Gael Poirier
email: gael.poirier@unifal-mg.edu.br

Lara Karam

Vincent Rodriguez

Frédéric Adamietz

Thierry Cardinal

Evelyne Fargin

Marc Dussauze
email: marc.dussauze@u-bordeaux.fr

Linear and non-linear optical microstructuring in sodium tantalum germanate glasses by thermal poling

Keywords: Glass, germanate, thermal micropoling, second harmonic generation, refractive index

Sodium tantalum germanate glasses were thermally poled using microstructured metallic anodes of two distinct geometries. Topological, structural and optical characterizations of the micro-imprinted structures revealed an accurate reproducibility of the electrode patterns on the glass surface with strong edge effects between the poled and unpoled areas. 100 nm-depth spatial reliefs were achieved and associated with glass network rearrangements due to sodium departure under the conductive anodic patterns. Second harmonic signals originating from both longitudinal and in-plane static electric fields were identified mainly near the borders of imprinted structures and related to a specific charge distribution model. Spatially controlled positive refractive index changes around 7 to 9.10 -3 could be induced, opening opportunities for active optical devices operating in the middle infrared.

-Introduction

Alkali niobium and tantalum germanate glasses are interesting materials thanks to their specific optical properties emerging from the mixed niobate/tantalate and germanate glassy network built upon MO6 (M=Nb or Ta) and GeO4 units [START_REF] De Pietro | Structural and Crystallization Properties of New Tantalum Alkali-Germanate Glasses[END_REF][START_REF] Marcondes | High Niobium Oxide Content in Germanate Glasses: Thermal, Structural and Optical Properties[END_REF][START_REF] Marcondes | Thermal and Spectroscopic Properties Studies of Er 3+doped and Er 3+ /Yb 3+ -codoped niobium germanate glasses for optical applications[END_REF]. In fact, several thermal and optical properties can be tuned by the M2O5 content along the glass forming domain. For example, low transition metal contents promote higher thermal stabilities against devitrification whereas higher contents close to the limit of the glass forming domain lead to strong crystallization tendency with formation of perovskite bronze-like crystalline phase of general formula A2M8O21 where A is an alkaline ion, mainly Na or K [START_REF] De Pietro | Structural and Crystallization Properties of New Tantalum Alkali-Germanate Glasses[END_REF][START_REF] Marcondes | High Niobium Oxide Content in Germanate Glasses: Thermal, Structural and Optical Properties[END_REF][START_REF] Da Cunha | Alkali Metal Tantalum Germanate Glasses and Glass-Ceramics Formation[END_REF][START_REF] Guedes | Effect of Alkaline Modifiers on the Structural, Optical and Crystallization Properties of Niobium Germanate Glasses and Glass-Ceramics[END_REF].

Optical properties which make these materials promising for photonic applications include their transparency in the middle infrared up to 6 m as well as the tunable rare earth visible and near infrared luminescent properties as a function of the M2O5 content or the degree of crystallinity in these compositions [START_REF] Marcondes | High Niobium Oxide Content in Germanate Glasses: Thermal, Structural and Optical Properties[END_REF][START_REF] Marcondes | Thermal and Spectroscopic Properties Studies of Er 3+doped and Er 3+ /Yb 3+ -codoped niobium germanate glasses for optical applications[END_REF][START_REF] Marcondes | Rare Earth Ion Doped Niobium Germanate Glasses and Glass-Ceramics for Optical Device Applications[END_REF][START_REF] Marcondes | Er 3+ -doped Niobium Alkali Germanate Glasses and glass-Ceramics: NIR and Visible Luminescence Properties[END_REF][START_REF] Marcondes | High Tantalum Oxide Content in Eu 3+ -doped Phosphate Glass and Glass-Ceramics for Photonic Applications[END_REF][START_REF] Marcondes | Multicolor tunable and NIR broadband emission from rare-earth-codoped tantalum germanate glasses and nanostructured glass-ceramics[END_REF]. However, besides the design of suitable glass compositions with the required physical specifications, photonic technologies and integrated optics also bring the need for a more precise control and/or modulation of the linear and non-linear optical properties at the microscale. Among many physical and chemical methodologies developed for such purpose, thermal poling, which can be understood as the application of a strong DC electric field on a heated noncrystalline material (usually a glass), has attracted attention in the past few years [START_REF] Alvarado | Patterning of the Surface Electrical Potential on Chalcogenide Glasses by a Thermoelectrical Imprinting Process[END_REF][START_REF] Karam | Electrically Micro-Polarized Amorphous Sodo-Niobate Film Competing with Crystalline Lithium Niobate Second-Order Optical Response[END_REF][START_REF] Karam | Second-Order Optical Response in Electrically Polarized Sodo-Niobate Amorphous Thin Films: Particularity of Multilayer Systems[END_REF][START_REF] Lepicard | Long-lived monolithic micro-optics for multispectral GRIN applications[END_REF]. First reports have demonstrated that such electric field applied on a glass heated below its glass transition temperature induce a migration of positive charges like alkaline ions from the anodic surface towards the cathode [START_REF] Myers | Large 2nd-order Nonlinearity in Poled Fused-Silica[END_REF][START_REF] Kazansky | Thermally Poled Glass-Frozen-in Electric Field or Oriented Dipoles[END_REF][START_REF] Mukherjee | Dynamics of Second-Harmonic Generation in Fused Silica[END_REF][START_REF] Pruneri | Thermal Poling of Silica in Air and under Vacuum: The Influence of Charge Transport on Second Harmonic Generation[END_REF].

After cooling back the sample to room temperature and then removing the high voltage, this electric field assisted space charge induced under the anode surface is "frozen" in the glass, generating a permanent static electric field (Eint). A few microns thick alkaline depleted layer with a high negative charge density is formed at the anodic side; it gives rise to specific modifications of the poled glass chemical and optical properties. For example, surface reactivity can be modified with respect to the atmospheric moisture resistance and/or hydrophobicity [START_REF] Lepicard | Surface Reactivity Control of a Borosilicate Glass using Thermal Poling[END_REF].

Thermal poling is also well known to promote second order non-linear optical properties such as second harmonic generation (SHG) associated with anisotropy generated orthogonally to the treated surface. Although some works suggest that SHG can be related with orientable species, it is well accepted that the main SHG mechanism is an electro-optic effect associated with the third order non-linear susceptibility  (3) and the internal electric field according to the relation  (2) =3. (3) .Eint, called the EFISH model for Electric Field Induced Second Harmonic [START_REF] Myers | Large 2nd-order Nonlinearity in Poled Fused-Silica[END_REF][START_REF] Kazansky | Thermally Poled Glass-Frozen-in Electric Field or Oriented Dipoles[END_REF][START_REF] Mukherjee | Dynamics of Second-Harmonic Generation in Fused Silica[END_REF][START_REF] Pruneri | Thermal Poling of Silica in Air and under Vacuum: The Influence of Charge Transport on Second Harmonic Generation[END_REF][START_REF] Quiquempois | Model of Charge Migration during Thermal Poling in Silica Glasses: Evidence of a Voltage Threshold for the Onset of a Second-Order Nonlinearity[END_REF]. Besides the non-linear optical properties associated with the space charge, cations depletion from the poled layer also promotes compositional changes associated with structural rearrangement for charge compensation [START_REF] Dussauze | How Does Thermal Poling affect the Structure of Soda-Lime Glass?[END_REF][START_REF] Dussauze | Thermal Poling of Optical Glasses: Mechanisms and Second-Order Optical Properties[END_REF][START_REF] Moncke | Thermal Poling induced Structural Changes in Sodium Borosilicate Glasses[END_REF][START_REF] Redkov | How does Thermal Poling produce Interstitial Oxygen Silicate Glasses?[END_REF][START_REF] Cremoux | Trapped Molecular Oxygen and Ionic Species in Poled Borosilicate Glasses: Toward a Rationalized Description of Thermal Poling in Glasses[END_REF][START_REF] Luo | Thermal Poling of Soda-Lime Silica Glass with Nonblocking Electrodes Part 1: Effects of Sodium Ion Migration and Water Ingres son Glass Surface Structure[END_REF][START_REF] Smith | Structural and Compositional Modification of a Barium Boroaluminosilicate Glass Surface by Thermal Poling[END_REF][START_REF] Mclaren | Depletion Layer Formation in Alkali Silicate Glasses by Electro-Thermal Poling[END_REF]. Lower refractive indices are usually induced in the poled layer when compared to the pristine glass, opening opportunities for waveguides design [START_REF] Li | Waveguide Electro-Optic Modulator in Fused Silica Fabricated by Femtosecond Laser Direct Writing and Thermal Poling[END_REF][START_REF] Li | Quasi-Phase Matched Second-Harmonic Generation through thermal Poling in Femtosecond Laser-Written Glass Waveguides[END_REF]. Even though thermal poling is an outstanding tool for optical materials, photonic technologies are in need of a microscale control of the optical properties for microdevices suitable for integrated optics. In this sense, deep efforts have been made for miniaturization of the thermal poling principle on glass surfaces.

Particularly, the use of micro structured electrodes with periodic conductive and insulating patterns has been proven useful for accurate micro-imprinting of the electrode structure on glass surfaces [START_REF] Lipovskii | Electric Field imprinting of Sub-micron Patterns in Glass-Metal Nanocomposites[END_REF][START_REF] Chervinskii | Formation of 2d-Patterning of Silver Nanoisland Film using Thermal Poling and Out-Diffusion from Glass[END_REF][START_REF] Lipovskii | Imprinting Phase/Amplitude Patterns in Glasses with Thermal Poling[END_REF][START_REF] Yang | Large Scale Microstructured Optical Second Harmonic Generation Response Imprinted on Glass Surface by Thermal Poling[END_REF]. This approach, sometimes reported as thermal micropoling, allows the control of surface relief as well as linear and non-linear optical properties at the microscale [START_REF] Yang | Large Scale Microstructured Optical Second Harmonic Generation Response Imprinted on Glass Surface by Thermal Poling[END_REF][START_REF] Brunkov | Submicron-Resolved Relief Formation in Poled Glasses and Glass-Metal Nanocomposites[END_REF][START_REF] Redkov | Nanoprofiling of Alkali-Silicate Glasses by Thermal Poling[END_REF][START_REF] Dussauze | Accurate Second Harmonic Generation Microimprinting in Glassy Oxide Materials[END_REF][START_REF] Karam | Electrically Micro-Polarized Amorphous Sodo-Niobate Film Competing with Crystalline Lithium Niobate Second-Order Optical Response[END_REF]. Charge distribution models are well described and accepted after classical poling treatment and are related with a homogeneous migration of mobile cations under the anode. However, thermal micropoling promotes more complex charge density distributions and strong edge effects between the poled and unpoled surfaces [START_REF] Dussauze | Accurate Second Harmonic Generation Microimprinting in Glassy Oxide Materials[END_REF]. Microstructuring of chemical and optical properties has been achieved by thermal poling in silicate and phosphate glasses but has not been reported in germanate glasses yet, despite their broader optical window in the middle infrared and higher refractive index compared to other oxide glasses. Since recent investigations have shown that thermally poled sodium tantalum germanate glasses exhibit stable second harmonic generation associated with sodium depletion [START_REF] Poirier | Second Harmonic Generation in Sodium Tantalum Germanate Glasses by Thermal Poling[END_REF], the present work investigates in details the effect of microstructured anodes during thermal poling on topological and structural modifications, and on the localization and geometry of the second harmonic generation as well as the refractive index changes in sodium tantalum germanate glass compositions.

-Experimental Part

Glass samples of composition 75GeO2-10Na2O-15Ta2O5 were prepared from reagent grades GeO2 99,9%, Ta2O5 99,9% and Na2CO3 (from Sigma Aldrich Corp.).

Starting powders were weighted and grounded in an agate mortar for a 30 g total batch and melted in a platinum crucible at 1500 ºC for 2 hours. In a second step, the crucible was cooled in cold water for 5 seconds and put in a furnace at 700 ºC during 12 hours for annealing before slow cooling to room temperature. The glass sample formed in the crucible was then cut and polished for final glass sizes of 1 mm in thickness and 25 mm in diameter.

The microstructured anodes consisted of a 50 nm thick titanium layer (for mechanical adherence) and a 100 nm thick platinum film deposited on a glass slide that were lithographically structured. Two different periodic patterns were used in this work. The first electrode, labeled E-70/4, presented insulating squares of 70 m (glass substrate free of metallic layer) separated by a 4 m-large conductive grid as depicted in Figure 1a. The second electrode labeled E-4/4 was constituted of 4 µm diameter insulating circles distant of 4 m one from the other (Figure 1c).The cathode was constituted of an n-doped silicon wafer under a 150m-thick borosilicate coverslip employed to keep the optical quality of the glass on this side.

The glass samples, respectively referred to as G-70/4 and G-4/4 depending of the anode employed for the treatment, are 1 mm-thick polished glass samples. They were pressed between two electrodes and heated from room temperature to 265 ºC at 5 ºC/min under flowing nitrogen atmosphere before applying a DC field between the electrodes during 30 min. The samples were then slowly cooled down with the DC field kept on until the sample reached room temperature. Based on previous studies [START_REF] Poirier | Second Harmonic Generation in Sodium Tantalum Germanate Glasses by Thermal Poling[END_REF], thermal poling treatments were first performed at 1350 V but the poled surface as observed by optical microscopy appeared strongly damaged. Decreasing poling voltages were tested until a clean microstructured surface was obtained for an 800 V poling voltage as illustrated by the Figure 1b and 1d for the samples G-70/4 and G-4/4 respectively.

Correlative Raman and SHG microscopies were recorded on the surface of the micropoled samples in backscattering mode using a modified micro-Raman spectrometer HR800 (Horiba/Jobin Yvon) equipped with a confocal microscope and a (x,y,z) motorized stage enabling 3D mapping with a spatial resolution around 0.5 m. Raman measurements were performed with a CW laser operating at 532 nm and a 1064 nm () picosecond laser was used as the excitation source for -SHG mapping recorded at 532 nm (2). Two different incident polarizations were employed to probe the SHG signal namely azimuthal and radial polarizations.

They were obtained using a polarization converter from Arcoptix relying on the special alignment of liquid crystal molecules. For both of them, the polarization states at the focal point were calculated following a methodology described in our previous work [START_REF] Karam | Second-Order Optical Response in Electrically Polarized Sodo-Niobate Amorphous Thin Films: Particularity of Multilayer Systems[END_REF] and using a program developed by Li [START_REF] Li | Optimization of point spread function of a high numerical aperture objective lens : application to high resolution optical imaging and fabrication[END_REF]. In the supplementary material S1, the intensity distribution profiles of the in-plane (Ixy) and out of the plane (Iz) components are shown for the two polarization states.

They were calculated for a 100×-0.9NA air objective that was employed for the µ-SHG measurements of the G-70/4 sample and for a 100-1.3NA oil objective that was used for the G-4/4 sample. These profiles show that the radial polarization allows for probing of the SHG response both in and out of the plane while the azimuthal polarization only probes the in-plane response.

Electrostatic simulations were achieved using the software COMSOL. Taking in account the electrode's geometry, we have calculated, for a wide range of charge distributions in the micropoled glasses, electrical potentials and electric field components. Calculation results were compared with SHG intensity profiles to give some insights about the poling patterning process. Atomic force microscopy (AFM) measurements were performed on the surface of the thermally poled glasses in PF-QNM (Peak Force Quantitative Nanoscale Mechanical characterization) mode using a Bruker Dimension ICON System and a PFQNE-AL cantilever. Refractive index changes along the imprinted microstructures were accessed by a phase contrast technique: a wave-front sensor SID4Bio by Phasics Inc placed inside an optical microscope was used to record the phase image of the microstructures. This measurement was performed in transmission mode under white light illumination using a band pass filter centered at 750 nm through a 100-1.3NA oil objective.

The refractive index variations were calculated by dividing the optical path difference along the microstructures by the thickness of the poled layer (estimated around 2.5 m by SHG microscopy on the micropoled glass cross-section).

-Results and discussion

Sodium tantalum germanate glass samples of composition 75GeO2-10Na2O-15Ta2O5 were thermally poled at 265 ºC under a 800 V DC electric field using the E-70/4 and E-4/4 microstructured electrodes whose periodic patterns are presented in Figures 1a and1c respectively. Optical micrographs of the surface of the corresponding poled glass samples are depicted in Figures 1b and1d. The inset of Figure 1d also brings the visual aspect of the poled glass where the poled area is clearly identified due to visible light diffraction. Under these poling conditions the microscaled patterns of the electrodes were perfectly reproduced on the glass surface, pointing out that micro-imprinting by thermal poling is effective and reproducible in these sodium tantalum germanate compositions.

Micro-Raman mapping measurements were performed at the boundary between the zones in contact (poled zone) and not in contact (unpoled region) with the metallic portions of the electrode for a better understanding of the glass network structural modifications under thermal poling. An optical microscopy image of this region on the G-70/4 sample is presented in Figure 2a. Raman mapping was performed in a 12 m35 m area delimited by the yellow rectangle with a 1 µm step along the X and Y axis. Two Raman spectra collected from the unpoled region (far from the boundary) and the poled area (under the metallic part of the electrode) were extracted and are compared in Figure 2b. Despite the overall similarities of these spectral profiles which were normalized at the most intense signal (480 cm -1 ), weak differences in several Raman mode intensities could be detected at 430 cm -1 (mode 1 in Figure 2b), 800 cm -1 (mode 2) and 1550 cm -1 (mode 3). Such weak variations on their own are hardly conclusive about structural changes promoted by thermal poling and could also be related with experimental conditions. However, Raman mappings comparing relative intensities of modes 1, 2 and 3 are depicted in Figure 2c1, 2c2 and 2c3 respectively and it appears that these signal intensities are well spatially correlated with the imprinted patterns. Previous -Raman investigations performed on homogeneously poled samples cross-section already related Raman mode variations centered at 430 cm -1 (mode 1) and 800 cm -1 (mode 2) to Ge-O-Ge bridging bonds in four-membered rings of GeO4 tetrahedra [START_REF] Poirier | Second Harmonic Generation in Sodium Tantalum Germanate Glasses by Thermal Poling[END_REF][START_REF] Henderson | The Structure of Glasses along the Na2O-GeO2 Join[END_REF][START_REF] Monteiro | Optical and Spectroscopic Properties of Germanotellurite Glasses[END_REF] and Ta-O stretching modes in isolated TaO6 units distributed inside the covalent germanate network [START_REF] Poirier | Second Harmonic Generation in Sodium Tantalum Germanate Glasses by Thermal Poling[END_REF][START_REF] Peng | Glass-forming Region and Enhanced Bi NIR Emission in Sodium Tantalum Silicate Laser Glass[END_REF][START_REF] Wetherall | The Atomic Structure of Niobium and Tantalum containing Borophosphate Glasses[END_REF], respectively. As reported, relative higher intensity of mode 1 after thermal poling can be interpreted by a polymerization of the germanate network where Ge-O -terminal bonds stabilized by Na + ions are converted to bridging Ge-O-Ge bonds in order to balance the sodium departure from the poled layer. On the other hand, a lower intensity in mode 2 suggests that tantalum oxide units are partially separated from the germanate network under thermal poling which promotes a nanoscaled phase separation between the germanate and tantalate species [START_REF] Poirier | Second Harmonic Generation in Sodium Tantalum Germanate Glasses by Thermal Poling[END_REF]. In the present work, similar spectral evolution are observed even if the spectral variations are less pronounced than for a homogeneous poling probed on the cross section [START_REF] Poirier | Second Harmonic Generation in Sodium Tantalum Germanate Glasses by Thermal Poling[END_REF]. This can be explained by the difference in probing geometry between these two studies (cross section vs. along the surface).

The weak spectral variations observed on a patterned glass surface are the consequence of the difference between longitudinal and in plane spatial resolution in confocal Raman microscopy as compared to the poled layer thickness. Besides these considerations, another weak Raman signal was detected around 1550 cm -1 only in the poled area as evidenced by Figures 2b and2c3. This feature, already reported in poled silicate and phosphate vitreous layers is associated with symmetric stretching of trapped molecular oxygen and support the structural model of a partial conversion of Ge-O -terminal bonds in Ge-O-Ge bridging linkages where the remaining oxygens are oxidized to molecular oxygen for charge compensation mechanisms [START_REF] Redkov | How does Thermal Poling produce Interstitial Oxygen Silicate Glasses?[END_REF][START_REF] Cremoux | Trapped Molecular Oxygen and Ionic Species in Poled Borosilicate Glasses: Toward a Rationalized Description of Thermal Poling in Glasses[END_REF][START_REF] Dussauze | Accurate Second Harmonic Generation Microimprinting in Glassy Oxide Materials[END_REF][START_REF] Guimbretière | Correlation between Second-Order Optical Response and Structure in Thermally Poled Sodium Niobium-Germanate Glass[END_REF].

The static electric field resulting from poling is known to break the glass' centrosymmetry and induce otherwise forbidden second order optical response such as SHG. This response was probed using the confocal -SHG setup described in the experimental section with both radial and azimuthal incident polarizations.

These results are gathered in the Figure 3 for both G-70/4 (Figures 3a) and G-4/4 (Figures 3b) glass samples. In each case, an optical micrograph highlights the areas (Figures 3a1 and3b1) that were probed under radial and azimuthal polarizations with respective -SHG mappings, I2ω-rad (Figures 3a2 and3b2) and azimuthal, I2ω-azi (Figures 3a3 and3b3) Let us first focus on the G-70/4 sample. The SHG response as probed under radial polarization is mainly localized at the poled/unpoled border (Figure 3a2), i.e. at the edges of the electrode's conductive part. In the poled zone (under the conductive grid of the electrode), the SHG intensity decreases by a factor of four, while in the unpoled region, no SHG signal can be measured under this polarization. When probed under azimuthal polarization (Figure 3a3), the SHG response is also localized at the edges of the electrode's borders. No SHG signal can be measured in the poled zone nor in the unpoled region: under azimuthal polarization, the border between these two regions is the only SHG active zone.

One must also note that, for the G-70/4 sample, there is a co-localization of the SHG response maxima as probed under the two polarizations. This behavior is different from the one observed for the G-4/4 sample. Indeed, on the G-4/4 sample, the SHG response as probed under radial polarization is maximal in the center of the circle.

That is, surprisingly, in the region where the electrode is not conductive. On the other hand, the maximum SHG intensity probed under azimuthal polarization is localized all around the imprinted circle.

To recapitulate, the electrodes employed to pole these two samples present opposite patterns: E-70/4 is constituted of thin conductive parts and large nonconductive zones while E-4/4 is composed of roughly equivalently large conductive and non-conductive areas. The resulting micro-poled samples exhibit different electric field geometry as evidenced by the SHG mappings. For G-70/4, the maximal intensities as probed under radial and azimuthal polarizations are colocalized, while it is very clear that for G-4/4, they are not. In order to gain a precise understanding of the underlying charge distributions at the origin of these responses, an electrostatic model was developed on the basis of our previous work on borophosphate glasses [START_REF] Dussauze | Accurate Second Harmonic Generation Microimprinting in Glassy Oxide Materials[END_REF]. The results of these calculations as well as a comparison with the experimental results are gathered in the Figure 4.

The Figures 4a and4b In order to ascertain the charge distribution at the origin of the measured SHG signal, the square of the calculated electric field was compared to the measured SHG intensity.

As a recall, two different polarizations were employed to probe the SHG signal, namely radial and azimuthal polarizations. As illustrated by the point spread functions presented in the supplementary material, an azimuthal incident polarization allows for probing the response only in the plane while a radial polarization probes the response both in and out of the plane. Therefore, the SHG intensity measured under azimuthal polarization was confronted to the calculated Ex 2 . The electric field along the Z axis is only be probed with a radial polarization, thus, the calculated Ez 2 was compared to the SHG intensity as measured under radial polarization.

In the Figure 4, are presented the results for a specific set of values for ρ1, ρ2 and ρ3 that best reproduced the measured SHG signals: C/m 3 and ρ3=-5E 2 C/m 3 for the sample G-4/4 in Figure 4b5. For both electrode's geometries, the SHG signal is simulated with similar models, i.e. with similar charge distributions at the edges. The rather good correspondences observed for both samples denote that the spatial control of the SHG response can be understood and managed on the basis of the charge distribution along one single electrode's edge. For more complex electrode geometries, it can then be deduced constructing electrostatic models on the base of the charge distribution expected for one electrode's edge. This constitutes a promising finding for the accurate control of such an imprinting process.

It is worth noting that the charge distribution at the origin of the SHG response in these germanate glasses is slightly different from the one evidenced in borophosphate glasses [START_REF] Dussauze | Accurate Second Harmonic Generation Microimprinting in Glassy Oxide Materials[END_REF]. Therefore, the way the glass reacts to this imprinting process depends on (i) the type of electrode and (ii) the glass composition.

However, we would like to emphasize that for both glass families, the model is the same one, only varying slightly in charge volumic concentration and edges effects sizes. This points out again that such an approach using an electrostatic model to estimate the second order optical properties in thermoelectrically imprinted glassy materials is robust.

Topological effects of micro-imprinting by thermal poling were also investigated by Atomic Force Microscopy, these results are gathered in the Figure For both samples, it appears that, in the poled area, the glass experiments a contraction with a depth variation of about 100 nm. AFM investigations also evidence intense edge effects as can be seen in the Figures 5c and5f. At the poled/unpoled frontier, stronger topology variations of the order of 300 nm are measured with a pronounced contraction on the conductive side of the conductive/nonconductive frontier and an opposite increase on the nonconductive side. This corresponds well to the charge distributions at the conductive/nonconductive borders presented in the Figure 4 and in particular the positive and negative charge accumulations at this frontier. Here, the topology of the poled glass seems to be modified by an electro-mechanical effect which is governed by charge accumulation and change of sign at electrode edges.

Since thermal micropoling promotes large compositional variations between poled and unpoled areas, linear optical properties should also be impacted by the treatment as already observed in other glassy systems [START_REF] Lepicard | Long-lived monolithic micro-optics for multispectral GRIN applications[END_REF]. In particular, the Figure 6 focuses on the refractive index modification and structuring induced by poling. In the Figures 6a and6c are presented the top-view phase contrast images for samples G-70/4 and G-4/4 respectively. These images show the optical path difference (OPD) which is related to (i) the topology change and (ii) the poled layer thickness and its modified refractive index. They demonstrate that regular optical patterns are successfully produced by thermal micro-poling. Refractive index difference profiles could not be accurately obtained from the OPD since the strong topological variations at the poled/unpoled frontiers as well as the wavelength used for the phase contrast measurements do not give a reliable resolution around these areas. However, one could also disregard these edge effects and focus on the variation of the OPD between the center of the poled and the unpoled regions. With these considerations, as can be seen on the Figures 6b and6d, the OPD is estimated to 60 nm for G-70/4 and to for a homogenous poling [START_REF] Poirier | Second Harmonic Generation in Sodium Tantalum Germanate Glasses by Thermal Poling[END_REF], the refractive index difference n (n=npoled-nunpoled) between the unpoled and poled areas after topology correction (methodology described in Supplementary Material S2) can be estimated respectively to 9.510 -3 and 7.110 -3 for G-70/4 and G-4/4. Positive values of n point out a higher refractive index under the poled surface in these sodium tantalum germanate glasses, in opposition with refractive index decreases of the order of 10 -2 observed in niobium borophosphate glasses [START_REF] Karam | The effect of the sodium content on the structure and the optical properties of thermally poled sodium and niobium borophosphate glasses[END_REF]. Since usual n decreases after poling are attributed to a correlated local density drop due to sodium depletion, our results can be understood by a local compression of the glass structure under poling promoting a higher number of highly polarizable tantalum atoms per unit volume.

Anyway, positive n values of the order of 10 -3 are compatible with waveguide production and reveal that the micro-imprinting process by thermal poling is a promising methodology for the microscale control of both linear and non linear optical properties.

-Conclusion

Glass samples of composition 75GeO2-10Na2O-15Ta2O5 were prepared by the melt-quenching technique at 1500 °C and thermally poled using microstructured metallic electrodes. The electrode microscale patterns could be accurately reproduced over large areas at the surface of the glass. Structural rearrangements observed after poling were attributed to a sodium depletion out of the poled layer and consequent repolymerization of the germanate and tantalate glass network through conversion of terminal oxygens to bridging bonds and molecular oxygen. Local SHG signals related with both longitudinal and in-plane static electric fields were evidenced out of the poled borders and were found to be confined over a 5 m region. A model of charge density distribution explaining the second order non-linear properties is proposed for these specific glass composition and poling conditions. Topological effects were also characterized with a contraction of the poled surface of about 100 nm and strong edge effects of the order of 300 nm at the poled boundaries. Homogeneous optical contrasts could be produced along the imprinted patterns with a refractive index increase of about 8.10 -3 in the poled layers. Our results support the efficiency of this glass composition and thermal micropoling for the design of microscale linear and nonlinear optical devices.

  correspond respectively to the glass samples G-70/4 and G-4/4. For both samples, a sketch of the charge density distributions employed to simulate the different observables is presented at the top of the figure (Figure 4a1 and 4b1). The micro structured poled layers were simulated using three different charge concentrations: a positive one, ρ1 and two negative charge concentrations, ρ2 and ρ3. All possible combinations of charge concentrations range values were tested for the following set of values: [1.10 3 ; 3.10 3 ; 5.10 3 ; 7.10 3 ; 1.10 4 ] C/m 3 for ρ1 , [-1.10 3 ; -3.10 3 ; -5.10 3 ; -7.10 3 ; -1.10 4 ] C/m 3 for ρ2 and [-1.10 2 ; -1.10 3 ; -5.10 3 ; -1.10 4 ] C/m 3 for ρ3 . For each cases the electrical potential, the electrical field in the plane (along X) and out of the plane (along Z) were calculated.

  ρ1=7E 3 C/m 3 ; ρ2=-1E 4 C/m 3 and ρ3=-1E 2 C/m 3 for the sample G-70/4 in Figure 4a5 and ρ1=8E 3 C/m 3 ; ρ2=-5E 3

5 .

 5 Figures 5a, 5b and 5c present an optical image of the probed area, the corresponding AFM measured 3D image and a topology profile for sample G-70/4. The same investigation for the sample G-4/4 is presented in Figures 5d, 5e and 5f.

Figure 1 .

 1 Figure 1. Optical micrographs of the surface of (a) electrode E-70/4, (b) glass

Figure 2 .

 2 Figure 2. (a) Optical micrograph of the sample 70/4 and studied area, (b) Raman

Figure 3 .

 3 Figure 3. Optical micrographs of poled samples (a1) G-70/4, (b1) G-4/4 with

Figure 4 .

 4 Figure 4. Scheme of the electrostatic model of charge distribution and resulting

Figure 5 .

 5 Figure 5. (a) and (d) Optical micrographs of the studied area in samples G-70/4

Figure 6 .

 6 Figure 6. (a) and (c) Phase contrast images in samples G-70/4 and G-4/4, (b) and

Acknowledgments

The authors gratefully acknowledge for financial support: IdEx Bordeaux (Cluster of Excellence LAPHIA and Visiting Scholar support) and the CNRS project EMERGENCE@INC2019. Facilities from the platform SIV. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 823941 (FUNGLASS). This article reflects only the author's view and that the Agency is not responsible for any use that may be made of the information it contains.


Alice Goillot

Alexis Maillard

Tigran Galstian

Younès Messaddeq

Frederic Adamietz

Vincent Rodriguez

Marc Dussauze
email: marc.dussauze@u-bordeaux.fr

Plasma assisted micro poling of glassy surfaces: a new tool to achieve liquid crystal multi-domain alignments

We propose an innovative approach to program the alignment of liquid crystal (LC) assemblies allowing for the formation of multi-domain alignments whose orientation axis and sizes are controlled at the micrometer scale by an electrically patterned glass surface. The glass surface preparation is based on a thermo-electrical imprinting process to induce localized space charge implantations in the glass matrix just below its anode surface. To demonstrate this new approach, a commercial soda-lime glass slide has been polarized using as anode a simple micrometric nickel grid. Characterizing the polarized glass surface by second harmonic generation polarized microscopy; we show an accurate control of both location and spatial components of frozen static fields embedded in the glass as a function of the electrode patterns. The polarized glassy surface is then used in the conception of a LC cell in which homeotropic or planar alignments can be controlled following the electrical pattern induced on the glass surface. This study also points out the importance of plasma discharges spatially controlled along the electrode pattern during the process in order to promote the inplane electrical polarization effects, which are essential for the programming of the in-plane LC alignment on the polarized glass surface.

Introduction

Since the beginning of liquid crystal (LC) displays' (LCD) development in the 1960's [START_REF] Yang | Fundamentals of Liquid Crystal Devices[END_REF], this field has reached high level of maturity and is now bringing unique possibilities for the development of many other optical devices in photonics such as LCs-based optical attenuators, polarization controllers, phase retarders and waveguides for instance [START_REF] Chigrinov | Photoaligning and Photopatterning -A New Challenge in Liquid Crystal Photonics[END_REF]. To control LCs properties, one should manage their orientations that are governed by surface interactions. To do so, rubbing methods are largely adopted by the LC industry, as they permit large scale homogenous LCs ordering [START_REF] De Gennes | The Physics of Liquid Crystals[END_REF][START_REF] Zhu | Atomic force microscopic study of rubbed polyimide films[END_REF][START_REF] Kim | Rubbed polyimide films studied by scanning force microscopy[END_REF]. To offer new possibilities in the design of LC devices, various top-down fabrication techniques have been successfully developed to modify the orientation of LC assemblies on various surfaces [START_REF] Xia | Tailoring surface patterns to direct the assembly of liquid crystalline materials[END_REF]. Most of them are based either on chemical [START_REF] Lind | Modifying the surface wetting behavior of soda-lime silicate glass substrates through thermal poling[END_REF][START_REF] Hess | Optical patterning of magnetic domains and defects in ferromagnetic liquid crystal colloids[END_REF][START_REF] Guo | High-Resolution and High-Throughput Plasmonic Photopatterning of Complex Molecular Orientations in Liquid Crystals[END_REF] or on topological surface patterns to taylor LCs alignments. Among these methods, a large variety of photoalignment processes has been reported. They could be referred to two main different mechanisms among others, first, the irradiation can be used to locally modify the surface chemistry of photosensitive polymers or of a self-assembled monolayers [START_REF] Schadt | Optical patterning of multi-domain liquid-crystal displays with wide viewing angles[END_REF][START_REF] Park | Multi-domain Liquid Crystal Display with Self-Aligned 4-Domains on Surface Relief Gratings of Photopolymer[END_REF][START_REF] Park | A self-aligned multi-domain liquid-crystal display on polymer gratings in a vertically aligned configuration[END_REF][START_REF] Zhao | High-resolution photoaligned liquid-crystal micropolarizer array for polarization imaging in visible spectrum[END_REF]. Second, the orientational changes of LCs matrices can be triggered by photochromic molecules, the alignment here is obtained by direct irradiation of the LC mesophase [START_REF] Wei | Generating Switchable and Reconfigurable Optical Vortices via Photopatterning of Liquid Crystals[END_REF][START_REF] Goubert | Light Controlled Capillarity of Liquid Crystals on Photo Anisotropic Surfaces[END_REF][START_REF] Nersisyan | Study of azo dye surface command photoalignment material for photonics applications[END_REF]. Without going more into technical details about these well documented methods to control the assembly of LC materials, one should point out their growing interest as they open the way to accurate 2D and 3D controls of LC molecular arrangements for innovative properties and functionalities in many applications. However, most of the described above approaches are using wet processing of surfaces (casting various liquid films on substrates and the further processing to solidify them), which become larger and larger (reaching several meters of diameter for last generation of LCDs). This is dramatically complicating the manufacturing process. In this context, it might be very desirable to have an alignment technique that might provide local orientational patterning capability while avoiding the above-mentioned wet processes. In this paper, we propose a new approach for multi-domain LC alignment based on the use of a polarized ("poled") glass surface. The basic principle of the glass surface polarization process consists in the application of a high DC voltage to a heated glass substrate in order to induce a depletion of ionic charge carriers, such as alkali cations, in the glassy matrix. Then, the temperature is decreased to freeze the polarized state of the glass before to turn off the DC field. The studies of electrically polarized glassy surfaces have been a topic in the early 1990's with works on second order optical properties in poled silica for photonic applications [START_REF] Myers | Large second-order nonlinearity in poled fused silica[END_REF], as well as for anodic bonding in microelectronic applications [START_REF] Wallis | Field Assisted Glass-Metal Sealing[END_REF][START_REF] Nitzsche | Ion Drift Processes in Pyrex-Type Alkali-Borosilicate Glass during Anodic Bonding[END_REF][START_REF] Dussauze | Structural Rearrangements and Second-Order Optical Response in the Space Charge Layer of Thermally Poled Sodium-Niobium Borophosphate Glasses[END_REF]. More recently this kind of DC poling process has been shown to be manageable at the micrometric scale resulting in thermo-electrical micro-imprinting treatments of glass surfaces [START_REF] Fleming | Imprinting of glass[END_REF]. When applied to specifically optimized glass compositions, an accurate control of various properties were reported such as optical properties (refractive index [START_REF] Dussauze | Refractive index distribution in the non-linear optical layer of thermally poled oxide glasses[END_REF] and second order optical response [START_REF] Karam | The effect of the sodium content on the structure and the optical properties of thermally poled sodium and niobium borophosphate glasses[END_REF][START_REF] Karam | Electrically Micro-Polarized Amorphous Sodo-Niobate Film Competing with Crystalline Lithium Niobate Second-Order Optical Response[END_REF]), surface electrical potential [START_REF] Alvarado | Patterning of the Surface Electrical Potential on Chalcogenide Glasses by a Thermoelectrical Imprinting Process[END_REF] but also chemical properties (durability [START_REF] Chazot | Enhancement of mechanical properties and chemical durability of Soda-lime silicate glasses treated by DC gas discharges[END_REF] and surface reactivity [START_REF] Lepicard | Microstructuring the surface reactivity of a borosilicate glass via thermal poling[END_REF][START_REF] Kamenskii | Effective diffraction gratings via acidic etching of thermally poled glass[END_REF]) and wettability [START_REF] Lind | Modifying the surface wetting behavior of soda-lime silicate glass substrates through thermal poling[END_REF]. Following the idea that such methodology allows to pattern surface electrical functions on a large variety of ionic glasses [START_REF] Alvarado | Patterning of the Surface Electrical Potential on Chalcogenide Glasses by a Thermoelectrical Imprinting Process[END_REF][START_REF] Lepicard | Demonstration of dimensional control and stabilization of second harmonic electro-optical response in chalcogenide glasses[END_REF][START_REF] Dussauze | Accurate Second Harmonic Generation Microimprinting in Glassy Oxide Materials[END_REF][START_REF] Rajaofara | Mapping the second and third order nonlinear susceptibilities in a thermally poled microimprinted niobium borophosphate glass[END_REF], in this work, we focus our attention on the use of frozen static electric fields patterned in a poled glass substrate to impose a so-called "easy axes" for LCs orientations on its surface. We have characterized the electrical fields' locations and spatial components, patterned on a commercial silicate glass surface, by using Second Harmonic Generation (SHG) polarized microscopy. A clear correlation is demonstrated between the glass surface electrical patterns and both orientations and domain formations of LCs characterized by cross polarization microscopy and polarized Raman imaging. Lastly, we highlight the importance of surface electrical current and plasma discharges during the imprinting polarization process in order to promote long-range in-plane electrical polarization effects, which are essential for a further control of in-plane LCs alignment on the polarized glass surface. We think that this approach can be developed into a step-by-step poling technique that may become a practical tool for modern LC device manufacturing, providing thus better performance and functionalities.

Thermo-electrical imprinting process and LC cell preparation

Figure 1 schematically shows various steps of the LC cell preparation which starts from an imprinting thermo-electrical process (Figure 1 (a)) to pattern the surface of a commercial soda lime silicate glass (SLG). The polarization treatment was done at 250 °C with a voltage of 1400 V during 30 min under nitrogen atmosphere. The anode configuration governing the final electrical pattern on the glass surface is a nickel grid having a thickness of 4µm and composed of 10 µm wide wires forming 40 µm wide squares. To finalize the treatment, the temperature is decreased to room temperature, the voltage is turn off and the poled SLG surface is extracted (Figure 1 (b)) in order to be used in the conception of a LC cell (Figure 1 (c)). The poled substrate is assembled with another SLG glass that was coated with a homeotropic polyimide polymer (PI) using a UV curing glue and silica balls as spacers to constitute a 5 µm thick LC cell (Figure 1(c)). The cell is then filled with the LC composition 4'-hexyl-biphenylcabonitrile (Figure 1(d)), sold by Merck. Before to characterize the poled glass surface and finally the LC cell, one should note the peculiarities of this thermo-electrical process by pointing out the generation of DC plasma occurring at the vicinity of the electrode edges and the glass surface. A video of localized plasma emissions has been recorded during the poling treatment using a 50x microscope objective that allows to observe the location and the dynamic of these DC gas discharges (see Visualization 1 for the complete video). In Figure 2(a) and (b), we have depicted respectively a picture of the nickel grid used as anode and a "stacking" picture corresponding to 1 min of the plasma emission video. Plasma-assisted poling processes have been reported previously [START_REF] Chazot | Enhancement of mechanical properties and chemical durability of Soda-lime silicate glasses treated by DC gas discharges[END_REF][START_REF] Cremoux | Trapped Molecular and Ionic Species in Poled Borosilicate Glasses: Toward a Rationalized Description of Thermal Poling in Glasses[END_REF], similarly, we observe in the current study (i) the same spectral emission from second positive system (SPS) electronic transition of N 2 (C 3 Π u → B 3 Π g ) [START_REF] Karam | Electrically Micro-Polarized Amorphous Sodo-Niobate Film Competing with Crystalline Lithium Niobate Second-Order Optical Response[END_REF] and (ii) a good correlation between temporal evolutions of electrical current and plasma emission ( The voltage increases with a slope of 280 V/min, reaching the target value of 1400 V at 300 sec and is constant until the end of the treatment, the temperature decrease at 2150 sec. On the inset is reported the emission spectrum measured within 300-450 nm spectral range.

Results

Glass composition and second harmonic generation response of the micro structured poled glass surface.

As reminded in the introduction, the main expected effects of such thermo-electrical polarization process concern (i) the formation of a mobile cations depletion and structural changes of the glassy matrix and (ii) the implantation of frozen charges and static electrical fields. [START_REF] Quiquempois | Model of charge migration during thermal poling in silica glasses: Evidence of a voltage threshold for the onset of a second-order nonlinearity[END_REF][START_REF] Dussauze | Génération de second harmonique dans des verres borophosphate de sodium et niobium par polarisation thermique[END_REF][START_REF] Dussauze | Thermal Poling of Optical Glasses: Mechanisms and Second-Order Optical Properties[END_REF][START_REF] Crémoux | Physico-chimie aux interfaces de systèmes vitreux à charge d'espace[END_REF][START_REF] Lepicard | Design of surface chemical reactivity and optical properties in glasses[END_REF][START_REF] Mclaren | Depletion Layer Formation in Alkali Silicate Glasses by Electro-Thermal Poling[END_REF][START_REF] Mclaren | Mechanism of electric field-induced softening (EFIS) of alkali silicate glasses[END_REF] These process outcomes on the glass surface properties were respectively characterized by Energy-dispersive X-ray (EDX) spectroscopy and SHG polarized imaging. In Figure 3 (a), we show the imprinted glass surface observed with an optical microscope.

The zones in contact with the grid have a rather uniform aspect with some topological defects linked to the influence of the grid roughness on the imprinting process [START_REF] Fleming | Imprinting of glass[END_REF]. The inner part of the patterns, corresponding to the location of the plasma discharges, presents an iridescence linked to refractive index variations as reported in one of our previous study [START_REF] Lepicard | Long-lived monolithic micro-optics for multispectral GRIN applications[END_REF]. ), the probed thicknesses have been estimated to 1.21 µm at 10 KeV and 3.88 µm at 20 KeV. [START_REF] Goldstein | Scanning Electron Microscopy and X-Ray Microanalysis[END_REF] At 10 KeV, the Na 2 O and K 2 O concentrations are always measured below 0.5 mol% for the whole surface. As the initial glass composition contains 15.45 mol% of Na 2 O and 0.8 mol% of K 2 O, it points out the complete alkaline ions depletion occurring at the surface. Concerning the alkaline earth oxides, at 10 KeV their concentration profiles show large variations with a strong concentration gradient at the boarder of the square which reach a plateau in the middle of the square patterns. A similar trend is observed for the Na 2 O profile probed at 20 KeV. A mapping of the Na 2 O concentration measured for a 20 keV electron beam (Figure 3 (c)) reveals the poling induced spatial gradients of mobile cations concentrations which patterns follow accurately the electrode geometry. The thickness of the sodium depletion layer is maximum at the electrode/glass surface contact area and decrease gradually from the electrode edge towards the center of the square patterns. If one compare these results to other micro-poling studies using patterned thin films as anode electrodes (metallic or ITO 100 nmthick films) [START_REF] Karam | The effect of the sodium content on the structure and the optical properties of thermally poled sodium and niobium borophosphate glasses[END_REF][START_REF] Karam | Electrically Micro-Polarized Amorphous Sodo-Niobate Film Competing with Crystalline Lithium Niobate Second-Order Optical Response[END_REF][START_REF] Alvarado | Patterning of the Surface Electrical Potential on Chalcogenide Glasses by a Thermoelectrical Imprinting Process[END_REF][START_REF] Lepicard | Microstructuring the surface reactivity of a borosilicate glass via thermal poling[END_REF][START_REF] Lepicard | Demonstration of dimensional control and stabilization of second harmonic electro-optical response in chalcogenide glasses[END_REF][START_REF] Lepicard | Long-lived monolithic micro-optics for multispectral GRIN applications[END_REF], the main difference concerns the spatial effects of the polarization treatment, i.e. the location of the induced depletion in mobile ions. In these previous studies using thin films as anode, the depletion is no more effective few micrometers out of the electrode contact zones. One could explain such difference by the larger thickness of the nickel grid anode (4 µm) that allows for localized plasma generation thanks to a sufficient quantity of gas within the volumes formed by the micrometric grid. This localized gaz discharges permit to carry surface electrical currents, which considerably extend the inplane polarization effects and thus allow the imprinting process to be effective on the entire glassy surface. polarization process on the glass matrix. SHG imaging of the polarized glass surface was achieved in reflection (epifluorescence) mode with four linear state configurations of light polarization. All technical details are available in the experimental section, but one should remind that the incident laser beam is focused on the poled glass surface with a numerical aperture of 0.40 and a linear incident polarization oriented either along the X or Y axis chosen to be parallel to the square patterns directions. Similarly, either the X or Y linear polarization of reflected SHG signals are analyzed. It forms a combination of four images of SHG intensity (I XX , I YY , I XY and I YX ; the first and second indexed letters correspond respectively to the incident light polarization and the SHG analyzed polarization). Note a SHG intensity image I IJ (I, J= X, Y) probe the second-order susceptibility χ (2) J;II . Such analysis allows a complete characterization of the in-plane components of the second order optical susceptibility tensor,  , originating from the in-plane poling effects on the glassy surface. Figure 4 shows the four polarized SHG images of a 50 µm wide zone centered on an imprinted square pattern. The SHG signals are located at the borders of the square pattern corresponding to the edges of the anode grid and are highly dependent on both incident light and SHG polarization states. By comparing intensities of SHG in parallel and crossed light polarization configuration, we observe that the terms   X;XX and   X;YY are maximum for a pattern orientation along the Y axis and null along the X axis. Similarly,   Y;YY and   Y;XX are maximum for a pattern orientation along the X axis and null along the Y axis. Moreover, one has to notice the high similarity of the SHG images measured with the same SHG polarization state. Such spatial correspondence allows evaluating polarization ratio (i.e. I XX /I YX and I YY /I XY ) which are found to be close to 9 (±10%) for all SHG active zones. These observations point out the following links between the patterned   components  X;XX =3.  X;YY and   Y;YY =3.  Y;XX . As expected from previous studies [START_REF] Myers | Large second-order nonlinearity in poled fused silica[END_REF][START_REF] Dussauze | Thermal Poling of Optical Glasses: Mechanisms and Second-Order Optical Properties[END_REF], this is in accordance with an electro optical origin of the poling induced loss of centrosymmetry for which the second order optical response originates from an interaction between a static electrical field, E stat , and the third order susceptibility of an isotropic media, χ (3) , in other words:     E stat [START_REF] Lepicard | Design of surface chemical reactivity and optical properties in glasses[END_REF][START_REF] Kazansky | Thermally poled glass: frozen-in electric field or oriented dipoles?[END_REF]. Finally, this polarized SHG characterization put in evidence the spatial patterning of multicomponent electric fields which in-plane orientation and location are accurately controlled. These spatially controlled polarization effects should be linked to the directional control of surface electrical current during the thermo-electrical polarization process, which allows to manage the geometry of both charge gradients and frozen static fields. After the characterization of the poled glass surface, the LC cell is fabricated as shown in Figure 1c. Figure 5 shows pictures of the cell examined between crossed polarizers for an orientation of 0°, 22.5° and 45°, the observations for 90° and 67.5° are respectively similar to the first two. There is a strong dependence of the light transmission with the LC cell rotation, which can lead to LC orientation deduction. At 0°, the cross polarizer are parallel to the square pattern directions, the aspect of the cell is dark, except a white cross along the diagonals AC and BD. For a rotation of 22.5°, the parts corresponding to the contact area with the anode grid during the poling process stay dark, the brightness increase inside four triangular domains formed by the cross (ABO, BCO, CDO, ADO), the brightness of the cross formed by the diagonal lines decrease. At 45°, the brightness in the four triangles is equal and maximum, the parts forming the contour of the square pattern stay dark. These observations demonstrate that (i) the LC alignment is homeotropic along the square pattern i.e. the glass surface that was in direct contact with the anode grid and (ii) inside the square patterns, i.e. at the location of the plasma discharges during the poling process, the LC alignment is planar. The triangular domains observed in this zone corresponds to planar alignments either parallel or perpendicular to the borders of the squares. To complete the molecular alignment description, we have carried out Raman polarized imaging characterizations, as Raman spectroscopy is well known to be sensitive to LC orientations [START_REF] Davies | Non-linear Raman spectroscopy of liquid crystals: Polarization measurements and relaxation processes in 4-cyano-4′-heptylbiphenyl (7CB)[END_REF][START_REF] Jen | Raman Scattering from a Nematic Liquid Crystal: Orientational Statistics[END_REF][START_REF] Jen | Polarized Raman scattering studies of orientational order in uniaxial liquid crystalline phases[END_REF][START_REF] Miyano | Raman depolarization ratios and order parameters of a nematic liquid crystal[END_REF]. The Raman spectra of the molecule used in this work (Figure 5 (b)) shows four strong bands which can be identify to: C-H in-plane bending vibration at 1175 cm -1 , inter-ring C-C stretching at 1280 cm -1 , benzene-ring stretching at 1606 cm -1 and C≡N stretching at 2226 cm -1 .

[51] The 4'-hexylbiphenylcabonitrile's triple bond C≡N leans toward the molecule axis and its stretching mode is known to be an accurate probe of the LC alignment by Raman methods [START_REF] Davies | Non-linear Raman spectroscopy of liquid crystals: Polarization measurements and relaxation processes in 4-cyano-4′-heptylbiphenyl (7CB)[END_REF][START_REF] Miyano | Raman depolarization ratios and order parameters of a nematic liquid crystal[END_REF]. Thus, two Raman intensity images of the C≡N stretching using polarization state of both incident laser and analyzed Raman (called also parallel polarization I // ) either along the X or Y laboratory axis (noted I XX and I YY ) are shown in Figure 5 (b).

The triangular domains with planar orientations are clearly observed by Raman imaging. The triangles pointing up or down towards the square centers are seen in the I YY polarization configuration. Inversely, triangles pointing horizontally towards the middle of the patterned squares are observed for the I XX Raman map. Of course, these results are consistent with the data obtained by observations with a pair of crossed polarizers. But they allow to precise that inside the triangular domains, LCs have a planar orientation perpendicular to the closer border of the square. One should also notice that for all triangular domains depicted in Figure 5, their optical responses are identical showing the same degree of alignment. These domains differ only by the in-plane orientation of their optical axis that appears to be dictated by the patterned glass surface. Finally, one needs to correlate the formation of LC multi domain of alignments with the polarized glass surface characterizations detailed above. One key observation of this study concerns the surface electrical field characterized by SHG measurements that appear to be accurately linked to the LCs planar alignments observed within the triangular domains formed in the square patterns. Similarly, for the areas forming the contour of the square patterns, the homeotropic LC orientation observed should be linked to an expected static field perpendicular to the surface due to its location at the contact zone with the anode grid during the poling process. Unfortunately, the out of plane electro optical response cannot be characterized by SHG microscopy using linear light polarization as carried out in this study. Nevertheless, such out of plane field components have been reported many times for classical planar electrodes using an adapted SHG Maker Fringes characterization method [START_REF] Dussauze | Thermal Poling of Optical Glasses: Mechanisms and Second-Order Optical Properties[END_REF] or by SHG microscopy using radial polarization state of the incident laser and high numerical aperture objectives [START_REF] Karam | The effect of the sodium content on the structure and the optical properties of thermally poled sodium and niobium borophosphate glasses[END_REF][START_REF] Karam | Electrically Micro-Polarized Amorphous Sodo-Niobate Film Competing with Crystalline Lithium Niobate Second-Order Optical Response[END_REF]. To summarize this correlation, in Figure 6 schematic representations of both static field components deduced from SHG measurements and LCs orientations are depicted. The static fields frozen within the sub surface of the glassy matrix induce uniform LC alignment parallel to their direction. At the boundary lines formed by the polarized pattern, the planar components of the static fields are maximum, which further guide the LCs planar alignment towards the middle of the patterned squares.

As a last comment, one should put an emphasis on the importance of surface electrical currents promoted by plasma discharges extending considerably the in-plane polarization effects. One should note that poling conditions without surface plasma ignitions (using patterned thin films as anode electrodes) did not permit to induce efficient LC alignments. This point supports that it is essential to polarize the entire glass surface using long range inplane poling effects for an accurate control of LC alignments. They might be at the origin of other surface mechanisms influencing the LC alignment. One can suppose the existence of some very weak poling-induced surface anisotropy which could not be observed with the characterization tools used in this study. Additionally, the surface charge density induced along the entire glass surface is expected to modify the surface energy [START_REF] Lind | Modifying the surface wetting behavior of soda-lime silicate glass substrates through thermal poling[END_REF][START_REF] Crémoux | Physico-chimie aux interfaces de systèmes vitreux à charge d'espace[END_REF][START_REF] Mugele | Electrowetting: from basics to applications[END_REF] and influence the LC surface anchoring mechanisms. Further experiments are in progress to tackle these assumptions.

Conclusion

Static electric fields can be imprinted on a commercial silicate glass by a thermo-electrical polarization process enabling an accurate spatial programming of LCs orientation, including the formation of complex multi domain alignments. The orientation of static fields, implanted at the surface of the glass substrate, were characterized by polarized SHG imaging and a clear correlation between LC alignments (characterized by polarized micro-Raman imaging) and both location and direction of implanted fields has been shown. The presence of plasma discharges allows extending the surface electrical currents enabling polarization effects on the whole surface with an accurate directional control. This study is a new proof of concept demonstrating that an accurate control of LC organization can be achieved by managing glass surface electrical properties. We think that this new surface electrical functionality has significant potential for the fabrication of next generation of LC devices.

Experimental Section/Methods

LC cell preparation:

The glass used was a 1 mm thick slide of a commercially available soda lime glass (SLG) with a composition of 72.20 wt% SiO 2 , 14.30 wt% Na 2 O, 6.40 wt% CaO, 4.30 wt% MgO, 1.20 wt% K 2 O, and 1.20 wt% Al 2 O 3 . A sample has been washed by solvents in ultrasound baths before to be poled with a nitrogen atmosphere at normal pressure and an atmospheric humidity lower than 1 %. The anode used is a nickel grid composed of 10 µm wide wires and 40 µm wide squares as shown in Figure 1a; the thickness of the grid is 4 µm. At the other side, a piece of silicon wafer was used as the cathode. All the system was heated to 250 °C and a voltage of 1400 V was then applied during 30 min. In the meanwhile, an acquisition of a video with a camera connected to an objective of 50x (NA = 0,42) has been done to record plasma emissions.

After having characterized the surface, the poled substrate is assembled with a soda-lime glass coated with a homeotropic polyimide (PI) using a UV curing glue and silica balls as spacers to constitute a 5 µm thick cell (Figure 1c). The cell is then filled with a liquid crystal composed of the molecule 4'-hexyl-biphenylcabonitrile (Figure 1d) sold by Merck.

Characterization:

A scanning electron microscopy Quanta FEI system coupled with an energy-dispersive xray spectroscopy detector (EDX) is used to quantify the atomic composition at the surface of the sample.

Polarized SHG images were recorded with a µ-SHG XY scanning system by optical microscopy combined with SHG spectroscopy on a custom-built scanning SHG microscope developed at the ISM lab [START_REF] Gouget | Isolating the Two Room-Temperature Polymorphs of NaNbO 3 : Structural Features, Optical Band Gap, and Reactivity[END_REF][START_REF] Chazot | Investigation of ZnSe stability and dissolution behavior in As-S-Se chalcogenide glasses[END_REF]. The excitation source used was a 1064 nm picosecond laser (Leukos Opera), which delivers 50 ps pulses at a repetition rate of 1 MHz. The laser incident light was set at an average power of 300 mW and focused into the sample with a near-IR 20 × objective (Mitutoyo M-PLAN APO, NA 0.4), and the resultant SHG at 532 nm was collected in the backward direction (epifluorescence mode) using a photomultiplier tube. Large polarized SHG images of 50 × 50 μm2 where recorded with a spatial resolution of 1 μm.

The first LC characterization method was transmission optical microscopy with a pair of crossed polarizers: a microscope with a 50x (NA = 0.42) objective is used to observe the LC cell placed in the XY plane, transmitted white light propagated along the Z axis, the analyzer and polarizer being respectively parallel to X and Y. The cell was then rotated along the Z axis. Second, we used a micro-Raman HR800 (Horiba/Jobin-Yvon) spectrometer with a 532 nm CW laser as source in the backscattering geometry at room temperature, the spectral resolution was 2.5 cm -1 . The liquid crystal cell was placed in XY plane and laser beam propagated along Z. Two polarized Raman maps were measured, using variable polarizations of both incident laser and analyzed Raman scattering either along X or Y directions.

Figure 1 .

 1 Figure 1. Schematics of LC cell fabrication steps: (a) thermo-electrical imprinting treatment, (b) Extraction of the patterned SLG substrate (c) LC cell conception formed of the assembly of the poled SLG surface with a homeotropic PI coated glass. The 5µm thick cell is then filled with 4'-hexyl-biphenylcabonitrile LCs ((d) LC chemical formula).

Figure 2 (Figure 2 .

 22 Figure 2. (a) anode picture before poling from the top, (b) "stacking" picture of 1 min of the plasma video during poling (see Visualization 1) and (c) recorded electrical current and plasma emission intensity during poling in function of time. The voltage increases with a slope of 280 V/min, reaching the target value of 1400 V at 300 sec and is constant until the end of the treatment, the temperature decrease at 2150 sec. On the inset is reported the emission spectrum measured within 300-450 nm spectral range.

Figure 3 .

 3 Figure 3. a) Observation of the surface after poling with an optical microscope. EDX characterisations: b) cation oxide concentration profiles for a beam energy of 10 keV, the straight lines materializing the initial oxide concentrations, [Na 2 O] = 15,45 mol%, [MgO] = 8,44 mol%, [CaO] = 8,09 mol%, [K 2 O] = 0,82 mol%, c) mapping representing Na EDX signal (arbitrary units in counts (cts)) and d) Na 2 O composition quantification with different electron beam energies, the 20keV smoothing is calculated by adjacent averaging method, with a window size of 10 points.

Figure 3 (

 3 b) contains the alkaline and alkaline earth oxides composition profiles measured with a 10 keV electron beam whereas in Figure 3 (d) we focus on the sodium oxide composition measured with respectively 10 and 20 keV electron beams. Adjusting the electron beam energy allows to probe different thicknesses of the polarized surface. By assuming a uniform density of the glass matrix ( g/cm 3

Figure 4 .

 4 Figure 4. Polarized SHG intensity image of the poled glass surface centered on a square.

8 3. 2 Figure 5 .

 825 Figure 5. (a) Observations between crossed polarizers of the LC cell for various rotation angles, A and P arrows respectively symbolize directions of the analyzer and polarizer. (b) Polarized Raman spectra of the liquid crystal 4'-hexyl-biphenylcabonitrile molecule, Raman mapping of the C≡N triple bond stretching mode with incident and analyzed polarization state either along the X or Y axis.

Figure 6 .

 6 Figure 6. Schematic representation of a) static electrical fields implanted at the glass surface and b) LC alignments.

Funding

This study has received financial support from the Canadian NSERC (05888) and CRC (230212) as well as French State in the framework of the Investments for the Future programme IdEx université de Bordeaux / GPR LIGHT. The authors gratefully acknowledge the financial support from the CNRS project EMERGENCE @INC2019. This project has received funding from the European Union's Horizon 2020 research program under the Marie SkłodowskaCurie grant agreement no. 823941 (FUNGLASS), from the Conseil Régional Aquitaine (IR Funglass) and from the Agence Nationale de la Recherche (Proteus). The Raman experiments were conducted using the SIV platform at the University of Bordeaux founded by the FEDER and the Region Aquitaine.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Disclosures 12

The authors declare no conflict of interest.