Roman Teisserenc
email: rteisserenc@gmail.com

Marc Lucotte

Ste ´phane Houel

Á M Lucotte

Á S Houel

S Houel

Terrestrial organic matter biomarkers as tracers of Hg sources in lake sediments

Keywords: Mercury, Lignin biomarker, Boreal forest lakes, Terrigenous organic matter, Sediment

Terrestrial organic matter (TOM) plays a key role in mercury (Hg) dynamics between watersheds and lakes. In this study we attempts to determine the role of TOM source and quality and not only quantity, in the fate and transport of total Hg (T-Hg) to boreal lakes. Integrating the watershed complexity is a daunting task. Within the scope of this project, we characterized this organic matter at a molecular level in order to determine Hg transfer conditions to the sediments. We sampled ten lakes in the Quebec boreal forest. In each lake, we took a sediment core at the deepest point in addition to analyzing T-Hg and a set of terrigenous biomarkers in recent sediments. Our results show no relationship between TOM quantity and T-Hg concentration in lake sediments. However, [T-Hg] variation is well explained by the increase of 3,5Bd/V ratios (R 2 = 0.84; p \ 0.0002) and the decrease of C/V ratios (R 2 = 0.5; p \ 0.0227). Our study shows that TOM source and quality are determinant for Hg loadings in lake sediments. More precisely, increasing TOM derived from humified soil horizons explains most of Hg level variation within sediments.

Introduction

Mercury (Hg) deposition in boreal lakes has increased significantly over the last century [START_REF] Jackson | Long-range atmospheric transport of mercury to ecosystems, and the importance of anthropogenic emissions-a critical review and evaluation of the published evidence[END_REF][START_REF] Lindberg | A synthesis of progress and uncertainties in attributing the sources of mercury in deposition[END_REF]. There is a consensus among the scientific community that this increase can be attributed to the anthropogenic emission of gaseous Hg that has been taking place since the beginning of the industrial era, primarily due to the combustion of fossils fuels [START_REF] Pacyna | Global anthropogenic mercury emission inventory for 2000[END_REF]. This anthropogenic Hg adds to Hg naturally present in ecosystems. Even in remote areas, high Hg levels in boreal ecosystems are observed. Indeed, Hg (anthropogenic, natural) can be carried over long distances far from point sources via atmospheric transport [START_REF] Fitzgerald | The case for atmospheric mercury contamination in remote areas[END_REF][START_REF] Pacyna | Global anthropogenic mercury emission inventory for 2000[END_REF]). Atmospheric Hg is then transferred to the environment by dry and wet depositions. Hg then tends to accumulate in lake sediments where increases in T-Hg are well recorded [START_REF] Lucotte | Anthropogenic mercury enrichment in remote lakes of northern Quebec (Canada)[END_REF][START_REF] Rognerud | Trace element contamination of Norwegian lake sediments[END_REF]. Previous studies measuring T-Hg concentrations [T-Hg] in recent boreal lake sediments reported values that vary between 50 and 500 ppb [START_REF] Lucotte | Anthropogenic mercury enrichment in remote lakes of northern Quebec (Canada)[END_REF][START_REF] Kainz | Mercury concentrations in lake sediments-revisiting the predictive power of catchment morphometry and organic matter composition[END_REF]. The role of TOM dynamics on the fate of Hg in these environments has often been proposed to explain [T-Hg] differences among lake sediments [START_REF] Kolka | Mercury and organic carbon relationships in streams draining forested upland/peatland watersheds[END_REF]. Indeed, organic matter is composed of a complex mixture of various compounds that bind heavy metals including Hg. Several studies have observed that the levels of T-Hg transported to lakes are related to TOM concentration [START_REF] Driscoll | The role of dissolved organic carbon in the chemistry and bioavailability of mercury in remote Adirondack lakes[END_REF][START_REF] Kolka | Mercury and organic carbon relationships in streams draining forested upland/peatland watersheds[END_REF][START_REF] Kainz | Relationships between organic matter composition and methyl mercury content of offshore and carbon-rich littoral sediments in an oligotrophic lake[END_REF][START_REF] Sanei | Relationship between organic matter and mercury in recent lake sediment: the physicalgeochemical aspects[END_REF]). More precisely, some studies raised the issue that TOM quality (source, composition), more than the sole quantity of TOM entering the lake, plays a key role in the fate of Hg in the environment [START_REF] Lucotte | Anthropogenic mercury enrichment in remote lakes of northern Quebec (Canada)[END_REF][START_REF] Kainz | Mercury concentrations in lake sediments-revisiting the predictive power of catchment morphometry and organic matter composition[END_REF][START_REF] Sanei | Relationship between organic matter and mercury in recent lake sediment: the physicalgeochemical aspects[END_REF][START_REF] Caron | Mercury transfer from watersheds to aquatic environments following the erosion of agrarian soils: a molecular biomarker approach[END_REF][START_REF] Ouellet | Lignin biomarkers as tracers of mercury sources in lakes water column[END_REF]. The regime of atmospheric Hg deposition on soil also varies according to vegetation [START_REF] Schroeder | Atmospheric mercury-an overview[END_REF][START_REF] Demers | Mercury cycling in litter and soil in different forest types in the Adirondack region, New York, USA[END_REF]. Furthermore, the hydrologic regime of forested watersheds will be modified by its vegetation composition, leading to differential Hg and TOM leaching into lakes.

Lignin phenol derivatives, obtained after a mild cupric oxidation (CuO), yield interesting information on TOM source and composition. Applicable in several environments, they have been broadly used to describe the TOM composition of sediments from various watersheds in addition to reconstructing past vegetation changes [START_REF] Hu | Lignin biomarkers and pollen in postglacial sediments of an Alaskan lake[END_REF][START_REF] Dalzell | The role of hydrology in annual organic carbon loads and terrestrial organic matter export from a midwestern agricultural watershed[END_REF]. Recent studies have used these biomarkers for environmental issues [START_REF] Louchouarn | Historical and geographical variations of sources and transport of terrigenous organic matter within a large-scale coastal environment[END_REF][START_REF] Houel | Translocation of soil organic matter following reservoir impoundment in boreal systems: implications for in situ productivity[END_REF]) such as the fate of contaminants in the environment [START_REF] Louchouarn | A historical reconstruction of organic and inorganic contamination events in the Saguenay Fjord/St. Lawrence system from preindustrial times to the present[END_REF][START_REF] Caron | Mercury transfer from watersheds to aquatic environments following the erosion of agrarian soils: a molecular biomarker approach[END_REF][START_REF] Ouellet | Lignin biomarkers as tracers of mercury sources in lakes water column[END_REF]. Earlier studies validated the use of CuO derived biomarkers to describe TOM composition variation due to watershed characteristics [START_REF] Teisserenc | Dynamique de la matie `re organique terrige `ne et du mercure dans les lacs et re ´servoirs bore ´aux[END_REF]. Here, we propose to follow the influence of TOM composition, revealed by CuO derived biomarkers, as a predictive variable on [T-Hg] in recently deposited lake sediments. By tracing TOM coming from deciduous and coniferous species as well as describing its state of degradation, we aim at determining the importance of TOM on Hg dynamics. This integration of watershed characteristics through molecular analysis should improve our understanding of [T-Hg] variation among lakes from the same region.

Materials and methods

Sampling sites

Ten oligotrophic lakes situated in the boreal forest were sampled. These lakes are located in two distinct administrative regions of North-eastern Canada: Outaouais and Temiscamingue (Fig. 1, Table 1). All lakes studied are part of the boreal forest ecosystem dominated by black spruce (Picea mariana), balsam fir (Abies balsamea), and grey pine (Pinus sabineana) for gymnosperm species and by white and yellow birch (Betula papyrifera, Betula alleghaniensis), maple (Acer spp.) and aspen (Populus sp.) for angiosperm species. Watersheds are covered by mixed wood forest dominated by deciduous species for the ten lakes and are located on the Grenville geological province (Fig. 1). These lakes lie on gneiss bedrock covered by thin glacial deposits. The soils are mainly podzolic, and overlay till or sand deposits.

Sampling

Sediment cores were sampled using a pneumatic Mackereth corer [START_REF] Mackereth | A portable core sampler for lake deposits[END_REF]) at maximum depth of each lake. The top 5 cm were subsampled at each centimeter in order to study the recent TOM and Hg deposition in these lakes. To avoid cross contamination, the contour in contact with the corer was removed. The samples were then freeze-dried prior to analysis.

Chemical analysis

Sediment samples were homogenized with a glass rod prior to total carbon and nitrogen analysis on a Carlo Erba (NA-1500) elemental analyzer with a reproducibility of 5%. Analyses of molecular biomarkers were performed based on the copper oxidation (CuO) method initially developed by [START_REF] Hedges | Characterization of lignin by gas capillary chromatography of cupric oxidation products[END_REF] and modified by Gon ˜i and Montgomery (2000). Extraction products were analyzed on a GC/MS system (VARIAN 3800/Saturn 2000) fitted with a fused capillary column (Varian FactorFour VF-1 ms 60 m, 0.32 mm). The most common CuO derivatives used in recent literature and analyzed for the purpose of our study are three lignin derived phenols families: Vanillyls (V: ubiquitous in all terrestrial plants), Cinnamyls (C: produced by nonwoody tissues) and Syringyls (S: specific for angiosperm plants) [START_REF] Hedges | The characterisation of plant tissues by their lignin oxidation products[END_REF]. These three families are used to determine the source of TOM along with its relative abundance (R8 normalized according to 10 g of sample: sum of V, C and S). p-Hydroxyl phenols and an aromatic carboxylic acid (3,5-dihydroxybenzoic acid) are also combined with V and S to describe the state of degradation and humification of TOM [START_REF] Houel | Translocation of soil organic matter following reservoir impoundment in boreal systems: implications for in situ productivity[END_REF][START_REF] Dickens | Sources and distribution of CuOderived benzene carboxylic acids in soils and sediments[END_REF]). Analyses of T-Hg concentrations were performed by cold vapour atomic fluorescence spectrometry detection (CVA-FS) following the protocol developed by [START_REF] Bloom | Determination of volatile mercury species at the picogram level by low-temperature gas chromatography with cold-vapour atomic fluorescence detection[END_REF] and adapted by [START_REF] Pichet | Analysis of total mercury and methylmercury in environmental samples[END_REF]. Briefly, a combination of acid HNO 3 :HCl (16:6 N) (10:1 ml) is added to approximately 250 mg of freeze dried, ground sediment and then heated to 120°C for 6 h. The remaining solution is brought back to a volume of 30 ml with NANOpureÒ water and analyzed by atomic fluorescence.

Results

In the following results we present the average values and standard deviation for the top 5 cm of each sediment core. Indeed, in order to integrate TOM dynamics between a lake and its surrounding watershed, we chose to analyze the first 5 cm of each sediment core. The first 5 cm represent between 20 and 30 years of sedimentation, estimated according to sedimentation rates measured in this region (sedimentation rate: 0.22 ± 0.06 cm year -1 n = 4) by [START_REF] Lucotte | Anthropogenic mercury enrichment in remote lakes of northern Quebec (Canada)[END_REF]. In order to evaluate potential changes due to early diagenesis in this 5 cm sediment layers, we plotted each indicator measured in the first centimeter against the mean value of 2-5 cm. For each indicator, the relationships are linear with regression coefficients varying between 0.83 and 0.96 and slopes close to 1 (0.76-0.96). The C/V, P/ (V ? S) and 3,5Bd/V ratios are less affected by early diagenesis than S/V ratio. However these changesdeduced from lower slopes of the regression diverging from 1-are limited and confirm that once reaching subaqueous condition, lignin macromolecules undergo limited degradation over a period of a few decades [START_REF] Opsahl | Early diagenesis of vascular plant tissues: lignin and cutin decomposition and biogeochemical implications[END_REF]. [START_REF] Kastner | Constancy in the vegetation of the Amazon Basin during the late Pleistocene: evidence from the organic matter composition of Amazon deep sea fan sediments[END_REF] also found high stability of lignin biomarkers measured in sediment cores. Ligneous compound accumulation in sediments thus appears well suited to hold long-term records of TOM sources [START_REF] Louchouarn | Sources and early diagenesis of lignin and bulk organic matter in the sediments of the lower St. Lawrence Estuary and the Saguenay Fjord[END_REF][START_REF] Hernes | Fractionation of lignin during leaching and sorption and implications for organic matter ''freshness[END_REF].

Figure 2 presents the relationship between [T-Hg] and percentage of organic carbon (%OC) in recently deposited sediments of the ten lakes. We observe a variation of %OC from 14 to 24% and a range of [T-Hg] from 120 to 390 ppb. No relationship is observed between these two variables. Figure 3 presents sedimentary [T-Hg] plotted against R8, which is the sum of C, V and S for 10 g of sample. This sum is used to estimate total lignin concentration and has been commonly used as indicator of TOM contribution to sediments [START_REF] Hedges | Land-derived organic matter in surface sediments from the Gulf of Mexico[END_REF][START_REF] Hedges | Characterization of lignin by gas capillary chromatography of cupric oxidation products[END_REF][START_REF] Onstad | Sources of particulate organic matter in rivers from the continental USA: lignin phenol and stable carbon isotope compositions[END_REF]. R8 values ranging from 24.5 to 43.1 mg/10 g of dw are recorded in these lakes. We do not observe any significant relationship between this variable and [T-Hg] variation.

In Figs. 4, 5, 6 and 7, T-Hg values are normalized according to R8. This normalization is driven by the fact Hg affinity for organic matter is well known and has been extensively described (e.g. [START_REF] Swain | Increasing rates of atmospheric mercury deposition in Midcontinental North America[END_REF][START_REF] Lucotte | Anthropogenic mercury enrichment in remote lakes of northern Quebec (Canada)[END_REF][START_REF] Kolka | Mercury and organic carbon relationships in streams draining forested upland/peatland watersheds[END_REF][START_REF] Kainz | Mercury concentrations in lake sediments-revisiting the predictive power of catchment morphometry and organic matter composition[END_REF]. Changes in organic matter quantity can carry important implications for Hg recruitment to sediments. To examine what influence the quality of terrigenous organic matter may play in the transport of Hg to lake sediments, normalization of Hg concentrations to organic matter concentrations allows for absolute comparisons of the influence of Fig. 2 Relationship between [T-Hg] and %OC in recent lake sediments specific TOM compounds as preferential vectors of the contaminant from the watershed to the aquatic system. Figure 4 presents the variation of [T-Hg]/R8 and S/V ratios in recent sediments. S/V ratio is an indicator of angiosperm-derived lignin in sediments [START_REF] Hedges | The characterisation of plant tissues by their lignin oxidation products[END_REF][START_REF] Tesi | Source and composition of organic matter in the Bari canyon (Italy): dense water cascading versus particulate export from the upper ocean[END_REF]. We observe variation of [T-Hg]/R8 ratios between 3 and 12 and S/V ratios between 0.13 and 0.39. No relationship is observed between the Hg associated with organic matter and angiosperm derived lignin compounds. C/V ratios vary between 0.25 and 0.65 (Fig. 5). This variation of non-woody and coniferous

Discussion

Hg and TOM in recent sediments

Percentages of organic carbon measured in recent lake sediments in this study (Fig. 2) are relatively high and correspond to the upper range of values measured in the same area by previous studies (2-18 %OC) (El [START_REF] Bilali | Role of sediment composition in trace metal distribution in lake sediments[END_REF][START_REF] Kainz | Mercury concentrations in lake sediments-revisiting the predictive power of catchment morphometry and organic matter composition[END_REF][START_REF] Sanei | Relationship between organic matter and mercury in recent lake sediment: the physicalgeochemical aspects[END_REF]. In oligotrophic lakes, %OC is often referred as an indicator of TOM inputs.

We observe here that the variation of %OC does not influence [T-Hg] in recent sediment among lakes under study. TOM loadings from watershed to lakes were also estimated thanks to R8 measurement in recent sediments. This indicator plotted against [T-Hg] allows highlighting that no variation of Hg is related to an increase of TOM in recent sediments. Indeed, we do observe elevated fluctuations of [T-Hg] in lake sediments but rather constant R8 values (Fig. 3). In these small headwater lakes, estimation of TOM inputs is not sufficient to understand the [T-Hg] variation in sediments. This result may be surprising as several studies have observed that the levels of T-Hg transported to lakes are related to TOM concentration in stream [START_REF] Kolka | Mercury and organic carbon relationships in streams draining forested upland/peatland watersheds[END_REF], water column [START_REF] Meili | Mercury in the surface water of Swedish forest lakes-concentrations, speciation and controlling factors[END_REF][START_REF] Driscoll | The role of dissolved organic carbon in the chemistry and bioavailability of mercury in remote Adirondack lakes[END_REF][START_REF] Selvendiran | Mercury dynamics and transport in two Adirondack lakes[END_REF]) and sediments [START_REF] Rasmussen | Mercury in lake sediments of the Precambrian Shield near Huntsville, Ontario, Canada[END_REF]. However this absence of relationship, within the range of organic carbon concentration observed, has been reported in recent studies [START_REF] Sanei | Relationship between organic matter and mercury in recent lake sediment: the physicalgeochemical aspects[END_REF][START_REF] Kainz | Mercury concentrations in lake sediments-revisiting the predictive power of catchment morphometry and organic matter composition[END_REF]). These authors raised the importance of the quality and particularly the source of TOM on Hg dynamics [START_REF] Kainz | Mercury concentrations in lake sediments-revisiting the predictive power of catchment morphometry and organic matter composition[END_REF]) instead of solely bulk estimation of TOM inputs [START_REF] Sanei | Relationship between organic matter and mercury in recent lake sediment: the physicalgeochemical aspects[END_REF][START_REF] Ouellet | Lignin biomarkers as tracers of mercury sources in lakes water column[END_REF]).

Hg and TOM sources

Lignin derived biomarkers hold precious information on the composition of TOM. S/V ratios trace the increasing influence of angiosperm stands in a given watershed on TOM found in lake sediments [START_REF] Hu | Lignin biomarkers and pollen in postglacial sediments of an Alaskan lake[END_REF]. C/V ratios are commonly used to trace grassland along with coniferous dominated watersheds in boreal ecosystems [START_REF] Hu | Lignin biomarkers and pollen in postglacial sediments of an Alaskan lake[END_REF][START_REF] Castan ˜eda | Late quaternary vegetation history of southeast Africa: the molecular isotopic record from lake Malawi[END_REF]. Our results indicate that variations in the presence of angiosperms on the watershed do not explain variations in sedimentary Hg levels from one lake to the next (Fig. 4). However the increasing presence of a non-woody or coniferous source in the watershed seems to lower the inputs of Hg to the lake (Fig. 5). These results tend to confirm that the increasing presence of open scrubland and coniferous forests corresponds to lower amounts of Hg leached out to lakes [START_REF] Demers | Mercury cycling in litter and soil in different forest types in the Adirondack region, New York, USA[END_REF]. Two main reasons may explain these observations. First, the incorporation of Hg to litter and soils are lower in coniferous stands than in deciduous one because of differences in litter dynamics (rate of foliage renewal between Fig. 7 Relationship between [T-Hg]/R8 and 3,5Bd/V ratios in recent lake sediments evergreen and deciduous trees, rate of organic matter degradation and accumulation, humification processes) [START_REF] Sheehan | Litterfall mercury in two forested watersheds at Acadia National Park, Maine, USA[END_REF][START_REF] Demers | Mercury cycling in litter and soil in different forest types in the Adirondack region, New York, USA[END_REF]. Moreover fluxes of T-Hg in forest floor leachates are lower in coniferous stands than in deciduous stand, with a difference in annual T-Hg fluxes estimated at 23% with respect to vegetation composition for lakes in the Adirondak region [START_REF] Demers | Mercury cycling in litter and soil in different forest types in the Adirondack region, New York, USA[END_REF]. Several studies have also shown that open forest areas, grasslands and scrublands are sites of lower Hg deposition leading to reduced [T-Hg] in litterfall as in addition to lower Hg fluxes in soils [START_REF] Sheehan | Litterfall mercury in two forested watersheds at Acadia National Park, Maine, USA[END_REF][START_REF] Poulain | Influence of temperate mixed and deciduous tree covers on Hg concentrations and photoredox transformations in snow[END_REF][START_REF] Nelson | Mass balances of mercury and nitrogen in burned and unburned forested watersheds at Acadia National Park, Maine, USA[END_REF][START_REF] Witt | Influence of the forest canopy on total and methyl mercury deposition in the Boreal forest[END_REF]. Second, in these studied watersheds, a previous study revealed that coniferous and open areas are mainly found in very low slope and illdrained areas that act as buffer zones for TOM transfer to the lake [START_REF] Teisserenc | Dynamique de la matie `re organique terrige `ne et du mercure dans les lacs et re ´servoirs bore ´aux[END_REF]). These results are particularly significant as the role of vegetation on Hg uptake and transfer in a watershed is a key parameter to understand Hg cycle in the boreal ecosystem [START_REF] Grigal | Mercury sequestration in forests and peatlands: a review[END_REF][START_REF] Sheehan | Litterfall mercury in two forested watersheds at Acadia National Park, Maine, USA[END_REF][START_REF] Demers | Mercury cycling in litter and soil in different forest types in the Adirondack region, New York, USA[END_REF][START_REF] Poulain | Influence of temperate mixed and deciduous tree covers on Hg concentrations and photoredox transformations in snow[END_REF][START_REF] Witt | Influence of the forest canopy on total and methyl mercury deposition in the Boreal forest[END_REF].

Hg and TOM quality

The ratio of p-hydroxy phenols over the sum of vanillyls and syringyls [P/(V ? S)] represents an indicator of lignin demethylation. Indeed, demethylation (e.g. by brown rot fungi) leads to the selective loss of vanillyl and syringyl phenol methoxylated groups, but does not affect the yield of phenols without methoxyl groups such as the p-hydroxyl phenols [START_REF] Ertel | Dissolved humic substances of the Amazon river system[END_REF][START_REF] Dittmar | Molecular evidence for lignin degradation in sulfate-reducing mangrove sediments (Amazo ˆnia, Brazil)[END_REF]. This process has led to the use of P/(V ? S) as an indicator of the state of TOM degradation. TOM freshness, estimated through P/(V ? S) ratios, does not influence Hg inputs to sediments of region A (Fig. 5). Yet we were expecting a relationship between this indicator and [T-Hg]/R8 as P/(V ? S) ratios increase in soils horizons [START_REF] Houel | Translocation of soil organic matter following reservoir impoundment in boreal systems: implications for in situ productivity[END_REF]) where [T-Hg] are higher [START_REF] Grondin | Mercury and lead profiles and burdens in soils of Quebec (Canada) before and after flooding[END_REF][START_REF] Obrist | Mercury concentrations and pools in four Sierra Nevada forest sites, and relationships to organic carbon and nitrogen[END_REF]). However, since the range of P/(V ? S) values is limited in these ten lakes, this ratio may not be appropriate for understanding the variation of [T-Hg] recorded in sediments. The variation of P/(V ? S) ratios variation is related to the demethylation of V and S phenols by fungal pathway (brown, white rot fungi). The close relationship between these small lakes and their watershed may limit their variations. Furthermore, we observed little variation of P/(V ? S) in angiosperm's soils between horizons, explaining the absence of relationship with Hg loadings in these southern lakes surrounded by deciduous vegetation [START_REF] Teisserenc | Dynamique de la matie `re organique terrige `ne et du mercure dans les lacs et re ´servoirs bore ´aux[END_REF].

Finally, 3,5Bd compound has been identified as a product of soil degradation [START_REF] Ugolini | Pedological, isotopic, and geochemical investigations of the soils at the boreal forest and alpine toundra transition in northern Alsaka[END_REF]. The precursors of this compound are tannins and other flavonoids (Gon ˜i and Hedges 1995). These polyphenolic precursors tend to accumulate within plant senescence and decaying cells (de [START_REF] Leeuw | A review of macromolecular organic compounds that comprise living organisms and their role in kerogen, coal and petroleum formation[END_REF]. The relative increase of 3,5Bd phenols in soils has been linked to the increase of degradation and humification of fresh plant tissues [START_REF] Houel | Translocation of soil organic matter following reservoir impoundment in boreal systems: implications for in situ productivity[END_REF]) and a recent study has confirmed the potential use of 3,5Bd/V as a tracer of TOM input to aquatic systems [START_REF] Dickens | Sources and distribution of CuOderived benzene carboxylic acids in soils and sediments[END_REF]). [START_REF] Houel | Translocation of soil organic matter following reservoir impoundment in boreal systems: implications for in situ productivity[END_REF] also used this ratio as model end-member between surface soil litter and mineral horizons of soils. This latter application is relevant to the study of Hg dynamics, as it tends to present variable concentrations along soil profiles [START_REF] Grigal | Mercury sequestration in forests and peatlands: a review[END_REF]. The relationship between [T-Hg]/R8 and 3,5Bd/V is quite significant (R 2 = 0.84; Fig. 7). This strong relationship leads to the explanation that more Hg is transferred to lake sediments when it is associated with more humified TOM. This observation is in contradiction with results observed in the water column of lakes [START_REF] Ouellet | Lignin biomarkers as tracers of mercury sources in lakes water column[END_REF]. However, in this study, anthropogenic activities (agriculture, forestry) drastically disturb the steady-state equilibrium of soil organic matter with selective erosion of soil humus and litter [START_REF] Lal | Soil erosion and the global carbon budget[END_REF]. Thus, in unperturbed watersheds, the leaching of more humified horizons below the surface litter will increase the association between Hg and TOM. This result confirms that strong mobilization of Hg is achieved in lower soils horizons and supports the simulated mobilization of T-Hg in soil by the water flow studied by [START_REF] Lee | Fluxes and turnover of methylmercury: mercury pools in forest soils[END_REF]. In a previous study, we observed that the mean slope of the watershed influences the 3,5Bd/V ratio in sediments [START_REF] Teisserenc | Dynamique de la matie `re organique terrige `ne et du mercure dans les lacs et re ´servoirs bore ´aux[END_REF]. Indeed, when the mean slope of the watershed decreases, water percolates more efficiently and accesses deeper soil horizons where 3,5Bd/V are higher and Hg is strongly associated with TOM [START_REF] Grigal | Inputs and outputs of mercury from terrestrila watersheds: a review[END_REF][START_REF] Houel | Translocation of soil organic matter following reservoir impoundment in boreal systems: implications for in situ productivity[END_REF][START_REF] Obrist | Mercury concentrations and pools in four Sierra Nevada forest sites, and relationships to organic carbon and nitrogen[END_REF]. While major research initiatives have tried to understand Hg retention in soils and its delayed release from watersheds [START_REF] Hintelmann | Reactivity and mobility of new and old mercury deposition in a boreal forest ecosystem during the first year of the METAALICUS study[END_REF][START_REF] Demers | Mercury cycling in litter and soil in different forest types in the Adirondack region, New York, USA[END_REF][START_REF] Johnson | Controls on mercury and methylmercury deposition for two watersheds in Acadia National Park, Maine[END_REF][START_REF] Graydon | Long-term wet and dry deposition of total and methyl mercury in the remote boreal ecoregion of Canada[END_REF]) none has achieve to assess the role of soils horizon on this dynamics.

The aim of this paper was to investigate whether variable TOM sources and quality could explain sedimentary [T-Hg] differences amongst nearby lakes in the boreal forest. TOM quality as defined by its humification state and its origin from various soil horizons plays a crucial role in Hg loadings towards lakes. The role of vegetation composition and soils on Hg dynamics has been addressed within several research project using extensive sampling and analytical efforts along with heavy logistic [START_REF] Ericksen | Accumulation of atmospheric mercury in forest foliage[END_REF][START_REF] Demers | Mercury cycling in litter and soil in different forest types in the Adirondack region, New York, USA[END_REF][START_REF] Graydon | Long-term wet and dry deposition of total and methyl mercury in the remote boreal ecoregion of Canada[END_REF]). In our study, the unique analysis of lignin biomarkers in sediments allowed to conclude on the preponderant influence of both humification process and coniferous stands in the watershed and open areas on terrestrial Hg transfers to a lake. Along with the two previous paper published by [START_REF] Caron | Mercury transfer from watersheds to aquatic environments following the erosion of agrarian soils: a molecular biomarker approach[END_REF] and [START_REF] Ouellet | Lignin biomarkers as tracers of mercury sources in lakes water column[END_REF], this study highlights the potential usage of lignin derived biomarkers to better understand the Hg cycle at the ecosystem level.

Fig. 1

 1 Fig. 1 Map of studied lakes

Fig. 5

 5 Fig. 5 Relationship between [T-Hg]/R8 and C/V ratios in recent lake sediments

Fig. 6

 6 Fig. 6 Relationship between [T-Hg]/R8 and P/(V ? S) ratios in recent lake sediments

Fig. 3

 3 Fig. 3 Relationship between [T-Hg] and R8 in recent lake sediments

Fig. 4

 4 Fig. 4 Relationship between [T-Hg]/R8 and S/V ratios in recent lake sediments

Table 1

 1 Localization of the ten study lakes and morphometric properties of their watersheds

	Lakes	Region	Lake area (km 2 )	Drainage area (km 2 )	DA/LA
	Joutel	Outaouais	0.66	4.72	7.15
	53699	Outaouais	0.30	4.18	13.93
	89750	Outaouais	0.44	1.63	3.70
	Cather	Outaouais	0.29	1.33	4.59
	Eygliers	Outaouais	0.38	3.49	9.18
	Hibou	Outaouais	0.40	1.50	3.75
	Lachaux	Outaouais	0.34	1.78	5.24
	Vera	Outaouais	0.36	4.60	12.78
	Desjardins east	Temiscamingue	10.26	38.84	3.79
	Desjardins west	Temiscamingue	8.88	46.95	5.29

Acknowledgments We would like to thank Sophie Chen and Isabelle Rheault for their assistance in the laboratory. We also acknowledge Jean Carreau for the sampling work. This research was supported by the Collaborative Mercury Research Network (COMERN), financed by the Natural Sciences and Engineering Research Council of Canada (NSERC). We are grateful to Mark Williams and an anonymous reviewer whose comments greatly improve the manuscript.


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Integrated Width-Modulated SiN Long Period Grating Designed for Refractometric Applications

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Integrated Width-Modulated SiN Long Period Grating Designed for Refractometric Applications Clément Deleau, Member, IEEE, Han Cheng Seat, Senior Member, IEEE, Frederic Surre, Senior Member, IEEE, Hélène Tap and Olivier D. Bernal, Member, IEEE Abstract-A novel integrated photonic structure based on Long Period Waveguide Gratings (LPWGs) relying on channel-width modulation is proposed and tested for refractometric applications. These LPWGs have been fabricated through a Silicon Nitride process and experimentally characterized in terms of both surface and bulk sensitivities. Surface sensing configuration is first achieved by propagating one of the coupling optical modes into an epoxy-based negative photoresist SU8 cladding region that is in contact with the analyte via its outer surface. We subsequently show that the proposed LPWGs cladding layer can be advantageously replaced by a gas-porous polymeric bulk layer such as Styrene-co-AcryloNitrile (SAN) as the cladding region to be directly sensed to anticipate future gas sensing applications. Here, bulk sensing is optimized by increasing the analyte's influence on the modal propagation constants as it is demonstrated to be currently the most promising solution to effectively enhance the figure of merit of long period gratings of given lengths. Using varying water-glycerol mixtures, the surface sensitivity of these LPWGs has been measured at up to 240 nm per RI unit (RIU) that is in agreement with simulation. In addition, the bulk sensitivity has been indirectly estimated to be ∼1900 nm/RIU via temperature measurements, which corroborates simulation results, thereby paving the way towards gas sensing applications.

Index Terms-Integrated photonics, long period grating, refractometry, coupled-local-mode theory, silicon photonics.

I. INTRODUCTION

I N recent years, integrated photonics has been intensely investigated for the development of highly sensitive labon-chip sensor applications. Due to their high degree of flexibility, they enable a multitude of functional designs to be implemented in a miniaturized circuit. The immunity of integrated photonic devices to electromagnetic and radiofrequency interferences coupled to their potential high resolution also render them very attractive [START_REF] Chrostowski | Silicon Photonics Design: From Devices to Systems[END_REF] for in situ measurements and monitoring in harsh environments. Numerous embedded functions, once implemented, can thus be simultaneously driven or interrogated by a unique optical source on a thermally and mechanically robust platform. These characteristics have led to growing interest from the industry to develop and commercialize integrated optical sensors for indoor chemical monitoring, elevating the limits of detection towards everincreasing sensitivities. Integrated optical chemical sensors can detect and measure the concentration of an analyte by C. Deleau accessing a particular optical parameter. Various designs for integrated refractometric measurements have been proposed over the years, including integrated interferometers [START_REF] Dullo | Sensitive on-chip methane detection with a cryptophane-a cladded mach-zehnder interferometer[END_REF], ring resonators [START_REF] Yebo | Selective and reversible ammonia gas detection with nanoporous film functionalized silicon photonic micro-ring resonator[END_REF], plasmonics [START_REF] Zaki | Integrated optical sensor using hybrid plasmonics for lab on chip applications[END_REF], photonic crystals [START_REF] Danaie | Design of a label-free photonic crystal refractive index sensor for biomedical applications[END_REF] and gratings [START_REF] Jain | Thermally stable optical filtering using silicon-based comb-like asymmetric grating for sensing applications[END_REF]. These are principally reagent-mediated sensors [START_REF] Mcdonagh | Optical chemical sensors[END_REF], implying that they monitor the optical response of an intermediate species (typically a solid porous matrix) whose optical properties depend on the presence of the target gaseous analyte. This is advantageous in several ways; firstly, a very high selectivity to a particular analyte can be achieved since some material matrices or chemical transducers are uniquely responsive to a specific biochemical species, and secondly, it permits chemical interaction enhancement by focusing effort on optically optimizing and sizing of the material matrix. Amongst the three principal interrogation techniques, namely intensity-based measurements, wavelength or spectral interrogation and phase demodulation, wavelength-based techniques technically guarantee measurements which are relatively independent of any input intensity variations from the optical source.

In this work we propose a novel type of integrated refractometer using a planar multimode Long Period Grating (LPG). LPGs are structures operating on wavelength-selective coupling of two or more co-propagative modes whose effective indices can be analyzed by using the resonance spectral features. The LPG structure typically consists of a periodic longitudinal index or spatial modulation of a multi-mode supporting architecture with the modulation of the order of several times the wavelength to allow selective optical mode resonance. Historically, LPGs have been principally implemented on fiberbased platforms, as the introduction of such modulation can simply be performed by irradiation or tapering of the fiber core or cladding but have recently found interest in the integrated platform [START_REF] Liu | Condition for the realization of a temperature-insensitive long-period waveguide grating[END_REF] [START_REF] Tripathi | Temperature insensitive long period waveguide gratings in rib waveguide[END_REF]. In fiber LPGs, which couple core modes to cladding modes, the interaction coefficient between the optical fields and the external sensing region is usually very low, of the order of 0.001 -0.01, ( ∼0.004) [START_REF] Simões | Characterization of optical fiber long period grating refractometer with nanocoating[END_REF] for conventional fibers and slightly higher (∼0.013) [START_REF] Hu | High sensitivity internal refractive index sensor based on a photonic crystal fiber long period grating[END_REF] for analyte-filled photonic crystal fibers. Nevertheless, the sensitivities that are obtained in these fiber-based devices are still within competitive levels. We hereby propose to exploit the design flexibility offered by integrated photonics in this work to create a highly sensitive and original chip-integrated sensor based on modal interaction optimization with the analyte of interest. Our design focuses on the coupling of the single core mode (in the silicon nitride layer) to cladding layer mode(s) by using periodic waveguide width-modulation as a pattern, as illustrated in Fig. 1. To Fig. 1. Illustration of the proposed SiN integrated Long Period Grating address future gas sensing applications, these LPGs could employ bulk sensing to benefit from the enhanced sensing matrix-optical field interaction with the cladding layer.

Section II describes the sensing scheme and structure features, and briefly discusses the different optimization methods that can be applied on an LPWG. The architecture's optical behavior is then modeled in Section III through EigenMode Expansion (EME) techniques whose advantages and limitations are discussed. Subsequently, Coupled-local-mode Theory (CLMT) [START_REF] Snyder | Optical waveguide theory[END_REF] is introduced as a means to provide more insight on the optical behavior of the design and to facilitate coupling rate optimization. In Section IV, the fabrication and characterization of the LPWGs are presented, and the effects of the process variations on the optical system are analyzed in detail. In the last section, to assess the performance of the proposed LPWG, experimental and simulation results of the LPWG transmission spectrum and surface sensitivity are first presented using a cladding layer of epoxy-based negative photoresist SU8. Regarding bulk sensitivity, we will then show that it can be inferred from the temperature dependence tests. Finally, the SU8 cladding layer is replaced by a gas porous layer of Styrene-co-AcryloNitrile (SAN) that is demonstrated to be compatible with our LPG, thereby paving the way towards future gas sensing applications.

II. DESIGN

A. Theory

Long Period Gratings have been successfully exploited in Fiber Optic Chemical Sensors due to their ease of fabrication and, in particular, their capacity for coupling energy to outer cladding modes, thereby allowing the optical power to interact with the external environment. As duly reported in various papers [START_REF] Jin | Coupled local-mode theory for strongly modulated long period gratings[END_REF] [14], a phase-matching condition between two co-propagative optical modes must be fulfilled to enable resonance to result in an exchange of energy :

n ef fj -n ef f l = λ res Ω (1)
where n ef fj and n ef f l are the effective indices (EIs) of the two coupled modes j and l, respectively, λ res the center resonant wavelength and Ω the grating period. The formula is derived from the well-known Coupled Mode Theory (CMT) [START_REF] Snyder | Optical waveguide theory[END_REF], from which coupling equations can be expressed as

db ±j dz ∓ iβ j b ±j = j (C ±j,l b l + C ±j,-l b -l ) (2)
where b ±j is the modal amplitude of the forward (+) or backward (-) propagating mode j, β j is the propagation constant of mode j, and C j,l is the mode coupling coefficient between modes j and l. Then, straightforward development and conservation of energy show that when the mode coupling coefficients C j,l are periodically modulated along the longitudinal axis, with a modulation period corresponding to the accumulated phase difference between the two modes, coupling can occur. The rate of energy exchange upon resonance further depends on other parameters, including the modulation amplitude and optical field superposition at the modulated guide interfaces, as previously detailed in [START_REF] Deleau | Integrated silicon nitride horizontal long period grating for refractometric gas sensing applications[END_REF]. In refractometric sensing schemes employing LPGs, the presence of the analyte generally modifies the refractive index (RI) of the equivalent sensing layer which, in turn, modifies the propagation constants of the incident modes propagating in the layer. The difference in EI variation between the two coupled modes leads to a spectral shift of the optical resonance. This spectral shift can finally be measured to determine the RI variations of either the analyte deposited on top of the cladding layer (i.e. surface sensing configuration) or of the cladding layer itself (i.e. bulk sensing configuration). To a certain extent, in correlation with the modal overlap, which is defined as the modal optical field superposition ratio to the region of interest, the dependency of the EI of the i th mode on the RI of the sensing layer n sens (used here as the cladding layer) can be expressed as the coefficient Γ i :

Γ i (λ, n ef f,i ) = dn ef f,i dn sens (λ, n ef f,i ) . (3)
Now, by considering the phase-matching condition (equation (1)), the sensitivity of the LPG can thus be established as

S = dλ res dn sens = λ Γ j (λ, n ef f,j ) -Γ l (λ, n ef f,l ) n g,j -n g,l (4)
where n g,j and n g,l are the group indices of the mode j and l, respectively. Subsequently, the sensitivity of an LPG can be improved either by increasing the numerator term or decreasing the denominator term in equation ( 4). Based on the former, we propose to enhance the sensitivity of the LPWG by extensively increasing the Γ l coefficients by improving the modal overlap of the modes to couple in the sensing region. This could be achieved by inducing one of the modes to directly propagate in the sensing region, which is particularly applicable to gas sensors using gas-porous solid cladding layers. Moreover, due to the relatively large spectral width of the typical LPG resonance, to the order of several nanometers, the minimum detectable spectral shift is typically limited by the full-width half-maximum (FWHM) of the resonance instead of the optical analyser spectral resolution [START_REF] Rindorf | Sensitivity of photonic crystal fiber grating sensors: Biosensing, refractive index, strain, and temperature sensing[END_REF]. By using the CMT approach and taking into account modal dispersion effects, the figure of merit (FOM) can be expressed as follows :

F.O.M. = S F W HM ≈ (Γ j -Γ l )L opt 0.8λ res (5)
where L opt is the minimum LPG length for full mode coupling at resonance. The expression shows that for an LPG of a given length the FOM is ultimately limited by the coefficients Γ j,l and that tailoring of the spectral features can be performed by engineering L opt which depends on the coupling coefficients C j,l , as will be detailed in the next section. Additionally, as it can be deduced from equations ( 4) and ( 5), improvements of the FWHM can be achieved by either reducing the coupling strength and proportionally increasing the grating length, or engineering the coupled modes propagation constants. The former method however decreases the optical transmission level with longer propagation in lossy integrated waveguides while the latter reduces the spectral sensitivity in proportion to the FWHM change, thus resulting in a constant FOM.

B. Structure

The proposed LPWG architecture consists of a Silicon Nitride (Si 3 N 4 ) width-modulated core integrated waveguide and a multimode cladding waveguide, as shown in Fig 1 . Smooth width modulation is advantageous as it allows continuous coupling, contrary to binary gratings where the waveguide is partly etched, thus potentially inducing loss of energy at the grating interfaces. In addition, the width modulation can be directly designed on the waveguide pattern, hence no additional process step is required.

The principal objective of our design is to obtain resonant coupling between the fundamental mode and a multi-mode in the cladding waveguide. As a main difference to fiber-based LPGs, whose cladding mode interaction with the sensing layer is generally very low, we elect to directly use the cladding cavity as the sensing layer, thus potentially increasing the coefficient Γ l to nearly 1. To perform this operation, a polymeric layer of Styrene-co-AcryloNitrile (SAN) is selected for its important material properties pertaining to future potential gas sensing applications. Firstly, SAN has been previously proven as a suitable gas sensing host layer [START_REF] Dullo | Sensitive on-chip methane detection with a cryptophane-a cladded mach-zehnder interferometer[END_REF], and allows incorporation of selective reagents such as Cryptophane for functionalization to methane, for instance. Secondly, its RI n SAN (=1.57) is superior to the standard oxide material index of n SiO2 =1.45, thereby enabling the confinement of modes in a sufficiently large sensing layer without significant field leakage to the bottom oxide layer. It was also previously demonstrated as an acceptable integrated waveguide [START_REF] Qureshi | Styrene acrylonitrile (san) based polymeric waveguides[END_REF], and is thus expected to exhibit relatively minor diffractive imperfections which could arise due to the porosity of the polymer. Considering suitable cross-sectional dimensions, the following relationship between material RIs permits confinement of core and cladding modes: n core > n ef f,1 > n clad > n ef f,n > n sub > n air where the indices are respectively the RI of the core n core = n Si3N4 =1.97, n ef f,1 the EI of the core's fundamental mode, n clad the RI of the cladding, n ef f,n the EI of the n th order cladding mode to couple, n sub the RI of the bottom SiO 2 layer and n air the RI of air.

The SiN waveguide is designed at standard dimensions with a cross-section of 1000×400 nm with a modulation width of ± 300 nm (see Fig. 2). Unlike waveguide Bragg grating reflectors whose periods are lower than the interrogating wavelength, waveguide LPGs could be subject to relatively higher energy loss at the period width minimas if the mode is too constrained. Preliminary experimental tests have, however, shown that no particular increase in optical loss is expected for both maximas or minimas of the waveguide width over a full modulation period. The cladding cavity dimensions are designed to be 1.1 µm thick and 32 µm wide, for a 1 mm long sensor, thus allowing to support multiple propagative cladding modes which can be coupled to the fundamental core waveguide mode.

III. MODELING

A. Mode calculation and Eigenmode Expansion

The waveguide structure supports a fundamental core mode, denoted by HE1, and multiple cladding modes (i.e. HEi with i= 2, 3, 4...), whose optical fields are shown in Fig. 3 for odd modes from HE7 to HE15. Each cladding mode possesses an EI slightly inferior to that of SAN that slowly decreases with the order of the mode. The cladding dimensions have been chosen to support up to eight hybrid odd HE modes which should result in eight resonant dips over a 200 nm spectral range. Moreover, as will be discussed in the next section, they also allow coupling parameters of different levels to be obtained which will translate into various dip amplitudes. As it is intended to couple the fundamental mode to cladding modes around 1550 nm, the LPWG modulation period values are chosen to be between 8 and 10 µm, depending on the selected mode(s) to be coupled to. This is achieved by satisfying equation (1) and using the cross-section of the waveguide at zero-modulation amplitude for modal calculation. It is, however, important to understand that due to the nonlinear EI dispersion of the modes, the period-averaged EI is slightly different from the average width profile's EI, hence a small resonance shift can be expected between calculated (equation ( 1)) and simulated / experimental results. EigenMode Expansion (EME) is found to be an efficient solution for analyzing Fig. 3. Optical fields of cross-sectional odd modes periodically-modulated structures. In EME, the structure is firstly divided into slices transverse to the axis of propagation. The optical fields and dispersion behaviors of the modes are then calculated for each cross-section after which a contingent iterative superposition of the scattering parameters is resolved to obtain the modulated modal information. Because of the post-mode-calculation analysis, which permits the setting of the structure's longitudinal profiles after the cross-sectional modal study, it is possible to optimize the LPWG in terms of length and periodicity with relative ease. Moreover, since EME studies the exchange of energy between modes, it is highly suitable for the design of our filter-type structure based on a multi-modal resonant coupling behavior. Figure 4 shows the output spectrum of the fundamental mode which exhibits multiple dips due to the different cladding mode resonances.

B. Coupled-local-mode Theory approach

Coupled-local-mode Theory (CLMT) provides an analytical model of the LPWG's response using parametric inputs such as its geometrical dimensions. Similar to EME, it requires the slicing of the structure and a modal calculation for each crosssection. However, mode coupling coefficients in CLMT are calculated analytically using the modulation parameters for each cross-section as shown in equation [START_REF] Jain | Thermally stable optical filtering using silicon-based comb-like asymmetric grating for sensing applications[END_REF]. The propagation calculation is then performed by the resolution of a set of differential equations as given in equation ( 2), contrary to CMT [START_REF] Snyder | Optical waveguide theory[END_REF]. In addition, CLMT takes into account the important waveguide dimensional variations as well as polarization effects by using the coupling coefficient between the j th and l th modes, denoted C j,l , calculated for a large number of cross-

∀j = l, C jl = k 4 ε 0 µ 0 1 2 1 β j -β l A∞ ê * j êl ∂n 2 ∂z dA, C jj = 0, (6)
where A ∞ is the infinite cross-section, 0 and µ 0 the freespace dielectric and permeability constants, respectively, Γ the free-space wavenumber 2π/λ and * denotes the complex conjugate. The development of the coupling coefficients provides important information. First, through the differential RI integration over the modulation interfaces, it is seen that only odd modes can be coupled to the fundamental mode for a structure with vertical plane symmetry along the propagation axis: the calculated coefficient becomes null for even modes because of the opposite polarization states of the fields at the two modulated waveguide interfaces as described in detail in [START_REF] Deleau | Integrated silicon nitride horizontal long period grating for refractometric gas sensing applications[END_REF]. Secondly, the coupling length at resonance for total energy transfer can be adjusted by controlling the amplitude of the coupling coefficients. This can firstly be performed by optimizing the electric field superposition at the lateral corecladding interface. As an example, from Fig. 3, it is observed that the HE9 mode has a higher optical field strength at the core-cladding interface than the HE7 mode, hence a greater coupling coefficient is achieved. Additionally, the coupling strength also depends on the modulation amplitude. A deeper modulation thus leads to longitudinal shortening of the optimized sensor, but can also increase extrinsic waveguide loss with thinner waveguide widths or widen the resonance spectral pattern as described in equation ( 5). In Fig. 4, one also notices the tendency of the coupling dips of the higher-order mode (HE15) to be smaller, despite having a greater Γ i coefficient, as previously explained. This is because the energy starts coupling back to the fundamental mode after being exchanged completely; the exchange of energy is periodic. In most fiberbased LPGs, the coupling coefficients vary only slightly over a full period. As a result, the optimal grating length L opt for the Fig. 5. LPWGs layout designed on Klayout j th and l th mode coupling can be approximated by π/(2C jl ) [START_REF] Rindorf | Sensitivity of photonic crystal fiber grating sensors: Biosensing, refractive index, strain, and temperature sensing[END_REF]. However, for LPWGs, as previously demonstrated in [START_REF] Deleau | Integrated silicon nitride horizontal long period grating for refractometric gas sensing applications[END_REF], L opt must be found numerically. This is due to larger variations of the coupling coefficient induced by typical profile modulations in integrated photonics.

IV. FABRICATION A. Materials and Cross Section

To validate the proposed LPWG architecture's operating principle and assess its surface sensitivity, a first set of LPWGs has been initially designed (Fig. 5) and fabricated using SU8 instead of SAN. Since both SU8 and SAN have very similar RIs and since SU8 has the particular advantage of being more easily deposited (in terms of flatness and thickness), SU8 is firstly used as cladding to investigate the operationality of the LPWG and characterize it as a prototype. Note that SU8 is an epoxy-based negative photoresist commonly used in photolithography, hence its optical and viscosity characteristics are widely known. This enables a greater control to be achieved on the cladding layer. It is, however, not porous to gaseous species and is only used here to validate the operating optical principle. For simplicity of fabrication, the cladding is delimited by incorporating SiO 2 walls using Hydrogen Silesquioxane (HSQ) resist, whose constitution and RI are found to be very similar to those of SiO 2 after curing. The HSQ walls are designed to be 3 µm wide and 0.6 µm thick to prevent multimode optical leakage as well as to ensure ease of coating and electron-patterning.

B. Process

To fabricate our waveguide, a 2 µm SiO 2 layer is first deposited by plasma-enhanced chemical vapor deposition (PECVD) on a clean Si wafer. Parasitic substrate optical leakage during waveguide modal propagation has been previously investigated for this material thickness and found to be negligible. A 400 nm thick Si 3 N 4 (or simply SiN) layer is next deposited on top by PECVD, with n core (∼1.97) measured by ellipsometry. An electron-sensitive resist MaN2405 is deposited by spin-coating, followed by an Electra92 resist layer, principally used for the dissipation of electronic charges that are induced during the electron-beam lithography stage. After development of the waveguide patterns, the unwanted parts of the SiN layer are removed by reactive ion etching (RIE). The remaining parts of the resist are then removed using acetone and Plasma O 2 cleaning. Both the HSQ and Electra92 resists are then deposited by spin-coating. After curing of the HSQ walls, a final layer of SU8 is deposited by spin-coating at a spin-rate of 1700 rpm. This layer amounts to 1.1 µm thick as measured by profilometry. Figure 6 shows optical microscope pictures and a zoomed scanning electron microscope (SEM) image of the fabricated LPWGs.

C. Post-Fabrication Characterization

Scanning electron microscopy has revealed a slight asymmetry of the structure, due to a minor translation shift between the two patterned layers. As will be shown in the next section, this asymmetry has only minor consequences on the output spectrum as well as on the sensor's sensitivity. The measured waveguide width has also been found to be slightly different from the design, which should induce a small resonance shift in the transmission spectrum since it slightly modifies the average EI of the core mode.

V. EXPERIMENTAL RESULTS

A. Experimental Setup

The experimental setup for characterizing our structure consists of a broadband light source (BBS), an optical spectrum analyzer (OSA), a fiber array and the chip under test, as illustrated in Fig. 7. The fiber array incorporates a set of multiple fibers bound and held together by a support at one end, with each fiber core separated by 127 µm. Each structure to be characterized is connected at each respective output to a grating coupler, which allows the injection and recovery of

B. Virtual Reconstruction Of The Entire Coupling Spectrum

As shown in equation ( 1), the position of the resonance peak due to coupling resonance within the structure depends proportionally on the period of the LPWG for a given crosssection. Furthermore, Fig. 4 shows that the theoretical transmission spectrum of the structure containing the first-order coupling resonance dip of every cladding mode is ∼200 nm wide and too large to be measured over a single wavelength scan by our setup. Hence, a set of LPWGs with different periods but identical cross-section and modulation amplitude has been designed and fabricated instead. It then becomes possible to virtually reconstruct the entire spectrum by firstly de-embedding the signal to isolate the LPWG's individual spectral contribution and, secondly, by shifting the processed signals respectively to the corresponding LPWGs periods. The LPWGs exhibit little or no additional energy loss when compared to non-modulated waveguides of equal length. After base-line correction, the LPWGs transmissions are shown on the reconstructed spectrum in Fig. 8(b). Subsequently, when fabrication defaults such as asymmetry or waveguide width defects are reintroduced into the model, a very similar spectra can be found as in 8(a).

Contrary to Fig. 4, shorter dips (1-3dB) have been observed between the main dips (3-10dB). They may be attributed to the slight asymmetry of the structure which disrupts the nullification condition of the optical modal field product at the lateral interfaces for even modes. This consequently leads to a minor rise in the coupling coefficients of the even modes, thus allowing partial coupling to these same even modes. Nonetheless, a flaw in the virtual spectrum reconstruction is highlighted by the differing measured amplitudes for the same coupling dips and can be attributed to the high spectral dispersion of the modal coupling coefficients in high indexcontrast gratings. This is because with higher wavelengths, the fundamental mode becomes more leaky and results in large variations of the optical field product at the waveguide's modulated interfaces, thereby changing the coupling strength. The different coupling dips are found to exhibit extinction ratios of several dBs. The dips also exhibit an average FWHM of approximately 5 nm in this work. Using the SANTEC tunable laser (TSL-550 C model) with its swept test system, which has a ± 1 pm repeatability and resolution, 200 wavelength scan measurements have been performed over an hour with a regulated temperature of 23°C to estimate the precision σ sensor of the resonance wavelength of the HE9 mode's transmission spectrum. After applying a Lorentzian curve fitting, σ sensor = 1.5 pm is obtained, which is similar to the laser system precision.

C. Refractometric measurements

A cladding refractometric measurement configuration is difficult to achieve here since a gas-porous sensing region is a solid layer which cannot be filled or saturated with liquids. We thereby propose a simple surface-based experimental configuration where the target liquid is poured onto the top surface of the sensor. Because of the relatively thin SU8 cladding, Γ l is of the order of 0.1 which remains higher than the coefficients of the cladding modes in most fiber LPGs, Water and glycerol mixtures of different proportions are then applied on different LPWGs and the resonance shifts of mode coupling dips tracked, as shown in Fig. 9 for the HE9 and HE15 modes. Using the RIs of water and glycerol around 1550 nm [START_REF] Saunders | Refractive indices of common solvents and solutions at 1550  nm[END_REF], the surface sensitivities are measured (Fig. 10) and compared to simulation, for both surface and cladding measurements in Table I. A sensitivity up to 240 nm/RIU has been measured for the HE15 mode's resonance dip, whose bandwidth and extinction ratio values are both found to agree with the simulated spectrum. Additionally, it is observed that when fleeting impurities interact with the cladding layer during measurement, the resonance features are not shifted, due to the inertial behavior of the LPWG. Because the modal energy exchange during propagation is driven by a coupling momentum, the LPWG sensor's resonance wavelength depends on the sensed layer's median RI and not the average RI, thus rendering it robust to disturbance by impurities. Additionally, a cross-sectional modification on a small segment of the LPWG does not lead to any significant shift in the LPWG resonance but can, however, contribute to reduce the coupled energy, making LPWGs highly interesting candidates for sensing of gases whose RI profiles are generally homogeneous within a given volume. As the measured and simulated sensitivities are found to be very similar for the surface measurement configuration, the experimental measurements are taken to corroborate the model and the subsequent simulations without loss of generality, thus validating the operation of our sensor with data-processed inputs. The comparison also suggests that the cladding measurements can further be expected to conform to the simulated values. Using our measured sensor resolution, a detection limit of 2 µRIU in the case of bulk sensing can be estimated.

D. Temperature dependence

The temperature behavior of the sensor is firstly simulated with EME using thermo-optical coefficients of SiN, SiO 2 and SU8, whose values at 1550 nm are respectively ∼24.5, 9.5 [START_REF] Arbabi | Measurements of the refractive indices and thermo-optic coefficients of si3n4 and siox using microring resonances[END_REF] and -130 µRIU/K [START_REF] Ibrahim | Athermal silicon waveguides with bridged subwavelength gratings for te and tm polarizations[END_REF]. The temperature sensitivity of the wavelength resonances is estimated to be ∼330 pm/K and is similar for each mode resonance. For experimental validation, the TEC temperature is swept from 15 to 30°C at 5°C steps. Linear interpolation of the measured values gives a temperature sensitivity of 340 pm/K as plotted in Fig. 11. In addition, from the temperature dependence analysis, an approximation of the bulk sensitivity can be inferred. This is estimated to be ∼1900 nm/RIU.

E. SAN coating

As previously mentioned, SU8 cannot, in practice, be used as a gas sensing layer as it is a hermetic layer. Instead, a porous polymeric layer of similar RI such as SAN can be used for gas sensing applications [START_REF] Dullo | Sensitive on-chip methane detection with a cryptophane-a cladded mach-zehnder interferometer[END_REF]. To ensure SAN compatibility with the proposed design architecture as the cladding, coating and characterization are performed on SAN as follows: 50 mg of SAN are dissolved in 10 mL of methylethylketone and the mixture is spin-coated onto the pre-cleaned photonic chip. As seen in Fig. 12, the coupling phenomenon occurs very similarly to that of the SU8-coated LPWG. Small changes of coupling are due to minor variations in the film thickness and layer RI deviation as compared to the previously-characterized LPWGs. Consequently, employing SAN as an external sensing layer provides a pathway to gas sensing based on the bulk sensitivity of the proposed LPWG. In addition, since the thermo-optical coefficients of SAN and SU8 are of the same order [START_REF] Sultanova | Characterization of optical properties of optical polymers[END_REF], the thermal behavior in a SAN-clad LPWG is not expected to significantly vary from the presented results.

VI. CONCLUSION

In this work, SiN width-modulated LPWGs have been designed, fabricated and characterized to achieve RI measurements with high sensitivity. Surface sensitivities up to 240 nm/RIU have been attained and agree with both the proposed CLMT model and EME simulations. In addition, from temperature tests, the bulk sensitivity has been estimated to be approximately 1900 nm/RIU, in accordance with EME simulations. This is an improvement of almost an order of magnitude and demonstrates possibly a very high sensitivity for potential gas sensing applications. A specific use of SAN's high RI is demonstrated to allow modal propagation, which could improve both the sensitivity and FOM of our sensor by eight-fold based on a bulk measurement configuration. The results from this work will serve as a baseline for the design of LPWGs combining modal interaction optimization with other sensitivity enhancement techniques such as phase-matching turning point optimization [START_REF] Wong | Optical fibre long-period grating sensors operating at and around the phase matching turning point[END_REF].

Fig. 2 .

 2 Fig. 2. Cross section material and refractive index profile of the proposed LPWG with n clad = 1.58 for SU8 and 1.57 for SAN

Fig. 4 .

 4 Fig. 4. Simulated transmission spectrum of 100-period LPWG showing coupling between fundamental and odd cladding modes. Insets illustrate various field profiles of coupled odd HEi modes

Fig. 6 .

 6 Fig. 6. Fabricated LPWGs die microscope photographies: (a) overview, (b) grating couplers zoom and (c) SEM image of the grating modulation

Fig. 7 .

 7 Fig. 7. Illustration of the experimental setup

Fig. 8 .

 8 Fig. 8. Transmission spectra for a 100-period long LPWG: (a) Simulated with parametric adjustment and (b) reconstructed from measurements

Fig. 9 .

 9 Fig. 9. Measured spectrum of HE9 and HE15 mode resonance of LPWGs using SU8 as cladding for different deposited concentrations of water and glycerol

Fig. 11 .

 11 Fig. 11. Measured temperature dependence of the wavelength resonance

Fig. 12 .

 12 Fig. 12. Measured transmission spectrum of HE9 mode resonance on LPWG with SAN cladding

ACKNOWLEDGMENT

The fabrication and characterization of the integrated photonic long period gratings are supported by a TTIL (Toulouse Tech Interlabs) 2019 grant and by LAAS-CNRs micro and nanotechnologies platform, a member of the Renatech french national network. The authors would like to thank A. Lecestre, F. Carcenac, J-B. Doucet, L. Mazenq and P-F. Calmon for their technical support during the fabrication and characterization processes of the photonic integrated circuits.


Clément Deleau
email: clement.deleau@laas.frseat@toulouse-inp.fr

Han-Cheng Seat

Hélène Tap
email: helene.tap@toulouse-inp.fr

Frédéric Surre

Olivier Bernal
email: olivier.bernal@toulouse-inp.frf.surre@ieee.org

Integrated Silicon Nitride Horizontal Long Period Grating for Refractometric Gas Sensing applications

Keywords: Integrated photonics, gas sensor, modeling, long period grating, coupled local mode theory. I

We designed an integrated long period grating based on the horizontal periodic tapering of a silicon nitride channel waveguide. The structure is studied for gas sensing applications, using Styrene AcryloNitrileas sensitive layer. Simulation results from the proposed architectureshow ahigh sensitivity beyond1700 nm/RIU using awavelength interrogation method centered at 1550 nm for a 20µm large and 300µm long structure.

INTRODUCTION

For the past two decades,long period fiber gratings (LPFGs) have beenintensely investigated for communication [START_REF] Chiang | Long-period grating devices for application in optical communication[END_REF] and sensing applications [START_REF] Tsuda | Characterization of long-period grating refractive index sensors and their applications[END_REF]. A wide diversity of LPFGbased systems has been demonstrated and used in various applications, such as optical filters [START_REF] Vengsarkar | Long-period Fiber gratings as band-rejection filters[END_REF], gain flatteners, polarization couplers, multiplexers and particularly refractometric sensors [START_REF] Barnes | Chemical sensing using a polymer coated long-period fiber grating interrogated by ring-down spectroscopy[END_REF][START_REF] Barnes | Chemical sensor based on a long period fibre grating modified by a functionalized polydimethylsiloxane coating[END_REF][START_REF] Ji | Highly sensitive refractive index sensor based on adiabatically tapered microfiber long period gratings[END_REF][START_REF] James | A long period grating-based chemical sensor insensitive to the influence of interfering parameters[END_REF]. However, to the best of our knowledge, the design of these structuresis typically limitedto standard dimensions and intrinsic parameters of the host fibers, rendering them unsuitable for integration and optimization.

Following the enormous impact of integrated electronics on our society, integrated photonicshave been subject to an exponentially growing interest since its earliest inception as laser diode devices for telecommunication applications in the 1960sand is now widely studied for the design of original, power-efficient and high-resolutioncompact sensors. In 2003, Tsoi and al. [START_REF] Tsoi | Polymeric long-period waveguide gratings[END_REF] demonstrated the first integration of a long period waveguide grating (LPWG)having similar properties to conventional LPFGs. The LPWGarchitectureusing a periodic perturbation of the width or height of the waveguide enables strong coupling between the fundamental mode and a copropagating cladding mode.It can thus be designed to selectively perform coupling under specific conditions, makingthem very interesting candidates for in-situ chemical monitoring. Using a suitablefunctionalizing chemical layer for the cladding window surrounding the LPWG core, the detection and quantification of a specific analyte has been demonstrated through various techniques [START_REF] Barnes | Chemical sensing using a polymer coated long-period fiber grating interrogated by ring-down spectroscopy[END_REF][START_REF] Barnes | Chemical sensor based on a long period fibre grating modified by a functionalized polydimethylsiloxane coating[END_REF][START_REF] James | A long period grating-based chemical sensor insensitive to the influence of interfering parameters[END_REF].

The fabrication of index-modulated structures required for long period gratings can be performed through local corrugation [START_REF] Pal | Realization of long-period corrugated grating in silica-on-silicon based channel Waveguide[END_REF], tapering [START_REF] Ji | Highly sensitive refractive index sensor based on adiabatically tapered microfiber long period gratings[END_REF], laser irradiation, ultraviolet inscription, arc discharge [START_REF] Estrudillo-Ayala | Long period fiber grating produced by arc discharges[END_REF]. We propose here to introduce a grating perturbation on the fundamental mode of a simple channel waveguide through a smooth periodic change of the waveguide width.Unlike binary gratings, this type of grating enables smooth power coupling and can be studied underthe slowly-varying envelope approximation assumptions. The design is studied to analyzethe LPWG response to a change of analyte concentration through the change of the sensing materialrefractive index. This paper is organized in three parts. First, in Section II, the general design of the horizontal LPWG is presented and compared to other reported types of LPWG. In Section III, the Coupled Local-Mode Theory (CLMT) [START_REF] Snyder | Optical waveguide theory[END_REF] is used to introduce and describe the principle of the LPWG's mechanism This approach is formulated as a proof-ofconcept but can subsequently beextended to accurately model the LPWG response and characteristics [START_REF] Li | Coupled-local-mode theory and study of optical peoperties of a gaussian fiber grating[END_REF][START_REF] Jin | Coupled local-mode theory for strongly modulated long period gratings[END_REF]. In Section IV, CLMT is applied on our structure andan EigenMode Expansion (EME) method is performed with Lumerical suite tools as a comparison and simulation results of the sensor's sensitivity are discussed.Finally, in section V,two fabrication methods are proposed.

II. ARCHITECTURE

A. Proposed structure

The proposed LPWG sensor structure consistsofa periodically-modulated(along the z-axis) channel width(xaxis) waveguide inside of a polymeric sensing regionas illustratedin Figure 1. As explained in the next section using CLMT [START_REF] Snyder | Optical waveguide theory[END_REF], the excitationof the coupling phenomenon between core and cladding modes is performedvia a periodic modification of the local modes along the propagation z-axis. Two different grating types can allow this mechanism. The most common grating is one with a local index variation inscribed in the waveguide or core [START_REF] Chiang | Long-period grating devices for application in optical communication[END_REF][START_REF] Estrudillo-Ayala | Long period fiber grating produced by arc discharges[END_REF]. It usually requires a specific and complex apparatus as well as accurate calibration on each material to be engraved. The second grating structure, more commonly employedin integrated photonics structures, are corrugatedwaveguides [START_REF] Pal | Realization of long-period corrugated grating in silica-on-silicon based channel Waveguide[END_REF][START_REF] Zhang | Long period grating in/on planar and channel waveguides: a theory description[END_REF], which can be achieved by an additional vertical etching step to createrelief, leading to optical coupling to cladding modes above the waveguide core. On the contrary, our structure is designed to incorporatea horizontal modulation via a periodic waveguide width variation and the design of a specific cladding box. Hence, no further process step is necessary. This is advantageous since the modulation pattern is directly drawn on the layout.

B. Materials and dimensions

The sensing mechanism is based on the coupling between two different modes; the fundamental core mode, HE1 of effective index n eff,1 , and an n th cladding mode of effective index n eff,n, which is mostly confined in the cladding whichcan later be functionalized to a specific chemical. Since grating-assisted coupling involves coupling the core mode to higher-order modes, which are modes with lower effective indices, the following conditionmust be fulfilledto have mode confinement n core > n eff,1 >n clad >n eff,n >n sub >n air where n core , n clad , n sub and n air are the refractive indexes of the Si 3 N 4 waveguide core, the cladding, the SiO 2 substrate, and the air respectively. Aspecific set of materials and structure dimensions must thenbeconsidered to allow both standard manufacturing process and functionalization for potential gas sensing. Silicon nitride (Si 3 N 4 or more commonly SiN)isemployed for its ease of growth in the domain of integrated photonics and optical properties(i.e. for its relatively mediumindexcontrast with silicon oxide). The sensitive layeremployed as cladding must be a porous polymer, in which the gas is soluble.In addition, the sensitivity and selectivity can be enhanced by employing supramolecular compounds which have a cage-like structure within which molecules can be reversibly trapped [START_REF] Ingvaldsen | Sensitivity to pressure and methane of a cryptophane-A doped polymer[END_REF].For example, Cryptophane-A which presents the smallest relative cavity, a methane trap,can be incorporated into a Styrene AcryloNitrile (SAN) film of index n=1.56, forming the sensing layer of a Mach-Zehnder-based methane sensor [START_REF] Dullo | Sensitive on-chip methane detection with a cryptophane-A cladded Mach-Zehnder interferometer[END_REF][START_REF] Apriyanto | Study, analysis and experimental validation of fiber refractometers based on single-mode, multimode and photonic crystal fibers for refractive index measurements with application for the detection of methane[END_REF]. It is referred to here as cladding, as it almost entirely encompasses the Silicon Nitride core(Fig. 1.(b) and 2.(a)) Figure 1. (b) describes the cross-sectional refractive index profile of the LPWG, with n core =2, n clad =1.56, n sub =1.45, n air =1. A sensing window thickness of ~1 µmallows uniform and relatively quick diffusion of the gas species to be detected as demonstrated in [START_REF] Barnes | Chemical sensor based on a long period fibre grating modified by a functionalized polydimethylsiloxane coating[END_REF][START_REF] James | A long period grating-based chemical sensor insensitive to the influence of interfering parameters[END_REF][START_REF] Tsoi | Polymeric long-period waveguide gratings[END_REF][START_REF] Dullo | Sensitive on-chip methane detection with a cryptophane-A cladded Mach-Zehnder interferometer[END_REF].The cladding and waveguide are respectively designed to have a20 and 0.8 (w core ) µm width and a 1.1µm and 0.6(h core )µmthicknessto ensure single mode propagation only within the core while allowing multiple higher order modes within the cladding.Moreover, the cladding dimensions determine the maximum order of the propagating cladding modes, which directly influences the coupling strength, as demonstrated later in section III and IV.Themaximum width variation Δ W (see Fig. 1. (a))and grating length period  are chosen to be 0.6µm and 8.76µm, respectively (Fig. 1 a)so that  corresponds to the standard LPG phase-matching condition [START_REF] Snyder | Optical waveguide theory[END_REF][START_REF] Li | Coupled-local-mode theory and study of optical peoperties of a gaussian fiber grating[END_REF][START_REF] Jin | Coupled local-mode theory for strongly modulated long period gratings[END_REF]on thepropagationconstants (z) β j and (z) β l of the two modes to couple at the resonance wavelength around 1550 nm:

 1 0 0     ) z ( β ) z ( β l j , (1)
Here, coupling occurs between the fundamental mode HE1, andhigher order propagating cladding modes, out of which one exhibits a higher coupling at a specific wavelength as described in the next section.More precisely, it will be further shown that only odd cladding modes can be coupled to the fundamental mode through the LPWG.Their respective effective indices and profiles were simulated with Lumerical,as shown in Fig. 2 for 2 higher-order modes only, to calculate the resonant grating period. We see that for the two multi-modes, most of the optical field is confined into the SAN, therefore called cladding-modes. These modes thus become inherently more affected by a change of the SAN refractive indexn clad .Using eq. ( 1), the resonance wavelength can be approximated by the average of the values of each coupled-mode effective indicesalong zpropagation. Note, however, that the real resonance wavelength values will be slightly shifted as the functions of the mode effective indicesversuscore width are not linear. LPG MODEL Different methods have been used to model the light propagation when introduced into the LPG. However, certain types of simulation methods find difficulty to model accurately this type of sensor as the behavior of the distribution of light is very continuous and highly depends on small structure variations.

A. Finite-Difference Time-Domain As an example, Finite-Difference Time-Domain (FDTD) gives an interesting insight of the overall sensor mechanism as shown in Fig 3, where coupling happens between HE1 and HE7, but its high dependence onfine discretization makes it inadequate for accurate modeling in our case using our computing resources.The need for both high temporal and mesh resolution over a relatively large area, especially at the interfaces where refraction happens, leads to large memory needs, otherwise simulations will present larger numerical errors than other methods. However, comparing Fig. 3. (a) and (b) clearly illustrates that, only at resonance, most of the optical power is transferred from the core mode to the higher order cladding mode after a brief propagating length. To circumvent these computing issues, two different methods can be used instead: the common EigenMode Expansion method and, more specific to our LPG application, the CLMT [START_REF] Snyder | Optical waveguide theory[END_REF].

B. Eigenmode Expansion method

The Eigenmode expansion method (EME), also referred to as mode matching method, is a rigorous technique used for modeling waveguides [START_REF] Eme | [END_REF][START_REF] Yue | Investigation of LPG-SPR sensors using the finite element method and eigenmode expansion method[END_REF], which relies on a scattering parameter superposition approach to calculate the amplitude of each mode at any propagation distance. This technique has very good efficiency for periodic and/or long components and provides flexible post-calculations analysis. It is thus ideal for modeling long period grating-based systems [START_REF] Yue | Investigation of LPG-SPR sensors using the finite element method and eigenmode expansion method[END_REF] as, due to the structure periodicity, it is possible to calculate the structure scattering parameters fromone single period. The method is available in various commercially available software such as Lumerical© suite tools, which was used to simulate the results presented on fig. 2.

C. Coupled Local-Mode Theory application

On the other hand, the CLMT application is performed through the characterization and calculation of the continuous refraction at the interfaces between the core and sensing window, which providesa more physical model on the coupling behavior in the LPG. The application of the theory was performed throughMatlab© and COMSOL© linked scripts.

Conventional Coupled Mode Theory (CMT) [START_REF] Snyder | Optical waveguide theory[END_REF]is usually used to describe the coupling between modes when small perturbations are assumedand modes remain almost unchanged along the propagation direction.Further, the general coupled mode equations are restricted to weakly guiding waveguides where polarization effects are ignored.CMT can thus model very accurately the first category of LPGs mentionedin Section II, where the waveguide dimensions remain constant and only local refractive indices are modified. However, in the presenceof significant cross-sectional dimension modulations [START_REF] Jin | Coupled local-mode theory for strongly modulated long period gratings[END_REF], CMT can no longer be applied, and a more specific approach, such as CLMT [START_REF] Snyder | Optical waveguide theory[END_REF], is required. CLMT achieves good results [START_REF] Li | Coupled-local-mode theory and study of optical peoperties of a gaussian fiber grating[END_REF][START_REF] Jin | Coupled local-mode theory for strongly modulated long period gratings[END_REF] when used to describestructures with large but slowly varying non-uniformitiesalong the waveguide and can thus be potentially used to describe our structure. In this section, a brief introduction to CLMT is formulated together with a method to calculate coupling coefficients. It will allow better understanding of the structure behavior and provide more insightto further optimize the design architecture.

Generally, there isno exact solution to Maxwell's equations for propagation along a perturbed waveguide.It is, however, possible to obtain accurate approximations of modes within local regions, known as local modes [START_REF] Snyder | Optical waveguide theory[END_REF]whichsuperpose to form the transverse field components as The coupling behavior between local modes is formulated by the general coupled local-mode equation [START_REF] Snyder | Optical waveguide theory[END_REF] 

      j j tj j j t (z)), β y, (x, ˆ (z) b (z) b z) y, (x,   (2)
          j l l , j l l , j j j j , ) b C b C b β i dz b d  (3)
withC jl the coupling coefficient between the local modes j and lwhich can be expressed as [START_REF] Snyder | Optical waveguide theory[END_REF] 

               A jj l * j l j 2 1 0 0 jl 0 C l; j dA, z n ê . ê β β 1 μ ε 4 1 C 2 (4)
The squared index component of the horizontal grating structure can be expressed here as

                         2 2 1 2 2 2 2 2 core box core n core core clad h y n h y )) z ( x ( H ( n h y n ) z , y , x ( n   , (5) with 2 2 1 core clad n n n    , 2 2 4 core w w z sin ) z (             and where 0   y x
at the center of the waveguide. H denotes the Heaviside function and ρ the periodic width variation of the LPWG along the z axis. By substituting eq. ( 5) into (4), we obtain the coupling coefficient for localmodes of an integrated horizontalgrating in the form of

                                            2 2 2 2 2     (6) with C jj =0.
Further, the transverse electric field at the interfaces of a step-index waveguide of relatively high index contrast is discontinuous, which complicates the calculation of the integrand. A bypass method [START_REF] Snyder | Optical waveguide theory[END_REF] is to recognize that n 2 e t is continuous across the interfaces. As a result, the transverse component of the integrand can be replaced by

                2 2 2 2 clad tl core * j , t n ê n . n ê n
As previously mentioned, one of the main advantages of this CLMT compared to the EME method consists in providing a better insight of the phenomena taking place in the LPG. In particular, important LPWG properties can be deduced from this equation (eq. 6):(1) onlycoupling of the fundamental mode to odd cladding modes is possible as the even mode coupling coefficients are null;(2) the coupling amplitude can be increasedby modifying the grating amplitude Δ W and period  (via ρ) or by optimizing the field superposition at the waveguide interfaces. The increase of the coupling coefficient amplitude fastens the rate at which energy is exchanged between modes, as described in eq. ( 3), thereby reducing the minimumrequiredLPWG's length to achieve maximum coupling.

To obtain a good estimation of the remaining integral in C jl (z) (eq. 6), COMSOL mode-solver, based on finiteelement method, can be used as it allows a convenient way to extractthe interface fields of each modes, their effective indices, and Poynting vectors for normalization. Ten crosssections were simulated by sweeping the waveguide width between minimum and maximum values to constitute a dataset of values.These calculations are only required over half a period of the 3D model because of the structure's periodicity. This dataset is then transferred to Matlab, coupling coefficients are calculated and extracted, and only then, the LPG geometry is taken into account to model energy distribution. Another advantage of the proposed model based on CLMT is thatusing this predetermined dataset, any LPG geometry can be designed and simulated easily. CLMT only requires a dataset of coupling coefficients for given cross-sections and directly calculates energy distribution as a function of C jl (z), while EME superposes each mode to calculate scattering parameter between each section. IV.

SIMULATIONRESULTS

A. Model validation

Figure4 shows the cladding mode power versus the propagating length along the LPWG for different wavelengths obtained withbothCLMT and EME techniques. It clearly shows that comparable results can be achieved with the CLMT.In addition, here, the highest order propagating mode (HE9, for our LPWG's dimensions)shows higher coupling than anylower order modes (e.g. HE7) at their respective resonant wavelengths (HE9@1540nm and HE7@1484nm), as previously demonstrated by the CLMT equations, due to a higher field product integrand at the core/cladding interface. This results in a reduced LPWG's length to achieve maximum coupling.The "HE9 normalized power" at wavelengths 1550nm and 1525nm clearly describes the coupling behavior of the LPWG when the injected wavelength drifts from the resonance, resulting in a reduction of the coupled energy at a the optimal sensor length (the shortest length where coupling reaches its peak at resonance), L opt = 300µm here.

B. Sensor sensitivity

The system interrogation can be performed through the wavelength interrogation method [START_REF] Barnes | Chemical sensing using a polymer coated long-period fiber grating interrogated by ring-down spectroscopy[END_REF][START_REF] Barnes | Chemical sensor based on a long period fibre grating modified by a functionalized polydimethylsiloxane coating[END_REF][START_REF] Ji | Highly sensitive refractive index sensor based on adiabatically tapered microfiber long period gratings[END_REF][START_REF] James | A long period grating-based chemical sensor insensitive to the influence of interfering parameters[END_REF]. The refractive index sensing mechanism relies on the disruption of the resonance of the LPWG which occurs when the cladding mode propagation constant changes. As a main difference with typical LPFG chemical sensors, which usuallyinvolve SPR as the cladding material cannot be modified easily, the cladding mode here is mostly confined in the sensing layer incorporated with the selective transducer. It is expected to lead to a relatively large modification of the mode propagation constant when the material indexchanges, i.e.analyte-inducedperturbations, which enhances sensor sensitivity. As it is difficult to measure the output spectra of the higher mode the measurement is made directly at the output of the core, which allows to get the same wavelength via detecting a dip in the light in the core.

We assume here that the output core intensity is equal to the input intensity minus the coupled energy to cladding modes along propagation, which could easily be measured using grating couplers, for example.

One can also notice a LPG peak is larger than other resonance peak found in integrated optics, which prevents it from large linewidth source issues.

V. FABRICATION PROPOSALS

This new type of integrated refractometric sensor is based on a specific coupling mechanism which allows several profile configurations, and therefore multiple realization processes. As described in the first section, the effective indices of each region must respect a certain relationship.Two different approaches can be employed to fabricate the LPWG. A first method would be to simply create an opening into the buried core of a photonic chip and cover it with a sensing film to fill the etched region as seen in Fig. 6. (a). A downsize to this method is the lack of control of the thickness of the film at certain areas where the cladding could form a rib multi mode waveguide instead of a strip one. It could simply be bypassed to a certain extent by performing spin coating to different speeds until the thickness reaches a value corresponding to a desired n eff,n of the rib cladding mode.

A second method (Fig. 6. (b)) currently being investigated would be to perform lithography on the polymer layer, creating polymer waveguides encompassing the core waveguide. [START_REF] Broglia | Rapid Fabrication of Periodic Patterns on Poly(styrene-co-acrylonitrile) Surfaces Using Direct Laser Interference Patterning[END_REF] This type of structure could also be translated to an electro optical multi-mode coupler, enabling selected coupling of the fundamental mode into a specific higher order mode. CONCLUSION We have presented a new sensor architecture based on a long period horizontal gratingstructure. We have also proposed to describe the LPWG using the CLMT which provides more insight on the physics of the structure.For example,it indicates that a higher index contrast and therefore higher n core values could increase the coupling, rendering the architecture an interesting candidate for silicon on-chip integration.This approach has been successfully compared to and verified using a standard method based on EME. Moreover,CLMT is more flexible to common grating profile modulations [START_REF] Li | Coupled-local-mode theory and study of optical peoperties of a gaussian fiber grating[END_REF][START_REF] Erdogan | Cladding-mode resonances in short-and long-period fibers[END_REF] as we work on the reconstruction of the coupling coefficient shape along propagation. The calculated overall sensor sensitivity reaches 1768 nm/RIU, and further improvement could increase the sensitivity to over 2000nm/RIU. Based on [START_REF] Ingvaldsen | Sensitivity to pressure and methane of a cryptophane-A doped polymer[END_REF], from the achieved Mach Zehnder sensitivity of 0.768 mrad/ppm, the SAN and Cryptophane layer sensitivity to methane in terms of RIU/ppm canbe estimated to be approximately 6.3 nRIU/ppm. As a result, using a similar sensitive layer with our proposed LPG architecture, an 11 fm/ppm theoretical wavelength sensitivity could be expected.This new type of design appears promising and can benefit from improvements or hybridations, potentiallyinvolving new sensing mechanisms, like plasmonics [START_REF] Yue | Investigation of LPG-SPR sensors using the finite element method and eigenmode expansion method[END_REF] or photonic crystals [START_REF] Steinvurzel | Long period grating resonances in photonic bandgap fiber[END_REF].

Fig. 1 .

 1 Fig. 1. (a)Horizontal LPWG coreprofiles and (b)cross-sectional material architecture where the Si3N4 and the Styrene AcryloNitrile(SAN) are the core and cladding waveguides respectively

Fig. 2 .

 2 Fig. 2. Mode profiles at 1550nm for Fundamental (a)HE1 mode, and cladding (b)HE9 and(c) HE7 modes calculated with Lumerical mode solver

Fig. 3 .

 3 Fig. 3. (a)Illustration of the intensity distribution seen from above at resonance (b)Normalizedintensity distribution seen from above with a slightly different cladding index

Figure 2 .

 2 Figure 2. shows (a) the fundamental mode profile and (b)-(c) the profile of two cladding modes that can couple to the fundamental mode at certain conditions. The gratingperiod is longitudinally divided into 40 block objects and the guided mode calculation considers 40 modes per block similarly to [12].

  of the j th mode, and j b ± (z)areboth modal amplitude and phase for forward (+) or backward (-) propagation.

Fig. 4 .

 4 Fig. 4. Cladding mode normalized power versus propagation length (SI) forHE7 and HE9 modes at different wavelengths simulated by CLMT application and EME

Figure 5 .

 5 Figure 5. (a) shows the coupling spectrafordifferent cladding refractive indices. From these results,thesensitivity can be calculated (cf. Fig. 5. (b)). The average sensitivity is found to be 1768nm/RIU (refractive index unit).

Fig. 5 .

 5 Fig.5. (a) HE9 normalized mode power spectra for a 33 periods long grating at different cladding refractive indices, calculated with EME method and (b) resulting resonance peak shift for wavelength interrogation

Fig. 6 .

 6 Fig. 6. (a)Rib cladding structure and (b)Strip cladding structure