurface structure with P = 140 nm, w = 20 nm, and VO2 thickness of 1 nm, which was heated at 95 °C and excited at 785 nm, yielded promising outcomes with a GH sensitivity in the order of 2.253 × 106 μm/RIU for ∆n= 1.2 × 10 -6 , 1.738 × 10 6 μm/RIU for ∆n= 10 -10 RIU, and a GH shift of 2.248 × 10 3 (Table 1). Further improvements increased the GH sensitivity to 2.919 × 107 μm/RIU for ∆n= 1.2 × 10 -6 when λ= 1030 nm, 1 nm thickness of VO2, P = 130 nm, and w = 50 nm, with a FWHM of 1.095°; and GH shift equals 2.997 × 10 3 μm when λ = 1000 nm VO2 is 2 nm thickness, P = 110 nm, and w = 50 nm, with a FWHM of 1.454° (Table S8 in supporting information). The influences of both the grooves' periodicity and width on the minimum reflectivity and thickness of VO2 are shown in the supporting information (Figures S8 and S9). Comparing the best configuration obtained in the simple continuous gold film case (thicknesses of 49 nm for gold and 1 nm for VO2, at 95 °C and an excitation o 735 nm) with that for a metasurface (continuous gold, metasurface, VO2 thicknesses of 30 20, and 2 nm, respectively, at a temperature of 20 °C, excitation of 1000 nm, periodicity and width of 110 and 50 nm, respectively), an increase of 772 μm (from 2.225 × 10 3 in the continuous gold configuration to 2.997 × 10 3 μm in the metasurface configuration) in GH shift is shown. According to Figure 3a-f, for a 630 nm excitation, the lowest reflectivity of ~3.075 × 10 -6 is set at 3 nm for a temperature of 95 • C; the maximum GH shift of ~264 µm is higher than that at 20 • C (69 µm), along with a more confined GH curve profile. Since this study is mainly based on the evaluation of the GH shift, a confined GH curve is needed for a fine angular tuning of the sensor. For a higher excitation wavelength of 785 nm, Figure 4a-f A decrease in the resonance angle is manifested by increased temperatures and excitation wavelengths, which may be explained by the reduction in the real part of the permittivity (Figures 3 and4) when subjected to these conditions. At the same excitation, ε real at 20 • C > ε real at 95 • C, and same temperature, ε real at 630 nm > ε real at 785 nm, this will, consequently, lead to a smaller k vector (Equation (S9) in supporting information) and, therefore, a smaller angle to excite the surface plasmon waves.

Tables S2-S5 and Equations (S13)-(S17) in supporting information demonstrate that the phase-related sensitivity yields more prominent results than the ones based on angular detection, with a-1.183 × 10 5 • /RIU difference in sensitivity between both, for ∆n = 1.2 × 10 -6 RIU (Equations (S15)-(S17) in supporting information and Table S2). Furthermore, the addition of the phase-change-material sensing layer significantly improved the GH shift for both wavelengths and temperatures (Tables S2 andS3), from 94.02 µm for the bare gold to 2.147 × 10 3 µm for VO 2 at 95 • C and excited at 630 nm, and the GH sensitivity (Tables S2 andS3), from 9.736 × 10 3 µm/RIU for the bare gold to 7.323 × 10 6 µm/RIU when ∆n = 1.2 × 10 -6 RIU and for VO 2 at 95 • C excited at 630 nm. Comparing the two excitation wavelengths, the best configuration is set when the sensor is excited at 630 nm, gold thickness is 47 nm, and VO 2 2 nm at 95 • C: 2.147 × 10 3 µm GH shift, 9.191 × 10 4 µm/RIU for ∆n = 0.02 GH sensitivity, and 7.323 × 10 6 µm/RIU for ∆n = 1.2 × 10 -6 GH sensitivity. Contrarily, for the higher excitation wavelength 785 nm, lower temperature yielded better GH shift (7.891 × 10 2 µm, when gold and VO 2 thicknesses are 48 and 2 nm, respectively).

In conclusion, according to Figures 3 and4 and Tables S2-S6 in supporting information:

1.

At higher temperatures and wavelengths, decreases in the resonance angles for each thickness of the phase-change material are shown;

2. At higher temperature, less VO 2 thickness is needed to reach the minimum reflectivity compared to low temperature; 3.

At longer wavelength, the minimum reflectivity occurs for less VO 2 thickness than for a shorter wavelength; 4.

The lowest reflectivity and highest GH shift occur at 630 nm and 95 • C, and, at a longer wavelength (785 nm), the lowest values occur at 20 • C.

Through performing a scan based on wavelength, the best configuration in terms of minimum reflectivity and GH shift, according to Table S6 in supporting information, is obtained when the sensor is excited at 735 nm, gold and VO 2 thicknesses are equal to 49 and 1 nm, respectively, and the temperature of the phase-change material is fixed at 95 • C (1.048 × 10 -7 minimum reflectivity and GH shift of 2.225 × 10 3 µm). The best GH sensitivity, when ∆n = 10 -10 is attained, is when the sensor is excited at 770 nm, gold and VO 2 thicknesses are equal to 46 and 4 nm, respectively, and the temperature of the phase-change material is fixed at 20 • C (1.393 × 10 8 µm/RIU).

To further detail the influence of each parameter alone, two distinct studies are performed: first, the VO 2 thickness is fixed, while that of the gold is tuned, and then vice versa. The results are then plotted and take the form of maximum GH shift and minimum reflectivity (Figures S2-S6 in supporting information).

Design with Metasurface

The GH shift can be further improved by replacing the continuous gold film with a metasurface based on a nanogroove configuration. The depth of the continuous film is chosen to be 30 nm, while that of the nanostructures is 20 nm (check Table S7 in supporting information). The width and periodicity of the grooves are the key variables of this setup and are optimized to yield the best results according to minimum reflectivity and GH shift.

Heating the phase-change material to 95 • C does not necessarily result in lower reflectivity and GH shift, even though the phase-change material has a higher absorption coefficient at higher temperature (Figure S8 in supporting information). Designing a metasurface structure with P = 140 nm, w = 20 nm, and VO 2 thickness of 1 nm, which was heated at 95 • C and excited at 785 nm, yielded promising outcomes with a GH sensitivity in the order of 2.253 × 106 µm/RIU for ∆n = 1.2 × 10 -6 , 1.738 × 10 6 µm/RIU for ∆n = 10 -10 RIU, and a GH shift of 2.248 × 10 3 (Table 1). Further improvements increased the GH sensitivity to 2.919 × 107 µm/RIU for ∆n = 1.2 × 10 -6 when λ = 1030 nm, 1 nm thickness of VO 2 , P = 130 nm, and w = 50 nm, with a FWHM of 1.095 • ; and GH shift equals 2.997 × 10 3 µm when λ = 1000 nm, VO 2 is 2 nm thickness, P = 110 nm, and w = 50 nm, with a FWHM of 1.454 • (Table S8 in supporting information). The influences of both the grooves' periodicity and width on the minimum reflectivity and thickness of VO 2 are shown in the supporting information (Figures S8 andS9). Comparing the best configuration obtained in the simple continuous gold film case (thicknesses of 49 nm for gold and 1 nm for VO 2 , at 95 • C and an excitation of 735 nm) with that for a metasurface (continuous gold, metasurface, VO 2 thicknesses of 30, 20, and 2 nm, respectively, at a temperature of 20 • C, excitation of 1000 nm, periodicity and width of 110 and 50 nm, respectively), an increase of 772 µm (from 2.225 × 10 3 in the continuous gold configuration to 2.997 × 10 3 µm in the metasurface configuration) in GH shift is shown. One method to enhance the performance of the sensor is through the introduction of metasurfaces; these subwavelength structures are responsible for (a) modulating the wavevector of the surface plasmons, (b) confining the surface plasmon waves (Figure 6), and (c) enhancing the GH shift (Figure 7). Through the periodic patterning of the gold, a 'double SPR' effect is created (Figure 6): at the surface, between the glass substrate and the continuous gold layer by way of the excitation of SPR (surface plasmon resonance) waves, and at the tip at of the nanogrooves, through the excitation of LSPR (localized surface plasmon). Additionally, the effective refractive index, at the tip and just below the VO 2 layer, is higher than that at the continuous gold film; this effect will confine the surface plasmon in their seats between the nanogrooves and VO 2 and enhance the electric field at the sensing layer [START_REF] Jiang | Multifunctional Hyperbolic Nanogroove Metasurface for Submolecular Detection[END_REF]. Accordingly, the metasurface was designed by tuning the periodicity and width of the nanogrooves. One method to enhance the performance of the sensor is through the introduction of metasurfaces; these subwavelength structures are responsible for (a) modulating the wavevector of the surface plasmons, (b) confining the surface plasmon waves (Figure 6), and (c) enhancing the GH shift (Figure 7). Through the periodic patterning of the gold, a 'double SPR' effect is created (Figure 6): at the surface, between the glass substrate and the continuous gold layer by way of the excitation of SPR (surface plasmon resonance) waves, and at the tip at of the nanogrooves, through the excitation of LSPR (localized surface plasmon). Additionally, the effective refractive index, at the tip and just below the VO2 layer, is higher than that at the continuous gold film; this effect will confine the surface plasmon in their seats between the nanogrooves and VO2 and enhance the electric field at the sensing layer [START_REF] Jiang | Multifunctional Hyperbolic Nanogroove Metasurface for Submolecular Detection[END_REF]. Accordingly, the metasurface was designed by tuning the periodicity and width of the nanogrooves.

Discussion

As the work function of gold, ~5.54 ev, is higher than that of VO2 [START_REF] Ko | Work Function of Vanadium Dioxide Thin Films Across the Metal-Insulator Transition and the Role of Surface Nonstoichiometry[END_REF] in its conducting state, 5.3 ev, the electron exchange takes place from the material with a lower work function (VO2) to the material with a higher work function (gold). Small reflectivity coefficients (in the order of ~10 -6 and lower) are obtained when approximately all of the reflected energy is absorbed by the phase-change material. For the same gold thickness, heating at 95 °C requires less VO2 thickness to reach the optimal value of the minimum reflectivity for both wavelengths (Tables S2-S5 in supporting information); this is due to the smaller real component of the dielectric function at higher temperature, and, therefore, a smaller k vector is needed to couple the incident radiation (Equation S9 and Table S1 in supporting information). Lower reflectivity values are obtained at 95 °C for a 630 nm excitation compared to 20 °C , due to the higher absorption coefficient related to the imaginary

Discussion

As the work function of gold, ~5.54 ev, is higher than that of VO 2 [START_REF] Ko | Work Function of Vanadium Dioxide Thin Films Across the Metal-Insulator Transition and the Role of Surface Nonstoichiometry[END_REF] in its conducting state, 5.3 ev, the electron exchange takes place from the material with a lower work function (VO 2 ) to the material with a higher work function (gold). Small reflectivity coefficients (in the order of ~10 -6 and lower) are obtained when approximately all of the reflected energy is absorbed by the phase-change material. For the same gold thickness, heating at 95 • C requires less VO 2 thickness to reach the optimal value of the minimum reflectivity for both wavelengths (Tables S2-S5 in supporting information); this is due to the smaller real component of the dielectric function at higher temperature, and, therefore, a smaller k vector is needed to couple the incident radiation (Equation S9 and Table S1 in supporting information). Lower reflectivity values are obtained at 95 • C for a 630 nm excitation compared to 20 • C, due to the higher absorption coefficient related to the imaginary component of the refractive index (Table S1 in supporting information). For a 785 nm excitation, better results (minimum reflectivity) are mostly obtained at 20 • C (Tables S4 and S5 in supporting information), even though the absorption coefficient is higher at 95 • C; in this case, the light will be mostly absorbed by the substrate, and less energy is transmitted to generate the surface plasmon waves. In general, for a high wavelength (above 700 nm), VO 2 at 20 • C will result in higher GH shifts (Table S8 in supporting information). The process of tuning the sensors according to their variables relies predominantly on finding an equilibrium between the absorption and energy losses linked to the excitation wavelength and the thicknesses of both gold and VO 2 .

The sensitivity to variation of phase for ∆n = 1.2 × 10 -6 is shown to be more pronounced than the resonant angular sensitivity. In the latter case, deeper VO 2 layers are required to promote a larger resonant angle variation, which will enlarge the FWHM and, therefore, decrease the detection efficiency, as the accurate point of minimum reflectivity cannot be found with precision. The increase in the FWHM is directly related to the thickness of VO 2 , due to the prominent energy losses found for deeper thicknesses. On the other hand, the phase sensitivity is linked to the value of minimum itself. When the reflectivity is in the order of 10 -6 and lower, a singular behavior of the phase is observed and, consequently, a higher phase sensitivity to refractive index variations, due to the significant electric field at the sensing layer. In simple terms, at the point of minimum reflectivity, a maximum transfer of incident energy to the surface plasmons is presented; this excitation leads to the enhancement of the electric field. Even if a minor increase in the FWHM occurs, the extensively large enhancement field created will eventually overcome this obstacle.

Even though better GH shifts are shown at a high temperature of VO 2 (at certain wavelengths), some antibodies (IgG, IgA, IgE, IgM) have no heat tolerance and can become irreversibly denatured [START_REF] Akazawa-Ogawa | Heat denaturation of the antibody, a multi-domain protein[END_REF]. One way to overcome this problem is by decreasing the transition temperature of VO 2 to some extent, to not deteriorate the antibodies. This can be done through several methods, by doping metal ions, niobium [START_REF] Piccirillo | Nb-Doped VO 2 Thin Films Prepared by Aerosol-Assisted Chemical Vapour Deposition[END_REF], molybdenum [START_REF] Khan | Room temperature tunability of Mo-doped VO 2 nanofilms across semiconductor to metal phase transition[END_REF], tungsten [START_REF] Piccirillo | Synthesis and characterisation of W-doped VO 2 by Aerosol Assisted Chemical Vapour Deposition[END_REF], terbium [START_REF] Wang | Terbium-Doped VO 2 Thin Films: Reduced Phase Transition Temperature and Largely Enhanced Luminous Transmittance[END_REF], or chromium [START_REF] Guan | A Novel Method for Notable Reducing Phase Transition Temperature of VO 2 Films for Smart Energy Efficient Windows[END_REF], into the VO 2 structure, by annealing [START_REF] Liu | Tuning phase transition temperature of VO 2 thin films by annealing atmosphere[END_REF] or by stress introduction into the structure [START_REF] Yuan | The large modification of phase transition characteristics of VO 2 films on SiO 2 /Si substrates[END_REF]. These techniques are shown to alter the optical properties of the phase-change material; for instance, the change in refractive index is affected by the percentage of the doping ions. However, at low concentrations of dopants and at visible frequencies, no significant change is recorded [START_REF] Piccirillo | Nb-Doped VO 2 Thin Films Prepared by Aerosol-Assisted Chemical Vapour Deposition[END_REF][START_REF] Khan | Room temperature tunability of Mo-doped VO 2 nanofilms across semiconductor to metal phase transition[END_REF][START_REF] Piccirillo | Synthesis and characterisation of W-doped VO 2 by Aerosol Assisted Chemical Vapour Deposition[END_REF][START_REF] Wang | Terbium-Doped VO 2 Thin Films: Reduced Phase Transition Temperature and Largely Enhanced Luminous Transmittance[END_REF][START_REF] Guan | A Novel Method for Notable Reducing Phase Transition Temperature of VO 2 Films for Smart Energy Efficient Windows[END_REF][START_REF] Pinto | Determination of the Optical Constants of VO 2 and Nb-Doped VO 2 Thin Films[END_REF][START_REF] Muller | Radio-Frequency Characteristics of Ge-Doped Vanadium Dioxide Thin Films with Increased Transition Temperature[END_REF]. Doping 1% of tungsten and 0.4% of niobium can lower the transition temperature by 25 • C and 13 • C respectively [START_REF] Piccirillo | Nb-Doped VO 2 Thin Films Prepared by Aerosol-Assisted Chemical Vapour Deposition[END_REF]. Additionally, by changing the wavelength of excitation, high GH shifts and sensitivities can still be obtained at low temperatures (Figure S8).

Conclusions

A surface plasmon SPR sensor, based on a VO 2 vanadium dioxide phase-change material as the sensing layer, has been systematically investigated based on several optimized parameters: gold and VO 2 thicknesses, excitation wavelength, and the dielectric constants of the phase-change materials based on temperature tuning. All of these parameters are optimized to a near-zero minimum reflectivity at SPR resonance, leading to a giant lateral position GH shift and an ultra-high sensitivity of the sensing head. The GH shift using an optimized periodic metasurface was considerably enhanced when comparted to the continuous gold configuration (2.997 × 10 3 µm). The enhancement effect induced was due to the coupling of surface plasmon resonance waves at the continuous gold surface and the localized SPR plasmonic effect introduced by the periodic structures. High GH sensitivities for both high (8.762 × 10 4 µm/RIU for ∆n = 0.02 RIU) and low (1.393 × 10 8 µm/RIU for ∆n = 10 -10 RIU) refractive index changes are discussed. Additionally, when comparing the GH shift of VO 2 with that of other well-known phase-change materials such as Sb 2 S 3 [START_REF] Sreekanth | Phase-Change-Material-Based Low-Loss Visible-Frequency Hyperbolic Metamaterials for Ultrasensitive Label-Free Biosensing[END_REF] and GST [START_REF] Sreekanth | Electrically Tunable Singular Phase and Goos-Hänchen Shifts in Phase-Change-Material-Based Thin-Film Coatings as Optical Absorbers[END_REF] (order of a few tens of micrometer GH shifts), a remarkable increase in the GH shift is shown. The precise tuning of the thickness and optical absorption of the phase-change materials as well as the period and width of the

Figure 1 .

 1 Figure 1. Schematic representing the Kretschmann SPR sensor based on a gold metasurface: prism, glass substrate, gold, and Vanadium dioxide as the sensing layer.

Figure 1 .

 1 Figure 1. Schematic representing the Kretschmann SPR sensor based on a gold metasurface: prism, glass substrate, gold, and Vanadium dioxide as the sensing layer.

Figure 2 .

 2 Figure 2. Experimental dielectric function: (a) real part and (b) imaginary part of VO2 at 20 °C and 95 °C.

Figure 2 .

 2 Figure 2. Experimental dielectric function: (a) real part and (b) imaginary part of VO 2 at 20 • C and 95 • C.

Figure 3 .

 3 Figure 3. SPR curves with respect to the thickness of VO2 calculated by TMM model, for an excitation of 630 nm, VO2 temperature of 20 °C (left) and 95 °C (right), and a gold thickness of 46 nm; (a,b) reflectivity, (c,d) phase, and (e,f) Goos-Hänchen shift (absolute value).

Figure 3 .

 3 Figure 3. SPR curves with respect to the thickness of VO 2 calculated by TMM model, for an excitation of 630 nm, VO 2 temperature of 20 • C (left) and 95 • C (right), and a gold thickness of 46 nm; (a,b) reflectivity, (c,d) phase, and (e,f) Goos-Hänchen shift (absolute value).

Figure 4 .

 4 Figure 4. SPR curves with respect to the thickness of VO2 calculated by TMM model, for an excitation of 785 nm, VO2 temperature of 20 °C (left) and 95 °C (right), and a gold thickness of 46 nm; (a,b) reflectivity, (c,d) phase, and (e,f) Goos-Hänchen shift (absolute value).

Figure 4 .

 4 Figure 4. SPR curves with respect to the thickness of VO 2 calculated by TMM model, for an excitation of 785 nm, VO 2 temperature of 20 • C (left) and 95 • C (right), and a gold thickness of 46 nm; (a,b) reflectivity, (c,d) phase, and (e,f) Goos-Hänchen shift (absolute value).

Figure 5 .

 5 Figure 5. Electric field (y component in V/m) distribution inside the structure, given that the thick nesses of the gold film and VO2 are 47 and 1 nm, respectively, excitation is 630 nm, and temperature is 20 °C.

Figure 5 .

 5 Figure 5. Electric field (y component in V/m) distribution inside the structure, given that the thicknesses of the gold film and VO 2 are 47 and 1 nm, respectively, excitation is 630 nm, and temperature is 20 • C.

  , the lowest reflectivity, at 20 and 95 • C, is comparable in value (8.239 × 10 -5 and 4.481 × 10 -5 , respectively) but occurs at different thicknesses of the phase-change material (4 nm at 20 • C and 2 nm at 95 • C).

Figure 6 .

 6 Figure 6. Electric field (norm in V/m) distribution inside the structure, given that the thickness of the continuous gold film, metasurface, and VO2 are 30, 20, and 4 nm, respectively, for excitation 630 nm, temperature 95 °C, periodicity 130 nm, and width 30 nm.

Figure 6 .

 6 Figure 6. Electric field (norm in V/m) distribution inside the structure, given that the thickness of the continuous gold film, metasurface, and VO 2 are 30, 20, and 4 nm, respectively, for excitation 630 nm, temperature 95 • C, periodicity 130 nm, and width 30 nm.

Figure 7 .

 7 Figure 7. SPR curves calculated by TMM model, comparing the continuous gold configuration and the one with a metasurface, for an excitation of 1000 nm and VO2 at 20°. The continuous gold thickness is equal to 50 nm, while the metasurface case includes a continuous gold layer of 30 nm and nanostructures at 20 nm depth; (a) schematic of the continuous gold configuration, (b) schematic of the metasurface configuration, (c) reflectivity, (d) phase, (e) Goos-Hänchen shift of continuous gold film (absolute value), and (f) Goos-Hänchen shift of gold metasurface (absolute value).

Figure 7 .

 7 Figure 7. SPR curves calculated by TMM model, comparing the continuous gold configuration and the one with a metasurface, for an excitation of 1000 nm and VO 2 at 20 • . The continuous gold thickness is equal to 50 nm, while the metasurface case includes a continuous gold layer of 30 nm and nanostructures at 20 nm depth; (a) schematic of the continuous gold configuration, (b) schematic of the metasurface configuration, (c) reflectivity, (d) phase, (e) Goos-Hänchen shift of continuous gold film (absolute value), and (f) Goos-Hänchen shift of gold metasurface (absolute value).

Table 1 .

 1 Summary of the best configurations, when the metasurface thickness is 20 nm on top of a 30 nm continuous gold film. The results are classified according to excitation wavelength, tempera ture, periodicity and width of the nanogrooves, thickness of VO2, minimum reflectivity, FWHM GH shift, and GH sensitivities, for ∆n = 1.2 × 10 -6 RIU and ∆n = 10 -10 RIU.

	λ (nm)	T (°C)	P (nm)	w (nm)	VO2 (nm)	Reflectivity	FWHM (°)	GH Shift (μm)	SGH (μm/RIU)	-6	SGH (μm/RIU)

-10

Table 1 .

 1 Summary of the best configurations, when the metasurface thickness is 20 nm on top of a 30 nm continuous gold film. The results are classified according to excitation wavelength, temperature, periodicity and width of the nanogrooves, thickness of VO 2 , minimum reflectivity, FWHM, GH shift, and GH sensitivities, for ∆n = 1.2 × 10 -6 RIU and ∆n = 10 -10 RIU.

	λ (nm)	T ( • C)	P (nm)	w (nm)	VO 2 (nm)	Reflectivity	FWHM ( • )	GH Shift (µm)	S GH (µm/RIU) ∆n = 1.2 × 10 -6	S GH (µm/RIU) ∆n = 1 × 10 -10
	785	95	140	20	1	1.549 × 10 -6	1.657	2.248 × 10 3	2.253 × 10 6	1.738 × 10 6
	785	20	130	20	2	3.542 × 10 -7	1.954	1.359 × 10 3	5.046 × 10 7	4.885 × 10 7

gold meta-arrays allow for the achievement of a high GH shift and ultra-high sensitivity to low refractive index changes.

Supplementary Materials:

The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/bios12100866/s1, Figure S1. SPR curves: minimum reflectivity versus wavelength and incident angle, VO 2 at 20 • with a thickness of 4 nm and a gold thickness of 46 nm; S1. Refractive index of VO 2 at 20 • C and 95 • C excited at 630 and 785 nm; Table S2. Summary of the best results of VO 2 at 20 • C with an excitation of 630 nm, taking into consideration the gold and VO 2 thicknesses, minimum reflectivity, FHWM, GH shift, GH sensitivity for ∆n = 0.02, angular sensitivity for ∆n = 1.2 × 10 -6 , phase sensitivity for ∆n = 1.2 × 10 -6 , and GH sensitivity for ∆n = 1.2 × 10 -6 ; Table S3. Summary of the best results of VO 2 at 95 • C with an excitation of 630 nm, taking into consideration the gold and VO 2 thicknesses, minimum reflectivity, FHWM, GH shift, GH sensitivity for ∆n = 0.02, angular sensitivity for ∆n = 1.2 × 10 -6 , phase sensitivity for ∆n = 1.2 × 10 -6 , and GH sensitivity for ∆n = 1.2 × 10 -6 ; Table S4. Summary of the best results of VO 2 at 20 • C with an excitation of 785 nm, taking into consideration the gold and VO 2 thicknesses, minimum reflectivity, FHWM, GH shift, GH sensitivity for ∆n = 0.02, angular sensitivity for ∆n = 1.2 × 10 -6 , and GH sensitivity for ∆n = 1.2 × 10 -6 ; Table S5. Summary of the best results of VO 2 at 95 • C with an excitation of 785 nm, taking into consideration the gold and VO 2 thicknesses, minimum reflectivity, FHWM, GH shift, GH sensitivity for ∆n = 0.02, angular sensitivity for ∆n = 1.2 × 10 -6 , and GH sensitivity for ∆n = 1.2 × 10 -6 ; Table S6. Summary of the best results of VO 2 , taking into consideration gold and VO 2 thicknesses, excitation wavelength, temperature, minimum reflectivity, FHWM, GH shift, and GH sensitivity for ∆n = 0.02, ∆n = 1.2 × 10 -6 , and ∆n = 1.2 × 10 -10 ; Table S7. Summary of the best results of VO 2 , while tuning the continuous and metasurface gold thickness, with an excitation of 630 nm, taking into consideration the temperature, periodicity, and width of the metasurface and thicknesses of continuous gold film, metasurface, and VO 2 , respectively, as well as minimum reflectivity, FHWM, GH shift, and GH sensitivity for ∆n = 0.02, ∆n = 1.2 × 10 -6 , and ∆n = 10 -10 ; Table S8. Summary of the best results obtained when the continuous gold and metasuraface thicknesses are 30 nm and 20 nm, respectively, with VO 2 optimized at 20 • C, taking into consideration the thickness of VO 2 and excitation wavelength, periodicity, and width of the metasurface, as well as minimum reflectivity, FHWM, GH shift, GH sensitivity for ∆n = 0.02 and ∆n = 10 -10 , and angular sensitivity for ∆n = 1.2 × 10 -6 ; Equations (S1)-(S20).

Conflicts of Interest:

The authors declare no conflict of interest.


domain: chim shs

text:
José Tapia

Myriam Eveno

Thomas Calligaro

Laurent Pichon

Eric Laval

Elisabeth Ravaud

Ina Reiche
email: ina.reiche@chimieparistech.psl.eu

Efficiency of combined MA-XRF and CXRF to give nondestructive insights about changes of a historical painting

Keywords: scanning Macro-XRF, confocal micro-XRF, elemental imaging, paints, stratigraphy, pigments

Historical paintings with important iconographical changes represent an analytical challenge. Considering the case study of a 15 th century French painting studied during its restoration, the efficiency of a combined non-invasive approach of two-dimensional scanning macro-X-ray fluorescence imaging (MA-XRF) and a laboratory-based depth resolved confocal micro-X-ray fluorescence (CXRF) is discussed. Large chemical maps of several elements were obtained by MA-XRF, enabling the identification of zones of interest representing changes in the painting composition. In these areas, depth profiles were measured with CXRF, allowing to evidence overlaying paint layers. The advantages of this technique are that it can give direct information on the stratigraphy of paint layers in a nondestructive way and can reduce the sampling needed, as well as increase the locations analyzed (in our study twenty-two depth-resolved scans). These results complement information obtained by scanning electron microscopy coupled with an energy-dispersive X-ray analyzing system (SEM-EDX) on three cross-sections samples taken in the areas of interest. Additionally, the three cross-sections of the painting were studied by CXRF lateral scans (y) in order to evaluate the efficiency of the CXRF analyses against SEM-EDX. The study shows the benefits of the combination of MA-XRF and CXRF for analyzing painting compositions, as such a high number of cross-sections would have been impossible to be sampled. From an art-historical and conservation perspective, this combined study provides an understanding of the original painting's paint sequence and its later retouches, helping to make informed conservation treatment decisions.

Graphical Abstract

Introduction

X-ray fluorescence (XRF) is an efficient, fast, non-invasive, safe and firmly established method for measuring single spots on artworks and obtaining information on the elemental composition [START_REF] Trojek | Confocal X-ray fluorescence spectrometer for in-situ analyses of paintings[END_REF], using an X-ray beam of small diameter and a detector [START_REF] Ravaud | Development of a versatile XRF scanner for the elemental imaging of paintworks[END_REF], [START_REF] Eveno | Confocal XRF depth profiling non-destructively reveals the original blue pigments in a Renaissance painting by Caroto[END_REF]. An evolution of this method is the two-dimensional (2D) scanning macro-X-ray fluorescence spectroscopy imaging (MA-XRF), that allows recording spectra point by point along the work area [START_REF] Eveno | Confocal XRF depth profiling non-destructively reveals the original blue pigments in a Renaissance painting by Caroto[END_REF], providing relatively large elemental maps of the painting down to trace concentrations (sometimes up to several square meters [START_REF] Alfeld | Strategies for processing mega-pixel X-ray fluorescence hyperspectral data: a case study on a version of Caravaggio's painting Supper at Emmaus[END_REF]). Moving the painting with a motorized X-Y stage [START_REF] Eveno | The Louvre Crucifix by Giotto -Unveiling the original decoration by 2D-XRF, X-ray radiography, Emissiography and SEM-EDX analysis[END_REF], a scan can be done in just hours, sometimes a few days for big paintings. It is a well-established method that can use both synchrotron radiation and laboratory X-ray generators [START_REF] Alfeld | Strategies for processing mega-pixel X-ray fluorescence hyperspectral data: a case study on a version of Caravaggio's painting Supper at Emmaus[END_REF], [START_REF] Eveno | The Louvre Crucifix by Giotto -Unveiling the original decoration by 2D-XRF, X-ray radiography, Emissiography and SEM-EDX analysis[END_REF]. However, MA-XRF presents limitations [START_REF] Ravaud | Development of a versatile XRF scanner for the elemental imaging of paintworks[END_REF] like the fact that the resolution is limited by the size of the X-ray beam or moreover, that the stratigraphy of the paintings cannot be directly resolved, which can be a major issue when investigating the painting's technique and the changes it might have undergone. The analysis of the stratigraphy of paintings is traditionally performed by means of an optical and electron microscopy coupled with an energy-dispersive X-ray system (OM and SEM-EDX) on cross-sections [START_REF] Reiche | Toward a three-dimensional vision of the different compositions and the stratigraphy of the painting L'Homme blessé by G. Courbet: coupling SEM-EDX and confocal micro-XRF[END_REF]. However, these analyses require micro-sampling, a damaging and in most cases not acceptable process [START_REF] Trojek | Confocal X-ray fluorescence spectrometer for in-situ analyses of paintings[END_REF]. To solve this last problem, a laboratory-based non-invasive depth-resolved confocal micro-Xray fluorescence (CXRF) spectrometer called LouX 3D was developed at the C2RMF laboratory a few years ago [START_REF] Reiche | Depth profiling reveals multiple paint layers of Louvre Renaissance paintings using non-invasive compact confocal micro-X-ray fluorescence[END_REF], [START_REF] Eveno | Confocal XRF depth profiling non-destructively reveals the original blue pigments in a Renaissance painting by Caroto[END_REF], [START_REF] Reiche | Toward a three-dimensional vision of the different compositions and the stratigraphy of the painting L'Homme blessé by G. Courbet: coupling SEM-EDX and confocal micro-XRF[END_REF]. By using a confocal system consisting of two X-ray optics, one in the excitation channel and the other in front of the detector, an ellipsoidal micro-volume can be defined by the overlap of the foci of both optics [START_REF] Reiche | Depth profiling reveals multiple paint layers of Louvre Renaissance paintings using non-invasive compact confocal micro-X-ray fluorescence[END_REF], the size of it depending on the X-ray energy [START_REF] Reiche | Toward a three-dimensional vision of the different compositions and the stratigraphy of the painting L'Homme blessé by G. Courbet: coupling SEM-EDX and confocal micro-XRF[END_REF]. First proposed by Gibson and Kumakhov in the 1990s [START_REF] Gibson | Applications of x-ray and neutron capillary optics[END_REF], this method allows to visualize the stratigraphy of the layers with a non-destructive approach. The first applications of such device used synchrotron radiation [START_REF] Trojek | Confocal X-ray fluorescence spectrometer for in-situ analyses of paintings[END_REF], [START_REF] Kanngießer | A new 3D micro X-ray fluorescence analysis set-up -First archaeometric applications[END_REF], [START_REF] Kanngießer | Three-dimensionnal micro-XRF investigations of paint layers with a tabletop setup[END_REF], but it can now be found in several laboratories due to the existence of relatively small X-ray generators [START_REF] Reiche | Depth profiling reveals multiple paint layers of Louvre Renaissance paintings using non-invasive compact confocal micro-X-ray fluorescence[END_REF], [START_REF] Trojek | Confocal X-ray fluorescence spectrometer for in-situ analyses of paintings[END_REF], [START_REF] Kanngießer | A new 3D micro X-ray fluorescence analysis set-up -First archaeometric applications[END_REF]- [START_REF] Müller | An in situ non-invasive study of paint layers on Early Netherlandish paintings: New insights into the paintings' history by portable CXRF[END_REF]. This analysis allows for the exploration of the paint layer construction, its chemistry and its stratigraphy, as complex layers and overpaints can be identified in depth-resolved scans. Thus, it is a promising analytical technique allowing for the non-destructive investigation of objects with a layered structure.

In this work the efficiency of CXRF is evaluated for the study of complex painting stratigraphy with respect to MA-XRF and SEM-EDX on cross-sections. A painting was studied, allowing to address the challenging questions arising from the multiple changes it had undergone through time, using a combination of CXRF and MA-XRF analysis, while at the same time confirming that the CXRF measurements are right. The goal of this study is to establish and characterize the original materials, the later additions and the paint palette used by the painter, helping in the decision-making process of the restoration. This complimentary approach therefore allowed revealing information about former compositions and gives insights into the genesis of the painting, unraveling the secrets hidden deep within the layers.

Experimental section 2.1 Materials

The painting Virgin and Child surrounded by saints and a donor (Anonymous, France, Inv. No. RFML.PE.2018.51.1, Fig. 1a andb) is considered to have been composed in France between 1420 and 1430, and is conserved in the Louvre Museum. It consists of a single oak panel, with a size of 23.7 x 42.5 cm 2 . It has been studied during the restoration process. Three crosssections were also taken at the C2RMF laboratory (A: no. 20041, B: no. 20042 and C: no. 20043), one of each of the three areas of interest found with the MA-XRF mapping, to be analyzed by SEM-EDX. This analysis, the lateral scan (y) on the cross-sections, and the three depth-resolved scans (z) in points adjacent to where the micro-samples had been taken from, allowed to compare between the SEM-EDX and CXRF results. After confirming that CXRF was indeed a correct alternative allowing to distinguish the layers and elements seen by SEM-EDX (when heavier than Si), nineteen other depth-resolved scans were performed in the three areas of interest. This technique thus changes the conditions and makes time, and not the permission to take micro-samples, the limit of the study.

Methods

Scanning macro-X-ray fluorescence (MA-XRF)

The detailed description of the instrument used in this study can be found in [START_REF] Ravaud | Development of a versatile XRF scanner for the elemental imaging of paintworks[END_REF], [START_REF] Reiche | New insights into the painting stratigraphy of L'Homme blessé by Gustave Courbet combining scanning macro-XRF and confocal micro-XRF[END_REF]. It consists of a head mounted on a motorized X-Y stage allowing for movement along the artwork (X max 50cm, Y max 60cm, ZABER). The 15kg head comprises an X-ray generator (ROENTEC X1 generator, Mo tube model RTW MCB 50-0.6, 50kV, 0.6 mA max), a fast silicon drift X-ray spectrometer collecting the XRF data (Amptek model X123, 70 mm 2 active area collimated to 50 µm 2 Fast SDD), and a laser allowing precise alignment working in concordance with a microvideo camera (Toshiba QP49H, 8mm objective). A 0.6-mm diameter Mo pinhole collimator is situated at the X-ray source end to shed a parallel and wide energy range beam (1.8 to 40 keV) on the painting. The detector was placed at a distance of 15 mm from the paintings' surface. In our case, 3 maps of 490 x 870, 340 x 420 and 250 x 250 pixels were acquired (whole painting, plus two details in the donor's tunic and the coat of arms) corresponding to sizes of (x,y) 24.5 x 42.5 cm 2 , 17 x 21 cm 2 and 5 x 5 cm 2 area. At max size, a scanning speed of 12.5 mm/s and a dwell time of 40 ms were used, taking 4.7h to collect the whole elemental maps. The two small scans were performed in areas selected according to the most interesting zones identified in the first scan. A dedicated program implemented in a portable computer running Windows ® using a Visual studio-built interface controls the instrument [START_REF] Ravaud | Development of a versatile XRF scanner for the elemental imaging of paintworks[END_REF]. Spectra are collected on the fly, and normalized to a common live time just after the transfer.

Data evaluation

The data (a matrix of pixels each containing a spectrum) is stored in EDF format, and processed with the open source program PyMCA [START_REF] Eveno | The Louvre Crucifix by Giotto -Unveiling the original decoration by 2D-XRF, X-ray radiography, Emissiography and SEM-EDX analysis[END_REF], [START_REF] Solé | A multiplatform code for the analysis of energy-dispersive X-ray fluorescence spectra[END_REF], developed for X-ray fluorescence at the European Synchrotron Facility (ESRF). With it, we can fit the peak area of different elements (in our study, namely Ca, Mn, Fe, Cu, Zn, As, Ba, Au, Hg and Pb), and obtain elemental maps in PNG format. These maps can then be represented in a linear or logarithmic black-and white-contrast scale in order to enhance the visibility (a higher value of white indicates a stronger signal). For all images, minimum and maximum intensity values were selected to enhance the readability.

Optical microscopy, and scanning electron microscopy coupled with an energydispersive X-ray analyzing system (SEM-EDX)

The three cross-sections were investigated by optical microscopy (OM; Nikon Eclipse LV-100ND coupled with a Nikon DS-Ri1 camera) under visible and UV lights. They were later analyzed using a scanning electron microscope (SEM; Philips XL30 CP: tungsten cathode, backscattered electron detector) coupled with energy-dispersive X-ray spectroscopy (EDX; Oxford Instruments, AZtec software) using an accelerating voltage of 20kV. The samples were polished and carbon-coated to avoid surface charging.

Confocal micro-X-ray fluorescence (CXRF) prototype LouX 3D

Confocal micro-X-ray fluorescence was performed on the painting using the LouX 3D spectrometer [START_REF] Reiche | Depth profiling reveals multiple paint layers of Louvre Renaissance paintings using non-invasive compact confocal micro-X-ray fluorescence[END_REF] installed at the C2RMF laboratory in Paris (Fig. 2). By moving the artwork through the probing volume with micrometer accuracy, a depth-scan can be performed, allowing the elemental distributions inside the sample to be explored. In this device, the object is placed on a motorized X-Y-Z stage, and moved away from the measurement head for security reasons. The device specifications can be found with more detail in [START_REF] Reiche | Depth profiling reveals multiple paint layers of Louvre Renaissance paintings using non-invasive compact confocal micro-X-ray fluorescence[END_REF]. The X-ray tube is a Rh anode (IMOXS), operated at 50 kV and 0.6 mA max, equipped with a full polycapillary lens at the exit providing a spot size of 50 µm and a working distance of about 6 mm. On the detection channel, an X-Flash detector (Bruker AXS, Rontec X Flash series 4 model 4010) is used with a poly-Conical Capillary Collimator (CCC) lens set up in front of it with a focal distance of 11 mm. The energy range of the systems is limited by the transmission of the optics between 3 and 20 keV. In previous studies [START_REF] Reiche | Depth profiling reveals multiple paint layers of Louvre Renaissance paintings using non-invasive compact confocal micro-X-ray fluorescence[END_REF], [START_REF] Reiche | Toward a three-dimensional vision of the different compositions and the stratigraphy of the painting L'Homme blessé by G. Courbet: coupling SEM-EDX and confocal micro-XRF[END_REF], paint layers up to 15-20 µm could be identified with the LouX 3D device by elemental profiling in the lateral direction on a painting's cross-section.

On the three cross sections, lateral CXRF scans (y) were applied to allow a comparison with optical microscopy (OM) and SEM-EDX measurements. For each lateral position (y), the acquisition time per spectrum was 100 s, with a step between measurements of 10 µm. Nevertheless, depth scans (z) were taken at different locations for the most part. The acquisition time per spectrum at each analysis depth was also set to 100 s. However, from the measurement of depth profiles, at greater depths an attenuation effect can be observed due to the attenuation and absorption of the X-rays by the surrounding and top layers. If heavy elements like Pb or Hg are on the outer layers of the painting, they will absorb even more the emission of elements of deep layers, thus getting less intensity and precluding the measurement of these deeper layers. Indeed, deeply buried layers often cannot be detected due to this absorption effects. If no heavy elements are present on the surface layers, a depth of 100-150 µm can be reached in paintings. Because of this, the time of acquisition of a complete depth-scan generally takes 35 (when many heavy elements are present on the surface) to 60 minutes. Depth scans were first performed in the vicinity of the three cross-sections sampling locations, to be extended to other locations in the areas of interest. For each depth scan, the object was placed on the motorized sample stage, positioned with the aid of the device's optical microscope, and subsequently submitted to two scans. The first one, a fast scan with a step of 50 µm, was mainly to locate the values of z were signal was measured. The second, a precise scan with a step of 10 µm was performed in the interval of interest by moving the painting away of the instrument starting at the deepest detectable layer, and measuring a spectrum per value of z.

Data evaluation

The XRF spectra obtained for each depth value was fitted by means of the PyMCA program [START_REF] Solé | A multiplatform code for the analysis of energy-dispersive X-ray fluorescence spectra[END_REF]. The peak areas of the different elements were adjusted, and the net peak intensities of the characteristic fluorescence lines were extracted and normalized to their maxima. These normalized values were then plotted against the depth z value, enabling an easier comparison of the intensity vs depth profiles. As in the MA-XRF case, the elements mainly found were Ca Mn, Fe, Cu, Zn, As, Ba, Au, Hg and Pb. The maximum intensities of the element peaks indicate the location of the different layers. These layers are labelled starting from the surface. This way is unconventional in the of paint layer succession (usually starting at the bottom), but is justified here because the deeper layers can often not be detected due to absorption effects by CXRF. It has to be noted that the distances depicted in the CXRF depth profiles do not correspond to real thicknesses of paint layers because of the absorption of X-rays in the successive layers crossed when transmitted and when reflected, which distorts the apparent distances.

Results and discussion

Characterization of the CXRF scan performances with respect to the study of the paint stratigraphy

The analytical volume was characterized with thin metallic films prior to the measurements presented in the following section. For this, several films of 1 µm of thickness were scanned in depth with a step size of 10 µm. Several elements were used (Cr, Fe, Ni, Cu, Zn, Pb). We measured the FWHM of each depth profile obtained representing the intensity of the peak of the different elements vs the position z. As expected, we obtained a FWHM decreasing with increasing energy: 61 µm at 6.4 keV and 36 µm at 12.6 keV for example.

Three samples for the cross-sections A, B and C were taken on the painting and their position is shown in Fig. 1b. They were first analyzed with optical microscopy (OM) and then by SEM-EDX. Fig. 3 shows the cross-sections under visible and UV light, as well as their corresponding back scattered electron micrographs. These techniques allow us to view the limits but also the advantages and precision of the CXRF set-up. In Table 1 In Fig. 4a is presented the CXRF sum spectrum for the depth scan (z) at the analysis point 1, adjacent to where the cross-section B was taken. This spectrum reveals the presence of Pb, Fe, Mn, Cu, Au, Hg and Ca at this position. The CXRF lateral profile (y) in the cross-section B shows the layers described in the Table 1. Indeed, we first see on the surface a layer with two peaks, Pb and Fe, followed by an Au layer (Fig. 4b), and then very well separated, a Cu-based layer. Almost the same results are found when performing a depth profile at the analysis location 1 adjacent to where the sample had been preserved (Fig. 4c).

As can be seen, CXRF resolves quite well the different layers. However, by using CXRF the number of cross-sections collected in an artwork can be limited. As can be seen here, only one sample is needed to verify that the gap between layers is a varnish, and many more CXRF depth analysis can be taken without the need to do more sampling. The varnish was also observed using Fourier transform infrared spectroscopy (FTIR) on some cross-sections (Fig

Chemical imaging for inferring characteristic pigments in the paint layers of the figurative depictions

A MA-XRF mapping of the whole painting was performed. Several areas of interest were identified: the coat of arms and the monk's tunic where several successive interventions were highlighted, and the cross. Indeed, on top of the original coat of arms had been applied two others, but it was difficult to understand the order and their shape as MA-XRF gives limited depth-resolved information. On top of the donor's short tunic had been applied a longer one, changing the iconography of the painting by turning him into a monk character. The cross could be original, but could have also been added at the same time as the iconographic change. Fig. 5A shows the sum MA-XRF spectrum produced by a 17 x 21 cm 2 area (340 x 420 pixels), presenting a detail of the whole painting including the monk's tunic, the coat of arms, and a part of the cross. The chemical maps of significant elements are shown in Fig. 5 b-f. A linear scale is applied here except in the case of lead and gold where a logarithmic greyscale is applied to compensate for the differences in recorded intensities. Comparing the Pb and Cu maps (Fig. 5b andc, respectively), we can see how they look very different in the monk's tunic, the coat of arms, and the cross. The Cu map shows a short tunic and the donor's legs, and a coat of arms composed of crescent moons of a different element surrounded by a Cu-based pigment. The cross does not seem to appear, even though some parts can be deduced from the missing intensity of the Cu triangles that has been absorbed by other elements. However, looking at the Pb map the composition seen is different: the tunic is long, the coat of arms is a rooster on a column, and the cross appears clearly. Furthermore, the Hg map (Fig. 5d) reveals a third different coat of arms conformed by a red pigment rectangle above spaced red stripes. Also, details appear on the tunic collar and cuffs that can only belong to the original underlying tunic, as the visible one is white and brown with no red. The Fe map (Fig. 5e) reinforces the existence of a shorter tunic, which then has to be blue/green with brown, and shows the same coat of arms as the lead map. The cross is perfectly visible, showing the colors we see, brown with white. The Au map (Fig. 5f) provides some golden details on the bishop's dress that are hidden in the visible composition, strengthening our knowledge on what is behind the long monk's tunic. Furthermore, details in the tunic collar and cuffs gives us information in addition to the Hg map that these might be red vermilion with some golden touches. The MA-XRF clearly shows here its ability to evidence distinct paint areas in a non-destructive way, even though it's lacking the ability to give depth-resolved information.

Depth profiling for elucidating the painting's stratigraphy and new information obtained on the three areas of interest

Twenty-two CXRF depth profiles (z) were performed on the painting (Fig. IIa-n in SI). The locations are marked in Fig. 1b in a detail of the painting at a moment prior to the analysis, when the restoration had already begun. The depth profiles taken at six representative locations are presented in Fig. 6a-f and discussed in this section, as well as the previously presented location 1. They comprise the three main areas of interest detected in the MA-XRF elemental maps: the monk's tunic, the coat of arms, and the cross. Location 1, 3 and 10 are located in the monk's tunic, location 11 and 12 in the coat of arms, and 8 and 22 in the cross. The combination of the results obtained by MA-XRF and CXRF, as well as the information provided by SEM-EDX analysis of the cross-sections, allows getting new insights into the different repaints and iconographic changes of the painting.

Monk's tunic. The profiles for the depth-scans analysis location 1, 3 and 10 correspond to this area. The CXRF depth profile at the analysis location 1 (Fig. 4c) indicates three main paint layers. At the surface of the painting, a Pb-and Fe-based layer containing lead white and earth pigments is identified, corresponding to the long white visible tunic. Below this layer, an Aubased one appears, attributed to a golden detail in the bishop's green cape hidden under the visible white monk's tunic. Under it, and clearly separated from the other layers, is a Cu-based layer that can be attributed to the bishop's green cape. Fig. 6a shows the element depth profiles obtained at analysis location 3 (over the original donor's dress). Two layers can be clearly separated. On the surface, a Pb-based layer with Fe and Ca (lead white and earth pigments) can be correlated to the white monk's tunic. The second one, deeper, is a Cu-based layer containing some Pb. It can be attributed to the short tunic, which should be blue or green (azurite or copper green). Fig. 6b shows the depth profiles at the analysis location 10, in a place of the tunic where the MA-XRF elemental map of Cu shows the feet of the donor. Three layers are identified here. First, a light Ca-based layer is identified on the surface that could indicate the presence of a slightly pigmented varnish. Underneath is found a Pb-and Fe-based layer also containing Ca (lead white with earth pigments), certainly corresponding to the white and brown monk's dress. Finally, at the furthest accessible probing volume is a Cu-based layer, which can be attributed to the feet/pants of the donor, as a little Hg (vermillion, not represented in the graph) content as well as some Fe are also found here.

A shorter tunic under the monk's long white and brown exists (MA-XRF elemental maps of Cu, Fe, Hg and Au). Its color should be dark blue-green, composed of a Cu-based pigment with vermillion and earth pigments at the collar and cuffs. The left side of the long tunic was painted on top of the bishop's Cu-based dress corresponding to a copper green glaze with some lead tin yellow, hiding as well some golden details of it. The CXRF depth-scans (locations 1, 2, 3, 10, 19, 20 and 21) find a good separation between the deeper layers (the Cu-based layers of the bishop's dress and the golden detail, the Cu-based layer of the tunic, the floor triangles) and the surface layer (the white tunic). This clear and somewhat big separation was shown to be due to a varnish thanks to the cross-section B sampled adjacent to CXRF location 1. This overpaint is important because it changes the iconography of the painting, as the donor was converted into a monk.

Coat of arms.

The profiles for the depths-scans at analysis location 11 and 12 correspond to the coat of arms. It must be noted here that the painting was analyzed during its restoration, and thus between the moment the MA-XRF elemental maps and cross-sections were taken and the moment the CXRF depth profile analysis was performed, some changes had already been undertaken to the painting. Mainly, the third coat of arms on the surface, a cock over a column, had already been partially removed, leaving place to analyze the second and first coat of arms.

The depth profiles at the analysis location 12 (on a beige vertical line in the second coat of arms) are shown in Fig. 6c. Two layers can be resolved very well by looking at the plot. The first one is a layer containing Pb (lead white), Hg (vermillion), Fe (earth pigments) and Ca (possibly calcium carbonate), and is well separated from the second one composed of Cu (likely azurite, as a blue underlayer appears through some small holes). They correspond, respectively, to the second and first coat of arms. We can see the predominance of red pigments in the first layer by looking at the values of the intensity maxima of the Fe Kα and Hg Lα fluorescence lines.

The CXRF depth scan at the analysis location 11 (on a vertical stripe in the second coat of arms over the gold in the first coat of arms) indicates again two different layers (Fig. 6d). Near the surface, a layer containing Pb, Hg, Fe and some Ca and Cu is found (again, the second coat of arms, lead white, vermillion and earth pigments). Very well separated appears a layer of Au, corresponding to the first coat of arms. The coat of arms consists in fact of three, painted one over the other. The first coat of arms and deepest is conformed of three golden crescent moons surrounded by a Cu-based pigment, probably azurite. The second is a dragon-shaped figure (location 18 in SI) on a red rectangle (mainly vermillion) in the upper part and alternating beige and red stripes in the lower part. The dragon-figure is made of earth pigments, vermillion and lead white, and perhaps red lake (not detectable by XRF analysis but visible to the observation under the microscope). The third most on the surface is a cock standing on a white column. The Cu MA-XRF elemental map gave information about the first coat of arms, Hg about the second, and Pb and Fe about the third. The Au map gave some insight about the crescent moons, but as the representative peaks of Au and Hg are very close, and the absorption effect at that depth is high, the crescent moons could not be clearly identified. By means of CXRF scans at depth-scan locations 11 to 17, the first and second coat of arms showed a clear separation between the different layers. This separation was also proven to be due to a varnish thanks to the observation of the crosssection A sampled adjacent to the depth-scan location 11. The third coat of arms could only be analyzed at location 13 as it had already been partially removed.

Cross. The profiles for the depths-scans at analysis location 8 and 22 correspond to the cross. The CXRF depth profiling at the analysis location 8 reveals five possible layers (Fig. 6e). At the surface of the painting, a Ca-and Hg-based layer is followed by a Pb-based layer with Fe. This could be attributed to the light beige cross which could be composed of lead white mixed with earth pigments and vermillion. Below these two, a third Cu-based (green copper pigment) layer followed by a Fe-based layer (earth pigments), corresponding to the dark triangle on the floor below the cross. Finally, the fifth layer containing Pb (lead white) and Hg (vermillion) likely corresponds to the beige floor. In Fig. 6f, the depth profiles at the analysis location 22 are shown. Four layers can be seen. On the surface of the painting, a Hg-and Ca-based layer (red vermillion) with some Cu can be found, followed by a Pb-and Fe-based layer (lead white with earth pigments). This likely corresponds to the cross. More in depth, a Cu-based layer is found, followed by a layer containing Pb. This could be the red cape from the saint. The color of the cape is probably made of red lake, not detectable by XRF analysis, mixed with lead white and a little Cu-based pigment.

The presence of the cross is likely linked to the iconographic change of the donor into the monk.

As can be seen in the MA-XRF maps of the Fe, the triangles in the floor are all painted under the cross. It was hypothesized that, when the donor was converted into a monk, the cross could have also been added. After the CXRF depth-scans at the locations 4, 8, 9 and 22, corresponding respectively to the cross over a triangle, a dark triangle, the hand and the red saint's cape, only a slight separation between the layers was found, unlike in the other two areas of interest. Taking this and the information obtained on the cross-section C that no varnish was found between the cross and the dark triangle, allows us to conclude that no or only a very thin varnish layer was placed between the cross and the triangles of the floor. Further art-historical studies are necessary to clarify the moment of the addition of the cross.

Conclusions

A combination of MA-XRF and CXRF supported by SEM-EDX cross-section analysis allowed the study of the hidden layers in the painting Virgin and Child surrounded by saints and donor conserved in the Louvre Museum collections in Paris, France. This study brought insights into its history and supported the decision-making process of its restoration. An in-depth vision of the stratigraphy was previously hampered by the fact that MA-XRF doesn't offer a depth resolution, and that the sampling required to study cross-sections with SEM-EDX is very restricted and has to be reduced as much as possible. The advantage of using CXRF is clear, as it can give spatially-resolved results on the painting stratigraphy close to those obtained by SEM-EDX on cross-sections but in a non-invasive way, allowing to freely increase the number of analysis points and reduce the sampling needed, making the time the main constraint.

Considering the elemental distributions related to the use of different pigments in several areas and depths, it is possible to discuss the changes in the areas of interest found in the MA-XRF scan. In the monk's tunic and in the coat of arms several successive interventions were separated. In the case of the monk's tunic, a shorter one was found under the visible one. In the coat of arms, three versions painted one on top of each other were found. The clear separation between the layers forming the monk's tunic and the donor's feet, donor's tunic, and bishop's dress, as well as between the different coat of arms, is due to an organic varnish layer, whose composing light elements cannot be evidenced by CXRF. This layer was confirmed to exist in two cross-sections analyzed with SEM-EDX and FTIR.

In the case of the cross, no well-separated layer system was found in contrast to the two other considered areas of the painting, perhaps indicating the absence of varnish between the layers. This could indicate that the cross was added at another moment than the other iconographic changes of the painting. This case study highlights the new non-invasive possibilities provided by MA-XRF scanning in combination with CXRF. These combined methods can be applied to other paintings presenting overpaints or compositional changes. The reproducibility of the analyzed point at the microscale is crucial in this methodological combination for correct data interpretation because of the highly heterogeneous nature of paints. Therefore, the development of a transportable equipment combining both methods in a single machine would allow for more precisely localized, easier and faster analyses, and is under way in the framework of the ANR DepthPaint program.

Fig. 1 a

 1 Fig. 1 a) Photograph of the painting Virgin and Child surrounded by saints and a donor (RFML.PE.2018.51.1). © C2RMF, T. Clot and b) detail showing the locations where the three cross-sections were taken in white (A, B and C), and in red the 22 locations where CXRF depth profiles were applied

Fig. 2

 2 Fig.2CXRF prototype LouX 3D used with the painting at the C2RMF, Paris

Fig. 3

 3 Fig. 3 Optical (left), UV (center) and back scattered electron micrographs (right) of cross-sections A, B, and C.

Fig. 4

 4 Fig. 4 CXRF results. The left side of the depth and lateral scan profiles represents the painting surface. The identified paint layers are indicated with the numbers on the depth profiles. a) Sum spectrum of the 36 XRF spectra (one per depth position (z) measured) for the depth scan at analysis Location 1, adjacent to the sample location for the cross section B. Normalized elemental profiles for: b) lateral scan of cross-section B (the intensity maxima of the Fe Kα, Cu Kα, Au Lα and Pb Lα fluorescence lines are 46, 1339, 128 and 18601, respectively) c) Depth-scan for analysis location 1 (adjacent to the sampling of cross section B) (the intensity maxima of the Fe Kα, Cu Kα, Au Lα and Pb Lα fluorescence lines are 376, 9402, 2024 and 11008, respectively).

Fig. 5

 5 Fig. 5 MA-XRF elemental distribution maps of an area measuring 17 x 21 cm 2 . a) experimental sum MA-XRF spectrum produced by that area together with the fitted spectrum (red line) b) Pb L in logarithmic scale c) Cu K d) Hg L e) Fe K f) Au L in logarithmic scale

Fig. 6

 6 Fig. 6 Results of the CXRF normalized elemental depth profiling. The identified paint layers are indicated with numbers on the depth profiles. a) analysis location 3 (the intensity maxima of the Ca Kα, Fe Kα, Cu Kα and Pb Lα fluorescence lines are 19, 1541, 3837 and 22068, respectively) b) analysis location 10 (the intensity maxima of the Ca Kα, Fe Kα, Cu Kα and Pb Lα fluorescence lines are 27, 3002, 3294 and 17546, respectively) c) analysis location 12 (the intensity maxima of the Ca Kα, Fe Kα, Cu Kα, Hg Lα and Pb Lα fluorescence lines are 16, 1453, 4298, 1963 and 29535, respectively) d) analysis location 11 (the intensity maxima of the Ca Kα, Fe Kα, Cu Kα, Au Lα, Hg Lα and Pb Lα fluorescence lines are 18, 1542, 42, 266, 2234 and 23805, respectively) e) analysis location 8 (the intensity maxima of the Ca Kα, Fe Kα, Cu Kα, Hg Lα and Pb Lα fluorescence lines are 61, 4356, 8209, 302 and 13905, respectively) f) analysis location 22 (the intensity maxima of the Ca Kα, Fe Kα, Cu Kα, Hg Lα and Pb Lα fluorescence lines are 44, 1550, 496, 129 and 11625, respectively)

  This allows us to perform another comparison between what can be detected by CXRF regarding a typical analysis on cross-sections by OM and SEM-EDX. The high proportion of layers detected by the lateral and depth CXRF scans is not a phenomenon unique to this artwork, but is also shared with other paintings analyzed with the Loux 3D set-up going from those of Italian Renaissance artists to 19th century French painters (Table A in the supplementary information, SI).

a detailed description of the layers in each cross-section obtained by OM and SEM-EDX observations can be found, enriched with the comparison with the CXRF lateral scan (y) of the cross-sections. The results from the CXRF depth scans (z) of the locations adjacent to the sampling are also presented. It can be recognized how the CXRF lateral scan (y) of cross-section A allows identifying four out of the nine (4/9) layers determined by OM/SEM-EDX, 4/8 for B, and 4/7 for C. In the case of the CXRF depth scans of the locations adjacent, we have 2/6 for A, 5/8 for B, and 3/7 for C.

Table 1

 1 OM and SEM-EDX descriptions of the paint layers compared with CXRF lateral scans (y) of the cross-sections and CXRF depth scans (z) of adjacent points. Layer one represents the outer layer closest to the surface of the painting. The element underlined (e.g., Cu) means it is the main identifiable element, without underline (e.g., Cu) that it is present, and between parenthesis, e.g., "(Cu)", that it is a minor element. Coat of arms 3 removed by the restorers between the cross-section sampling and the CXRF depth scan.

	Cross-	Layer and composition determined by OM/ SEM-EDX observations	Elements identified by	Elements identified by CXRF depth	Identification
	section		CXRF lateral scan (y)	scans (z) of adjacent locations
	A			Location 11
		1. Thin fluorescent under UV layer (several µm)
		2. Thin organic layer with big orange grains (red ochre; Al, Si, Fe) (several µm)	(Fe) right next to Cu		Coat of arms 3
		3. Light beige layer (lead white; Pb, Ca) with small red, black and blue grains (Cu) as well	Cu
		as grains of green earth (10-30 µm)
		4. Organic layer, possible varnish (several µm)			Coat of arms 2
		5. Beige-orange layer of lead white (Pb, Fe, Ca) with red, white and black grains (earth	Fe, Hg, Pb	Fe, Hg, Pb
		pigments, vermillion; Ca, Fe, Hg, S, Mg) (15-25 µm)
		6. Organic layer, possible varnish (several µm)			Coat of arms 1
		7. Gold leaf (Au)	Au	Au
		8. Bole (earth pigments; Al, Si, Mg, Fe) (several µm)	Not clear. Fe, Hg
		9. White ground layer (calcium carbonate with several alumina silicates; Ca, Al, Si) (66 µm)
	B			Location 1
		1. Organic layer with orange and yellow grains (Pb, Ca). Possibly tinted varnish (several		(Fe), Pb	Monk's tunic
		µm)
		2. Lead white and earth pigments (Mg, Al, Si, Fe) with a P, Cl, Pb and Ca layer on the	Fe, Pb	Fe, Pb	Monk's tunic
		surface (13-16 µm)
		3. Brown organic non fluorescent under UV layer with some earth elements (Al, Si) (13 µm)			Golden detail
		4. Gold leaf (Au)	Au	Au	Golden detail
		5. Beige mordant layer (lead white, earth pigments, lead tin yellow ; Pb, Sn, Al, Si, Fe) (13-	Not clear	Not identified	Golden detail
		17 µm)
		6. Organic layer, possibly varnish (~7 µm)			Bishop's green tunic
		7. Copper green glaze non-UV-fluorescent layer (Cu, Pb, Sn) (5-6 µm)	Cu	Cu, Pb	Bishop's green tunic
		8. Green copper layer with some grains of lead tin yellow (Cl, Sn and Pb) (30 µm)	Cu	Cu, Pb	Bishop's green tunic
		No ground layer present in this cross section
	C			Location 4
		1. Slightly fluorescent under UV organic layer, perhaps a tinted varnish (several µm)	Fe, Pb	Fe, Hg	Cross
		2. Light beige layer with lead white, earth pigments, blue copper pigment, orange iron oxide	(Fe), Cu, Pb	Pb	Cross
		and carbon black (20-25 µm)
		3. Thick non-fluorescent under UV organic layer with some Cu and Pb (5-6 µm)	Not clear	Not clear	Triangle
		4. Thick organic varnish layer fluorescent under UV (8-20 µm)			Floor
		5. Beige layer (lead white, orange iron oxide, vermilion) (13-16 µm)	Fe, Hg, Pb	Cu, Hg, Pb	Floor
		6. Beige layer (lead white, earth pigments; Al, Si, Fe) (15-25 µm)	Pb	Not identified	Floor
		7. Thin organic layer of impregnation (several µm)
		No ground layer present in this cross section

Acknowledgements

We thank Brice Moignard, Antoine Zink and Frédéric Leblanc from the C2RMF laboratory for their help during the reinstallation of the confocal X-ray fluorescence spectrometer. We also thank Gilles Bastian, Clarisse Delmas, Rosaria Motta, Matthieu Gilles and Sophie Caron for the insight they gave us regarding the painting's history and the discussions regarding its restoration. Funding was provided by ANR DepthPaint (ANR-20-CE29-0018) for the CXRF measurements and the PhD of J.T.R. at PSL university, ED 388 (2021-24).

Data availability statement

All data presented and discussed in this manuscript are either presented in the main manuscript file or in the supplementary information. Further information can be provided on demand by the authors institution.

Author contributions

The manuscript was written through contributions of J.T., I.R., M.E., T.C and L.P. E.L. performed the MA-XRF data acquisition. M.E. performed the SEM-EDX and FTIR on cross sections data acquisition. J.T., I.R., M.E., T.C. and L.P. have contributed to the CXRF data acquisition. All authors have given approval to the final version of the manuscript.

Conflicts of interest

There is no conflict of interest to declare.