Papa Malick Ndiaye
email: ndiaye.papa-malick@ugb.edu.sn

Ansoumana Bodian
email: bodianansoumana@gmail.com

Lamine Diop
email: lamine.diop@ugb.edu.sn

Alain Dezetter
email: alain.dezetter@ird.fr

Etienne Guilpart
email: etienne.guilpart@gmail.com

Abdoulaye Deme
email: abdoulaye.deme@ugb.edu.sn

Andrew Ogilvie
email: andrew.ogilvie@ird.fr

Future trend and sensitivity analysis of evapotranspiration in the Senegal River Basin

Keywords:

Study region: Senegal River Basin in West Africa. Study focus: This work aimed to assess reference evapotranspiration (ET 0 ) trends and its sensitivity to climate variables on the period 2036-2065 in the Senegal River basin. Seven General Circulation Models (GCMs) and seven Regional Climate Models (RCMs) of the CMIP5 project were used under the scenarios RCP4.5 and RCP8.5. The performance of GCMs and RCMs was first evaluated by comparing their outputs with the reanalyses data. The change of ET 0 is determined between the periods 1971-2000 and 2036-2065. A sensitivity coefficient was calculated to analyze the influence of climatic variables on ET 0 . Finally, the Mann Kendall test and Sen slope were used to detect future trends in ET 0 and climate variables. New hydrological insights for the region: It was found that RCMs were here more robust than GCMs in estimating reference evapotranspiration over the period 1984-2000. Compared to the period 1971-2000, the RCMs show that ET 0 will increase by 14-293 mm under RCP4.5 and by 55-387 mm under RCP8.5 according to the climatic zones. The maximum values are observed in Sahelian zone and the minimum one in Guinean area. The sensitivity analysis shows that ET 0 is more sensitive to relative humidity, maximum temperature and solar radiation. The trend analysis reveals, generally, a significant increase in ET 0 and in maximum and minimum temperatures in the period 2036-2065 under the RCP4.5 and RCP8.5 scenarios. This means that ET 0 will not be stationary and may continue to increase after 2065 because of the increase of temperature.

Introduction

Climate change are now affecting both natural and anthropic ecosystems, and are of major concern to the scientific community and policy makers (IPCC, 2018;[START_REF] Ouhamdouch | Assessment the climate change impact on the future evapotranspiration and flows from a semiarid environment[END_REF][START_REF] Bahir | Climate change effect on groundwater characteristics within semi-arid zones from western Morocco[END_REF]. According to the latest estimations from the Intergovernmental Panel on Climate Change (IPCC, 2018), human activities have caused global warming of 1 • C above pre-industrial levels, with a range of 0.8-1.2 • C. This warming could reach 1.5 • C between 2030 and 2052 if it continues to increase at the current rate (IPCC, 2018). This climate change could impact a large panel of sector and activities, by raising pressure on water resources, reducing agricultural productivity, and greater development of vector-borne and water-borne diseases (IPCC, 2014). In addition, a continuous increase in temperatures could intensify the hydrological cycle and lead to the more frequent occurrence of extreme weather events [START_REF] Chaouche | Analyses of precipitation, temperature and evapotranspiration in a French Mediterranean region in the context of climate change[END_REF][START_REF] Tao | Analysis and prediction of reference evapotranspiration with climate change in Xiangjiang River Basin, China[END_REF][START_REF] Rahman | Analysis of reference evapotranspiration (ET0) trends under climate change in Bangladesh using observed and CMIP5 data sets[END_REF][START_REF] Wilcox | Trends in hydrological extremes in the Senegal and niger rivers[END_REF][START_REF] Ouhamdouch | Assessment the climate change impact on the future evapotranspiration and flows from a semiarid environment[END_REF]. Therefore, it is important to determine the potential impacts of climate change on water resources and the spatiotemporal variation of hydrological processes.

Reference evapotranspiration (ET 0 ), a key indicator of climate change, is one of those hydrological processes that directly links the energy balance to the water balance. Evapotranspiration rates mainly depend on the water and energy available and the vapor pressure [START_REF] Dong | The response of reference evapotranspiration to climate change in Xinjiang, China: historical changes, driving forces, and future projections[END_REF]. However, these three factors are strongly affected by climate change [START_REF] Sarkar | A review on impact of climate change on evapotranspiration[END_REF]. Detecting future changes in evapotranspiration can help to determine the impact of climate change on water resources and to constitute a benchmark for the management of water resources and the optimization of agricultural water demands [START_REF] Lin | Impacts of climate change on reference evapotranspiration in the Qilian Mountains of China: historical trends and projected changes[END_REF][START_REF] Dong | The response of reference evapotranspiration to climate change in Xinjiang, China: historical changes, driving forces, and future projections[END_REF][START_REF] Mubialiwo | Historical rainfall and evapotranspiration changes over mpologoma catchment in Uganda, hindawi[END_REF]. Furthermore, analysis of trends in climatic variables (temperature, wind speed, relative humidity and solar radiation) provides a better understanding of the sensitivity of ET 0 to climate variables and helps determine the potential impacts of climate changes on evapotranspiration [START_REF] Lin | Impacts of climate change on reference evapotranspiration in the Qilian Mountains of China: historical trends and projected changes[END_REF].

In recent years, several authors [START_REF] Moratiel | Trends in climatic variables and future reference evapotranspiration in Duero Valley (Spain)[END_REF][START_REF] Huo | Effect of climate change on reference evapotranspiration and aridity index in arid region of China[END_REF][START_REF] Delghandi | Climate change impacts on spatial-temporal variations of reference evapotranspiration in Iran[END_REF][START_REF] Giménez | Assessing regional climate models (RCMs) ensemble-driven reference evapotranspiration over Spain[END_REF][START_REF] Dong | The response of reference evapotranspiration to climate change in Xinjiang, China: historical changes, driving forces, and future projections[END_REF][START_REF] Yang | Spatio-temporal Variation of Reference Evapotranspiration in Northwest China Based on CORDEX-EA[END_REF][START_REF] Ouhamdouch | Assessment the climate change impact on the future evapotranspiration and flows from a semiarid environment[END_REF] used General Circulation Models (GCMs) or Regional Climatic Models (RCMs) to assess the potential impacts of climate change on evapotranspiration. For example, [START_REF] Dong | The response of reference evapotranspiration to climate change in Xinjiang, China: historical changes, driving forces, and future projections[END_REF] used four GCMs to analyze current and future trend of evapotranspiration in an arid and sub-humid climate of Xinjiang province in China according to the RCP4.5 and RCP8.5 scenarios. They concluded that evapotranspiration will continue to increase during the 21 st century. [START_REF] Delghandi | Climate change impacts on spatial-temporal variations of reference evapotranspiration in Iran[END_REF] assessed the impacts of climate change on the spatiotemporal variation of ET 0 in an arid and semi-arid climate of Iran using fifteen GCMs. Their results show an increase in evapotranspiration during the periods 2015-2045 and 2070-2099 compared to the period 1971-2000. In the semi-arid zone of Spain, [START_REF] Giménez | Assessing regional climate models (RCMs) ensemble-driven reference evapotranspiration over Spain[END_REF] used the average of sixteen regional models to estimate evapotranspiration by the method of Hargreaves and Samani (1985) by 2035 (2021-2050). They noted that ET 0 will continue to rise due to rising temperatures. In West Africa, [START_REF] Obada | Trends and changes in recent and future penman-monteith potential evapotranspiration in Benin (West Africa)[END_REF] used three regional models from the COordinated Regional-climate Downscaling Experiment (CORDEX) project to estimate the annual evapotranspiration in Benin over the period 1951-2100. Their results show an increase in evapotranspiration by 2100 according to the RCP4.5 and RCP8.5 scenarios. To our knowledge, the study of [START_REF] Obada | Trends and changes in recent and future penman-monteith potential evapotranspiration in Benin (West Africa)[END_REF] is the only one that looks at future trends and rate of change in evapotranspiration in West Africa. However, this study did not take into account the sensitivity analysis of ET 0 to climate variables which is an effective way to understand the impact of climate change on evapotranspiration [START_REF] Wang | Spatial and temporal characteristics of reference evapotranspiration and its climatic driving factors over China from 1979-2015[END_REF], and climate projections are not homogeneous across West Africa.

The objective of this work is to analyze the trends of evapotranspiration as well as its sensitivity to climatic variables in the Senegal River basin on the period 2036-2065. Specifically, it seeks to: (i) evaluate the performance of climate models (GCMs and RCMs) compared to reference data for estimating evapotranspiration, (ii) detect future trends in evapotranspiration and climatic variables (temperature, wind speed, relative humidity, radiation solar), (iii) analyze the sensitivity of ET 0 to climatic variables and determine the change rate of ET 0 between the periods 1971-2000 and 2036-2065. Understanding future trends in evapotranspiration is essential to assess the impact of climate change on water resources and develop adequate and efficient management strategies, notably in the Senegal River Basin where resources are under increasing pressure to supply agriculture, hydroelectric production, drinking water, navigation, etc.

Materials and methods

Study area

The Senegal River basin is the second largest transboundary basin in West Africa. It covers an area over of 300,000 km 2 and its population is estimated at 6.5 million in 2015 and could reach 9.5 million in 2025 [START_REF] Sdage-Omvs | Etat Des Lieux Et Diagnostique ; Rapport Provisoire 2009, Rapport De Phase III[END_REF]. The basin spans four states (Guinea, Mali, Mauritania, Senegal) which created the Organization for the Development of the Senegal River (in french, l'Organisation pour la Mise en Valeur du fleuve Sénégal, OMVS). The Senegal River basin is at the heart of the socio-economic development strategies of the riparian countries. The establishment of hydraulic infrastructure (Fig. 1a) has enabled agricultural development, hydroelectric production and the exploitation of mineral resources. From a climatic point of view, the longitudinal distribution of precipitation divides the basin into three climatic zones: Sahelian, Sudanian and Guinean [START_REF] Dione | Evolution Climatique Récente Et Dynamique Fluviale Dans Les Hauts Bassins Des Fleuves Sénégal Et Gambie (Recent Climate Evolution and Fluvial Dynamics in the High Basins of the Senegal and Gambia Rivers)[END_REF]Fig. 1b). The Sahelian zone occupies 37 % of the basin and the average annual rainfall is less than 500 mm over the period 1951-2004. In the Sudanian zone (62 % of the basin area), the annual average precipitation varies between 500 and 1500 mm. The Guinean zone (1%) records the most abundant precipitations with an average greater than 1500 mm. The daily maximum temperature can reach 43 • C in Guinean area, 48 • C in the Sahelian zone and 49 • C in Sudanian area over the period 1984-2017. The Sahelian zone is here influenced by the sea leading to a dampening of temperatures.

Data

In this study, data from reanalysis, General Circulation Models (GCMs) and Regional Climate Models (RCMs) are used. Reanalysis weather data from the NASA Langley Research Center (LaRC) POWER project driven by NASA Earth Science/Applied Science program (https://power. larc.nasa.gov/data-accessviewer, accessed December 20, 2018) are used as alternatives to observed data generally sparse and inaccessible in Africa [START_REF] Poccard-Leclercq | Etude Diagnostique De Nouvelles Données Climatiques : Les Réanalyses. Exemples d'application Aux Précipitations En Afrique Tropicale[END_REF][START_REF] Bodian | Recent trend in hydroclimatic conditions in the Senegal River Basin[END_REF]Ndiaye et al., 2020a, b). Indeed, too few stations with long time series are available, which represents a major obstacle both to use data from these meteorological stations, but also to carry out an evaluation of any data sets of reanalyses. Thus, NASA reanalyses are used as reference data to assess the spatiotemporal consistency of the outputs of climate models.

In this study, we take into account seven GCMs included in the Coupled Model Intercomparison Project (CMIP5). The seven RCMs datasets used were extracted from the CORDEX-Africa project and the r1i1p1 set, and correspond to the Rossby Center regional atmospheric model (RCA4) which has been forced by the seven GCMs mentioned above (Table 1). The simulation domain spans Longitude: 24 • W-60 • E and Latitude: 45 • S-42 • N. The characteristics of the models used are summarized in Table 1.

The scenarios used are RCP4.5 and RCP8.5. The RCP4.5 scenario recommends stabilizing the concentration of CO 2 with an increase in temperatures of 2.4 • C by 2100 (IPCC, 2014). RCP8.5 is the pessimistic scenario which predicts a high concentration of CO 2 and an increase in temperatures of over 4 • C by 2100 (IPCC, 2014). The multi-model ensemble represents a variety of best effort attempts to simulate the climate system and can provide a consensus representation of the climate system [START_REF] Taylor | An overview of CMIP5 and the experiment design[END_REF][START_REF] Yin | Projections of aridity and its regional variability over China in the mid-21st century[END_REF][START_REF] Dong | The response of reference evapotranspiration to climate change in Xinjiang, China: historical changes, driving forces, and future projections[END_REF]. In this study, the multi-model is considered as the average (ENSEMBLE) of the seven models in GCMs and RCMs.

For both climate models, monthly data of air temperature (max and min), relative humidity, wind speed and solar radiation are used to estimate evapotranspiration in three periods. Indeed, the period 1984-2000 is used to assess the performance of climate models against reanalyses for estimating ET 0 by the Penman-Monteith method [START_REF] Allen | Crop Evapotranspiration. Guideline for Computing Crop Requirements[END_REF]. This assessment only concerns the historical period of climate models (1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000). The period 1984-2000 is used not only because of the length of the data series available but also to have a homogeneous period for reanalyses and climate models. For the same reason of data availability, the historical period is 1971-2000 and the projection one is 2036-2065. The annual and seasonal ET 0 are obtained by summing monthly ET 0 values. For climate variables, the averages values are used. Two seasons are considered: a dry season (November to May) and a rainy season (June to October) even though, the length of the seasons varies according to the climatic zones of the basin (Ndiaye et al., 2020b). The coordinates of 31 OMVS weather stations and 33 virtual stations (Fig. 1, Ndiaye et al., 2020b) were used to extract both reanalyses and outputs of climate models.

Methodology

The methodology employed here consists of (i) the performance evaluation of reanalyses compared to observations, (ii) the performance evaluation of the GCMs and RCMs compared to the reanalyses for the estimation of reference evapotranspiration (ET 0 ) over the period 1984-2000, (iii) evaluation of the change of ET 0 and climate variables between the periods 1971-2000 and 2036-2065, (iv) the sensitivity analysis of ET 0 to climatic variables and detection of the trends of ET 0 and climate variables over the period 2036-2065.

Performance evaluation of reanalyses data

Due to the lack of sufficient climate observations in the Senegal River Basin, reanalyses data were used here. The meteorological variables extracted from the NASA databases were first evaluated against ground based observations, to establish their temporal consistency and verify if they reproduce the same trend.

For this, we chose the stations which have at least three meteorological variables available on a daily scale. These are the stations of Kayes, Kita, Nioro du Sahel and Bamako Senou. These four stations cover the range of climatic zones found in the Senegal River basin (Fig. 1b). For each station, for the sake of better legibility of the results, a single year was chosen to represent the trend of climatic variables. To evaluate the agreement between the reanalyses and the observed data, the Kling Gupta Efficiency [START_REF] Gupta | Decomposition of the mean squared error and NSE performance criteria: implications for improving hydrological modeling[END_REF] is used (Eq. 2). In order to take into account the climate zones (sahelian, sudanian and guinean) of the basin, two stations (Labe and Mamou) are added to the four previous ones for assessing the KGE.

Evaluating the performance of climate model projections

The performance of climate models' projections is assessed in two steps. First, the difference between the yearly average of ET 0 of reanalyses and that of GCMs and RCMs is assessed over the period 1984-2000 by using the following equation:

ΔET 0rea-model = 1 n ∑ (ET 0model -ET 0rea ) (1)
Where ΔET 0rea-model is the difference between ET 0 of reanalyses and models, ET 0rea is the ET 0 calculated with reanalyses data, ET 0model is ET 0 calculated with GCMs and RCMs and n the length of the series.

Then, the Kling Gupta Efficiency (KGE- [START_REF] Gupta | Decomposition of the mean squared error and NSE performance criteria: implications for improving hydrological modeling[END_REF] and the Percentage of Bias (PBIAS) are used as evaluation criteria at monthly scale. The KGE combines the correlation coefficient (r), the biases (β) and the variability (α). It varies from -∞ to 1 and its optimal value is 1. The formulation of the KGE is as follows: r -1) 2 + (β -1) 2 + (α -1) 2

KGE = 1 - ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ (

√

(2)

Percent bias (PBIAS) indicates the underestimation / overestimation of ET 0 by climate models. It varies from -∞ to + ∞ and its optimal value is 0. Its formulation is as follows:

PBIAS = ⎡ ⎢ ⎢ ⎢ ⎣ 1 n ∑ n i=1 (ET ocm -ET 0rea ) 1 n ∑ n i=1 (ET o cm ) ⎤ ⎥ ⎥ ⎥ ⎦ * 100 (3)
Where, ET ocm is the reference evapotranspiration estimated from the climate models, ET 0rea is the ET 0 estimated by the reanalysis and n is the length of the data.

Sensitivity analysis and calculation of the rate of change

The sensitivity analysis allows to determine the impact of climate variables on the reference evapotranspiration [START_REF] Zhao | Climatic characteristics of reference evapotranspiration in the Hai River Basin and their attribution[END_REF]. The influence of each variable is determined by calculating a sensitivity coefficient. Its wording is as follows:

S vi = ∂ET 0 ∂ vi × vi ET 0 (4)
Where, S vi is the sensitivity coefficient, ∂ET 0 variation of the reference evapotranspiration (ET 0 ) caused by the change of a variable ∂ vi , is the considered variable. A positive (negative) sensitivity coefficient indicates that the variable causes an increase (decrease) in ET 0 . The higher the absolute value of the sensitivity coefficient, the more influence the variable has on ET 0 [START_REF] Li | Variation of aridity index and the role of climate variables in the Southwest China[END_REF].

The rate of change of ET 0 is calculated between the mean of ET 0 on the historical period and the projections (2036-2065) according to the following formula:

RC = ET 0 Pro -ET 0Hist ET 0Hist × 100 (5)
Where, RC is the rate of change in %, ET 0Hist is the mean reference evapotranspiration calculated over the historical period and ET 0Pro is the mean reference evapotranspiration calculated in the future. A positive (negative) value for the rate of change indicates an increase (decrease) in evapotranspiration in the future. The same Eq. ( 4) is used for calculating the rate change of climate variables.

Trend in reference evapotranspiration and climatic variables

The Mann Kendall test [START_REF] Mann | Non-parametric test against trend[END_REF]Kendall, 1975) is used to detect the trend of annual and seasonal ET 0 and climate variables on the period 2036-2065 according to the RCP4.5 and RCP8.5 scenarios. The Mann Kendall test is based on two hypotheses: hypothesis (denoted H0) which assumes that the series is stationary, without trend and the alternative hypothesis (H1) which indicates the existence of a trend by rejecting H0. A positive/negative trend is obtained from the +/-sign of the Z value of the Mann Kendall test. The trend obtained is measured by its degree of significance, that is to say the probability associated with the rejection or not of the null hypothesis. The significance level used in this study is 0.05. When |Z|> 1.96 the null hypothesis is rejected and the trend is significant at 5%. The amplitude of the trend is measured by the slope of Sen (Sen, 1968) denoted (β).

The method of interpolation of the Inverse Distance Weighting (IDW) [START_REF] Chu | Changes in reference evapotranspiration and its contributing factors in Jiangsu, a major economic and agricultural province of Eastern China[END_REF] is used to spatialize the ET 0 and climate variables on an annual and seasonal scale. The IDW interpolation technique is widely used to analyze the spatial distribution of evapotranspiration [START_REF] Qi | Spatiotemporal changes of reference evapotranspiration in the highest-latitude region of China[END_REF][START_REF] Malamos | Spatial interpolation of potential evapotranspiration for precision irrigation purposes[END_REF]Ndiaye et al., 2020b).

Results and discussion

Performance of reanalyses against observed data

The climate variables available for the four weather stations (Bamako Senou, Kayes, Kita and Nioro du Sahel) are maximum and minimum temperature, relative humidity and wind speed. The latter is only available for Bamako Senou weather station. The temporal consistency between observed data and reanalyses is shown in Fig. 2 for a given year. Table 2 provides the KGE values and its components (r, alpha, beta) according to climate variables available and climate zones. Fig. 2 shows good consistency for Tmax, Tmin, and lesser for Rh. Table 2 confirms good performance for Tmax with KGE above 0.5 for all stations. KGE for Tmin is also high, except on Guinean stations. This may be explained by the coarse resolution of reanalyse data and the fact that their reliability appears to vary with the location, time period and variables considered [START_REF] Martins | Assessing reference evapotranspiration estimation from reanalysis weather products. An application to the Iberian Peninsula[END_REF]. For Rh, despite some variability in Fig. 2, KGE remains high. Wind speed KGE values are much lower around 0.2 but Fig. 2 shows relative agreement in the overall amplitude of the wind.

Overall, these results show acceptable consistency between the observed data and the reanalyses for the key climatic variables at the Kayes, Kita, Nioro du Sahel and Bamako Senou stations. Accordingly, the reanalyses were used as reference here for assessing the performance of climate models.

Performance of GCMS and RCMs against reanalyses data

Fig. 3 shows the spatial distribution of the difference in the annual ET 0 of climate models and reanalyses over the period 1984-2000. Results show that the difference in annual ET 0 between reanalyses and GCMs varies from -1560 to +820 mm depending on the models (Fig. 3). The maximum negative values are obtained by IPSL-CM5A-RC and CSIRO-MK3-6-0 models in Sahelian and Sudanian climate zones. For the ENSEMBLE average of all models, the difference ranges from -747 to +283 mm. individually, the HADGEM, CNRM, and CANESM models exhibit ET 0 values closer to reanalyses. RCMs, on the other hand, show ET 0 values that are closer to reanalyses compared to GCMs. However, they generally tend to overestimate evapotranspiration, while GCMs here tend to underestimate it. For example, the difference in annual ET 0 between reanalyses and regional models ranges from -483 to +1110 mm depending on the model. The ENSEMBLE average of all regional models shows a difference ranging from -139 to +720 mm (Fig. 4). The ET 0 values of the regional models CANESM2.RCA4, CNRM-CM5.RCA4 and HadGEM2-ES.RCA4 are closer to those obtained with reanalyses.

Overall, the results show that the differences between ET 0 values from reanalysis data and climate models are relatively high. This may be explained by the difficulty of climate models to reproduce correctly the climate variables used for estimating reference evapotranspiration. Indeed, the ET 0 values obtained from reanalyses are closer to those of Bodian (2011) and Djaman et al. (2015) in Senegal River Basin. According to Bodian (2011), at Labé and Siguiri (Guinean zone) weather stations, the observed values of ET 0 were 1611 mm and 1969 mm over the period 1960-1996. For these two stations, the values of reanalyses are 1838 mm and 1936 mm over the period 1984-2017. Moreover, in Sahelian zone, Djaman et al. (2015) used the observed data of Africa Rice Center research stations at Ndiaye and Fanaye (Sahelian Regional station, Senegal) for estimation reference evapotranspiration over February 2013 and May 2014. They showed that reference evapotranspiration varies from 1 to 14 mm/day with an average of 6 mm/day (2190 mm/year) at Ndiaye and from 3 to 18 mm/day with an average of 10 mm/day (3650 mm/year) at Fanaye. For the reanalyses, ET 0 varies between 1-18 mm/day with an average of 8 mm/day (2920 mm/year) over the period 1984-2017 at Fanaye.

Figs. 4 and 5 respectively give the spatial distribution of KGE and PBIAS and Fig. 6 gives a synthesis of KGE and PBIAS as a function of climatic zones. For the GCMs, the KGE vary from -0.35 to 0.68. The highest values are obtained by the CANESM2 and GDFL-ESM2M models and the lowest by CSIRO-MK3-6-0 and HadGEM2-ES. The biases vary from -124 % to 38 %. The mean values of PBIAS show that GCMs underestimate evapotranspiration in 91 % of stations in the basin. The average of all GCMs shows KGE values of 0.09 to 0.48 and biases of -58 % to 24 %. From a spatial point of view, the results are almost similar depending on the climatic zones. From the Guinean zone to the Sahelian one, the GCMs have KGE of less than 0.60 and underestimate the evapotranspiration. These results obtained show that GCMs are less robust for the estimation of evapotranspiration. This can be explained by the coarse resolution of the GCMs and their uncertainty in estimating the climate variables necessary for the estimation of evapotranspiration. Fig. 4 shows that the KGE of RCMs are greater than 0.60 in the most of the stations and are more in agreement with the reanalyses than the GCMs. The average KGE and PBIAS of the regional models vary from -0.21 to 0.87 and from -8% to 27 % respectively. Unlike GCMs, RCMs overestimate ET 0 at 88 % of stations. From a spatial point of view, the mean KGE values of multi-models ENSEMBLE are 0.70 (min and max vary from 0.54 to 0.87) in Guinean zone, 0.72 (0.43 to 0.83) in Sudanian area and 0.67 (0.36 to 0.85) in the Sahelian zone. The PBIAS show that all RCMs overestimate evapotranspiration in all climate zones, with the exception of CSIRO-Mk3-6-0.RCA4 and MIROC5RC.RCA4 which underestimate it in the Guinean zone. Moreover, some regional models have better performances than the ENSEMBLE average of all models in some climate zones. For example, in Guinean zone, the KGE values of CSIRO-Mk3-6-0.RCA4, HadGEM2-ES.RCA4 and MIROC5RC.RCA4 are respectively 0.73, 0.74 and 0.76 and that of the ENSEMBLE average models is 0.70. However, in Sahelian and Sudanian zones, the ENSEMBLE performs better than the individual models.

Overall, RCMs are more robust than GCMs for estimating evapotranspiration in the Senegal River basin. For this purpose, only RCMs will be taken into account in subsequent analyses. The reanalyses data used to perform climate models seem coherent with observed data used by Bodian (2011) and Djaman et al. (2015) in the High Basin and the Valley of Senegal River. Moreover, the different values of KGE and PBIAS obtained by the models in the climate zones may be explained by the structure of the models, the heterogeneity of the landscape and the number of stations used in each climate zones. For example, in Guinean zone (1% of the basin) only the mean values of five stations are analyzed against 33 and 26 stations in Sudanian (37 %) and Sahelian zones (62 %), respectively. The reanalyses used as a reference are not validated by observed data; which can influence the calculation of the rate of reference evapotranspiration. The difficulty of climate models in correctly simulating the variables necessary for estimating ET 0 would also be a source of uncertainty.

Change in evapotranspiration by 2065

All the models agree on a positive variation in evapotranspiration on the period 2036-2065. Fig. 7 shows mean values of annual evapotranspiration in both historical and projection periods according to the climate zones. Fig. 8 gives the spatial distribution of the ET 0 change at annual and seasonal scales. In the Guinean zone, the minimum and maximum values of annual ET 0 vary from 1355 to 2521 mm on the period 1971-2000 according to climate models. During the period 2036-2065, these values vary from 1455 to 2657 mm for RCP4.5 and 1457-2696 mm for RCP8.5. The maximum values were obtained by IPSL-CM5A-MR.RCA4. The increase of ET 0 in the Guinean zone varies from 14 to 173 mm (i.e. 2-11%) for RCP4.5 and from 55 to 196 mm (i.e. 2.4-11%) for RCP8.5 according to the models. In Sudanian zone, the ET 0 values vary from 1902 to 2390 mm over the period 1971-2000. The ET 0 for the period 2036-2065 vary from 2046 to 2386 for RCP4.5 and 2051-4056 mm for RCP8.5. This means that, according to the models, ET 0 will increase by 2-9% (56-285 mm) for RCP4.5 and 4-11% (99-365 mm) for RCP8.5 until 2065. The ET 0 values will reach 4095 mm for RCP4.5 and 4153 mm for RCP8.5 compared to the period 1971-2000 where the maximum value of ET 0 was 3810 mm in the Sahelian zone. The increase of ET 0 varies between 3-10 % (63 and 293 mm) for RCP4.5 and 3-12 % (106-387 mm) for RCP8.5. Moreover, it is interesting to note that among the models, MIROC5.RCA4 shows higher values of ET 0 for RCP4.5 than RCP8.5 in the three climate zones. This surprising result may be explained by the interactions between local climatic processes and the reduced maximum temperature and wind speed modelled by this RCMs under scenario RCP8.5 (Section 3.4.2). At the seasonal scale, the models show that, until 2065, evapotranspiration will increase during the dry and wet season. For example, in the Sahelian zone, the ET 0 will increase between 27 and 181 mm (2-9 %) for RCP4.5 and 72-189 mm (4-10 %) for RCP8.5. In the Guinean and Sudanian zones the maximum values of ET 0 will respectively reach 123-150 mm for RCP4.5 and 128-176 mm for RCP8.5. During the rainy season, ET 0 will increase at a rate of 0-18 % in Sahelian and Sudanian zones according to the models and the two scenarios. It will increase from 3 to 15 % in the Guinean zone.

Overall, according to the RCMs, the ET 0 will continue to increase until 2065 in Senegal River Basin. Similar results have been obtained in different regions of the world. Thus, [START_REF] Obada | Trends and changes in recent and future penman-monteith potential evapotranspiration in Benin (West Africa)[END_REF] noted that all three models they used project an increase in ET 0 from 3% to 10.91 % in Benin (West Africa) over the period 2041-2070. In a semi climate arid in Spain, [START_REF] Giménez | Assessing regional climate models (RCMs) ensemble-driven reference evapotranspiration over Spain[END_REF] predict an increase in ET 0 from 4.42 % to 16.21 % by 2050, compared to the average for the period 1960-1990. The increase in ET 0 by 2050 could be accompanied by a decrease in flows. Indeed, according to [START_REF] Bodian | Future climate change impacts on streamflows of Two Main West Africa river basins: senegal and Gambia[END_REF], compared to the period 1971-2000, the annual flows of the Bafing, the main tributary of the Senegal River, will decrease by 8% according to the RCP4.5 scenario and by 16 % under RCP8.5 scenario by 2050 in West Africa. This means that the annual flows depend on precipitation variability and evapotranspiration. The continued increase of the latter may affect the water resources and exacerbate competition between users. Moreover, it is important to note that Ndiaye et al. (2020b) highlighted a significant decrease of evapotranspiration in the Sahelian zone and mentioned the existence of an "evaporation paradox" in the Senegal River Basin on the period 1987-2017. However, no model has highlighted a significant decrease of evapotranspiration on the period 2036-2065. Therefore the "evaporation paradox" will not exist on the period 2036-2065 according to the RCMs.

Sensitivity of future evapotranspiration to climatic variables

The influence of climatic variables on evapotranspiration is determined by calculating a sensitivity coefficient. Thus, Fig. 9 gives the spatial distribution of the annual sensitivity coefficients according to the models and Table 2 indicates the average values of the coefficients according to climatic zones. With the exception of relative humidity, all variables have positive sensitivity coefficients. In other words, their increase leads to an increase in evapotranspiration.

Table 3 shows that the relative humidity sensitivity coefficients vary from -0.90 to -8. from -0.90 to -8.4 depending on the models, under both the RCP4.5 and RCP8.5 scenarios. The maximum values of relative humidity are observed in the Guinean zone and those minimum in the Sahelian zone. The maximum temperature coefficients range from 1.35 to 2.59 under RCP4.5 and from 1.35 to 2.49 under RCP8.5. The influence of maximum temperature on evapotranspiration is greater in the Sahelian and Sudanian areas. Solar radiation is the third variable that has the most influence on ET 0 with coefficients varying from 0.60 to 0.97 under the two scenarios. Its maximum values are noted in the Guinean zone. Wind speed and minimum temperature have less influence on ET 0 with coefficients below 0.35. Wind speed has more influence on ET 0 in the Sahelian and Sudanian areas. The results obtained confirm those of Ndiaye et al. (2020b) who noted that evapotranspiration is more sensitive to relative humidity, maximum temperature and solar radiation in the Senegal River basin over the period 1984-2017. On a seasonal scale, relative humidity, maximum temperature and solar radiation are always the variables that have the most influence on evapotranspiration. The influence of relative humidity on ET 0 is more significant during the rainy season and in the Guinean zone with coefficients varying from -0.86 to -3.49 under RCP4.5 and from -8.07 to -15.36 under RCP8. 5. ET 0 is more sensitive to maximum temperature during the dry season and in the Sudanese and Sahelian areas. Solar radiation has more influence on ET 0 in the Guinean area and during the rainy season.

The sensitivity analysis shows that future evapotranspiration will be more influenced by relative humidity, maximum temperature and solar radiation. Therefore, it would be important to pay more attention to the measurement and/or estimation of these climatic variables in order to ensure a good estimate of evapotranspiration. It is also important to note that the climate variable influence on ET 0 depend on climate zones. The influence of relative humidity and solar radiation is more significant in Guinean zone than in Sahelian and Sudanian ones. However, in Sudanian and Sahelian zones, the ET 0 is most sensible to maximum temperature, minimum temperature and wind.

Is the climate stationary in 2036-2065?

Future trends in evapotranspiration

The spatial distribution of Mann Kendall's Z of annual and seasonal evapotranspiration on the period 2036-2065 is given in Fig. 10. The average of all regional models shows a significant increase (p < 0.05) in annual and seasonal ET 0 over the entire basin according to the RCP4.5 and RCP8.5 scenarios. The HadGEM2-ES.RCA4, IPSL-CM5A-MR.RCA4, CSIRO-Mk3-6-0.RCA4 and CANESM2.RCA4 models show a significant increase in annual evapotranspiration. For all the models, only GFDL-ESM2M.RCA4 shows a non-significant trend in annual and seasonal ET 0 over the entire basin. Fig. 11 shows the magnitude of the ET 0 trends depending on the models. In the Guinean zone, the annual ET 0 increases by 1.78 mm/year according to the RCP4.5 scenario and by 3.06 mm/year according to RCP8.5 Table 3 : Summary of the sensitivity coefficients of ET 0 to climate variables at the annual scale (CA : CANESM2.RCA4, CN : CNRM-CM5.RCA4, SIR : CSIRO-Mk3-6-0.RCA4, GD : GFDL-ESM2M.RCA4, IP : IPSL-CM5A-MR.RCA4, MI : MIROC5.RCA4, MO : HadGEM2-ES.RCA4, ENS : ENSEMBLE). by 2065. According to the two scenarios, the annual average ET 0 increases respectively by 2.55 mm/year to 3.78 mm/year in the Sudanian zone and from 2.83 mm/year to 4.4 mm/year in the Sahelian zone.

The trend analysis shows that overall evapotranspiration will increase significantly (p < 0.05) by 2065 in the Senegal River Basin. Similar results are obtained by some studies across the world. Indeed, the work of [START_REF] Dong | The response of reference evapotranspiration to climate change in Xinjiang, China: historical changes, driving forces, and future projections[END_REF] pointed out a continuous increase in evapotranspiration throughout the 21 st century in China's semi-arid climate. Ndiaye et al. (2020b) showed a significant increase in the annual ET 0 in 32 % of the Senegal river basin during the period 1984-2017. However, Ndiaye et al. (2020b) also showed a significant drop in ET 0 in Sahelian area of the basin despite the increase in temperature. Here, projections do not reveal a drop in ET 0 and results indicate that this evaporation paradox will disappear from the basin by 2050. The increase in ET 0 could have impacts on the hydrological cycle and on agriculture. Indeed, from a hydrological point of view, the continuous increase in ET 0 can affect the rainfall effective and exacerbate the arid conditions of a given environment [START_REF] Goyal | Sensitivity of evapotranspiration to global warming:a case study of arid zone of Rajasthan (India)[END_REF]. In agriculture sector, increasing ET 0 tends to increase aridity, decrease soil moisture and effective rainfall [START_REF] Aubé | Impacts Du Changement Climatique Dans Le Domaine De l'eau Sur Les Bassins Rhône-méditerranée Et Corse -Bilan Actualisé Des Connaissances[END_REF]. This increase in ET 0 could also lead to an increase in crop water demand and an increase in irrigation costs [START_REF] Rahman | Analysis of reference evapotranspiration (ET0) trends under climate change in Bangladesh using observed and CMIP5 data sets[END_REF].

Future trends in climate variables

Fig. 12 shows the future spatial distribution of Mann Kendall's Z of climate variables at the annual scale. All models agree on a significant increase in minimum and maximum temperatures with the exception of the RCP4.5 scenario of the NOAA-GFDL-ESM2M. RCA4 and MIROC5.RCA4 models which shows a non-significant trend in these two climate variables. A non-significant decrease (p > 0.05) in relative humidity was also noted over the entire basin.

Of all the models, only CANESM2.RCA4, HadGEM2-ES.RCA4, MIROC5.RCA4 and multi-model exhibit a significant decrease in wind speed and solar radiation. HadGEM2-ES.RCA4 showed a decrease in wind speed in 8% of the basin area for the RCP4.5 scenario and in 12 % of this for RCP8.5. This decrease in wind speed mentioned in Ndiaye et al. (2020b) is confirmed in future projections. In addition to the decrease in wind speed, some models show a significant decrease in solar radiation. Indeed, the ENSEMBLE shows a significant decrease in solar radiation for 46 % of the basin area according to the two scenarios. A significant decrease in radiation is also highlighted by IPSL-CM5A-MR.RCA4 in 11 % and 99 % of the basin according to the RCP4.5 and RCP8.5 scenarios, respectively. According to the RCP8.5 scenario, MIROC5.RCA4 and CANESM2.RCA4 respectively show a significant decrease in radiation in 21 % and 83 % of the basin area.

Table 4 gives a summary of Sen 'slope values of climate variables over the period 2036-2065 according to climatic zones. Considering the average of all the models, the minimum temperature varies from 0.02 • C/ year to 0.04 • C/year according to the RCP4.5 and RCP8.5 scenarios. The maximum temperature increases from 0.05 • C/year to 0.06 • C/year for RCP4.5 and from 0.01 • C/ year to 0.02 • C/year for RCP8.5. For maximum temperature, the low values obtained by ENSEMBLE RCP8.5 can be explained by the low values of CSIRO-Mk3-6-0.RCA4, HadGEM2-ES.RCA4 and MIROC5.RCA4. This indicates that the multi-model ensemble is not always preferable as it here leads to a lower, incongruous increase in temperature with RCP8.5 than with RCP4.5. Moreover, for the RCP4.5, the models show that the maximum temperature will increase from 1.3 to 2.5 • C in Guinean zone, 1.3-2.7 • C in Sudanian zone and from 1.3 to 2.8 • C in Sahelian one. For the RCP8.5 the high values of maximum temperature vary between 3.1 and 3.3 • C depending on climate zones. The minimum temperature will respectively increase by 2.9, 3.2 and 3.3 • C in Guinean, Sudanian and Sahelian zones under RCP4.5. According to RCP8.5, the minimum temperature will vary between 3.2-3.9 • C according to the climate models. The maximum values are noted in Sahelian and Sudanian zones. It is also important to note that the minimum temperatures increase faster than the maximum ones. The same results are obtained by [START_REF] Ly | Evolution of some observed climate extremes in the West African Sahel[END_REF] in West Africa and [START_REF] Samba | Minimum and maximum temperature trends in Congo-Brazzaville: 1932-2010[END_REF] in Congo Brazzaville who noted that the increase of minimum temperature is more important than the maximum. This situation may be explained by the concentration of aerosol which reduce the solar radiation reaching the earth surface [START_REF] Ringard | Évolution des pics de températures en Afrique de l'ouest : étude comparative entre Abidjan et Niamey », 27. 27e[END_REF]. This increase in temperature can also affect crops. For example, [START_REF] Diop | Les Bilans Hydriques Dans La Moyenne Vallée Du Fleuve Sénégal-contribution à l'étude Des Besoins En Eau[END_REF] mentioned that ecological monitoring carried out in Nianga (Podor, Senegal River Basin) showed that certain varieties of rice have abortion rates of 33-57% when the temperature exceeds 35 • C. Relative humidity varies from 0.17 to 7%/year in the Guinean zone, from -0.6-7% in the Sudanese one and from -0.9 to 6%/year in the Sahelian zone according to the two scenarios. Wind speed and solar radiation vary respectively from -0.025 to 4.11 m/year and from -1.6 to 1.7 MJ.m -2-D -1 /year depending on both scenarios and depending on climatic zones. On a seasonal scale, all models predict a significant increase in temperatures during the dry and rainy season. The models also predict an insignificant decrease in wind speed and relative humidity during both seasons. The downward trend in solar radiation is generally insignificant on a seasonal scale.

Trend analysis show a significant increase in temperatures in the Senegal River basin. This rise in temperatures would be considered the main reason for the significant increase in evapotranspiration in the period 2036-2065. This information associated with the trend of ET 0 and climate variable allow to note that horizon 2036-2065 will not be stationary and the climate will continue to change if the temperature increase at the current rate. Indeed, significant positive trend is both ET 0 and temperatures, is showed by RCMs. This confirms the studies by [START_REF] Abiye | Potential Evapotranspiration Trends in West Africa From 1906 to 2015[END_REF] and Ndiaye et al. (2020b) according to which the temperature (maximum and minimum) is the main factor of variation of evapotranspiration during the periods 1906-2015 and 1984-2017 in West Africa and in the Senegal river basin. Of all the variables, only wind speed and solar radiation show a significant decrease depending on the models. The decrease in wind speed (Wind Stilling) and solar radiation (Global Dimming) explains the decrease in evapotranspiration mentioned by some authors [START_REF] Mcvicar | Global review and synthesis of trends in observed terrestrial near-surface wind speeds: implications for evaporation[END_REF][START_REF] Chu | Changes in reference evapotranspiration and its contributing factors in Jiangsu, a major economic and agricultural province of Eastern China[END_REF][START_REF] Han | Effects of different land use types on potential evapotranspiration in the Beijing-Tianjin Hebei region, North China[END_REF][START_REF] Bian | Spatial distribution of potential evapotranspiration trends in the Inner Mongolia autonomous Region (1971-2016[END_REF]Ndiaye et al., 2020b). This decrease in solar radiation is linked to the concentration of aerosols in the atmosphere due to human activities [START_REF] Han | Effects of different land use types on potential evapotranspiration in the Beijing-Tianjin Hebei region, North China[END_REF].

Conclusion

The results of this study show that the ET 0 values obtained by the RCMs are closer to those of the reanalyses than the GCMs, though they tend to overestimate ET 0 . Trend analysis shows almost all models agree on a significant increase in reference evapotranspiration in the period 2036-2065 under the RCP4.5 and RCP8.5 scenarios. The ENSEMBLE provides an increase in ET 0 of 39 mm for RCP4.5 and 144 mm for RCP8.5 in the Guinean zone. In the Sudanese and Sahelian zones, ET 0 will increase respectively from 48 mm to 266 mm and from 57 mm to 277 mm according to the two scenarios. Trends in climate variables show a significant increase in maximum and minimum temperatures. This rise in temperatures is shown to be the primary explanation for the increase in ET 0 though some models also highlight a significant decrease in wind speed and solar radiation. Sensitivity analysis reveals that ET 0 is more sensitive to relative humidity, maximum temperature and solar radiation. The increase in the future will increase crop water requirements, accentuate water losses in reservoirs, reduce hydroelectric deliverability and increase competition between different users. It is important to note that this increase of ET 0 will not be stationary in 2065 and may continue to increase if the temperatures rise at the same rate. Furthermore, this work underlines the discrepancies between results based on GCMs and RCMs as well as those between individual RCMs when estimating evapotranspiration. These differences highlight the importance of improving the performance of climate circulation models (both GCMs and RCMs) to allow for a more accurate and reliable estimate of climate variables needed to analyze long-term ET 0 variations/projections. It would also be important to have complete in-situ meteorological observations to fill in the gaps and improve climate simulations.

Fig. 2 .

 2 Fig. 2. Temporal consistency of observed climatic variables and those of reanalyses.

Fig. 3 .Fig. 4 .Fig. 5 .

 345 Fig. 3. Difference between annual average of ET 0 calculated by reanalyses and GCMs & RCMs models over the period 1984-2000.

Fig. 6 .

 6 Fig. 6. KGE and PBIAS between climate models and reanalyses at monthly scale (CAN : CANESM2, CNR : CNRM, CSI : CSIRO-MK3-6-0, GDF : GDFL-ESM2G, HAD : HADGEM2-ES, IPS : IPSL-CM5A-MR, MIR : MIROC5, CA : CANESM2.RCA4, CN : CNRM-CM5.RCA4, SIR : CSIRO-Mk3-6-0.RCA4, GD : GFDL-ESM2M.RCA4, IP : IPSL-CM5A-MR.RCA4, MI : MIROC5.RCA4, MO : HadGEM2-ES.RCA4, ENS : ENSEMBLE).

Fig. 7 .

 7 Fig. 7. Annual average of evapotranspiration (mm) on historical and projection periods.

Fig. 8 .

 8 Fig. 8. Spatial distribution of change of the ET 0 of the RCMs calculated between the historical period 1971-2000 and that of the 2036-2065 projections.

Fig. 9 .

 9 Fig.9. Spatial distribution of the sensitivity coefficients of ET 0 to climate variables of regional models at the annual scale over the period 2036-2065.

Fig. 10 .

 10 Fig. 10. Spatial distribution of Mann Kendall's Z of regional models over the period 2036-2065.

Fig. 11 .

 11 Fig. 11. Sen's slope of regional models at annual and seasonal scale over the period 2036-2065 (A: Guinean zone, B: Sudanian zone, C: Sahelian zone).

Fig. 12 .

 12 Fig. 12. Spatial distribution of Mann Kendall's Z of the climate variables of regional models at annual scale over the period 2036 -2065.

Table 1

 1 Characteristics of GCMs and RCMs used.

	Institute

• Centre National de Recherche Météorologique-Groupe d'étude de l'Atmosphère Météorologique and Centre Européen de Recherche et de Formation Avancée • National Institute for Environmental Studies, and Japan Agency for Marine-Earth Science and Technology MIROC5 1.40 • × 1.40 • MIROC5.RCA4 0.44 • × 0.44 • Institut Pierre-Simon Laplace IPSL-CM5A-MR 1.25 • x2.5 • IPSL-CM5A-MR. RCA4 0.44 • × 0.44 • Commonwealth Scientific and Industrial Research Organization CSIRO-MK3-6-0 1.87 • × 1.87 • CSIRO-Mk3-6-0.RCA4 0.44 • × 0.44 • P.M. Ndiaye et al.

Table 2

 2 KGE values for the four selected weather stations.

	Weather stations	Climate zones	Climate variables	Periods	r	α	β	KGE
			Tmax	2002-2003	0.66	0.99	0.99	0.66
	Bamako Senou	Sudanian	Tmin Rh	2002-2003 2002-2003	0.58 0.84	0.8 1.04	1.06 0.84	0.53 0.77
			u2	2002-2003	0.24	1.19	1.23	0.19
			Tmax	1984-1996	0.6	1.06	0.98	0.59
	Kayes	Sudanian	Tmin	1984-1996	0.71	0.78	1.01	0.63
			Rh	1984-1996	0.83	1.19	0.81	0.68
			Tmax	1984-1987	0.8	1.11	0.99	0.77
	Kita	Sahelian	Tmin	1984-1987	0.75	0.85	1	0.71
			Rh	1984-1987	0.88	1.19	0.85	0.73
			Tmax	2002-2003	0.76	1.04	1	0.75
	Nioro du Sahel	Sahelian	Tmin	2002-2003	0.8	0.79	0.95	0.71
			Rh	2002-2003	0.76	0.88	0.67	0.57
	Labé	Guinean	Tmax Tmin	1986-1996 1986-1996	0.69 0.26	1.33 0.67	1.07 1.41	0.54 0.09
	Mamou	Guinean	Tmax Tmin	1984-1998 1984-1998	0.75 0.30	1.26 0.79	1.01 1.19	0.64 0.25

Read: Tmax maximum temperature, Tmin minimum temperature, Rh Relative humidity, u2 wind speed.

Table 4

 4 Summary of Sen's slope values (β per year) of climate variables at the annual scale (CA : CANESM2.RCA4, CN : CNRM-CM5.RCA4, SIR : CSIRO-Mk3-6-0.RCA4, GD : GFDL-ESM2M.RCA4, IP : IPSL-CM5A-MR.RCA4, MI : MIROC5.RCA4, MO : HadGEM2-ES.RCA4, ENS : ENSEMBLE).

	Climate zones	Modèles	β(Minimum temperature)	β (Maximum temperature)	β (Wind speed)	β(Relative humidity)	β(Solar radiation)
			RCP4.5	RCP8.5	RCP4.5	RCP8.5	RCP4.5	RCP8.5	RCP4.5	RCP8.5	RCP4.5	RCP8.5
		CA	0.029	0.088	0.030	0.074	¡0.001	¡0.001	¡0.008	¡0.014	¡0.004	¡0.007
		CN	0.006	0.029	0.039	0.058	0.001	1.026	4.261	3.397	1.259	0.568
		CS	0.010	0.043	0.072	¡0.042	0.002	1.251	3.971	5.117	¡0.730	0.779
	Sudanian	GD	0.015	0.037	0.008	0.033	¡0.002	¡0.001	0.030	0.049	¡0.008	¡0.001
		MO	0.013	0.042	0.072	¡0.061	0.002	1.850	5.150	5.080	¡1.093	0.734
		IP	0.040	0.077	0.037	0.066	0.001	¡0.001	¡0.050	0.022	¡0.004	¡0.010
		MI	¡0.005	0.015	0.056	¡0.052	0.003	¡0.743	1.199	3.531	¡1.040	0.754
		ENS	0.004	0.031	0.060	0.001	¡0.025	3.911	¡0.553	6.864	0.625	¡0.731
		CA	0.030	0.084	0.027	0.070	¡0.001	0.000	¡0.019	0.002	¡0.002	0.001
		CN	¡0.001	0.026	0.035	0.101	¡0.001	¡0.029	4.057	3.829	1.542	¡0.478
		CS	0.018	0.035	0.074	¡0.001	0.003	1.342	4.610	5.370	0.068	1.735
	Guinean	GD MO	0.015 0.025	0.042 0.032	0.014 0.062	0.035 ¡0.015	¡0.003 0.006	0.001 1.891	0.047 5.789	0.008 5.142	0.000 ¡0.285	0.003 ¡0.750
		IP	0.034	0.074	0.034	0.065	0.001	0.001	¡0.009	0.005	0.002	¡0.011
		MI	0.004	0.012	0.063	¡0.071	0.001	0.332	1.131	3.854	¡1.656	0.532
		ENS	0.002	0.025	0.058	0.000	¡0.001	4.118	¡0.178	6.994	0.634	0.612
		CA	0.027	0.078	0.029	0.063	0.001	0.000	1.844	5.127	¡0.003	¡0.007
		CN	0.003	0.029	0.040	0.004	0.001	0.877	3.866	3.259	0.108	0.466
		CS	0.001	0.049	0.063	0.022	0.003	0.197	3.911	4.648	0.294	0.810
	Sahelian	GD MO	0.012 0.004	0.043 0.034	0.008 0.066	0.039 ¡0.019	¡0.001 0.000	¡0.002 0.675	0.050 3.257	0.036 4.891	¡0.008 ¡0.484	¡0.003 1.989
		IP	0.035	0.076	0.031	0.068	0.001	0.001	¡0.019	0.012	¡0.004	¡0.009
		MI	¡0.004	0.017	0.051	¡0.035	0.002	¡0.655	1.166	3.452	¡0.710	0.659
		ENS	0.005	0.030	0.056	0.002	¡0.025	3.627	¡0.862	6.420	1.759	¡1.603

Journal of Hydrology: Regional Studies 35 (2021) 100820

Acknowledgments

Reanalysis weather data used in this study were obtained from the NASA Langley Research Center (LaRC) POWER Project funded through the NASA Earth Science. The authors also wish to thank the two anonymous reviewers and the special academic editor for their suggestions, which helped improve the manuscript.

Funding

This research was partially funded by the AICS/UE N. 03/2020/WEFE-SENEGAL project. P.M. Ndiaye et al.

Declaration of Competing Interest

The authors declare that there is no conflict of interests regarding publishing this article.

Appendix A. Supplementary data

Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.ejrh.2021. 100820.


Karim Dogheche

Bandar Alshehri

Namarig Taha Abdulrahmane

Abderrahim Ramdane

Hadj El

Dogheche

El Hadj Dogheche

Fabrication of µLEDS for light fidelity optical transmission

Keywords: Gallium nitride, photonics, LED, light fidelity

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Gallium Nitride based SC have attracted a lot of interest for new generation of optoelectronic devices [START_REF] Nakamura | Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes[END_REF]. The advantage with these materials is the flexible bandgap varying from 0.7 to 6 eV hence covering a large spectrum, from deep ultraviolet up to near infrared [START_REF] Castiglia | InGaN laser diodes emitting at 500nm with p-layers grown by molecular beam epitaxy[END_REF], allowing the development of microelectronics and high spped photonics [START_REF] Wu | Superior radiation resistance of In 1-xGa xN alloys: Fullsolar-spectrum photovoltaic material system[END_REF][START_REF] Mishra | GaN-based RF power devices and amplifiers[END_REF][START_REF] Walker | AlxGa1-xN (0≤x≤1) ultraviolet photodetectors grown on sapphire by metal-organic chemical-vapor deposition[END_REF][START_REF] Zhang | 1.5 Gbit/s Multi-Channel Visible Light Communications Using CMOS-Controlled GaN-Based LEDs[END_REF][START_REF] Skierbiszewski | Growth and characterization of AlInN/GaInN quantum wells for highspeed intersubband devices at telecom wavelengths[END_REF]. The recent years have announced the emergence of novel photonic technologies based on III-nitrides semiconductors. Gathering the progress in materials maturity and the advance in manufacturing process, SolidState Lighting based upon GaN-based light-emitting diodes (LEDs) has emerged as one the dominant technology for indoor/outdoor lighting as in hospital and transportation. In addition, the opportunity to apply LED for indoor/outdoor communication is a research innovation for the community. This well-known concept is identified light fidelity (LiFi), as a wireless technology that uses optical light to transmit informations more fast and reliable data transmission than conventional Wi-Fi. Higher Frequency results from smaller dimensions for the devices.

EXPERIMENTS

The proposed PIN structure consists of a thick not-intentionally-doped (n.i.d) GaN buffer layer (called also undoped GaN) on c-plane (0001) sapphire. In order to ensure a high crystalline quality for GaN and to move away from the GaN/sapphire interface, the thickness of this layer is chosen to be 2.5µm. This is followed by a 3.5µm thick Si-doped n-type GaN layer with a carrier concentration of 3×10 18 cm -3 . The thickness of the "i" intrinsic-absorption-layer, is ~ 145 nm in order to efficiently absorb the incidentlight. The MQW structure is gown with 10 pairs of InGaN/GaN with thicknesses of 2.5nm for InGaN and 12nm for GaN within the InGaN/GaN well. 100nm Mg-doped p-type GaN layer is grown as the top layer with a carrier concentration of 5×10 17 cm -3 .

Fabrication process of photodiode consists of four steps starting by p-type top contact deposition, etching process to reach n-GaN layer, n-type contact deposition and finally thermal annealing of n and p contacts. Metals have been optimized to be Pd/Au with respective thicknesses of 35nm/120nm for p-type top contact demonstrating the high work function of Pd metal associated with its high reactivity with low contact resistance. Ti/Al/Au metals with respective thicknesses of 10nm/30nm/300nm for n-type bottom contact have been used. Global experiments have been conducted by reducing the LED dimension (from 300 to 5µm) to lower the capacitance, the internal electric field of InGaN MQWs and therefore to increase the LED's emission efficiency. Proper etching and metallization optimization processes have been developed to create large or small mesa that allows a controlled parasite capacitance for the global configuration [START_REF] Dogheche | Development of micron sized photonic devices based on deep GaN etching[END_REF][START_REF] Alshehri | Synthesis of In0.1Ga0.9N/GaN structures grown[END_REF]. For RF experimens, coplanar transmission lines have been designed and fabricated on top of the samples.

CHARACTERIZATION OF PHOTONIC DEVICES

The measurement of photocurrent relies on two important factors, the wavelength of incident light and the output power. For this reason, a laser source has been used for powerful input light. Besides, fiber-coupled laser source is the optimal choice due to the ease to focus a laser beam using stripped and cleaved optical fiber. The wavelength of fiber-coupled laser source is 405nm and its output power reaches100mWatts. In order to estimate the cut-off frequency, we have first theoretically calculated it from the average value of capacitance C. For RF analysis, coplanar transmission lines have been designed and fabricated on top of LEDs samples. Previously, we have investigated the capacitance values using a C-V setup, for photodiode areas ranging from 100×100 µm 2 to 1000×1000 µm 2 . The extraction of capacitance permits us to estimate the cut-off frequency and compare these results to the theoretical values. This approach gives some indications in order to optimize the design of the photodiodes and more generally to reduce the capacitive effects. Actually, any methods exist that allows the direct measurement of the photodiode cut-off frequency in UV-Vis region. For the frequency experiments, due to the lack of modulated laser source (in the wavelength range 400 to 633nm), we have performed noise figure techniques already used for III-V semiconductors technologies samples but in the IR range. This experiment is related to the noise figure measurement.

RESULTS AND DISCUSSION

Samples with different dimensions have been investigated by photocurrent measurement in order to evaluate the photodiode response. The investigation of size-dependent capacitance has been performed for large-scale photodiodes (from 100×100 to 1000×1000 µm 2 ) using a C-V setup. The capacitance is proportional to the photodiode size and particularly to the diameter of the mesa produced by dry etching. Dynamic measurements are performed under reverse bias both in the dark and under illumination by laser source. This method is considered as one of the most convenient technique to extract the cut-off frequency for photodiodes. It consists in the noise measurement as function of the frequency. The evolution of noise response clearly indicates a limitation in the photodiode behavior when the frequency increases, allowing the estimate of the 3dB cut-off frequency, a very convenient way to assess the dynamic response of fabricated photodiodes. Lower cut-off frequency of 9MHz is observed for 1000×1000 µm 2 demonstrating the influence of the capacitance on the dynamic response.

Fig. 2 shows the evolution of the noise intensity as function of frequency: we have selected a photodiode with diameter of 100µm and using coplanar lines for the probe connection. The photodiode has been biased under reverse voltage in dark and under illumination of laser source in order to measure the shot noise. The curve shows a drop of shot noise related to the photodiode current when frequency is increased. The difference in noise intensity between dark (Ndark) and under illumination (Nphotocurrent) is observed very small when bias voltage of -4 V is applied for small photodiode dimensions. Difference (Nphotocurrent -Ndark) in average value is roughly about 0.8 dB. From fig. 2, the -3dB cut-off frequency is estimated to be 300MHz for a photodiode diameter of 100µm.

CONCLUSION

In this research activity, the design, the material characterization and the device fabrication have been performed for InGaN/GaN based photodiodes. The InGaN absorbent layer has been defined with 10% of indium content. The objective of this work has been directed towards fabrication of high speed photodiodes. The first step of this work is to optimize the photodiode design and fabrication in order to reduce the capacitive effects. Firstly, large-scale photodiodes have been employed to extract the photocurrent and the cut-off frequency. The increase of photocurrents is observed once the laser power is increased and attains 1.2 mA with EQE value of 13 %. Theoretical calculation of the photodiode frequency has been performed in order to compare it with the experimented values issued from C-V setup and Noise measurement.

Results demonstrate a cut-off frequency at -3dB of 300 MHz using Noise measurement for 100×100 µm 2 photodiode. This study offers the possibility to work toward the InGaN-based µPhotodiode such as a perspective work towards LiFi configuration.

Fig1:

  Fig1: Configuration of PIN structure using RF coplanar transmission lines (a) for dark measurement (b) under illumination

Fig 2 :

 2 Fig 2: Noise measurement for 100×100 µm 2 photodiode


David González-Andrade

Diego Pérez-Galacho

Miguel Montesinos-Ballester

Xavier Le Roux

Eric Cassan

Delphine Marris-Morini

Pavel Cheben

Nathalie Vulliet

Stephane Monfray

Frédéric Boeuf

Miguel Montesinos- Ballester

Laurent Vivien

Aitor V Velasco

Carlos Alonso-Ramos

Dual-band fiber-chip grating

come

The silicon-on-insulator (SOI) platform leverages microelectronics fabrication processes to achieve cost-effective mass-scale production of high-performance photonic circuits [1]. However, the tight modal confinement in SOI waveguides results in a large mode size mismatch with standard single-mode optical fibers that seriously hampers the efficiency of fiber-chip light coupling [2,3]. Surface grating couplers have been widely used for this purpose.

These couplers rely on diffractive structures that can be positioned anywhere on the chip surface, allowing wafer-scale testing, and circumventing the need for optical facet preparation. Compared to edge couplers, surface grating couplers also provide an easier alignment process along with more relaxed tolerances to fabrication deviations [4]. Nevertheless, the operation of conventional grating couplers relies on radiation of a single beam at a given angle to couple the light between the chip and the optical fiber, which generally limits operation to wavelength ranges on the order of a few tens of nanometers. This restriction inherently arises from the phase-matching condition relating radiation angle, wavelength and refractive index [5,6]. While broadband grating couplers can yield a bandwidth of ~100 -150 nm [7,8], this is still insufficient for emerging applications like next-generation passive optical networks (PON) [9]. By way of illustration, 10 Gbit symmetric PONs (XGS-PON) utilize upstream and downstream channels that are 307 nm apart (𝜆 1 = 1270 nm and 𝜆 2 = 1577 nm) [10]. Although these access network applications have been successfully deployed using bulk optics components, silicon photonics has been identified as an enabling technology to further improve the performance in terms of bandwidth, power consumption and cost [11][12][13]. Efficient fiber-chip couplers operating at distinct wavelength bands are therefore key components to combine or split different optical bands.

Dual-band grating couplers working as wavelength multiplexer or demultiplexer (mux/demux) in the SOI platform were initially proposed by Roelkens et al. [14,15] and have since attracted growing attention for coupling and splitting optical signals at [15] 1300.0 -6.0 1520.0 -4.0 TE [16] 1485.0 -6.5 1530.0 -6.0 TE [21] 1310.0 -8.2 1550.0 -7.1 TE&TM [22] 1486.0 -7.4 1594.5 -7.0 TE [22] 1481.5 -8.4 1661.5 -7.6 TE [23] 1289.0 -7.3 1551.0 -8.2 TE [25] 1560.0 -7.0 2255.0 -5.9 TE [25] 1487.0 -6.9 2331.0 -5.7 TE This work 1270.0 -4.9 1577.0 -5.2 TE a The worst CE was considered in polarization-independent devices. different wavelength bands. Leveraging this concept, and using an index matching fluid to mitigate reflections, a 1D dual-band coupler was demonstrated in [15] with coupling efficiencies better than -7 dB and -8 dB at 1310 nm and 1550 nm wavelengths, respectively. A dual-wavelength 2D grating coupler with coupling efficiencies of -6.5 dB and -6 dB at the wavelengths of 1490 nm and 1530 nm, respectively, was also demonstrated [16]. Wavelength demultiplexing couplers operating at normal incidence have been reported using different design strategies, including inverse design [17], gradient-based optimization algorithm [18] and finitedifference time-domain (FDTD) methods [19]. The latter employs a gold mirror formed underneath the structure to increase the coupling efficiency, but this requires additional (not CMOS compatible) steps during fabrication process. A novel subwavelength engineered dual-band grating coupler was recently proposed [20], exhibiting a calculated polarization-independent behavior with coupling efficiencies near -4.5 dB. Finally, couplers have also been developed that operate at different wavelength bands but without multiplexing/demultiplexing the optical signals [21][22][23][24][25]. Table 1 summarizes the performance of state-of-the-art dual-band grating couplers that have been experimentally demonstrated. Most of these devices have been fabricated using electron beam lithography and not yet demonstrated with 193-nm deep-ultraviolet (deep-UV) photolithography. Furthermore, some of them imply increased complexity (e.g. using index matching fluid [15] or requiring small feature sizes around 60 nm [22] and 80 nm [25]), and no grating coupler has yet been reported operating according to the ITU-PON wavelength roadmap [10]. Therefore, our results open promising prospects for the implementation of efficient and low-cost fiber-chip coupling interfaces for access network applications.

In this Letter, we propose and experimentally demonstrate an efficient dual-band grating coupler, which operates as a wavelength mux/demux in the O and C+L telecom bands in compliance with the XGS-PON wavelengths. The 1D grating section of our device is engineered to achieve opposite radiation angles, and thus combine or separate two optical signals at 𝜆 1 = 1270 nm and 𝜆 2 = 1577 nm wavelengths. Additionally, the material platform was optimized as a tradeoff between the waveguide propagation loss and the substrate reflectivity for higher coupler efficiency. The fabrication of our device, with a minimum feature size of 225 nm, was performed using 193-nm deep-UV process on 300-mm SOI platform [26], compatible with large-volume production.

A 3D schematic representation of the coupler is shown in Fig. 1(a). We use an SOI platform with thicknesses of 𝑇 𝑆𝑖 = 310 nm for the Si waveguides and 𝑇 𝐵𝑂𝑋 = 720 nm for the buried oxide (BOX) The principle of operation of the coupler relies on the intrinsic change of the radiation angle with the wavelength, according to the grating equation [27]:

𝑛 𝐹𝐵 + 𝑝𝜆 Λ ⁄ = 𝑛 𝑐 sin 𝜃. (1)
Here 𝑛 𝐹𝐵 is the effective index of the fundamental Floquet-Bloch mode supported by the periodic structure, 𝑝 is the diffraction order, 𝜆 is the operating wavelength, Λ is the grating period, 𝑛 𝑐 is the refractive index of the upper cladding (here, 𝑛 𝑐 = 1), and 𝜃 is the radiation angle. In demux configuration, the light of two different wavelengths 𝜆 1 = 1270 nm and 𝜆 2 = 1577 nm is coupled from the SMF-28 fiber to the chip and separated into two different waveguides, which is achieved by designing the grating to operate with opposite radiation angles for the two wavelengths. The input fields at 𝜆 1 = 1270 nm and 𝜆 2 = 1577 nm fulfill Eq. ( 1) with a positive radiation angle 𝜃 and a negative radiation angle -𝜃, respectively. Conversely, when the coupler operates as a multiplexer, the two modes propagating in the opposite waveguides are combined and simultaneously coupled into the optical fiber. Figure 1(b) shows a side view schematic of the grating coupler. Since the width of the grating coupler (𝑊 𝐺𝐶 ) is much larger than the operating wavelength, the structure can be considered as invariant in the 𝑥 direction [27]. The device is designed for transverse-electric (TE) polarization. The dual-wavelength band operation of the 1D grating can be achieved by judiciously selecting the values of Λ and DC so that the radiation angle at 𝜆 1 = 1270 nm is the opposite of that at 𝜆 2 = 1577 nm, i.e. 𝜃(𝜆 1 = 1270) = -𝜃(𝜆 2 = 1577).

In the first step of our design, we examined both the radiation angle and the power radiated upward as a function of the grating pitch and the duty cycle via 2D FDTD simulations (see Fig. 2). Figure 2(a) shows the absolute value of the radiation angle as a function of grating period for different duty cycles. We choose a period of Λ = 500 nm and DC = 55%, yielding the same absolute value for radiation angle for both wavelengths. In this case, the minimum feature size of the shallow-etch trench is 225 nm, thereby ensuring compatibility with 193-nm deep-UV optical lithography considered for fabrication. The width and the length of the grating were set to 𝑊 𝐺𝐶 = 17 µm and 𝐿 𝐺𝐶 ≈ 10 µm, to maximize the overlap between the fundamental mode of the SMF-28 fiber (near-Gaussian distribution) and the radiated fields (exponential distribution). The width mismatch between the interconnection waveguides (𝑊 𝐼 ) and the grating coupler (𝑊 𝐺𝐶 ) requires a spot-size converter. For this purpose, we selected linear adiabatic tapers with a length of 𝐿 𝑇 = 500 µm to minimize the transition loss. Figure 3 shows the calculated coupling efficiency of the coupler. The efficiency for the design wavelengths of 𝜆 1 = 1270 nm and 𝜆 2 = 1577 nm is as high as -4.28 dB and -2.71 dB, respectively. The simulated crosstalk is below -31 dB at 𝜆 1 = 1270 nm and -28 dB at 𝜆 2 = 1577 nm. In addition, the coupling efficiency spectra show a 3-dB bandwidth of 42 nm for the O-band channel, whereas the 3-dB bandwidth for the C+L channel is 75 nm. Moreover, we calculate tolerances to variations in etching depth (𝑇 𝐸 ), and thickness of Si (𝑇 𝑆𝑖 ) and BOX (𝑇 𝐵𝑂𝑋 ). The coupling efficiency penalty is 0.74 dB for 𝑇 𝐸 ± 10 nm, 0.53 dB for 𝑇 𝑆𝑖 ± 10 nm, and 1.34 dB for 𝑇 𝐵𝑂𝑋 ± 200 nm. Finally, simulations also show that a one-step antireflection stage [28] with length of 150 nm, silicon width of 200 nm and gap width of 200 nm is enough to reduce back-reflections of the proposed coupler below 3% for both 1270 nm and 1577 nm wavelengths.

The coupler was fabricated using STMicroelectronics' silicon photonics R&D and manufacturing platform based on 300-mm SOI wafers [26]. The 310-nm-thick Si layer was patterned using 193-nm deep-UV optical lithography based on a CMOS 55 nm process. A two-step etch process was used to define shallow-and full-etch trenches of the grating section and the strip waveguides. No material was deposited as upper cladding, exposing devices to air. Two different flavours with DC = 55% and DC = 50% were included in the mask. The best performance was found for the nominal design. Scanning electron microscope (SEM) images the fabricated nominal device are shown in Figs. 4(a) and 4(b).

The experimental characterization was performed on test structures comprising a dual-band grating coupler connected to two different focusing grating couplers, each optimized for either Oband or C-band operation, as shown in Fig. 4(c). The grating trenches of the focusing couplers are described by different ellipses with common focal point between the interconnection waveguide and the grating [29]. The focusing grating coupler operating at 𝜆 1 = 1270 nm is connected to port 𝑃 1 of our device, whereas the ⁄ . Note that IL 𝑠𝑒𝑡𝑢𝑝 refers to the loss that the signal suffers when passing through the setup elements in absence of the chip (i.e. no light coupling to the chip). The devices were characterized using two tunable lasers (Yenista T100S-HP-O and T100S-HP-CL), which were connected by means of a passive component tester Yenista CT400 to sweep the 1260 -1300 nm and the 1525 -1630 nm wavelength ranges. The light was coupled to the chip and collected from the chip using cleaved SMF-28 fibers. First, measurements of the auxiliary structures were carried out to find the optimum tilt angle of the optical fiber for the focusing grating couplers and determine their coupling efficiencies. Subsequently, the test structures were measured maintaining the optimum tilt angle for the focusing grating couplers (~17° for the coupler operating at O-band and ~7° for the coupler operating at C+L-bands). An optimum angle of 𝜃 ≈ 21° was found for the fabricated dual-band grating coupler, in good agreement with our 2D FDTD simulations. The coupling efficiency of our bandwidth of 27 nm is measured at the wavelength of 𝜆 1 = 1270 nm, limited at the lower bound by the wavelength range of our laser. Conversely, for 𝜆 2 = 1577 nm, the coupling efficiency is as large as -5.2 dB with a 3-dB bandwidth of 56 nm. Peak coupling efficiencies of -4.3 dB and -4.6 dB were measured at the wavelengths of 1280 nm and 1600 nm, respectively. It should be noted that crosstalk is difficult to measure using this test structure due to the high rejection of the focusing grating couplers on the nonoptimized bands. Ripples observed in CE measurements are due to back-reflections in the test structure. Although the contribution of our device and the focusing grating couplers to this ripple cannot be accurately separated from experimental data, larger ripples are expected in the C+L band, as the corresponding focusing grating coupler operates near the Bragg condition, with a comparatively small coupling angle of ~7°. Nevertheless, our results compare favorably to state-of-the-art dual-band couplers (see Table 1).

In summary, we report on the demonstration of a dual-band grating coupler implemented with 193-nm deep-UV lithography. The device relies on the engineering of the 1D diffractive grating to achieve opposite radiation angles, and therefore spatially separate two wavelength bands. 2D FDTD simulations show that dual-band operation is achieved with a minimal trade-off between coupling efficiency, radiation angle and fabricable design parameters. The device was fabricated using industrial-scale 300 mm silicon photonics platform. The fabricated devices show some of the highest coupling efficiencies compared to state-of-the-art dualband grating couplers. Specifically, fiber-chip coupling efficiencies of -4.3 dB and -4.6 dB were achieved near the wavelengths of 1280 nm and 1600 nm. At XGS-PON wavelengths, the measured coupling efficiencies were -4.9 dB (𝜆 1 = 1270 nm) and -5.2 dB (𝜆 2 = 1577 nm) with a 3-dB bandwidth of 27 nm and 56 nm, respectively. The performance of the coupler could be further enhanced with apodization and even achieve dual-polarization operation with the introduction of transversal subwavelength gratings [3,20]. Nevertheless, these results prove the compatibility of our dual-band grating coupler with large-volume fabrication processes, paving the way towards a cost-effective deployment of efficient fiber-chip interfaces operating simultaneously in different spectral band, including applications in XGS-PON networks.

Fig. 1 .

 1 Fig. 1. (a) 3D schematic view of the dual-band fiber-chip grating coupler. The two fields that propagate through the optical fiber core at 𝜆 1 = 1270 nm (blue curve) and 𝜆 2 = 1577 nm (red curve) are coupled to port 𝑃 1 and 𝑃 2 , respectively. (b) 2D side view of the grating coupler used during the design process. layer. The complete device consists of two distinct parts: a taperbased spot-size converter of length 𝐿 𝑇 , and a 1D diffraction grating with a period Λ, duty cycle DC = 𝑎/Λ, and total length 𝐿 𝐺𝐶 . The diffractive grating comprises unetched silicon strips (𝑎) and shallow-etched trenches (Λ -𝑎) with an etch depth of 𝑇 𝐸 = 150 nm. A cleaved single mode optical fiber (SMF-28) is positioned over the coupler with a tilt angle 𝜃 with respect to the vertical axis. The principle of operation of the coupler relies on the intrinsic change of the radiation angle with the wavelength, according to the grating equation [27]:

Fig. 2 .

 2 Fig. 2. (a) Radiation angle and (b) fraction of power radiated upward as a function of the grating period for different duty cycles, calculated at 𝜆 1 = 1270 nm (blue curves) and 𝜆 2 = 1577 nm (red curves).

Fig. 3 .

 3 Fig. 3. Calculated coupling efficiency as a function of the wavelength near (a) 𝜆 1 = 1270 nm and (b) 𝜆 2 = 1577 nm.

Fig. 4 .

 4 Fig. 4. (a) and (b) SEM images of the fabricated device. (c) Schematic of the test structure employed for the experimental characterization. focusing grating coupler operating at 𝜆 1 = 1577 nm was connected to port 𝑃 2 (see Figs. 1(a) and 4(c)). Other auxiliary test structures were also included, such as two identical focusing couplers arranged in a back-to-back configuration for both O-and C+L bands. These allowed us to determine the coupling efficiency of a single focusing grating coupler (CE 𝐹𝐺𝐶 ) from the insertion loss measurements (IL 𝑎𝑢𝑥 ) and the setup insertion loss (IL 𝑠𝑒𝑡𝑢𝑝 ): CE 𝐹𝐺𝐶 = (IL 𝑎𝑢𝑥 -IL 𝑠𝑒𝑡𝑢𝑝 ) 2 ⁄ . Note that IL 𝑠𝑒𝑡𝑢𝑝 refers to the

Fig. 5 .

 5 Fig. 5. Extracted coupling efficiencies near (a) 𝜆 1 = 1270 nm and (b) 𝜆 2 = 1577 nm.

Table 1 . Experimental coupling efficiency (CE) and operating wavelengths (λ) of demonstrated dual-band grating couplers a Refs. λ1 (nm) CE1 (dB) λ2 (nm) CE2 (dB) TE/TM

 1

Funding. Spanish Ministry of Science, Innovation and Universities (MICINN) (RTI2018-097957-B-C33, TEC2015-71127-C2-1-R FPI scholarship BES-2016-077798); Community of Madrid -FEDER funds (S2018/NMT-4326); Horizon 2020 Research and Innovation Program (Marie Sklodowska-Curie 734331); H2020 European Research Council (ERC POPSTAR 647342); European Commission (H2020-ICT-26127-2017 COSMICC 688516); French Industry Ministry (Nano2022 project under IPCEI program); Agence Nationale de la Recherche (ANR-MIRSPEC-17-CE09-0041).

Disclosures. The authors declare no conflicts of interest.


Thi Thuy

Duong Dinh

David González-Andrade

Miguel Montesinos-Ballester

Lucas Deniel

Bertrand Szelag

Xavier Le Roux

Eric Cassan

Delphine Marris-Morini

Laurent Vivien

Pavel Cheben

Thuy Thi

Duong Dinh

Aitor V Velasco

Carlos Alonso-Ramos

Silicon photonic on-chip spatial heterodyne Fourier transform spectrometer exploiting the Jacquinot's advantage

come

Silicon photonics on-chip spectrometers are finding important applications in medical diagnostics, pollution monitoring and astrophysics. Spatial heterodyne Fourier-transform spectrometers (SHFTS) provide a particularly interesting architecture with a powerful passive error correction capability and high spectral resolution. Despite having an intrinsically large optical throughput (étendue, also referred as Jaquinot's advantage), state-of-the-art silicon SHFTS have not exploited this advantage yet. Here, we propose and experimentally demonstrate for the first time an SHFTS implementing a wide-area light collection system simultaneously feeding an array of 16 interferometers, with an input aperture as large as 90 µm × 60 µm formed by a twoway-fed grating coupler. We experimentally demonstrate 85 pm spectral resolution, 600 pm bandwidth and 13 dB étendue increase, compared with a device with a conventional grating coupler input. The SHFTS was fabricated using 193-nm deep-UV optical lithography and integrates the large-size input aperture with the interferometer array and monolithic Ge photodetectors, in a 4.5 mm 2 footprint. © 2021 Optical Society of America http://dx.doi.org/10.1364/ao.XX.XXXXXX Miniaturized on-chip silicon photonics spectrometers have been identified as an enabling tool for a wide range of applications, including medical diagnostics, biological and environmental monitoring, astrophysics and planetary science [0], to name a few. In integrated photonic spectrometers, light is collected and processed with a dispersive [0, 0, 0, 0, 0, 0] or a Fourier transform device [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]. Dispersive devices [0], e.g. arrayed waveguide gratings (AWGs) [0, 0] and waveguide echelle gratings [0, 0], have a single input waveguide, limit-ing the optical throughput, and therefore, compromising the signal-to-noise ratio. In addition, dispersive elements are quite sensitive to fabrication imperfections. Conversely, Fourier transform circuits enable multi-aperture inputs, where input area can be enlarged by increasing the number of apertures, benefiting from wider solid angles and thus an intrinsically large étendue, i.e., the Jacquinot's advantage [0]. A particularly promising architecture for miniaturized on-chip Fourier transform circuits is the spatial heterodyne Fourier transform spectrometer (SHFTS) [0, 0, 0, 0, 0, 0, 0]. SHFTS relies on an array of Mach-Zehnder interferometers (MZIs) with a linearly increasing optical path length imbalance, to form a spatial interferogram from which the input spectrum is retrieved [0]. SHFTS allows passive calibration techniques to correct amplitude and phase errors due to fabrication imperfections and achieve a high spectral resolution both in the near-IR (40 pm) [0] and the mid-IR ( Here, we propose and experimentally demonstrate a novel silicon on-chip SHFTS exploiting the Jacquinot's advantage, implementing on a wide-area collecting input formed by two grating couplers, side by side (see Fig.

In our SHFTS, a free-space propagating beam is collected and coupled into the chip using surface grating couplers. Due to the large difference between grating width and thickness, the design of transversal (along y axis) and longitudinal (along x axis) geometries can be treated separately [0]. On the one hand, grating couplers can be made arbitrarily wide. Thus, they can be readily designed to match any desired input beam width. On the other hand, the maximum effective grating length that can be implemented is limited by grating radiation strength. The effective grating length can be increased, weakening the radiation strength by reducing the grating contrast, e.g. using subwavelength index engineering [0]. Nevertheless, the minimum achievable strength may be limited by fabrication constraints like minimum feature size or sensitivity to imperfections. Here, we propose an alternative approach to increase the grating length, based on connecting two grating couplers with opposite radiation angles. This approach allows doubling the total length of the light collecting region without the need to halve the grating strength, while facilitating excitation of multiple waveguides as light is coupled towards the two sides of the grating.

Let us consider the 2D grating geometry shown in Fig.

To illustrate the advantage of this two-way-fed configuration, we calculate the coupling efficiency as a function of the grating length, L = L A + L B , when a plane wave truncated to 100 µm width is used as input. The plane-wave propagation angle θ, defined in Fig.

The single-mode operation. Length imbalance in the MZIs is implemented using spirals with bending radius ranging from 10 µm to 100 µm. The MZIs are implemented with 2×2 multi-mode interference couplers. One input of each MZI is connected to the wide-area two-way-fed grating coupler, and one MZI output is connected to an integrated germanium photodetector, with the responsivity of 0.6 A/W. The other two ports of the MZI are connected to conventional fibre-chip grating couplers, for reference. Conventional fiber-chip grating couplers have a period of 600 nm, a duty cycle of 0.5 and size of ∼ 20 × 20 µm 2 . The MZIs in the SHFTS can be excited simultaneously using the twoway-fed grating, or one by one using conventional fiber-chip couplers. The output of each MZI is readout either using integrated photodetectors, or with SMF-28 fibers and analyzed using external photodetectors. To illuminate the wide-area grating, we use a fiber gradient-index (GRIN) lens collimator with a beam diameter of 0.5 mm, at full-width at half maximum (FWHM).

As shown in Fig.

First, we characterize the étendue improvement of the twoway-fed grating. The étendue is the product of the input area, the coupling efficiency and the solid angle [0]. For comparison, we use a conventional grating coupler, with a size of 20 × 20 µm 2 , similar to the size of the individual inputs of our coupler, of 10 × 30 µm 2 each. Having comparable areas, they will have similar angular apertures, allowing direct comparison of the étendue using the peak coupling efficiency. We illuminate the widearea grating with the GRIN collimator and collect the output of the 16 MZIs, using an SMF-28 fiber and the ports connected to conventional fiber-chip grating couplers. The signal collected at each output port is normalized by the transmittance of two conventional grating couplers in a back-to-back configuration when using the GRIN collimator at the input and SMF-28 fiber at the output. The transmittance of the 16 MZIs near 1570 nm wavelength is shown in Fig. We have compared the spectral retrieval of the SHFTS using four possible configurations combining the two inputs (widearea two-way-fed and conventional grating) and the two outputs (integrated Ge photodetector and conventional fiber-chip coupler) of the MZIs. In each case, a different calibration matrix is recorded and used for spectral retrieval. As an example, Fig.

To optimize the signal-to-noise ratio of the retrieved spectrum, we truncate the callibration matrix to 600 pm wavelength range. Figure In summary, we report on the experimental demonstration of the SHFTS fabricated using 193-nm deep-UV optical lithography, comprising a wide-area light collecting aperture of 90 µm × 60 µm and integrated Ge photodetector array. The device relies on a novel two-way-fed grating geometry, combining two grating couplers with opposite radiation angle to simultaneously feed 16 Mach-Zehnder interferometers. We experimentally show a ∼13 dB increase in étendue, compared with a conventional input grating coupler aperture, when using a wide-area illumination beam of 0.5 mm FWHM. We compared different device configurations, illuminating all MZI simultaneously with wide-area collection input or one by one with conventional fiberchip couplers, and recording the MZI outputs with integrated Ge photodetectors and external photodetectors. The large étendue of the proposed configuration and the powerful phase and amplitude corrections provided by the pseudoinverse technique allowed the demonstration of 85 pm resolution using wide-area input aperture and integrated photodetectors, with no significant performance degradation compared to individual illumination of each MZI and readout with external photodetectors. These results open a new route to large-volume production of miniaturized silicon photonic on-chip spectrometers exploiting the Jaquinot's advantage, which can be particularly interesting for sensing applications in embarked systems where weight, robustness, and étendue are key parameters [0].

  3 nm) [0]. The parallel acquisition of the entire interferogram can be exploited to implement a multi-aperture light collection covering wide areas [0, 0]. However, silicon photonics on-chip SHFTSs reported to date have not yet exploited parallel acquisition with multi-aperture input, i.e. the Jacquinot's advantage. State-of-the-art SHFTS demonstrations use single-waveguide input and power splitting trees [0, 0, 0] or multiple inputs that are accessed separately, one by one [0, 0]. Reported SHFTSs rely on conventional fiber-chip grating couplers [0, 0] or facet couplers based on subwavelength engineered tapers [0, 0] of multimodal waveguides [0]. SHFTS have been monolithically integrated with one photodetector and one MZI [0].

Fig. 1 .

 1 Fig. 1. Optical images of: (a) wide-area two-way-fed input grating coupler, and (b) complete SHFTS device, comprising the wide-area coupler, 16 MZIs and Ge photodetectors.

Fig. 2 .

 2 Fig. 2. (a) Schematic 2D view of the two-way-fed grating coupler. (b) Coupling efficiency as a function of the grating length, when a plane wave of 100 µm length is used as the input. (c) Angular aperture as a function of the grating length.

Fig. 3 .

 3 Fig. 3. Transmittance of the 16 MZIs in the SHFTS near 1570 nm wavelength, when simultaneously illuminated with a GRIN lens collimator and the two-way-fed grating.

Fig. 4 .

 4 Fig. 4. Calibration matrix measured for the 16 MZIs and the input aperture illuminated using GRIN lens collimator, and output with integrated Ge photodetectors.

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Fig. 5 .

 5 Fig. 5. Retrieved spectrum of a monochromatic input and a doublet with peak-to-peak separation of 85 pm, for: (a) illumination with conventional grating coupler, readout with external photodetector, (b) illumination with conventional grating coupler, readout with integrated Ge photodetectors, (c) illumination with two-way-fed grating, readout with external photodetector, and (d) illumination with two-way-fed grating, readout with integrated Ge photodetectors.

FUNDING

French Industry Ministry (Nano2022 project under IPCEI program); Agence Nationale de la Recherche (ANR-MIRSPEC-17-CE09-0041); Spanish Ministry of Science, Innovation and Universities (MICINN) (RTI2018-097957-B-C33, TEC2015-71127-C2-1-R FPI scholarship BES-2016-077798); Community of Madrid -FEDER funds (S2018/NMT-4326); Horizon 2020 Research and Innovation Program (Marie Sklodowska-Curie 734331);

DISCLOSURES

The authors declare no conflicts of interest.