Dounia El Hamrani

PhD Véronique Vives

MSc Rebecca Buchholz

PhD William Même

Cécile Factor

PhD Stefanie Fingerhut

PhD Michael Sperling

Uwe Kärst

PhD Philippe Robert

PhD Sandra Même
email: sandra.meme@cnrs.fr

PhD Dounia El Hamrani

PhD Cecile Factor

PhD Uwe Karst

Effect of Long-Term Retention of Gadolinium on Metabolism of Deep Cerebellar Nuclei After Repeated Injections of Gadodiamide in Rats

Keywords: gadolinium based contrast agent, cerebellum, deep cerebellar nuclei, gadolinium retention, MRI, 1 H MRS, LA-ICP-MS, histology

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

Introduction

Gadolinium is a lanthanide metal with paramagnetic properties extensively used as a contrast agent for magnetic resonance imaging (MRI). For the last 30 years, over 450 million patients have received gadolinium based contrast agent (GBCA) and these have been prescribed in 30-45% of clinical protocols. [START_REF] Hao | MRI contrast agents: Basic chemistry and safety[END_REF][START_REF] Kanal | Gadolinium based contrast agents (GBCA): Safety overview after 3 decades of clinical experience[END_REF][START_REF] Mcdonald | Gadolinium Retention: A Research Roadmap from the 2018 NIH/ACR/RSNA Workshop on Gadolinium Chelates[END_REF] However, non-chelated gadolinium (Gd 3+ form) is highly toxic in biological systems given its similar size as calcium ion (Ca 2+ ). [START_REF] Sherry | Primer on gadolinium chemistry[END_REF] To avoid this toxicity, Gd 3+ is chelated with polyaminocarboxylate ligands which can be either macrocyclic or linear. In terms of thermodynamic and kinetic stability, it has been shown that macrocyclic chelates are more stable than their linear counterparts as they demonstrate a lower potential of gadolinium release. [START_REF] Tedeschi | Gadolinium retention in the body: what we know and what we can do[END_REF] GBCA are extracellular agents which are rapidly cleared from the intravascular space through kidney excretion in patients with normal renal function (90% eliminated during the first 12 hours). [START_REF] Aime | Biodistribution of gadolinium-based contrast agents, including gadolinium deposition[END_REF] Consequently, GBCA are not supposed to distribute into the central nervous system (CNS) extracellular fluid except if the blood-brain barrier (BBB) is impaired (e.g. tumors, multiple sclerosis, inflammation, irradiation treatment). [START_REF] Errante | Progressive Increase of T1 Signal Intensity of the Dentate Nucleus on Unenhanced Magnetic Resonance Images Is Associated With Cumulative Doses of Intravenously Administered Gadodiamide in Patients With Normal Renal Function, Suggesting Dechelation[END_REF][START_REF] Quattrocchi | Gadodiamide and Dentate Nucleus T1 Hyperintensity in Patients With Meningioma Evaluated by Multiple Follow-Up Contrast-Enhanced Magnetic Resonance Examinations With No Systemic Interval Therapy[END_REF] Nevertheless, Kanda et al. highlighted the presence of a hypersignal on unenhanced T1-weighed MR images in deep grey matter structures of the brain (deep cerebellar nuclei, DCN and globus pallidus, GP) among patients with normal renal function who had received cumulative doses of GBCA. [START_REF] Kanda | High Signal Intensity in the Dentate Nucleus and Globus Pallidus on Unenhanced T1-weighted MR Images: Relationship with Increasing Cumulative Dose of a Gadolinium-based Contrast Material[END_REF] Since their seminal article, a positive correlation between this hypersignal in GP and DCN on unenhanced T1-weighed images and the number of repeated intravenous injections of GBCA (up to 6) for MRI exams has been clearly established. [START_REF] Errante | Progressive Increase of T1 Signal Intensity of the Dentate Nucleus on Unenhanced Magnetic Resonance Images Is Associated With Cumulative Doses of Intravenously Administered Gadodiamide in Patients With Normal Renal Function, Suggesting Dechelation[END_REF][START_REF] Quattrocchi | Gadodiamide and Dentate Nucleus T1 Hyperintensity in Patients With Meningioma Evaluated by Multiple Follow-Up Contrast-Enhanced Magnetic Resonance Examinations With No Systemic Interval Therapy[END_REF][START_REF] Kanda | High Signal Intensity in the Dentate Nucleus and Globus Pallidus on Unenhanced T1-weighted MR Images: Relationship with Increasing Cumulative Dose of a Gadolinium-based Contrast Material[END_REF][START_REF] Kanda | High Signal Intensity in Dentate Nucleus on Unenhanced T1weighted MR Images: Association with Linear versus Macrocyclic Gadolinium Chelate Administration[END_REF][START_REF] Ramalho | High Signal Intensity in Globus Pallidus and Dentate Nucleus on Unenhanced T1-weighted MR Images: Evaluation of Two Linear Gadolinium-based Contrast Agents[END_REF] Moreover, it has been extensively documented that repeated injections of linear GBCAs lead to gadolinium deposition in DCN as opposed to macrocyclic GBCAs. [START_REF] Kanda | High Signal Intensity in Dentate Nucleus on Unenhanced T1weighted MR Images: Association with Linear versus Macrocyclic Gadolinium Chelate Administration[END_REF][START_REF] Cao | Signal Change in the Dentate Nucleus on T1-Weighted MR Images After Multiple Administrations of Gadopentetate Dimeglumine Versus Gadobutrol[END_REF][START_REF] Yoo | Evaluation of Gadolinium Retention After Serial Administrations of a Macrocyclic Gadolinium-Based Contrast Agent (Gadobutrol): A Single-Institution Experience With 189 Patients[END_REF][START_REF] Bae | Gadolinium deposition in the brain: association with various GBCAs using a generalized additive model[END_REF][START_REF] Radbruch | Gadolinium Retention in the Dentate Nucleus and Globus Pallidus Is Dependent on the Class of Contrast Agent[END_REF] Most of the studies were conducted by inductively coupled plasma mass spectrometry (ICP-MS) on post-mortem samples or resections pieces. They have shown the presence of non-negligible quantities of gadolinium in brain tissue of patients. [START_REF] Mcdonald | Intracranial Gadolinium Deposition after Contrastenhanced MR Imaging[END_REF][START_REF] Kanda | Gadolinium-based Contrast Agent Accumulates in the Brain Even in Subjects without Severe Renal Dysfunction: Evaluation of Autopsy Brain Specimens with Inductively Coupled Plasma Mass Spectroscopy[END_REF] Several histological studies have demonstrated that gadolinium retention occurred without alterations of the BBB. [START_REF] Mcdonald | Intracranial Gadolinium Deposition after Contrastenhanced MR Imaging[END_REF][START_REF] Kanda | Gadolinium-based Contrast Agent Accumulates in the Brain Even in Subjects without Severe Renal Dysfunction: Evaluation of Autopsy Brain Specimens with Inductively Coupled Plasma Mass Spectroscopy[END_REF] Similar findings were reported in non-clinical rodent models assessed by MRI, ICP-MS and histology. [START_REF] Robert | Methodological Aspects for Preclinical Evaluation of Gadolinium Presence in Brain Tissue: Critical Appraisal and Suggestions for Harmonization-A Joint Initiative[END_REF] Recently, Robert et al. have demonstrated that gadolinium presence persists at longterm post-injections in brain rats. [START_REF] Robert | One-year Retention of Gadolinium in the Brain: Comparison of Gadodiamide and Gadoterate Meglumine in a Rodent Model[END_REF] One year after the last injection of one linear GBCA (gadodiamide), gadolinium has been detected by ICP-MS in cerebellum (2.45 nmol/g), cortical brain (1.23 nmol/g), subcortical brain (1.52 nmol/g) and brainstem (0.74 nmol/g). In the case of macrocyclic GBCA (gadoterate), gadolinium concentrations were in the range of the background noise in these structures (from 0.05 to 0.09 nmol/g). Moreover, gadolinium detected after gadodiamide was found to be no longer in its original form but bound to macromolecules.

Several questions are still remaining, including if long-term gadolinium deposition has potential adverse health effects. In our study, we decided to address this question by following rats throughout one year after they received cumulative doses of a linear GBCA (gadodiamide).

Thereby, we investigated until one year post-injections if : (i) deposition of GBCA could induce cellular alterations detectable by 1 H magnetic resonance spectroscopy ( 1 H MRS); (ii) long-term hypersignal on unenhanced T1-weighted MR images is correlated to gadolinium deposition within DCN by laser ablation ICP-MS (LA-ICP-MS) and (iii) histological integrity of cerebellar tissue is compromised.

Materials and Methods

Animals and contrast agent injection

All animal experiments were conducted in accordance with French regulations and in compliance with the European Union Directives 2010/63/EU. Twenty female Sprague-Dawley rats aged 10 weeks (SPF/OFA female rats, Charles River, L'Arbresle, France) were used in this study. The animals were housed under a 12 h light/dark cycle at constant temperature of 23±1°C with free access to food and water.

Two experimental groups (10 rats per group) were compared: one group received gadodiamide intravenous injections and the other control group received 0.9% saline intravenous injections.

All injections were performed following a defined published protocol under general anesthesia (3%-3.5% isoflurane; IsoFlo, Axience, Pantin, France). [START_REF] Robert | T1-Weighted Hypersignal in the Deep Cerebellar Nuclei After Repeated Administrations of Gadolinium-Based Contrast Agents in Healthy Rats: Difference Between Linear and Macrocyclic Agents[END_REF] The gadodiamide (Omniscan®, 0.5 M, GE Healthcare, Chalfont-St-Giles, United Kingdom) group received 20 intravenous injections of 0.6 mmol of gadolinium per kilogram (1.2 mL/kg) over a period of 5 weeks (4 daily and consecutive injections per week). The daily dose of 0.6 mmol gadolinium per kilogram is equivalent to the usual human dose of GBCAs (0.1 mmol of gadolinium per kilogram or 0.2 mL/kg), after adjustment for body surface area as recommended by the Food and Drug Administration [START_REF] Fda | Guidance for Industry: Estimating the Maximum Safe Starting Dose in Initial Clinical Trials for Therapeutics in Adult Healthy Volunteers[END_REF] . A clinical follow up of animals was regularly performed.

MR experiments

During the MR experiments, the animals were positioned in a custom-built cradle to immobilize the head. They were anesthetized during the MR experiment with 1.5%-2% isoflurane and a mixture of O2/N2O (1:1) with an output of 0.5 L/min. Respiration was monitored during the whole experiment using an air pillow and body temperature was maintained constant at 37°C by a warm-water circulation system. MR acquisitions were performed on a 7T horizontal ultrashielded superconducting magnet dedicated to small animal imaging (70/16 Bruker Pharmascan, Wissembourg, France) and equipped with a 230 mT/m gradient set. A Bruker 38 mm inner diameter birdcage coil was used for both [START_REF] Hao | MRI contrast agents: Basic chemistry and safety[END_REF] H transmission and reception.

All rats underwent the same protocol (figure 1). MR experiments were performed at M0 (one week after the last injection; 0 month of washout period), M1 (six weeks after the last injection; 1 month of washout period) and M13 (54-55 weeks after the last injection; 13 months of washout period). for water suppression was achieved to assess only cerebellar metabolites. An OVS module (outer volume suppression) was used to eliminate signal outside the voxel. Localized first and second order shim terms were adjusted within the voxel.

Quantification of T1-weighted MR Image

Quantification was performed in a blinded manner. Two regions of interest (ROI) were positioned in the most visible right or left deep cerebellar nuclei (DCN), and in the brainstem (reference). Signal intensity was calculated as the ratio between the signal of the more visible of the two DCN signal and the brainstem signal (taken as a reference).

Spectral analysis and quantification

Spectra were analyzed on CSIapo software developed by Yann Le Fur (CRMBM, Marseille, France) and Helene Ratiney (CREATIS -INSA, Lyon, France) which is an interface for quantification algorithm QUEST (quantitation based on quantum estimation). [START_REF] Ratiney | Time-domain semi-parametric estimation based on a metabolite basis set[END_REF] QUEST is a linear combination model decomposing free induction decay (FID) signal in temporal domain.

QUEST uses a database to fit a weighted combination of metabolite signals and then to obtain a quantitation in arbitrary unit (A.U). This database is simulated through GAVA (GAmma Visual Analysis) which is used for modelling metabolites signals including their characteristics (chemical shift, amplitude and phase) and also experimental parameters (magnetic field and echo time). [START_REF] Soher | GAVA: Spectral simulation for in vivo MRS applications[END_REF] Cerebral metabolites quantified in DCN are the following: creatine and phosphocreatine (Cr+PCr); N-Acetyl Aspartate (NAA); choline, phosphocholine and glycérophosphocholine (tCho); glutamate (Glu); glutamate+glutamine (Glx); Taurine (Tau) and myo-Inositol (mI) (figure 2).

Sample collection

Following MR experiments, animals were sacrificed under general anesthesia and analgesia (isoflurane, 5%). The sacrifice consisted in exsanguination and perfusion of the blood system with saline. Immediately after euthanasia of rats, the skull was opened and the brain was taken off. The cerebellum was sampled and placed in OCT medium and then immediately cooled down in isopenthane (-60°C) until complete freezing. Frozen specimens were stored at -80°C.

The cerebellum was cut at -20°C in serial 7 µm-thick sections at the level of deep nuclei, according to the atlas of Paxinos and Watson [START_REF] Paxinos | The Rat Brain in Stereotaxic Coordinates[END_REF] . The appropriate level of section were validated with cresyl violet staining. The rostral sections of the DCN were used for immunostaining protocols and the caudal portions were sampled for LA-ICP-MS experiments.

Histology

Slides at the level of DCN were used for the immunostaining protocol (n=6/group) in purpose to detect 3 targets of interest: GFAP (glial fibrillary acidic protein, astrocytes maker), synaptophysin (SYP; neurons) and CD68 (microglial cells). Alexa 488 was chosen as the fluorescent dye to detect the targeted molecule. The primary antibodies and corresponding secondary antibody were selected as shown in table 1. The immunostaining protocol was performed for each marker as detailed in table 2. At the end of the immunostaining, slides were cover slipped with a medium containing DAPI (4′,6-diamidino-2-phenylindole) for nuclear counterstain.

After immunostaining, images of DCN slides were acquired by epifluorescence microscopy using a FITC filter cube with similar image acquisition parameters for all slides (1280 x 1024 pixels, exposure time 300 ms, gain 1, medium contrast). Semi-quantitative analysis of GFAP, SYP and CD68 signals were performed by evaluating the signal distribution and its prevalence on a scale from 0 (no signal) to 3 (high density of signal) within the deep cerebellar nuclei area.

LA-ICP-MS

For quantitative LA-ICP-MS analysis, matrix matched standards based on gelatin were used for external calibration. Seven gadolinium standards with concentrations ranging from 0 to 50 µg/g were prepared by diluting Gd ICP Standard (TraceCERT®, 1000 mg/L Gd, Sigma-Aldrich, MO, USA) and spiking 10% w/w gelatin (Grüssing GmbH, Filsum, Germany). These standards were heated up to 40°C and homogenized. For quantification of iron, copper and zinc, multielement standards with concentrations ranging from 0 to 100 µg/g per element were prepared in the same way as the Gd standards. Concentrations of the prepared standards were verified by bulk analysis with ICP-MS (iCap TQ, Thermo Fisher, Bremen, Germany) after acidic digestions.

Gelatin-based standards and the samples (n=6/group) were sliced into 10 µm thick sections with a cryotome (CryoStar NX70, Thermo Fisher, Bremen, Germany) and mounted onto glass slides.

LA-ICP-MS analysis was performed with a laser ablation system (LSX G2+, Cetac Technologies, Omaha, USA) equipped with 213 nm Nd:YAG laser, a two-volume HelEX ablation cell and connective tygon tubings, connected to a ICP-MS (iCap TQ, Thermo Fisher, Bremen, Germany) equipped with Ni sampler and skimmer cone and a quartz injector with an inner diameter of 2.5 mm.

Laser energy was adjusted to allow for complete ablation of the samples. For calibration, ten parallel lines and for the samples, the whole brain section was ablated linewise with a laser spot size of 25 µm and a scan speed of 75 µm/s.

Statistical analysis

Data are given as mean ± SEM. Statistical analyses were performed using Prism 5.1 (GraphPad, La Jolla, CA, USA). Non-parametric t test Mann-Whitney was used on weight, MRI and 1 H MRS data for comparison between saline and gadodiamide groups. A p<0.05 was considered statistically significant.

Results

Sanitary following of animals

Four rats of the gadodiamide group died during the study period: 1 unexplained death (at M0), 3 ethically sacrificed (one at M0 and 2 at M1) because signs of pain induced by visible ulcerative and squamous skin lesions. One rat in the saline group died at M0 during the anesthesia.

Qualitative analysis of T1-weighted MR images

Figure 3 shows examples of typical non enhanced T1-weighted images obtained for both groups (saline and gadodiamide) 1 week (M0), 6 weeks (M1) and 54-55 weeks (M13) after the end of the injections. Specific DCN signal enhancement (arrows) is present for all rats of the gadodiamide group.

The hyperintensity was present on the images as early as the week following the end of the injections and persisted over time even 1 year after the end of the injections.

Quantitative analysis of signal intensity in T1-weighed images

The ratio between the signals of the DCN and the brainstem for M0, M1 and M13 are presented on figure 4. There is a significant increase of the ratio DCN/brainstem for the gadodiamide group at M0 (1 week after the end of the injections) and M1 (6 weeks after the end of the injections). This increase in DCN signal intensity lasted up to 1 year after the end of the injections.

At M0, the ratio for DCN signal intensity to brainstem increased by 7.2% in gadodiamide group (1.060±0.010) compared to saline group (0.989±0.01). At M1, the ratio for DCN signal intensity to brainstem was elevated of 7.6% for gadodiamide group (1.078±0.014) vs saline group (1.002±0.018). At M13, the ratio for DCN signal intensity to brainstem was greater of 4.7% for gadodiamide group (1.033±0.011) in comparison of saline group (0.9862±0.008).

MR Spectroscopy

Figure 5 represents the concentration of metabolites measured in the DCN at M0 (1 week postinjections), M1 (6 weeks post-injections) and M13 (54-55 weeks post-injections). MRS allows to detect three categories of metabolites: (i) cellular homeostasis (creatine, choline, taurine); (ii) excitatory neurotransmitter (glutamate) and (iii) metabolites specific to a cellular compartment (NAA for neurons and myo-Inositol for glial cells). No variation among these markers was detected between gadodiamide and saline groups at M0, M1 and M13.

LA-ICP-MS

The element distribution for Gd, P, Fe, Cu and Zn in rat brain observed after repeated injection of either gadodiamide (left side) or saline solution (right side) are shown in figure 6.

Corresponding microscopic images of the analysed thin sections are also shown (a,b) for comparison. Concentrations up to 64 nmol/g, in a few cases even higher, were found in the brain of rats treated with gadodiamide. Highest concentrations were found in the region of DCN, with average concentrations ranging from 25 to 35 nmol/g in the three substructures. For the rat brain injected with saline solution, no Gd could be detected.

No clear correlation between gadolinium and phosphorous, copper or zinc can be observed, but the highest Gd concentrations are found in the region with highest iron concentrations. The average iron concentrations are slightly lower (497 nmol/g) in the DCN of the gadodiamide sample compared to the untreated animal (665 nmol/g).

Immunofluorescent analysis

Semi-quantitative analysis of cerebellar cell populations (astrocytes, neurons and glial cells) were performed at 1-year post-injections in gadodiamide and saline groups.

GFAP is a marker for astrocyte cells (density and thickness of astrocyte processes) and allowed to determine their distribution (perineuronal and perivascular). Synaptophysin is a neuronal marker which provide a morphological information on perikaryon. CD68 is a marker for microglial cells which indicate their distribution (perivascular activated microglial) and their morphology (diffuse neuropil) (figure 7a).

No morphological changes were observed between gadodiamide and saline groups based on the evaluation of immunofluorescent analysis of various cells populations in the deep cerebellar nuclei area (figure 7b).

Discussion

The main goal of our study was to evaluate the long-term retention of a linear gadolinium based contrast agent (GBCA; gadodiamide) within the cerebellum, and more specifically in the deep cerebellar nuclei (DCN) after 1-year post-injections. We used both in vivo MR techniques (MRI and 1 H MRS) as well as quantitative chemical (LA-ICP-MS) and histological approaches.

In our experimental design, we used a rodent model receiving cumulative doses of a linear GBCA (12 mmol of gadolinium per kilogram) which was previously demonstrated to lead to a cerebellar gadolinium accumulation at 5 weeks post-injections and also at 1 year postinjections. [START_REF] Robert | One-year Retention of Gadolinium in the Brain: Comparison of Gadodiamide and Gadoterate Meglumine in a Rodent Model[END_REF][START_REF] Robert | T1-Weighted Hypersignal in the Deep Cerebellar Nuclei After Repeated Administrations of Gadolinium-Based Contrast Agents in Healthy Rats: Difference Between Linear and Macrocyclic Agents[END_REF][START_REF] Robert | Linear Gadolinium-Based Contrast Agents Are Associated With Brain Gadolinium Retention in Healthy Rats[END_REF] Animal welfare was followed throughout our longitudinal MR study to monitor any physiological changes induced by repeated injections of gadodiamide.

This clinical monitoring allowed us to notice the apparition of skin lesions among our animals (3 out of 10 rats) between 1 and 5 weeks post-injections. Lohrke et al. have reported similar observations of skin injuries among 4 out of 10 rats exposed to cumulative doses of gadodiamide (50 mmol of gadolinium per kilogram; 4 times higher than in our protocol). [START_REF] Lohrke | Histology and Gadolinium Distribution in the Rodent Brain After the Administration of Cumulative High Doses of Linear and Macrocyclic Gadolinium-Based Contrast Agents[END_REF] In their protocol, a high concentration of gadolinium was quantified in the skin after gadodiamide exposure (1472 nmol/g) and not in the case of others GBCAs (gadopentetate dimeglumine, gadobutrol and gadoteridol). Moreover, several studies have shown that there is an accumulation of gadolinium in tissues such as bone and skin both in humans and rats with normal renal function. [START_REF] Tweedle | Biodistribution of radiolabeled, formulated gadopentetate, gadoteridol, gadoterate, and gadodiamide in mice and rats[END_REF][START_REF] Pietsch | Long-term retention of gadolinium in the skin of rodents following the administration of gadolinium-based contrast agents[END_REF][START_REF] White | Comparison of Gd(DTPA-BMA) (Omniscan) Versus Gd(HP-DO3A) (ProHance) Relative to Gadolinium Retention in Human Bone Tissue by Inductively Coupled Plasma Mass Spectroscopy[END_REF] Throughout our longitudinal study, we observed a T1 hypersignal in cerebellum on unenhanced MR images at 1 and 5-weeks post-injections which was persistent until 13 months postinjections. This observation is in agreement with a previous report on the same rat model at 1year post-injections, gadolinium concentration was quantified up to 2.45 nmol/g within cerebellum. [START_REF] Robert | One-year Retention of Gadolinium in the Brain: Comparison of Gadodiamide and Gadoterate Meglumine in a Rodent Model[END_REF] Our results obtained by LA-ICP-MS demonstrated that long-term gadolinium retention occurred preferentially in DCN. This result is consistent with previous studies that showed preferential gadolinium accumulation in this cerebellar structure at an earlier point (8 weeks post-injections). [START_REF] Lohrke | Histology and Gadolinium Distribution in the Rodent Brain After the Administration of Cumulative High Doses of Linear and Macrocyclic Gadolinium-Based Contrast Agents[END_REF] Given the high concentration of metals within DCN, the most likely hypothesis would be that GBCA dechelated through a transmetalation of gadolinium to iron, cupper or zinc. The limit of LA-ICP-MS method lies in its incapacity to identify whether gadolinium is present under its chelated or dechelated form.

Despite gadolinium retention within DCN, we did not observed any morphological modification of various cellular populations (neurons, astrocytes and microglia) at 1-year postinjections. Previous studies at earlier time points (8 and 20 weeks post-injections) are concordant with our results. [START_REF] Lohrke | Histology and Gadolinium Distribution in the Rodent Brain After the Administration of Cumulative High Doses of Linear and Macrocyclic Gadolinium-Based Contrast Agents[END_REF][START_REF] Smith | Clearance of Gadolinium from the Brain with No Pathologic Effect after Repeated Administration of Gadodiamide in Healthy Rats: An Analytical and Histologic Study[END_REF] So far, histological studies only explored morphological features. Furthers studies should focus on inflammatory markers to determine whether gadolinium retention in DCN could induce a local inflammation.

Our main goal was to identify whether repeated injections of gadodiamide could lead to metabolic alterations at short (1 and 6 weeks post-injections) and long-term (1-year postinjections) using 1 H MRS. To date, few data are available for cerebellar metabolism following repeated injections of linear GCBA. Our main observation was that long-term retention of gadodiamide did not induce any detectable metabolic changes in the cerebellum after 1-year post-injections. In accordance with literature, [START_REF] Robert | Methodological Aspects for Preclinical Evaluation of Gadolinium Presence in Brain Tissue: Critical Appraisal and Suggestions for Harmonization-A Joint Initiative[END_REF] F-fluorodeoxyglucose positron emission tomography ( 18 F-FDG-PET) imaging of rats who had received a cumulative dose of gadodiamide (13.2 mmol/kg over 7 weeks) did not reveal any abnormal glucose uptake in the DCN, and thus even with chronic cerebral hypoperfusion (model of aging and neurodegenerative diseases). [START_REF] Arena | Gadolinium presence, MRI hyperintensities, and glucose uptake in the hypoperfused rat brain after repeated administrations of gadodiamide[END_REF] However, a [START_REF] Robert | Methodological Aspects for Preclinical Evaluation of Gadolinium Presence in Brain Tissue: Critical Appraisal and Suggestions for Harmonization-A Joint Initiative[END_REF] F-FDG-PET study had shown a lower maximum standardized uptake value (SUVmax) in DCN of patients who had received repeated injections of GBCAs (3 to 6 injections without distinction between macrocyclic and linear forms) compared to those who had not received, which might indicate a decrease of glucose metabolism. [START_REF] Bauer | Do Gadolinium-Based Contrast Agents Affect 18 F-FDG PET/CT Uptake in the Dentate Nucleus and the Globus Pallidus? A Pilot Study[END_REF] Nevertheless, it should be taken under consideration that 1 H MRS may not be sensitive enough to detect any subtle modifications of cerebellar metabolism. Indeed, one technical limit of 1 H MRS is its inability to detect molecules below mM range. It also appears that metabolites involved in cellular homeostasis and excitatory neurotransmitter (glutamate) which are detectable by 1 H MRS may not be a target of dechelated gadolinium. Another methodological limit of in vivo [START_REF] Hao | MRI contrast agents: Basic chemistry and safety[END_REF] H MRS is that a technique sensitive only to molecules with a high degree of rotational molecular motion. [START_REF] Williams | Natural Abundance Carbon-13 Nuclear Magnetic Resonance Spectra of the Canine Sciatic Nerve[END_REF] Moreover, it has been recently reported that gadolinium linked preferentially to macromolecules (larger to 66.5 kDa in insoluble fraction). [START_REF] Robert | One-year Retention of Gadolinium in the Brain: Comparison of Gadodiamide and Gadoterate Meglumine in a Rodent Model[END_REF] In the case of gadolinium bounded to macromolecules such as proteins or lipids and especially within the membrane bilayer, any alteration could not be detectable by [START_REF] Hao | MRI contrast agents: Basic chemistry and safety[END_REF] H MRS.

In our study, we studied only one representative of linear GBCAs which is neutral in terms of charge. Indeed, linear ionic GBCAs such as gadobenate dimeglumine and gadopentetate dimeglumine induce also gadolinium retention in the cerebellum of patients. [START_REF] Ramalho | High Signal Intensity in Globus Pallidus and Dentate Nucleus on Unenhanced T1-weighted MR Images: Evaluation of Two Linear Gadolinium-based Contrast Agents[END_REF][START_REF] Radbruch | Gadolinium Retention in the Dentate Nucleus and Globus Pallidus Is Dependent on the Class of Contrast Agent[END_REF][START_REF] Schlemm | Gadopentetate but not gadobutrol accumulates in the dentate nucleus of multiple sclerosis patients[END_REF] Furthermore, linear ionic GBCA have been previously shown to decrease the area under the peak of choline in breast and cerebral tumors. [START_REF] Lenkinski | Interaction of gadolinium-based MR contrast agents with choline: Implications for MR spectroscopy (MRS) of the breast[END_REF][START_REF] Baltzer | Effect of contrast agent on the results of in vivo1H MRS of breast tumors -is it clinically significant?: EFFECT OF CONTRAST AGENT ON 1H MRS OF BREAST TUMORS[END_REF][START_REF] Murphy | The effect of Gd-DTPA on T1-weighted choline signal in human brain tumours[END_REF] The peak of choline is widely used in diagnostic as an index for cellular density of the tumor and the degree of tumor infiltration into brain tissue. [START_REF] Horská | Imaging of Brain Tumors: MR Spectroscopy and Metabolic Imaging[END_REF] It will be highly interesting to investigate the impact of linear ionic GBCAs on 1 H MRS spectra in brain. In this purpose, further studies must be conducted to evaluate if they can alter choline peak signal and thereby diagnostic.

To conclude, we demonstrate that cumulative administration of a linear and nonionic GBCA (gadodiamide) induces a retention of gadolinium within DCN at 1-year post-injections and thus without altering metabolic biomarkers of cellular homeostasis and an excitatory neurotransmitter (glutamate). Although, histological analysis did not show any alterations of Tables

  38 seconds. PRESS (point resolved spectroscopy) sequence was acquired with the following parameters: voxel size= 3 x 2 x 1.5 mm 3 ; TR/TE=2775 ms/16 ms; spectral bandwidth= 4006.41 Hz (13.34 ppm); 2048 points; 970 averages; acquisition time= 44 min 52 seconds. T1-weighted images were used to place the voxel in the left DCN with an extended care to avoid brainstem and subcutaneous lipids. A VAPOR module (variable pulse power and optimized relaxation delays)

Figure 1 :

 1 Figure 1: MRI, 1 H MRS and injection scheme. MR experiments are performed at M0 (Week

Figure 2 :

 2 Figure 2: (A) Voxel position in the left dentate cerebellar nuclei (DCN) on T1-weighed

Figure 3 :

 3 Figure 3: T1-weighted Ig-FLASH images at 7T of saline and gadodiamide rats at M0, M1

Figure 4 :

 4 Figure 4: Delay Effect -Quantitative analysis of enhancement at M0, M1 and M13.

Figure 5 :

 5 Figure 5: MR Spectroscopy quantitation obtained with QUEST algorithm at delay M0,

Figure 6 :

 6 Figure 6: LA-ICP-MS analysis of rat brains after repeated injections of gadodiamide (left)

Figure 7 :

 7 Figure 7: (a) Representative images of GFAP and CD68 immunostaining within deep

Table 1 : Primary antibodies and corresponding antibodies for immunostaining protocol

 1

	Primary antibody	Clone	Secondary antibody
	Mouse anti-CD68 IgG1	ED1	Anti-mouse IgG1 A488
	Rabbit anti-SYP	YE269	Anti-rabbit IgG A488
	Rabbit anti-GFAP	polyclonal	Anti-rabbit IgG A488

Table 2 : Steps for immunostaining protocol

 2

	Step	Reagent	Condition
	Fixation of slides	Formalin 4%	10 min at room temperature
	Rinsing	PBS1x	3 x 5 min
		BSA 3% /
	Serum blocking		1h at room temperature
		Goat serum 10% in PBS1x
		Anti-GFAP 1/1000 e	1h at room temperature
	Primary antibody incubation	Anti-CD68 1/200 e	1h at room temperature
		Anti-SYP 1/600 e	1h at room temperature
	Rinsing	PBS 1x	3 x 5 min
	Secondary antibody	Anti-IgG A488 1/500 e	1h at room temperature
	Rinsing	PBS1x	3 x 5 min

J. Leiten and M. Rasschaert (Guerbet Group, FranceThis work was supported by Region Centre-Val de Loire (France) (Grant number: n°201400093609).

DCN, further studies are required to elucidate the putative clinical long-term consequences of gadolinium retention (e.g. inflammatory markers) as well as the mechanism underlying such a retention.


Richard-Nicolas Verrone

Charles Moisset

Fabien Lemarchand

Andrea Campos

Martiane Cabié

Carine Perrin-Pellegrino

Julien Lumeau

Jean-Yves Natoli

Konstantinos Iliopoulos
email: konstantinos.iliopoulos@fresnel.fr

Thickness-Dependent Optical Nonlinearities of Nanometer-Thick Sb 2 Te 3 Thin Films: Implications for Mode-locking and Super-Resolved Direct Laser Writing

Keywords: Ultrafast nonlinear optics, 2D materials, Z-scan, chalcogenides, thin films

come

INTRODUCTION

After the successful isolation of graphene layers and the intense research carried out concerning their nonlinear optical properties, 2D materials are very widely investigated in order to be used for photonic applications. This is currently a field of very intense scientific research and many publications are already existing. [START_REF] You | Nonlinear Optical Properties and Applications of 2D Materials: Theoretical and Experimental Aspects[END_REF][START_REF] Yamashita | Nonlinear Optics in Carbon Nanotube, Graphene, and Related 2D Materials[END_REF][START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF][START_REF] Liu | Recent Advances of 2D Materials in Nonlinear Photonics and Fiber Lasers[END_REF][START_REF] Guo | 2D Layered Materials: Synthesis, Nonlinear Optical Properties, and Device Applications[END_REF][START_REF] Autere | Nonlinear Optics Based on Two-dimensional Layered Materials[END_REF][START_REF] Wang | Saturable Absorption in 2D Nanomaterials and Related Photonic Devices[END_REF][START_REF] Wu | Kerr Nonlinearity in 2D Graphdiyne for Passive Photonic Diodes[END_REF][START_REF] Ge | Broadband Nonlinear Photoresponse of 2D TiS 2 for Ultrashort Pulse Generation and All-Optical Thresholding Devices[END_REF][START_REF] Jiang | Ultrathin Metal-Organic Framework: An Emerging Broadband Nonlinear Optical Material for Ultrafast Photonics[END_REF][START_REF] Lu | Broadband Nonlinear Optical Response in Few-Layer Antimonene and Antimonene Quantum Dots: A Promising Optical Kerr Media with Enhanced Stability[END_REF][START_REF] Jiang | Two-Dimensional MXenes: From Morphological to Optical, Electric, and Magnetic Properties and Applications[END_REF][START_REF] Liu | Optical Properties and Applications for MoS 2 -Sb 2 Te 3 -MoS 2 Heterostructure Materials[END_REF] Several 2D materials exhibit unique optical and nonlinear optical (NLO) properties which are mainly due to their topological insulating characters. [START_REF] Liu | Recent Advances of 2D Materials in Nonlinear Photonics and Fiber Lasers[END_REF][START_REF] Wang | Ultrafast Nonlinear Excitation Dynamics of Black Phosphorus Nanosheets from Visible to Mid-Infrared[END_REF] More specifically, these materials have an insulating character in the bulk, while conducting states appear at the surface. This results to a band structure which is similar to that of graphene, showing a Dirac-like linear band dispersion. [START_REF] Zhang | Topological Insulators in Bi 2 Se 3 , Bi 2 Te 3 and Sb 2 Te 3 with a Single Dirac Cone on the Surface[END_REF] Such materials are currently the most promising candidates for applications requiring significant NLO responses and in several cases it has been shown that they can have superior performances compared to those of graphene. [START_REF] Guo | 2D Layered Materials: Synthesis, Nonlinear Optical Properties, and Device Applications[END_REF][START_REF] Moisset | Giant Ultrafast Optical Nonlinearities of Annealed Sb 2 Te 3 Layers[END_REF] Moreover, the broadband character of their optical and nonlinear optical responses enhances their importance for photonic applications. [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF][START_REF] Moisset | Saturable Absorption Optimization of Silica Protected Thin Sb 2 Te 3 Layers towards Super-Resolution Applications[END_REF] The relation between the thickness of 2D materials and their nonlinearities is still unclear, despite their importance for many different fields of photonics and the intense research currently carried out in this scientific domain. This is a significant scientific problem nowadays which requires more and thorough studies. Shedding light on this aspect will provide strong enhancements to the efficiency of 2D materials in terms of applications. Research in this field has been significantly triggered by the rise of graphene, for this reason it is the mostly investigated material in this domain.

Among 2D materials, the Sb 2 Te 3 is well known for its very high nonlinear optical responses. More specifically, it has been shown in the past, that it exhibits a very high saturable absorption at the ns regime. [START_REF] Wei | Nano-Optical Information Storage Induced by the Nonlinear Saturable Absorption Effect[END_REF][START_REF] Liu | Origin of the Giant Optical Nonlinearity of Sb 2 Te 3 Phase Change Materials[END_REF][START_REF] Liu | Nonlinear Absorption of Sb-Based Phase Change Materials Due to the Weakening of the Resonant Bond[END_REF] This has been employed in order to surpass the diffraction limit and increase the information density of optical data storage media. [START_REF] Wei | Nano-Optical Information Storage Induced by the Nonlinear Saturable Absorption Effect[END_REF] Due to their topological insulator character, Sb 2 Te 3 thin films can have broadband optical nonlinearities. Indeed our group has demonstrated that such films can exhibit significant NLO responses at the visible and the IR parts of the spectrum (532 nm and 1064 nm respectively) using nanosecond laser pulses. [START_REF] Moisset | Saturable Absorption Optimization of Silica Protected Thin Sb 2 Te 3 Layers towards Super-Resolution Applications[END_REF] Very recently we have demonstrated the same broadband character at the ultrafast regime employing 600 fs duration laser pulses at both 515nm and 1030 nm. [START_REF] Moisset | Giant Ultrafast Optical Nonlinearities of Annealed Sb 2 Te 3 Layers[END_REF] More specifically, a very high saturable absorption has been obtained, which has been compared with current state-of-theart materials. [START_REF] Moisset | Giant Ultrafast Optical Nonlinearities of Annealed Sb 2 Te 3 Layers[END_REF] Due to its high saturable absorption, the Sb 2 Te 3 material is very widely used nowadays for modelocking of ultrafast laser systems. [START_REF] Boguslawski | Mode-Locked Er-Doped Fiber Laser Based on Liquid Phase Exfoliated Sb 2 Te 3 Topological Insulator[END_REF][START_REF] Kowalczyk | Sb 2 Te 3 -Deposited D-Shaped Fiber as a Saturable Absorber for Mode-Locked Yb-Doped Fiber Lasers[END_REF][START_REF] Liu | Generation of Dark Solitons in Erbium-Doped Fiber Lasers Based Sb 2 Te 3 Saturable Absorbers[END_REF][START_REF] Liu | 70-Fs Mode-Locked Erbium-Doped Fiber Laser with Topological Insulator[END_REF] Despite of the importance of this material for photonic applications, its nonlinear optical parameters are not sufficiently investigated.

An enhanced NLO response will improve the efficiency of currently used mode-locking systems and will provide novel ways to obtain super-resolved nanostructuring at the ultrafast regime. Indeed, the fabrication of efficient mode-locking materials requires a significantly high saturable absorption. The same NLO mechanism can result to the decrease of the size of a focused Gaussian beam. This can offer sub-wavelength resolutions during nanostructuring of a material with femtosecond pulses. In order to enhance the NLO efficiency of Sb 2 Te 3 thin films thorough studies of the optical nonlinearities are required. These studies are highly complex because they require a deep understanding of the laser-matter interaction of this material under femtosecond pulse irradiation. The difficulty is further increased, due to the fact that enhancing the NLO response requires a well-defined crystalline structure. This has been previously achieved by our group by means of a precise annealing of the Sb 2 Te 3 thin layers. [START_REF] Moisset | Giant Ultrafast Optical Nonlinearities of Annealed Sb 2 Te 3 Layers[END_REF] The enhancement of the optical nonlinearities is also expected to depend on the nanocrystal size. Moreover, taking into account that the significant nonlinearities of Sb 2 Te 3 thin films are attributed to their topological insulator character, a high dependence of the NLO response on the thin film thickness can be expected. Such studies have been carried out in the case of other materials, such as graphene and resulted to an enhancement of their NLO performances. [START_REF] Bao | Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers[END_REF] It has to be noted that there is currently no evidence concerning the relation of the nonlinear absorption and nonlinear refraction parameters of the Sb 2 Te 3 material with the film thickness and the nanocrystal size at the ultrafast regime.

The target of this work is to shed light upon this matter and trigger further research in this field.

The article is structured as follows. Firstly the thin film preparation is presented. Then the results obtained by X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), Energy-Dispersive X-Ray Spectroscopy (EDS) and Vis-IR spectroscopy studies are shown. All the aforementioned studies are of significant importance because they allow a precise and complete identification of the structure, morphology and optical properties of the layers. This is necessary in order to relate the NLO properties with the thin film structure and shed light upon the complex laser-matter interactions in the case of the Sb 2 Te 3 material. Finally, the NLO properties are investigated by means of the Z-scan technique employing 400 fs laser pulses at 1030 nm. The results are compared with those previously obtained in the literature for other 2D photonic materials.

RESULTS AND DISCUSSION

Thin films preparation. Sb 2 Te 3 thin films have been deposited on 2 mm thick B270 substrate using Electron Beam Deposition (EBD) by a Bühler SYRUSpro 710 machine, at room temperature with a 0.5 nmsec -1 deposition rate. A previously calibrated quartz microbalance has been employed during the thin film deposition in order to measure the thickness of the Sb 2 Te layers with a precision of ±0.2 nm. The Sb 2 Te 3 thin films thicknesses are ranging from 2.5 nm to 50 nm. The nanometer-thick Sb 2 Te 3 thin films have been then protected by a 2 nm thick SiO layer in order to avoid their oxidation after the deposition.

A proper annealing of the thin films is necessary in order to obtain a high nonlinearity, as the latter is highly dependent on the crystal structure. [START_REF] Moisset | Giant Ultrafast Optical Nonlinearities of Annealed Sb 2 Te 3 Layers[END_REF] The crystallization has been obtained by performing a 24 hour annealing at 300°C as previously demonstrated by our group. [START_REF] Moisset | Giant Ultrafast Optical Nonlinearities of Annealed Sb 2 Te 3 Layers[END_REF][START_REF] Moisset | Saturable Absorption Optimization of Silica Protected Thin Sb 2 Te 3 Layers towards Super-Resolution Applications[END_REF] Morphological studies and elemental analysis. The annealed layers have been initially visualized by Scanning Electron Microscopy using a backscatter electron detector that delivers a signal response from deeper subsurface layers of the sample and also shows crystal orientation contrast. [START_REF] Goldstein | Scanning Electron Microscopy and X-Ray Microanalysis[END_REF] SEM images were acquired at 10 kV acceleration voltage, which was the optimal one to observe the Sb 2 Te 3 surface between the silica protection layer and the substrate. Figures 1a-c, acquired at the same magnification for comparison, show nanocrystals with different sizes and contrasts, revealing their polycrystalline nature. Additionally, the observation of the total area shows that the crystallization occurs all over the films. Figure 1a corresponds to the 10 nm thick film, exhibiting nanocrystal length size ranging from 15 nm to 127 nm, with an average length of 46 nm. In Figures 1b and1c SEM images of the 30 nm and the 50 nm thick layers are shown, respectively. Figure 1b shows nanocrystal sizes ranging from 30 to 310 nm with an average length of 104 nm, whereas in Figure 1c the nanocrystal size varies from 46 to 447 nm, with an average length of 164 nm.

To further investigate the film growth and perform elemental analysis, a Scanning Transmission Electron Microscopy (STEM) study coupled to Energy-dispersive X-ray spectroscopy analyses have been performed. For this study, the samples were first carbon coated to prevent any charging effects, and ultrathin electron transparent cross sections were prepared by Focused Ion Beam (FIB) milling. In Figures 2a,b cross-sectional bright field STEM images of the 10 nm and 30 nm thick Sb 2 Te 3 films are presented, respectively. The annealed surfaces have been found to be slightly rough and the film thicknesses were in very good agreement with the nominal thicknesses. EDS spectra were acquired to check the chemical composition of the layers. (see scanned zones in Figures 2a and2b). The focused electron beam was in the range of a few nanometers, allowing to probe only the layer and prevent any contribution from either the glass substrate or the protective silicon oxide layer on top. The obtained spectra are presented in Figures 2c and2d for the two different sample thicknesses. The concentration deduced from the Sb (K) and Te (K) ionization peaks is respectively equal to 37 and 63 atomic percents in very good agreement with the nominal concentrations of the Sb 2 Te 3 thin films. For this measurement, K lines were preferred to L lines, as they are less absorbed by the sample itself.

X-Ray diffraction studies. X-Ray diffraction studies have been performed for all annealed films studied in this work. The studies have been carried out with a theta-theta configuration and CuKα radiation (λ=0.15418 nm) using an X'Pert MPD diffractometer, equipped with a rapid detector. The representative diagrams shown in Figures 1d-f have been obtained for the same thin films used for the SEM studies (10 nm, 30 nm, 50 nm samples, Figures 1a-c) to facilitate the comparison of the results. The XRD peaks obtained belong to the rhombohedral crystalline structure R m with 00l preferred orientation of the Sb 2 Te 3 material, in accordance with the results previously obtained by our group and other scientific groups. [START_REF] Moisset | Saturable Absorption Optimization of Silica Protected Thin Sb 2 Te 3 Layers towards Super-Resolution Applications[END_REF][START_REF] Moisset | Giant Ultrafast Optical Nonlinearities of Annealed Sb 2 Te 3 Layers[END_REF][START_REF] Wang | Characterization of Cr-Doped Sb 2 Te 3 Films and Their Application to Phase-Change Memory[END_REF][START_REF] Yin | Characterization of Nitrogen-Doped Sb 2 Te 3 Films and Their Application to Phase-Change Memory[END_REF][START_REF] Liu | Structural, Optical and Electrical Properties of Sb 2 Te 3 Films Prepared by Pulsed Laser Deposition[END_REF][30][START_REF] Lv | Preparation and Characterization of Sb 2 Te 3 Thin Films by Coevaporation[END_REF] In the case of the 7 nm thick layers and for lower film thicknesses no peaks appeared during the XRD studies. These films are though well crystallized (see Figure S1 in Supporting information for the 7 nm thick layer). We attribute this to a very low size of the crystallized grains which are under the detection level of the XRD technique. It has been also found that the XRD peaks were becoming narrower by increasing the film thickness. This indicates that the nanocrystals formed during the annealing become larger as the film thickness increases which is in very good agreement with the SEM studies. It is important to note that with the theta-theta configuration used, the families of probed diffracted planes are parallel to the substrate. Thus, the information deduced from the diffracted peak is only linked to these planes. It is the case for the crystal sizes that have been determined by means of the Scherrer equation [START_REF] Cullity | Elements of X-Ray Diffraction[END_REF] for each film and are shown in Table 1. It can be seen that the determined crystal sizes are similar to the thickness of the films, which demonstrates that the crystallization took place everywhere between the substrate and the silica protection layer, on the totality of the thickness.

Optical studies. Vis-NIR spectrophotometric studies have been performed by means of a

Perkin-Elmer Lambda 1050 with a specific module that allows performing the reflectance and transmittance measurement at 8° angle of incidence on the same point of a sample. The measurements have been performed from 400 nm to 1200 nm. Representative transmittance and reflectance curves are presented in Figures 3a, 3b for 6 different film thicknesses. The obtained curves indicate the broadband optical characteristics of the Sb 2 Te 3 , which are due to its low bandgap (between 0.14 eV and 0.20 eV). [START_REF] Park | Optical Properties of Pseudobinary GeTe, Ge 2 Sb 2 Te 5 , GeSb 2 Te 4 , GeSb 4 Te 7 , and Sb 2 Te 3 from Ellipsometry and Density Functional Theory[END_REF][START_REF] Olson | Optical Properties of Amorphous GeTe, Sb 2 Te 3 , and Ge 2 Sb 2 Te 5 : The Role of Oxygen[END_REF] In Figure 3c the reflectance, the transmittance and the absorption at the laser excitation wavelength used for the NLO studies (i.e. 1030 nm) are shown as a function of the film thickness for all the thin films investigated. Films with thicknesses up to 5 nm exhibit transmittances higher than 60%. The transmittance gradually decreases with increasing the film thickness. This is mainly due to a significant increase of the reflectance of the thin film layers as the thickness increases. Indeed a very high reflectance, of about 70% has been obtained in the case of the 30 nm thick Sb 2 Te 3 film. The absorption of the thin films has been found to increase with increasing the thin film thicknesses. An absorption maximum of about 35% has been obtained for the 8 nm thick Sb 2 Te 3 layer. A slight, gradual decrease of the absorption has been obtained for films thicker than 11 nm. This can be attributed to the fact that the crystal sizes and morphology highly depend on the film thickness, as shown in the previous paragraphs, which can have a high impact on the optical properties of the investigated layers.

The refractive index of all annealed Sb 2 Te 3 layers was determined in the range [400-1200 nm].

The technique followed, based on spectrophotometric analysis, is the curve fitting method, which requires an optical dispersion model. This model is capable of integrating several spectral information, such as transmittance and reflectance, allowing the index determination process. In addition, it is also capable of handling complicated cases, such as strongly absorbing layers.

In this case, the complex refractive index of annealed Sb 2 Te 3 films of different thicknesses is estimated from the reflectance and transmittance values. The theoretical reflectance and transmittance were calculated using the matrix method, taking into account backside reflectance.

They depend on the measurement wavelength, the substrate refractive index n s , the complex refractive index (n, k) and the layer thickness (d). There are several optical dispersion models describing the laws of the complex refractive index of the layer under consideration. In this study, we focused on a Forouhi-Bloomer model combined with a Drude model. [START_REF] Gao | Comparison of Different Dispersion Models for Single Layer Optical Thin Film Index Determination[END_REF] Several considerations justify this choice. The Forouhi-Bloomer model is one of the optical dispersion models derived from Kramers-Kronig integration. All the parameters describing the real and imaginary parts of the refractive index have a physical meaning. Finally, this model shows excellent performance with some crystalline and amorphous semiconductors, but also with dielectric thin films over a wide energy range.

The determination of the index consists of minimizing an error function, denoting the difference between the calculated and experimental reflectance or transmittance values in the whole spectral domain, and as a function of the 8 Forouhi Bloomer and Drude parameters injected on the n and k model.

Of course, with a relatively large number (8) of variables needed to calculate the refractive index n and k, and thus the error function, a simple local non-linear least squares optimization technique is inefficient, and a global optimization procedure is needed. As indicated in our previous study, [START_REF] Gao | Comparison of Different Dispersion Models for Single Layer Optical Thin Film Index Determination[END_REF] a global clustering optimization (GCO) algorithm is very efficient for the determination of a multiparametric index. GCO methods can be considered as an advanced form of a standard Multistart procedure, in which a local search is performed from several starting points distributed over the entire search initial domain.

The real and imaginary parts of the refractive index, corresponding to those leading to the overall minimization of the error function, are shown in Figures 3d,e. The validity and accuracy of index determination increases with the thickness. Indeed, we consider a homogeneous layer, which generally cannot be guarantee for very thin layers, in the 0-5nm range. Moreover, spectral signatures are not specific in the case of very thin layers, and several n and k dispersion curves may give a good agreement. Regarding our results, index determination seems reliable for samples with thicknesses higher than 10 nm, but should be considered carefully for thinner layers.

However, the values determined in this work are in good agreement with the values previously reported in the literature. [START_REF] Kuwahara | Approach for Measuring Complex Refractive Index of Molten Sb 2 Te 3 by Spectroscopic Ellipsometry[END_REF] In Figure 3f, the same parameters are presented at 1030 nm as a function of the layer thickness.

Nonlinear optical studies. For the needs of the nonlinear optical studies the Z-scan technique has been employed (see also experimental section). The studies have been performed using 400 fs duration pulses, at 1030 nm with a 100 Hz repetition rate. Many different thin films (annealed and amorphous) exhibiting thicknesses from 2.5 nm to 30 nm have been studied during this work. Higher thicknesses have not been studied in order to avoid low laser beam transmittances.

It has to be noted that in all cases the amorphous layers have been found to exhibit negligible nonlinearities, compared with the annealed ones (see for example Figure S2 in the supporting information), showing the importance of the annealing to obtain high NLO responses. The results shown in the next paragraphs concern the annealed Sb 2 Te 3 layers. The substrates used for the thin film deposition have been separately studied, under identical experimental conditions, revealing that they do not contribute to the nonlinear refraction and the nonlinear absorption of the investigated structures. Many Z-scan studies have been performed for every thin film and in many different areas of the surface of the samples. Moreover measurements have been done for many different laser intensities in order to find the most suitable range of intensities to be employed for this work and verify that no modification of the thin film layers was occurring during the nonlinear optical investigations. The range of intensities used for the Z-scan studies was 0.4 GW/cm 2 to 10 GW/cm 2 , which is significantly lower than the damage threshold, which is about 20 GW/cm 2 under the same experimental conditions.

In Figure 4a representative normalized "open aperture" Z-scan curves obtained with a 6 GW/cm 2 incident laser intensity are presented. For film thicknesses lower than 5 nm the obtained signals were found to be very low corresponding to negligible optical nonlinearities. For thicknesses higher than 5 nm a transmission peak has been observed (see for example the obtained experimental curve for the 6 nm thin film), indicating the saturable absorption character of the Sb 2 Te 3 layers. The obtained peaks were gradually increasing with the film thickness and a maximum peak has been obtained for the 9 nm -11 nm thick Sb 2 Te 3 layers. In Figure 4a a representative "Open aperture" Z-scan obtained for the 10 nm layer is presented. Then a decrease of the nonlinearity has been observed for thicker films. In Figures S3 andS4 The nonlinear absorption coefficient (β), as well as the imaginary part of the third order nonlinear susceptibility (Imχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] ) have been determined by many experimental curves, following the procedure described in the experimental section. Table 1 presents the nonlinear optical parameters for all thin films investigated during this work. The Imχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] is also presented in Figure 5a as a function of the thin film thickness. In Figure 5b the figure of merit, defined as the Imχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] divided by the linear absorption coefficient of the thin film layers at 1030 nm, is also presented.

It is obvious that the imaginary part of the third order nonlinear susceptibility and the figure of merit obtain their maximum values for a film thickness of 9-11 nm. The nonlinear absorption gradually decreases for thicker and thinner films. This finding is in accordance with the experimental curves shown in Figure 4a. It has to be noted that the choice of the thin film thicknesses employed for this investigation have been gradually done during the studies in order to allow a high precision determination of the highest nonlinear absorption that can be obtained by the Sb 2 Te 3 material.

In order to study the nonlinear refraction of the investigated materials "closed aperture" and "divided" Z-scans have been recorded. The determination of the nonlinear refraction of the Sb 2 Te 3 layers is a very challenging procedure for the following reasons. For thin films thicker than 6 nm the nonlinear absorption exhibits giant values and consequently it is dominating the optical nonlinearities. In such cases the Reχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] becomes much lower than Imχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] and it cannot be detected by the Z-scan technique. [START_REF] Sheik-Bahae | Sensitive Measurement of Optical Nonlinearities Using a Single Beam[END_REF] Decreasing the thickness can aid to surpass this difficulty, however very low thicknesses result to negligible nonlinearities (both nonlinear refraction and nonlinear absorption). For these reasons the nonlinear refractive parameters of the Sb 2 Te 3 material at the ultrafast regime are unknown. These measurements can be accurately done for 5-6 nm thick layers. This is due to the fact that these layers exhibit low nonlinear absorption, allowing a precise determination of the nonlinear refraction. A representative "divided" Z-scan obtained for the 5 nm thin film layer with an incident laser intensity of 6 GW/cm 2 is presented in Figure 4b. The "divided" Z-scan curves obtained during at this work show a peak-valley configuration, which indicates a self-defocusing character and consequently negative Reχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] values. The nonlinear refractive parameters have been determined in the case of the 5 and 6 nm layers following the procedure shown in the experimental section and are shown in Table 1.

Similar thickness dependent studies of the Sb 2 Te 3 material do not currently exist, despite the importance of this material for applications. Our work demonstrates the significant dependence of both nonlinear refraction and absorption on the thickness of the 2D layers. By a careful examination of Table 1 one can identify five different regimes, which result to different NLO behaviours. The first regime corresponds to very thin films (i.e. 2.5 nm) which exhibit negligible nonlinear refraction and nonlinear absorption. The lack of high optical nonlinearities can be attributed to the fact that in this case there is not sufficient matter to provide a uniform crystallization of the layers. A second, different behaviour has been observed in the case of the 5 nm thick films. In that case there is a significant nonlinear refraction, while the thin films exhibit a negligible nonlinear absorption. The nonlinear refractive parameter ( ) and Reχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] obtained in this work are of the order of 10 -9 cm 2 /W and 10 -7 esu respectively. These values are significantly high, showing that the Sb 2 Te 3 material can exhibit a strong nonlinear refractive character if its thickness is properly adjusted. It is interesting to make a comparison with the nonlinear refraction values previously obtained for graphene layers, as they are currently a reference 2D material for nonlinear optics. The published nonlinear optical properties of graphene vary a lot due to an apparent strong dependence on the pulse duration, the excitation wavelength, the repetition rate and the graphene preparation conditions. Chen et al. [START_REF] Chen | The Nonlinear Optical Properties of Coupling and Decoupling Graphene Layers[END_REF] reported a nonlinear refractive index of the order of 1.4x10 -9 cm 2 /W, which is slightly higher than the values reported in this work. The repetition rate employed by Chen et al. has been high (i.e. 80 MHz). In another work similar values have been found (10 -7 ~10 -6 esu) by employing the same repetition rate. [START_REF] Ahn | Wavelength and Fluence-Dependent Third-Order Optical Nonlinearity of Monoand Multi-Layer Graphene[END_REF] Very recently Karampitsos et al. [START_REF] Karampitsos | On the Measurement of the Nonlinear Optical Response of Graphene Dispersions Using fs Lasers[END_REF] have investigated graphene dispersions and have demonstrated that the repetition rate of the laser plays a very important role on the NLO response of graphene. Using a high repetition rate (i.e. 80 MHz) they have shown that thermal effects dominate the nonlinearities. To avoid this fact the repetition rate has been kept low (i.e. 100 Hz) during our work. Demetriou et al. [START_REF] Demetriou | Nonlinear Optical Properties of Multilayer Graphene in the Infrared[END_REF] investigated the optical nonlinearities of few-layer graphene (5 to 7 layers) by wavelength-dependent measurements in the infrared. In order to assure that no thermal effects arise they used a repetition rate of 1 kHz. The nonlinear refractive index obtained using an excitation wavelength at 1150 nm is of the same order of magnitude with our reported values for the Sb 2 Te 3 layers. It has to be noted that the negative nonlinear refraction obtained here (self-defocusing) is in accordance with several previous experimental and theoretical studies on graphene systems. [START_REF] Karampitsos | On the Measurement of the Nonlinear Optical Response of Graphene Dispersions Using fs Lasers[END_REF][START_REF] Demetriou | Nonlinear Optical Properties of Multilayer Graphene in the Infrared[END_REF][START_REF] Ooi | Waveguide Engineering of Graphene's Nonlinearity[END_REF] A negative nonlinear refraction has been also presented in Reference [START_REF] Xu | Size-Dependent Nonlinear Optical Properties of Black Phosphorus Nanosheets and Their Applications in Ultrafast Photonics[END_REF] in the case of another 2D material, black phosphorus, while the nonlinear refraction is 6-7 orders of magnitude lower than that reported in this work.

A third regime can be observed in Table 1 for the 6 nm layers. In this case there is a simultaneous existence of a nonlinear refraction and absorption. By further increasing the 2D layer thickness a transition to a fourth regime occurs, where the nonlinear absorption reaches record values, while gradually the nonlinear refraction disappears. This happens for thin films of 9-11 nm thickness. The nonlinear absorption coefficient has been found to be about an order of magnitude higher than that published by Liu et al for the same material. [START_REF] Liu | Contrastive Investigation on Linear Optical Properties and Nonlinear Absorption Behaviors between Sb 2 Se 3 and Sb 2 Te 3 Thin Films[END_REF] The higher values obtained here can be attributed to an enhancement of the nonlinear absorption achieved through the thickness optimization that we present in this work and an annealing optimization that has been previously detailed by our group. [START_REF] Moisset | Giant Ultrafast Optical Nonlinearities of Annealed Sb 2 Te 3 Layers[END_REF] It has to be mentioned that the nonlinear absorption coefficients found in this work are slightly lower than those that we have previously reported, which is due to the shorter pulse duration of the laser system employed here (400 fs instead of 600 fs used in Reference [START_REF] Moisset | Giant Ultrafast Optical Nonlinearities of Annealed Sb 2 Te 3 Layers[END_REF] ). The pulse duration is well-known to have a significant impact on the NLO response of 2D materials. For example Tang et al. have shown that a decrease of the pulse duration from 1 ps to 100 fs can result to a decrease of the nonlinear absorption coefficient of black phosphorus dispersions by about one order of magnitude. [START_REF] Tang | Pulse Duration Dependent Nonlinear Optical Response in Black Phosphorus Dispersions[END_REF] The giant nonlinear absorption obtained for the annealed Sb 2 Te 3 thin films is among the highest ever reported. A detailed comparison and discussion of these nonlinear optical absorption efficiencies with current state-of-the-art materials such as other chalcogenides, [START_REF] Fang | Thickness Dependence of a Giant Nonlinear Saturable Absorption Response in GeSb 4 Te 7 Thin Films[END_REF][START_REF] Wang | Ultra-Broadband Nonlinear Saturable Absorption for Two-Dimensional Bi 2 Te x Se 3-x Nanosheets[END_REF] perovskites, [START_REF] Kalanoor | Third-Order Optical Nonlinearities in Organometallic Methylammonium Lead Iodide Perovskite Thin Films[END_REF][START_REF] Li | CsPbBr 3 Perovskite Quantum Dots: Saturable Absorption Properties and Passively Q-Switched Visible Lasers[END_REF][START_REF] Li | Two-Dimensional CH 3 NH 3 PbI 3 Perovskite Nanosheets for Ultrafast Pulsed Fiber Lasers[END_REF] graphene, [START_REF] Kumar | Femtosecond Carrier Dynamics and Saturable Absorption in Graphene Suspensions[END_REF][START_REF] He | Enhanced Nonlinear Saturable Absorption of MoS 2 /Graphene Nanocomposite Films[END_REF] carbon nanotubes [START_REF] Tatsuura | Semiconductor Carbon Nanotubes as Ultrafast Switching Materials for Optical Telecommunications[END_REF] and 2D α-Mo 2 C 54 has been carried out by our group in Reference [START_REF] Moisset | Giant Ultrafast Optical Nonlinearities of Annealed Sb 2 Te 3 Layers[END_REF] (see Table 1 therein). The nonlinear optical mechanism which gives rise to these giant β values is the following. The Sb 2 Te 3 material exhibits a very low bandgap of about 0.14-0.20 eV, which offers to this material a broadband absorption character. [START_REF] Moisset | Giant Ultrafast Optical Nonlinearities of Annealed Sb 2 Te 3 Layers[END_REF][START_REF] Park | Optical Properties of Pseudobinary GeTe, Ge 2 Sb 2 Te 5 , GeSb 2 Te 4 , GeSb 4 Te 7 , and Sb 2 Te 3 from Ellipsometry and Density Functional Theory[END_REF][START_REF] Olson | Optical Properties of Amorphous GeTe, Sb 2 Te 3 , and Ge 2 Sb 2 Te 5 : The Role of Oxygen[END_REF] The excitation wavelength employed in this work (i.e. 1030 nm) excites the electrons from the valence band to the conduction band.

Increasing the laser intensity results to an increase of the number of carriers in the conduction band. Since electrons are fermions, when all energy states are occupied, the Sb 2 Te 3 material is not able to absorb more light due to the Pauli blocking. This bleaching results to an increase of the transmission and leads to high NLO responses. The significant contribution of this mechanism to the NLO response of 2D materials has been previously demonstrated by our and other scientific groups. [START_REF] You | Nonlinear Optical Properties and Applications of 2D Materials: Theoretical and Experimental Aspects[END_REF][START_REF] Liu | Recent Advances of 2D Materials in Nonlinear Photonics and Fiber Lasers[END_REF][START_REF] Moisset | Giant Ultrafast Optical Nonlinearities of Annealed Sb 2 Te 3 Layers[END_REF] Finally a fifth regime can be defined for thicker films. An increase of the film thickness over 10 nm results to a gradual decrease of the nonlinear absorption coefficients. For thicknesses over 24 nm lower optical nonlinearities are observed, while the optical losses of the layers become significant.

The high dependence of the NLO response on the film thickness is attributed to the topological insulator behaviour of the thin film layers. Even slight modifications of the optimal thicknesses can result to a significant loss of the NLO performances. There is no evidence of this thickness dependence in the literature so a further comparison with the literature is not feasible. However thickness dependent studies have been performed for other 2D materials. Ahn et al. have recently investigated the optical nonlinearities of mono and multilayer graphene by means of Z-scan and Optical Kerr gate experiments showing a high dependence on the number of graphene layers. [START_REF] Ahn | Wavelength and Fluence-Dependent Third-Order Optical Nonlinearity of Monoand Multi-Layer Graphene[END_REF] Chen et al. studied the nonlinear refraction and the nonlinear absorption from monolayers to multilayers in the case of graphene in the ultrafast regime. [START_REF] Chen | The Nonlinear Optical Properties of Coupling and Decoupling Graphene Layers[END_REF] They demonstrated that the nonlinear optical response is not proportional to the number of layers. This has been attributed to the interlayer coupling. In another work it has been demonstrated that monolayer graphene acts as a more effective saturable absorber than multilayer graphene. [START_REF] Bao | Monolayer Graphene as a Saturable Absorber in a Mode-Locked Laser[END_REF] More specifically the monolayer graphene has been found to provide a better pulse shaping ability, pulse stability and output energy. On the contrary, as we show in this work, in the case of the Sb 2 Te 3 material higher thicknesses are needed to obtain giant optical nonlinearities. This is related to the different nature of these two 2D materials. Graphene is obtained through the isolation of a single sheet of graphite and it already has the necessary structure to obtain the NLO response. In the case of the Sb 2 Te 3 material, formation of nanocrystals is necessary to achieve high nonlinear absorption or nonlinear refraction, which is obtained through a precise annealing of the deposited layers. Bao et al. [START_REF] Bao | Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers[END_REF] demonstrated that the saturation intensity of graphene systems can vary from 0.71 to 0.61 MW cm -2 by changing the number of layers from 3 ± 1 to 10 ± 1. They also found that the modulation depth can be reduced from 66.5% to 6.2% by changing the number of graphene layers. Other 2D materials have been also previously investigated. Thickness-dependent studies have been also carried out in the case of SnS 2 nanolayers in order to optimize their performance for fibre lasers. [START_REF] Liu | Thickness-Dependent Ultrafast Photonics of SnS 2 Nanolayers for Optimizing Fiber Lasers[END_REF] In this case three different thicknesses have been studied and an increase of the modulation depth with increasing the film thickness has been found, while the best performance has been acquired by a 108.7 nm thick layer. In another work the nonlinear refraction and the nonlinear absorption has been studied as a function of the size of black phosphorus nanosheets. [START_REF] Xu | Size-Dependent Nonlinear Optical Properties of Black Phosphorus Nanosheets and Their Applications in Ultrafast Photonics[END_REF] Three different thicknesses have been studied showing an increase of both real and imaginary part of the third order nonlinear optical susceptibilities by decreasing the nanosheets size. Tuo et al studied 2D α-Mo2C crystals and find out that by changing the crystal thickness and the laser intensity a significant tunability of the NLO parameters can be achieved. [START_REF] Tuo | Ultrathin 2D Transition Metal Carbides for Ultrafast Pulsed Fiber Lasers[END_REF] The results reported in this work are of significant importance for the field of nonlinear optics of 2D materials. They show that a precise tuning of the film thickness is necessary in order to enhance the optical nonlinearities of the Sb 2 Te 3 layers. On the contrary, avoiding such adjustment can result to poor performances in terms of applications, as for example modelocking of fibre lasers. Moreover the thickness adjustment can result to a switching between different NLO behaviours, so it can be employed in order to adapt the Sb 2 Te 3 performance for specific needs. More specifically, careful adjustment of the crystallized Sb 2 Te 3 thickness can provide a switching from a purely nonlinear refractive NLO regime to a regime where the nonlinear absorption dominates the nonlinearities. Another important point has to be highlighted.

The nonlinear optical parameters found in this work demonstrate a non-monotonic dependence on the film thickness. Such behaviour can only be detected by thorough NLO studies of many different thin films. It is very possible that a similar behaviour will be unveiled for many other 2D materials by investigating a large number of samples, having appropriately adjusted thicknesses.

CONCLUSIONS

The nonlinear optical properties of nanometer-thick 2D Sb 2 Te 3 thin films have been studied by the Z-scan technique employing 400 fs laser pulses at 1030 nm with a low repetition rate of 100 Hz in order to avoid the appearance of thermal effects. Significant NLO properties have been found, which are highly dependent on the film thickness. A nonlinear refractive parameter of the order of 10 -9 cm 2 /W has been obtained for 5-6 nm thick layers. This refraction if very high, comparable with that of other state-of-the-art nonlinear optical materials. A giant nonlinear absorption coefficient of the order of 10 -6 m/W has been obtained for 9-11 nm thick films. The nonlinear absorption dominates in that case the optical nonlinearities. These results show the importance of the precise adjustment of the film thickness for mode locking and super-resolved nanostructuring. We believe that these findings will trigger further research in the field of the optical nonlinearities of 2D photonic materials.

METHODS

Sample Characterization. SEM analysis was performed with a Zeiss GeminiSEM 500 ultrahigh resolution Field Emission Scanning Electron Microscope operating at 10 kV. A backscatter electron detector was used for imaging in nanoscale. Grain sizes were measured using the Image J software.

For TEM analysis, the samples were observed with a FEI Tecnaï G2 microscope operating at 200KV. This microscope is equipped with an X-Max Silicon Drift Detector (Oxford) which allows Energy-dispersive X-ray spectroscopy measurements. The Cliff-Lorimer method as implemented in the Aztec software package from Oxford is used for quantitative chemical analysis.

Nonlinear Optical Studies. The nonlinear optical measurements have been performed by means of the Z-scan technique. The Z-scan technique [START_REF] Sheik-Bahae | Sensitive Measurement of Optical Nonlinearities Using a Single Beam[END_REF] employs two different experimental arms, the so called "closed aperture" and "open aperture" Z-scans allowing a determination of the nonlinear refraction and the nonlinear absorption of a material respectively. For the Z-scan studies an Amplitude, Yuja, femtosecond laser system has been employed. This is a hybrid (crystal/fiber), passively mode-locked laser delivering 400 fs duration pulses at 1030 nm. The oscillator provides pulses at a 40 MHz repetition rate. By means of a pulse picker and an acousto-optic modulator, both integrated in the laser system, the repetition rate can be adjusted. For the Z-scan measurements a 100 Hz repetition rate has been employed in order to avoid thermal effect contribution to the measured nonlinear optical responses. The laser beam has been focused by a 10 cm focal length lens on the sample, which has been moved around the focal plane by means of a computer controlled translation stage. The beam waist at the focal plane has been measured to be 20 μm.

The recorded "Closed aperture" and "Open aperture" Z-scans allow the determination of the real and imaginary parts of the third order nonlinear optical susceptibility (Reχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] and Imχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] ) respectively. The nonlinear absorption coefficient β has been determined by fitting the "open aperture" Z-scan curves by means of the following equation: (1) where I 0 is the on-axis irradiance at the focus, L eff is defined as L eff =(1-exp(-α 0 L))/α 0 and α 0 is the linear absorption coefficient of the sample (at 1030 nm and at 515 nm respectively). The Imχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] can be then calculated by means of the following equation: (2) where c is the speed of light in cm s -1 , n 0 is the linear refractive index and ω is the fundamental frequency in cycles per sec.

The nonlinear refraction parameters have been obtained by dividing the "closed aperture" Zscans by the "open aperture" Z-scans, obtaining the so-called "divided" Z-scans. The "divided" Z-scans allowed the determination of the nonlinear refractive parameters following the experimental analysis procedure previously detailed. [START_REF] Iliopoulos | Ultrafast Third Order Nonlinearities of Organic Solvents[END_REF] The γ´ values have been determined as follows:

(3

)
where k is the wave number in vacuum, S is the linear transmittance of the aperture and ΔΤ P-V is the difference between the transmittance minima and maxima of the recorded experimental curves.

The real part of the third order nonlinear optical susceptibility has been then obtained by means of the following equation: (4) where c is the speed of light in cm s -1 and has to be given in cm 2 W -1 .

FIGURES

  (Supporting information) additional "Open aperture" curves obtained for thin films of different thicknesses are presented. All the curves have been recorded using the same incident laser intensity (6 GW/cm 2 ). Moreover in FigureS5(Supporting information) three curves obtained at three different zones of the 10 nm thin film layer are presented, revealing the excellent repeatability of the measurements.

Figure 1 .

 1 Figure 1. a-c) SEM images obtained in backscattered mode for the a) 10 nm b) 30 nm and c) 50 nm Sb 2 Te 3 layers. d-f) Corresponding XRD diagrams ( = 0.15418 nm) for the d) 10 nm e) 30 nm f) 50 nm samples.

Figure 2

 2 Figure 2

Figure 2 .

 2 Figure 2. Cross-sectional STEM bright field images for the a) 10 nm and b) 30 nm annealed Sb 2 Te 3 layers. The rectangle indicates the area scanned by the beam for the EDX analysis. EDX Spectra obtained for the c) 10 nm and d) 30 nm samples. The Sb(K) and Te(K) ionization peaks used for quantitative analysis are located at 26.4 keV and 27.4 keV.

Figure 3 Figure 3 .

 33 Figure 3

Figure 4

 4 Figure 4

Figure 4 .

 4 Figure 4. a) "Open aperture" Z-scan curves for three different Sb 2 Te 3 thicknesses. b) "Divided" Z-scan obtained for the 5 nm thick layer.

ACKNOWLEDGMENTS

The authors would like to thank Dr. Jean-Benoît Claude for his participation in the surface morphology studies. The authors acknowledge financial support from the French National Research Agency (ANR-19-CE09-0002-01), from the Ministry for Armed Forces (DGA) and Aix-Marseille University.

Crystal sizes (nm) β (10 -7 mW -1 ) Imχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] (10 -7 esu) Imχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] /α (10 -16 m esu) γ' (10 -10 cm 2 W -1 ) Reχ [START_REF] Liu | Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics[END_REF] (10 -7 esu)

NOTES

The authors declare no competing financial interest.