IRSTEA Delphine Bertin
email: delphine.bertin@irstea.fr

Benoît J D Ferrari

Pierre Labadie
email: pierre.labadie@u-bordeaux1.fr

Alexandre Sapin
email: alexandre.sapin@irstea.fr

Jeanne Garric
email: jeanne.garric@irstea.fr

Hélène Budzinski
email: h.budzinski@epoc.u-bordeaux1.fr

Magali Houde
email: magali.houde@ec.gc.ca

Marc Babut
email: marc.babut@irstea.fr

Bioaccumulation of perfluoroalkyl compounds in midge (Chironomus riparius) larvae exposed to sediment

Keywords: Perfluoroalkyl compounds, sediment, Chironomus riparius, bioaccumulation

Midge larvae (Chironomus riparius) were exposed to sediments from a deposition sampled at a site along the Rhône River (France) downstream of an industrial site releasing various perfluorinated chemicals. This sediment is characterized by high concentrations of perfluoroundecanoic acid (PFUnA) and perfluorotridecanoic acid (PFTrDA) and a low perfluorooctane sulfonate (PFOS) concentration. Concentrations of 23 perfluoroalkyl compounds, including C 4 -C 14 carboxylate acids, C 4 -C 10 sulfonates, and seven precursors, were analyzed in overlying and pore water, sediment, and larvae.

Midge larvae accumulated carboxylate acids (C 11 -C 14 ), PFOS, and two precursors (perfluorooctane sulfonamide: FOSA and 6:2 fluorotelomer sulfonic acid, 6:2 FTSA).

These substances accumulated mainly during the fourth instar larvae exponential growth phase. Accumulation of 6:2 FTSA, PFUnA, and PFOS occured via trophic and tegumentary routes. Other compounds mainly accumulated from food. Kinetics followed a partition model, from which uptake and elimination constants were derived.

Introduction

Polyfluoroalkyl and perfluoroalkyl substances (PFASs) have been produced since the early 1950s. The production and use of these compounds have resulted in their

Author-produced version of the article published in Environmental Pollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

global distribution in the environment [START_REF] Houde | Monitoring of Perfluorinated Compounds in Aquatic Biota: An Updated Review[END_REF][START_REF] Houde | Biological monitoring of polyfluoroalkyl substances: A review[END_REF][START_REF] Prevedouros | Sources, fate and transport of perfluorocarboxylates[END_REF]. In 2000, the 3M company voluntarily phased -out C 8 -basedchemicals (i.e., sulfonamide based polymers), at the base of the formation of perfluorooctane sulfonate (PFOS) and perfluorooctanoic acid (PFOA), and replaced them with shorter-chain chemicals (e.g., perfluorobutane sulfonate, PFBS) [START_REF] Renner | The long and the short of perfl uorinated replacements[END_REF][START_REF] Lindstrom | Polyfluorinated Compounds: Past, Present, and Future[END_REF]. In 2009, PFOS was listed under Annex B of the Stockholm convention (United Nations Environmental Program -UNEP) on Persistent Organic Pollutants (POPs) [START_REF] Lindstrom | Polyfluorinated Compounds: Past, Present, and Future[END_REF].

PFASs have been found in all aquatic media [START_REF] Houde | Monitoring of Perfluorinated Compounds in Aquatic Biota: An Updated Review[END_REF][START_REF] Houde | Biological monitoring of polyfluoroalkyl substances: A review[END_REF]. On the basis of global modelling, marine sediments have been designated as the ultimate containment for PFASs [START_REF] Armitage | Modeling global-scale fate and transport of perfluorooctanoate emitted from direct sources[END_REF]. Several studies have shown the presence of PFASs in sediment with concentrations ranging from 0.5 ± 0.1 to 38.3 ± 16.8 ng.g -1 dw [START_REF] Ahrens | Partitioning Behavior of Per-and Polyfluoroalkyl Compounds between Pore Water and Sediment in Two Sediment Cores from Tokyo Bay, Japan[END_REF][START_REF] Bao | Perfluorinated compounds in sediments from the Daliao River system of northeast China[END_REF][START_REF] Bao | Perfluorinated compounds in urban river sediments from Guangzhou and Shanghai of China[END_REF][START_REF] Higgins | Quantitative determination of perfluorochemicals in sediments and domestic sludge[END_REF][START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF][START_REF] Myers | Fate, distribution, and contrasting temporal trends of Author-produced version of the article[END_REF][START_REF] Zushi | Time trends of perfluorinated compounds from the sediment core of Tokyo Bay, Japan (1950s-2004)[END_REF]. Sediment has been suggested as a major source of contamination of aquatic organisms [START_REF] Martin | Perfluoroalkyl contaminants in a food web from lake Ontario[END_REF]. However, the distribution of water, sediment, and biota as well as the role of the sediment compartment in biota contamination is still poorly understood. The length of the fluorocarbon chain is an important criterion for PFAS distribution in the environment [START_REF] Ahrens | Partitioning Behavior of Per-and Polyfluoroalkyl Compounds between Pore Water and Sediment in Two Sediment Cores from Tokyo Bay, Japan[END_REF][START_REF] Higgins | Sorption of perfluorinated surfactants on sediments[END_REF][START_REF] Myers | Fate, distribution, and contrasting temporal trends of Author-produced version of the article[END_REF]. PFASs with eight or more carbon atom backbones are known to be bioaccumulative [START_REF] Kannan | Perfluorinated compounds in aquatic organisms at various trophic levels in a Great Lakes food chain[END_REF][START_REF] Kelly | Perfluoroalkyl contaminants in an arctic marine food web: Trophic magnification and wildlife exposure[END_REF][START_REF] Loi | Trophic Magnification of Poly-and Perfluorinated Compounds in a Subtropical Food Web[END_REF][START_REF] Tomy | Fluorinated organic compounds in an Eastern arctic marine food web[END_REF].

In France, PFASs were found in fish from the Rhône River near Lyon [START_REF] Miège | Occurrence of priority and emerging organic substances in fishes from the Rhone river in the area of Lyon[END_REF]. Highest levels of PFASs were found in fish from this latter river (mean total PFAS concentration: 241.5 ng.g -1 dry weight (dw)), the Rhône River was therefore

Author-produced version of the article published in Environmental Pollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

chosen as the study site for this research which aimed to better understand the origin of PFAS contamination in aquatic organisms by evaluating the transfer of these compounds from sediment to invertebrates.

A benthic invertebrate, the non-biting midge Chironomus riparius, is found in sediment from the Rhône River and is recommended by the OECD for toxicity testing (OECD, 2004). Midges are holometabolous, that is they go through complete metamorphosis consisting of egg, larva, pupa, and adult stages. C. riparius mates in aerial swarms. After mating, the female deposits the eggs on the water surface. Larvae undergo four instars; the first (L1) is planktonic and the second to fourth larval stages (L2, L3, L4) are in direct contact with sediment (Fig. S1). Larvae L2 to L4 are collectorgatherers, feeding mainly on detritus and its associated bacteria and fungi. This species represents an important food source for fish, making it a useful species for documenting the bioaccumulation of perfluoroalkyl compounds [START_REF] Armitage | The Chironomidae: Biology and Ecology of Non-Biting Midges[END_REF].

The objectives of the present study were (i) to experimentally determine the role played by sediment in the accumulation of eleven carboxylic acids (from 4 to 14 carbons), five sulfonates (ranging from 4 to 10 carbons), and seven precursors by C.

riparius larvae and (ii) to describe the kinetics of the bioaccumulation process.

Materials and Methods

The study site, Beurre Island (BER), is a fluvial annex of the Rhône River (eastern central France, N45°28'17,0"E4°46'43,4", Fig. 1) and located downstream of a fluoropolymer manufacturing plant that has been found to be an important source of PFAS contamination with a typical profile [START_REF] Dauchy | Relationship between indusrial discharges and contamination of raw water ressources by perfluorinated compounds. Part I: Case study of a fluoropolymer manufacturing plant[END_REF].

Sediments

Author-produced version of the article published in Environmental Pollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

In 2012, 50 L of natural sediments were collected from the river bed with a Van-Veen grab, kept on ice and brought to the laboratory, where they were sieved at 2 mm, pooled in a polypropylene (PP) jar, and stored at 4°C. Six aquaria (38 × 20 × 24.5 cm in polystyrene) were prepared with 4 L of homogenized sediment and 15 L of groundwater mixed with treated water via an osmosis system in order to reach a conductivity of 300 µS.cm -1 . Each aquarium was allowed to settle for 1 week before introducing the chironomids. Three control aquaria were prepared in the same manner with silica sand (particle size distribution: 90% 50-200µm, 10% <50µm) [START_REF] Péry | A modeling approach to link food availability, growth, emergence, and reproduction for the midge Chironomus riparius[END_REF].

The sediment was characterized for water content, nitrogen, carbonate using a

Bernard calcimeter, and loss on ignition (LOI) [START_REF] Afnor | Determination of the toxicity of fresh water sediments to Chironomous riparius -Part 1 : natural sediments Water quality Author-produced version of the article[END_REF][START_REF] Afnor | Determination of the toxicity of fresh water sediments to Chironomous riparius -Part 1 : natural sediments Water quality Author-produced version of the article[END_REF][START_REF] Afnor | Determination of the toxicity of fresh water sediments to Chironomous riparius -Part 1 : natural sediments Water quality Author-produced version of the article[END_REF][START_REF] Vatan | Manuel de sédimentologie[END_REF]) and showed a water content of 43.4%, an organic carbon content of 4.3%, a carbonate content of 27.4%, and a nitrogen content of 0.19%. The particle size distribution was determined by laser diffractometry (Cilas 1190, France) and found to be 10% clay -silt (< 5.83µm), 40% silt (5.83 -52.24 µm), and 50% of silt -very fine sand (>52.24 mm).

C. riparius exposure

Chironomids were obtained from laboratory cultures made according to standard methods [START_REF] Afnor | Determination of the toxicity of fresh water sediments to Chironomous riparius -Part 1 : natural sediments Water quality Author-produced version of the article[END_REF]OECD, 2004). Chironomids were exposed to the BER sediment at standard temperature (21°C). Two experiments were conducted to examine the extent to which developmental stage influences the amount of accumulated chemicals in C. riparius (experimental designs shown in Fig. S2). The first experiment (E1) started with L2 larvae until the end of the L4 stage and lasted for 9 days. The second experiment (E2) started directly with L4 larvae. In experiment E1, 2400 L2 larvae (2-day-old larvae post-hatching) were added to three study aquaria, and to three control aquaria (400 in each aquarium). In experiment E2, 1200 early L4 larvae (7-day-old larvae post-hatching) were exposed in three aquaria. Overlying water (OW) was continuously renewed (four times a day) to maintain adequate water quality and oxygenated under a 16:8-h light: dark photoperiod during the experiment. Larvae were fed ad libitum each day with 1mg commercial food (Tetramin ® ) per organism per day. We decided to feed the chironomids during the experiment because previous experiments showed that larvae did not survive without an external supply of food in this sediment. A quantity of 1mg Tetramin ® per organism per day was selected because preliminary tests (data not shown) conducted with 0.6mg

Tetramin ® per organism per day showed low survival and growth. E1 organisms were sacrificed after 11 post-hatching days, i.e., 9 days (Tfinal, Tf) after being introduced in the aquaria. E2 organisms were sacrificed at 2 (T1), 3 (T2), and 4 (T3) days, respectively, after introducing L4 chironomids. The water quality parameters (pH, concentration of dissolved oxygen, conductivity, NO 2 -, and NH 4 + ) were monitored once a week and at the beginning and the end of the exposure period (Fig. S2).

Sample collection and chironomid measurements

Overlying water (OW), pore water (PW), and sediment were sampled at T1, T2, T3, and Tf. E1 organisms were sampled only at Tf. E2 chironomids were sampled at T0

(fourth instar larvae), T1, T2 and T3, and Tf. Water samples were each spiked with 2 ng of IS and processed using Srata X-AW cartridges as described by [START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF].

Eluates were concentrated to 400 µL under a nitrogen stream at 40°C and transferred into PP vials (final volume: 250-300 µL). Extracts were stored at -20°C until analysis.

Sediment sample

Sediment samples were extracted by sonication, using a method adapted from [START_REF] Sun | Long-chain perfluorinated chemicals in digested sewage sludges in Switzerland[END_REF]. Samples (1 g dw) were spiked with ISs (1.8 ng each) and extracted with 5 mL of MeOH for 20 min, prior to centrifugation for 3 min (20°C, 2900 g). This procedure was repeated with 2.5 mL of MeOH and the two extracts were combined and concentrated to 800 µL under a nitrogen stream at 40°C. Samples were purified using ENVI-Carb cartridges previously conditioned with 4 mL of MeOH and eluted with 2× 4 mL of MeOH. Eluates were concentrated to 400 µL under a nitrogen stream at 40°C and transferred into injection vials.

Author-produced version of the article published in Environmental Pollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

C. riparius samples and Tetramin ® samples

Extraction of PFASs in 120 mg dw C. riparius (800 mg wet weight (ww)) and in 540 mg Tetramin ® followed the same protocol used for the sediment samples. Extract clean-up was adapted from Ballesteros-Gomez et al. (2010). Extracts were diluted 20 times with ultra-pure water (5% extract in water) and then passed through a Strata X-AW cartridge previously conditioned as described above. After extract loading, cartridges were washed with 5 mL of sodium acetate buffer (pH=4.5, 25 mM). They

Isotopic analysis

Isotopic analysis ( 13 C and 15 N) was performed by the INRA-Nancy laboratory (PTEF-isotopy pole, France) on decarbonated sediment, Tetramin ® , and chironomids (i.e., chironomids that have eliminated their gut content following 48h in a beaker containing silicate, overlying water with food, and chironomids with gut content).

LC-MS/MS analysis

Author-produced version of the article published in Environmental Pollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

PFAS analyses were performed using an Agilent 1200 LC system (Agilent Technologie, Massy, France) interfaced with an Agilent 6460 triple quadrupole mass spectrometer (details in Table S2).

Quality control and performance methods

Analyte recoveries were determined using spiked samples for each matrix (surface and pore water, sediment, and chironomids). Native PFAS recoveries ranged from 50 to 110% (except for PFTeDA, MeFOSA and EtFOSA), with a relative standard deviation below 15% (Table S3).

Mean IS recoveries, estimated by external calibration, were in the range 70 -135% for the different matrices. Replicate procedural blanks were analyzed for each series of samples. The predominant compounds in surface water blanks were PFHpA (mean level: 166 pg) and PFHxA (115 pg). For solid samples, the prevailing analytes in blanks were PFOA (63 pg) and PFPA (26 pg). PFAS concentrations were therefore blank-corrected. For compounds present in blanks, the limits of detection (LDs) were defined as three times the standard deviation, and the limits of quantification (LQs)

were set at ten times the standard deviation of the blank. For analytes not detected in the blanks, LDs and LQs were determined as the concentration with a signal-to-noise ratio of 3 and 9, respectively. This calculation was performed on matrices spiked at 2-5 ng.g -1 (sediment and C. riparius) and 2-3 pg.L -1 (Vittel ® mineral water samples) (Table S4). were performed using the software package R (version 2.11.0) (R Development Core

Data processing

Team, 2013). For calculating data below the LQ, 0.5*LQ was used.

When relevant, accumulation data were fit to an exponential rise model (Eq.1)

with Sigma Plot 10.0 software (Systat software Inc., Point Richmond, CA, USAwww.systat.com).

C org (t) = a.(1-e -bt ) Eq. ( 1)

Where C org is the concentrations in chironomids (ng. g -1 ww), t the time in (h), a and b are defined in the discussion.

This model has been adapted to existing bioaccumulation models, including the model described by [START_REF] Spacie | Bioaccumulation[END_REF] and Landrum [START_REF] Landrum | Bioavailability and toxicokinetics of polycyclic aromatic hydrocarbons sorbed to sediments for the amphipod Pontoporeia hoyi[END_REF]. PFTrDA (2.54 ± 0.23 ng.g -1 dw), PFUnA (1.70 ± 0.22 ng.g -1 dw), PFDoA (1.54 ± 0.63 ng.g -1 dw), PFTeDA and PFDA (0.99 ± 0.58 ng.g -1 dw and 0.91 ± 0.43 ng.g -1 dw respectively), whereas PFOS was lower (0.26 ± 0.02 ng.g -1 dw). In sediment control samples, only PFPA and PFOA results were between LDs and LQs; the other compounds were <LDs.

Results

3

The analysis of Tetramin ® indicated the presence of 4 PFASs: PFNA (0.20 ± 0.05 ng.g -1 dw), PFUnA (0.34 ± 0.32 ng.g -1 dw), PFOS (1.43 ± 0.17 ng.g -1 dw), and FOSA (0.39 ± 0.03 ng.g -1 dw). The range of PFAS concentrations in chironomids at the end of E1 and E2 exposures are presented in Table 1, PFAS concentrations in chironomids control were <LDs.

Growth and accumulation kinetics

Survival throughout the experiments (E1 and E2) was greater than 80%.

Chironomid weight was significantly different (p < 0.001) between growth in sediment (two at fourth instar larvae: 7.15 ± 0.60 mg) and in silica (5.84 ± 0.83 mg) at 11 days post-hatching (Fig. S3). However, no adverse effect of contaminated sediment on chironomid growth was observed. In addition, fourth instar larvae weight data (E2) fit an exponential growth curve well (R 2 = 0.999, p <0.0001); growth rate (g) 0.0148 (± 0.0001).

The results indicated that C. riparius accumulated four long-chain PFCAs (> 10 carbons: PFUnA, PFTrDA, PFDoA, and PFTeDA), PFOS, one precursor (FOSA), and one fluorotelomer (6:2 FTSA); the other compounds were all <LDs (Fig. 2). Fourth instar chironomid larvae accumulated PFASs as early as the second day of exposure and a steady state was observed at the end of exposure for most of the accumulated compounds, except for PFTeDA (LD< PFTeDA concentration < LQ) and perhaps for 6:2 FTSA. No differences in accumulation were observed between organisms exposed only at the fourth instar and those exposed from the second to the fourth instar (Fig. 3, Table 1).

The chironomids were not depurated before PFAS analyses; therefore the gut content estimation was based on [START_REF] Brooke | Gut content weight and clearance rate for three species of freshwater invertebrates[END_REF]. According to this calculation there was no difference in PFAS concentrations between chironomids in which gut content was or was not estimated. Therefore, the data without gut content correction were kept for further interpretation.

The biota-to-sediment accumulation factor (BSAF) between organisms was calculated according to [START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF]:

BSAF ww = C org / C sed,oc Eq. ( 2
)
where C org (ng.g -1 ww) is the PFAS concentration in the organism (at steady state) and C sed,oc (ng.g oc -1 dw) is the PFAS concentration in sediment normalized by the organic carbon content (Table 2).

Isotopic analysis

δ 13 C signatures of -27.57 ± 0.005‰ and -23.11‰ and δ 15 N signatures of 4.12 ± 0.64‰ and 7.58‰ were found in sediment and chironomid food (Tetramin ® ) respectively. No differences were observed between depurated or non-depurated chironomids: the δ 13 C signature was -20.37 ± 0.42‰ and the δ 15 N signature 11.61 ± 0.80‰ (Fig. S4).

Discussion

PFAS distribution in water, sediment, food, and C. riparius

The sediment from the study site was characterized by high concentrations of with the data reported in the literature (Table S6). This pattern of PFAS contamination may be characteristic of the upstream industrial discharge from a fluoropolymer and polyvinylidene fluoride facility [START_REF] Dauchy | Relationship between indusrial discharges and contamination of raw water ressources by perfluorinated compounds. Part I: Case study of a fluoropolymer manufacturing plant[END_REF]. In most published studies from other sites, PFUnA and PFDA were usually below 1 ng.g -1 dw [START_REF] Clara | Perfluorinated alkylated substances in the aquatic environment: An Austrian case study[END_REF][START_REF] Higgins | Quantitative determination of perfluorochemicals in sediments and domestic sludge[END_REF][START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF][START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF], except for the Coosa River in Alabama (3.80 ng.g -1 dw) and Tennessee, USA (4.66 ng.g -1 dw) [START_REF] Lasier | Perfluorinated chemicals in surface waters and sediments from northwest Georgia, USA, and their bioaccumulation in Lumbriculus variegatus[END_REF]. Detection of other long-chain PFCAs was scarce: a maximum value of 1.19 ng.g -1 dw for PFTrDA was reported in Tokyo Bay, Japan [START_REF] Zushi | Time trends of perfluorinated compounds from the sediment core of Tokyo Bay, Japan (1950s-2004)[END_REF], and

PFDoA and PFTeDA values were below 1 ng.g -1 dw in the Orge River (near Paris, France) [START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF], whereas in the Coosa River, USA, concentrations above 1 ng.g -1 dw (1.7 and 4.64 ng.g -1 dw respectively) were found [START_REF] Lasier | Perfluorinated chemicals in surface waters and sediments from northwest Georgia, USA, and their bioaccumulation in Lumbriculus variegatus[END_REF]. For PFOS, BER sediment concentrations (0.247 -0.294 ng.g -1 dw)

were in the same range as reported in other studies around the world (Table S6) [START_REF] Bao | Perfluorinated compounds in sediments from the Daliao River system of northeast China[END_REF][START_REF] Benskin | Observation of a Novel PFOS-Precursor, the Perfluorooctane Sulfonamido Ethanol-Based Phosphate (SAmPAP) Diester, in Marine Sediments[END_REF][START_REF] Nakata | Perfluorinated contaminants in sediments and aquatic organisms collected from shallow water and tidal flat areas of the Ariake Sea, Japan: Environmental fate of perfluorooctane sulfonate in aquatic ecosystems[END_REF] and lower than PFOS levels in the Orge River (France), Coosa River (USA), Sydney Harbor (Australia), and the North and Baltic Seas [START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF][START_REF] Lasier | Perfluorinated chemicals in surface waters and sediments from northwest Georgia, USA, and their bioaccumulation in Lumbriculus variegatus[END_REF][START_REF] Theobald | Occurrence of perfluorinated organic acids in the North and Baltic Seas. Part 2: distribution in sediments[END_REF][START_REF] Thompson | Perfluorinated alkyl acids in water, sediment and wildlife from Sydney Harbour and surroundings[END_REF].

Comparison of the respective concentration ranges for the PFASs measured in control and test aquaria make it possible to design a conceptual diagram of PFASs transport between compartments (Fig. 4). Since PFBA, PFPA, PFHxA, PFNA, PFDA, PFBS, and PFHxS display the same concentrations on overlying waters in control and test aquaria, we inferred that sediment is not a source for these compounds to water.

PFASs in benthic invertebrates

Chironomids bioaccumulated four PFCAs, one PFSA (PFOS), and two PFASs precursors. Among these, 6:2 FTSA was found to bioaccumulate poorly in fish and rats [START_REF] Zonyl | Fluorotelomer Products in the Environment -An Update NFPA[END_REF]. Reported concentrations were generally higher for benthic invertebrates than chironomids, especially for PFOS; ranges of PFOS in Capitellidae and Nereidae were 0.82 -12.6 ng.g -1 ww and 0.26 -0.67 ng.g -1 ww [START_REF] Loi | Trophic Magnification of Poly-and Perfluorinated Compounds in a Subtropical Food Web[END_REF].

Mean PFAS concentrations reported for lugworm were 0.41 ng.g -1 ww [START_REF] Nakata | Perfluorinated contaminants in sediments and aquatic organisms collected from shallow water and tidal flat areas of the Ariake Sea, Japan: Environmental fate of perfluorooctane sulfonate in aquatic ecosystems[END_REF] and 280 ± 33 ng.g -1 ww for Diporeia hoyi [START_REF] Martin | Perfluoroalkyl contaminants in a food web from lake Ontario[END_REF]. The latter study also reported that concentrations of PFUnA, PFDoA, PFTrDA, and PFTeDA were higher in Diporeia hoyi than in chironomids [START_REF] Martin | Perfluoroalkyl contaminants in a food web from lake Ontario[END_REF]. In Nereidae and Capillidae worms, concentrations of PFUnA were lower than in chironomids [START_REF] Loi | Trophic Magnification of Poly-and Perfluorinated Compounds in a Subtropical Food Web[END_REF]. Compared to chironomids from the present study, lower concentrations were also reported for PFDoA in Capillidae [START_REF] Loi | Trophic Magnification of Poly-and Perfluorinated Compounds in a Subtropical Food Web[END_REF], for PFOS in clams (Nakata et al 2006; [START_REF] Nania | Monitoring of perfluorinated compounds in edible fish from the Mediterranean Sea[END_REF], for FOSA in clams and lugworms [START_REF] Nakata | Perfluorinated contaminants in sediments and aquatic organisms collected from shallow water and tidal flat areas of the Ariake Sea, Japan: Environmental fate of perfluorooctane sulfonate in aquatic ecosystems[END_REF], and for PFTeDA in Nereidae worms [START_REF] Loi | Trophic Magnification of Poly-and Perfluorinated Compounds in a Subtropical Food Web[END_REF]. However, comparisons between freshwater and marine organisms should be interpreted with caution because salt may affect the chemical activity (Jeon et al., 2010a;Jeon et al., 2010b).

Accumulation kinetics

The biota-to-sediment accumulation factors (BSAFs; Eq. 2) indicated values for FOSA > PFTrDA > PFOS > PFUnA > 6:2 FTSA > PFTeDA > PFDoA, and no trend was observed between BSAF and PFAS chain length. In contrast, [START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF] observed that BSAF values tended to decrease with increasing chain length [START_REF] Lasier | Perfluorinated chemicals in surface waters and sediments from northwest Georgia, USA, and their bioaccumulation in Lumbriculus variegatus[END_REF] reported that BSAF values increased with increasing chain length. BSAF values in the present study were lower than BSAFs reported by [START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF] and Lasier et al. ( 2011) (e.g., PFUnA BSAF ww chironomid = 0.020; BSAF ww = 0.44 ± 0.11; BSAF ww = 0.29, CV = 40, respectively). This might be explained by the fact to the food added during the present experiment, in contrast to the absence of fedding in previous studies [START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF][START_REF] Lasier | Perfluorinated chemicals in surface waters and sediments from northwest Georgia, USA, and their bioaccumulation in Lumbriculus variegatus[END_REF]. Adding food may decrease the exposure and dilute the contamination because without this addition the chironomids would have fed only on sediment organic matter. Our experiment was conducted in this manner because preliminary trials showed that survival rates were too low when no food was added to the aquaria.

In the [START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF] PFHpA, PFOA, PFNA, and PFDA, although they were measured in sediment. This could be explained by the difference in feeding habits between the two organisms [START_REF] Nogaro | Ecosystem engineering at the sediment-water interface: Bioturbation and consumer-substrate interaction[END_REF]. In addition, chironomid growth during the accumulation phase is not negligible, unlike for L. variegatus, which lost weight (because it went unfed), as growth dilutes contamination. PFAS accumulation in chironomids was as effective when exposure started at 2 nd instar as when it started at 4 th instar. PFASs concentrations were the same between the end of E1 and E2 exposures (Table 1, Fig. 3). At the latter stage, growth is more rapid than at previous stages [START_REF] Péry | A modeling approach to link food availability, growth, emergence, and reproduction for the midge Chironomus riparius[END_REF]. These results

suggest that the sole use of the 4 th instar in could be included in the design of future experimental studies with this organism.

For PFTrDA, PFUnA, PFOS, and FOSA, accumulation data obtained in the present study fit an exponential rise model well (Eq. 1), with R² values ranging from 0.99 (PFOS) to 0.97 (PFUnA). Equation ( 1) supports either a classical two-compartment partition model [START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF][START_REF] Landrum | Bioavailability and toxicokinetics of polycyclic aromatic hydrocarbons sorbed to sediments for the amphipod Pontoporeia hoyi[END_REF] or a more sophisticated adsorption-like accumulation model [START_REF] Liu | Novel Perspectives on the Bioaccumulation of PFCsthe Concentration Dependency[END_REF]. Model parameter a is related to the exposure concentration (C sed-oc ) and uptake and depuration rates (k u and k e respectively).

Model parameter b is related to the elimination rate (k e ). As chironomids grow during the experiment, the elimination rate (k e' ) should be corrected according to Eq. ( 3) [START_REF] Spacie | Bioaccumulation[END_REF],

k e ' = k e + g Eq. (3)
The complete two-compartment model includes a  term in order to account for the chemical concentration decline in sediment. This term is set to 1, as in eq. 1, when sediment concentrations do not vary significantly during the experiment (that is, if the flux from sediment to organisms is much lower than the overall compound mass in sediment). This was the case in the current experiment (Table S5). In this case, equation

(1) can be solved easily, with b being the apparent elimination rate (k e ' in h -1 ), and a = (k u /k e )*C sed-oc eq. ( 4)

with k u the uptake rate (g oc .g ww .h -1 ) and C sed-oc the concentration in sediment normalized to the organic carbon content (ng.g oc -1 ).

Applying this approach, yields (k u , k e , and k e' ) were obtained for PFTrDA, PFUnA, PFOS, and FOSA) (Table 3). These data are only informative because no depuration data were available.

The adsorption-like model [START_REF] Liu | Novel Perspectives on the Bioaccumulation of PFCsthe Concentration Dependency[END_REF] was developed initially for an uptake experiment from water. We assumed that it could also apply to accumulation from sediment and food as in our study. Nevertheless, it cannot be solved without depuration data because three variables are included in the terms a and b instead of two as in the two-compartment model:

a = (n*k u *C sed )/(k u *C sed + k e )
Eq. ( 5)

b = k u *C sed + k e Eq. ( 6
)
where n is the number of adsorption sites.

Contamination routes

All compounds accumulated by the chironomids were detected in sediment. PFUnA, PFOS, and 6:2 FTSA were also quantified in both pore and overlying water and PFTrDA was detected in overlying water. In addition, some compounds, such as PFUnA, PFOS, and FOSA, were found in food added (Tetramin ® ) to chironomids, which did not affect accumulation in chironomids (i.e., the balance between

Author-produced version of the article published in Environmental Pollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018 accumulation and depuration) because these compounds were not detected in control chironomids (PFAS concentrations <LDs).

These results therefore suggest that there are two contamination routes for the PFASs, which differ according to the compounds. The contamination routes for substances found in both pore water and sediment (particles) were via food and tegument. For other compounds, found only in sediment, the contamination route was only trophic.

These observations are supported by the growth data: larvae grew more in test sediments than in the control setting, although they received the same quantity of Tetramin ® . These results indicate that larvae fed on organic carbon from the sediment and thus may have absorbed the PFAS associated with particles. On the other hand, the chironomid δ 13 C values were almost identical in test and control organisms, suggesting that the proportion of C obtained by the larvae from the sediment was limited. This is consistent with the findings reported by [START_REF] Goedkoop | Trophic fractionation of carbon and nitrogen stable isotopes in Chironomus riparius reared on food of aquatic and terrestrial origin[END_REF], which showed that about 90% of the carbon intake was from added food. However, both δ 13 C and δ 15 N values for Tetramin ® were mean values because Tetramin ® is a mixture of animal (fish, crustaceans, mollusks) and plant (cereals) ingredients, each having its own isotopic composition. Chironomids may feed selectively on certain components of the added food [START_REF] Goedkoop | Trophic fractionation of carbon and nitrogen stable isotopes in Chironomus riparius reared on food of aquatic and terrestrial origin[END_REF]. Therefore, the observed chironomid δ 13 C signature may be influenced by sediment organic carbon.

Conclusion

Results apparent uptake and elimination constants can thus be proposed on the basis of the classical partition model [START_REF] Landrum | Bioavailability and toxicokinetics of polycyclic aromatic hydrocarbons sorbed to sediments for the amphipod Pontoporeia hoyi[END_REF][START_REF] Spacie | Bioaccumulation[END_REF]. Elimination experiments should be conducted to determine the elimination kinetics experimentally in this species. Table 1: PFAS concentrations in chironomids at the end of E1 and E2 exposures (ng.g -1 ww). E1 with standard deviation (n = 3) and E2 with analytical error calculation relative to spiked samples (Table S3). PFTeDA "trace" means that concentrations were between LD and LQ. S3). S3); on the right graph they represent the standard deviation between three replicates (n = 3).

Author

  were vacuum-dried (30-40 min) and connected via a polyethylene adaptor cap to an ENVI-Carb cartridge previously conditioned with 8 mL of MeOH. Neutral PFASs were eluted with 8 mL of MeOH (fraction A). The ENVI-Carb cartridge was then replaced and a second fraction (fraction B) containing acidic analytes was eluted with 8 mL of MeOH containing 0.2% NH 4 OH. Fraction A eluates were concentrated to 300 µL and then transferred into PP injection vials. Fraction B eluates were processed almost to dryness before adding 200 µL of acetonitrile and 200 µL ultrapure water. Extracts were then passed through MeOH-rinsed centrifuge tube filters and transferred into PP injection vials.

Figure 2 :

 2 Figure 2: Kinetics of PFASs accumulation in fourth instar larvae of C. riparius, in the

Figure 3 :

 3 Figure 3: PFCA accumulation in E1 (left, LD < PFTeDA concentrations < LQ) and E2

Figure 1 :Figure 2 :

 12 Figure 1 : Study site

FigureFigure 3 :

 3 Figure Click here to download Figure: Fig 2-01-14.doc Author-produced version of the article published in Environmental Pollution (2014), vol. 189, 27-34The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

Figure

  Figure Click here to download Figure: Fig 3-01-14.doc Author-produced version of the article published in Environmental Pollution (2014), vol. 189, 27-34The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

Figure 4 :

 4 Figure 4: Partition between different compartments

  Data were analyzed using the Student' t-test. All data were checked for normality and homogeneity of variance using the Shapiro-Wilk test and the Bartlett test, respectively. For all statistical tests, the significance level (alpha) was set at 0.05 and calculationsAuthor-produced version of the article published in EnvironmentalPollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

  Author-produced version of the article published in EnvironmentalPollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

	PFHxS were detected at levels lower than PW from test aquaria (n =3, p-value<0.001).
	In sediment, short-(PFBA to PFHpA) and long-chain (PFOA to PFTeDA) PFCAs,
	PFOS, and two precursors (6:2 FTSA and FOSA) were detected > LQs and EtFOSAA

.1 PFAS distribution in water, sediment, food, and C. riparius Short-(PFBA to PFHxA) and long-chain PFCAs (PFOA, PFNA, PFDA, PFUnA, and PFTrDA), short-and long-chain PFSAs (PFBS, PFHxS, and PFOS) and one precursor (6:2 FTSA) were detected in OW test aquaria. PFBA, PFPA, PFHxA, PFNA, PFDA, PFBS, PFHxS, and PFOS were also detected in OW control aquaria, at levels comparable to those observed in test aquaria. Concentrations were consistent throughout the replicates (test and control) (Table

S5

). The same compounds were observed in pore water, except PFDA and PFTrDA; PFHpA was also measured in this compartment. In PW samples from control aquaria, PFBA, PFPA, PFHxA, PFHpA, and were detected < LQs. Concentration of long-chain PFCAs were higher in sediment:

  Author-produced version of the article published in EnvironmentalPollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

  Author-produced version of the article published in EnvironmentalPollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018PFHxA, PFOA, PFNA, PFUnA, PFOS, and 6:2 FTSA associated with test sediments were in much higher concentrations in PW from test aquaria than in PW from controls.

	Therefore, their presence in PW cannot be related to OW. PFNA and PFOS were
	measured in both food (Tetramin ® ) and OW controls aquaria. As a consequence, it
	could not be exclude that PFNA and PFOS in Tetramin ® were dissolved into OW.
	However, all the PFASs measured were <LD in control chironomids; therefore
	Tetramin ® is not a source of PFASs. PFUnA, PFOS, and 6:2 FTSA were present in
	sediment, PW, and chironomids: both PW (respiration) and sediment (food) contribute
	to the contamination. Conversely, PFDoA, PFTrDA, PFTeDA, and FOSA present only
	in sediment and chironomids contributed to the contamination by the ingestion of
	sediment particles.
	Conversely, PFUnA, PFTrDA, and 6:2 FTSA, which were present only in OW test

aquaria and therefore were clearly released from the sediment. Similarly, PFBA, PFPA,

  Author-produced version of the article published in EnvironmentalPollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

.,

  study, Lumbriculus variegatus reached steady state for PFOA and PFDS but not for PFNA, PFOS, PFDA, PFUnA, and PFDoA. In this experiment C. riparius reached a steady state both for PFCAs > C 11 (PFUnA, PFDoA, PFTrDA) and PFOS and FOSA. However, in Lasier et al. (2011), L. variegatus accumulated other compounds that were not accumulated by chironomids such as Author-produced version of the article published in Environmental Pollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

  Author-produced version of the article published in EnvironmentalPollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

  Author-produced version of the article published in EnvironmentalPollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018No short-chain PFAS, detected mostly in water, were accumulated by chironomids. No trends were observed for BSAFs, in contrast to studies by[START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF] and

	Lasier et al. (2011). The contamination pathways appeared to be trophic (sediment
	particles) and tegumentary (pore water) for PFUnA, PFOS, and 6:2 FTSA and only via
	the trophic pathway for the other compounds. Growth data support the trophic
	contamination route but isotopic data are difficult to interpret because of food added
	during the experiments. PFUnA, PFTrDA, and PFOS data fit an exponential rise model;
	from this study indicate that C. riparius accumulated four long-chain
	perfluoroalkyl carboxylates (PFUnA, PFDoA, PFTrDA, and PFTeDA), a perfluoroalkyl
	sulfonate (PFOS), a precursor (FOSA), and a fluorotelomer (6:2 FTSA) from sediment.

Table 2 :

 2 BSAF ww (g oc .g ww -1 ) for chironomids and for Lumbriculus variegatus[START_REF] Higgins | Bioaccumulation of perfluorochemicals in sediments by the aquatic oligochaete Lumbriculus variegatus[END_REF][START_REF] Lasier | Perfluorinated chemicals in surface waters and sediments from northwest Georgia, USA, and their bioaccumulation in Lumbriculus variegatus[END_REF]; n.d, not detected, *PFTeDA, as guidelines only (because LD < PFTeDA concentrations in chironomids < LQ).

Table 3 :

 3 Model parameters with (k e ') and without growth correction (k u , k

e ) Figure 1: Study site of the Rhône River, France. BER = Beurre Island, Plant = PFAS production plant. The river runs from north to south.

Table 1 :

 1 -produced version of the article published in Environmental Pollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018 Figure 4: Partitioning between different compartments: green represents PFASs in food or from a food source, and brown, in the same manner, for sediment. For chironomids, Author-produced version of the article published in Environmental Pollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018 PFAS concentrations in chironomids at the end of E1 and E2 exposures

	the blue frames represent both sediment (brown) and pore water (blue) sources for
	PFASs.

Table Click here to download Table: Table 1_01_14.doc

 Click Author-produced version of the article published in EnvironmentalPollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

Table 2 :

 2 BSAF ww (g oc .g ww -1 )

	Compounds	Fluorinated carbon number	BSAF ww chironomid	BSAF ww Higgins et al., 2007	BSAF ww Lasier et al., 2011
	PFUnA	10	0.020	0.44 ± 0.11 0.29, CV= 40
	PFDoA	11	0.004	0.45 ± 0.08	0.34, CV=40
	PFTrDA	12	0.042	n.d	0.62, CV=44
	PFTeDA*	13	0.004	n.d	0.63, CV=47
	PFOS	8	0.023	0.83 ± 0.20	0.49, CV=50
	6:2 FTSA	6	0.018	n.d	n.d
	FOSA	8	0.098	n.d	n.d

Table Click here to download Table: Table 2.doc

 Click Author-produced version of the article published in EnvironmentalPollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

Table 3 :

 3 Model parameters

	Compounds	a	ku	ke' (b)	ke
	PFUnA	0.83 ± 0.03	0,0009	0.04 ± 0.01	0,03
	PFTrDA	2.56 ± 0.11	0,0015	0.03 ± 0.01	0,02
	PFOS	0.14 ± 0.008	0,0009	0.04 ± 0.01	0,03
	FOSA	0.06 ± 0.01	0,0022	0.02 ± 0.01	0,01

Table Click here to download Table: Table 3_01_14.doc

 Click Author-produced version of the article published in EnvironmentalPollution (2014), vol. 189, 27-34 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.envpol.2014.02.018

Acknowledgments

This study was funded by the Rhone-Mediterranean and Corsica Water Agency and the Rhone-Alpes Region within the Rhone ecological restoration plan. We thank Bernard Motte (IRSTEA), Raphael Barlon, and the Centre d'Observation de l'Ile du Beurre team (Condrieu, France) for their assistance during the sampling campaigns and chemical laboratory analysis (UR MALY, IRSTEA Lyon-Villeurbanne) for monitoring the physicochemical characterization of sediment, and Linda Northrup for copyediting the text as well as two anonymous reviewers for their constructive remarks.

Author-produced version of the article published in Environmental Pollution (2014), vol. 189, 27-34 The


D H Phung

M Merzougui

M Lintz

C Alexandre

Keywords: Photodetectors, Phase measurement, Phase noise, Heating, Optical modulation, Microwave frequency conversion

High accuracy and low noise measurement of the phase of a microwave signal requires that spurious contributions are adequately dealt with. In this paper we investigate the power-to-phase coupling in two commercial high bandwidth P-I-N, near-IR photodetectors. We observe that a sudden change of the optical power induces a transient of the phase of the 20 GHz signal, at different time scales. The temperature rise of the photodetector junction is likely to be involved in this dynamical behaviour. The value of the bias voltage applied to the photodetector appears to control the size of the phase transients, as well as the optical power for which the slope of the amplitude-to-phase coupling cancels. The most efficient way to reduce amplitude to phase couplings consists in implementing optical demodulation, instead of electrical demodulation, of the microwave signal.

I. INTRODUCTION

ICROWAVE modulation of an optical beam is becoming increasingly important for the transfer of a high frequency reference, with applications in antenna synchronisation for radio-astronomy, optical clock comparison in metrology, photonic analogue-to-digital conversion [START_REF] Valley | Photonic analog-to-digital converters[END_REF], ... In all these applications, where a very low phase noise is required, photodetectors are critical parts of the chain. P-I-N InGaAs photodiodes are capable of very low intrinsic phase noise [START_REF] Rubiola | Flicker noise in high-speed p-i-n photodiodes[END_REF]. However, reaching low phase noise and high accuracy in the detection process requires that any additional contribution be reduced to the desired level. The amplitude-to-phase (AM-to-PM) coupling is a known problem [START_REF] Ivanov | Study of the excess noise associated with demodulation of ultra-short infrared pulses[END_REF] because it exacerbates phase noise as soon as the optical power varies, and can place stringent limits to the relative intensity noise of the laser source. This has been studied in the framework of microwave optical links, as the amplitude noise cannot exceed the desired phase noise divided by the AM-to-PM conversion factor. In the case of mode-locked lasers the AM-to-PM coupling has been related to the distortion and broadening of the photodetection pulses, recorded with a high speed sampling oscilloscope [START_REF] Currie | Microwave phase retardation in saturated InGaAs photodetectors[END_REF]. In [START_REF] Taylor | Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes[END_REF] the observation is made that when increasing the energy/pulse one can find conditions where the AM-to-PM slope turns to zero, thus relaxing the requirements on the laser intensity noise. The screening of the electric field accross the photodiode junction by the charges of the photocurrent, which is responsible for saturation and pulsed signal distortion [START_REF] Kuhl | Influence of space charges on the impulse response of InGaAs metal-semiconductor-metal photodetectors[END_REF] can be reduced by modifying the photodiode design. The modified unitravelling carrier photodiode of [START_REF] Fortier | Photonic microwave generation with high-power photodiodes[END_REF] has shown lower saturation and lower AM-to-PM coupling. In [START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF], the zeroes of the AM-to-PM coefficient were Phase measurement of a microwave optical modulation: characterisation and reduction of amplitude-to-phase conversion in 1.5 µm high bandwidth photodiodes

Duy-Ha Phung, Mourad Merzougui, Christophe Alexandre, Michel Lintz M explained, in the model of the triangular shape temporal response of the photodetector. In the case of a high-frequency modulated laser beam, reference [START_REF] Eliyahu | RF amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator[END_REF] has also observed that the AM-to-PM coupling can change sign and cross zero at a certain optical power. The coincidence with the optical power at which the photodiode saturates was also explained through the collapse of the electric field in the photodiode junction [START_REF] Kuhl | Influence of space charges on the impulse response of InGaAs metal-semiconductor-metal photodetectors[END_REF]. The screening of the electric field takes place at very short time scales, typically picoseconds (Fig. 1 in [START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF]). It can be considered as instantaneous in what we discuss in this paper. Ref. [START_REF] Wu | Frequency response of the noise conversion from relative intensity noise to phase noise in the photodetection of an optical pulse train[END_REF] has reported a ≈1/f frequency dependence of the AM-to-PM coefficient when the power of sub-ps pulses was modulated at audio frequencies. The method consisted in modulating the current in the pump diode of the (free running) mode-locked laser and in using a spectrum analyser to observe both the amplitude and the phase modulations in the photodiode signal. But the normalized conversion ratio reported ( [START_REF] Wu | Frequency response of the noise conversion from relative intensity noise to phase noise in the photodetection of an optical pulse train[END_REF], figure 3 and figure 4-c) does not change when inserting optical attenuators before the photodiode, which suggests that the phase modulations reported in [START_REF] Wu | Frequency response of the noise conversion from relative intensity noise to phase noise in the photodetection of an optical pulse train[END_REF] do not originate in the photodiode.

Thermal processes are known to be involved in the runaway failure of photodiodes, due to the combination of the Joule power dissipated in the junction and the decrease of the thermal conductivity of the substrate with increasing temperature [START_REF] Paslaski | High-power microwave photodiode for improving performance of RF fiber optic links[END_REF]. Addressing this problem, other studies [START_REF] Williams | Design considerations for high-current photodetectors[END_REF] have brought quantitative insight into thermal management of photodiodes. In particular, by observing the responsivity change caused by the thermal bandgap redshift in the junction material, [START_REF] Chen | A Method to Estimate the Junction Temperature of Photodetectors Operating at High Photocurrent[END_REF] has indirectly measured the junction temperature rise of photodiodes submitted to strong illumination, and confirmed that the heating power is equal to the product of the photocurrent and the reverse bias voltage. Temperature is also known to affect carrier mobility [START_REF] Williams | Design considerations for high-current photodetectors[END_REF]. Thermal processes can give rise to time scales much longer than the ps-scale photodetector response time. Nevertheless, none of Refs [START_REF] Taylor | Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes[END_REF][START_REF] Kuhl | Influence of space charges on the impulse response of InGaAs metal-semiconductor-metal photodetectors[END_REF][START_REF] Fortier | Photonic microwave generation with high-power photodiodes[END_REF][START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF][START_REF] Eliyahu | RF amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator[END_REF] considers self-heating of photodiodes illuminated by a strong laser power as relevant to the problem of AM-to-PM coupling.

In order to identify the conditions for optimal rejection of noise and systematic deviations in optical microwave links, we perform a systematic study of the phase of the RF signal, and of its dependence on the two prominent parameters, optical power and applied reverse bias. This is done with two P-I-N, InGaAs, 20 and 25 GHz bandwidth, commercial photodiodes. After a sudden change of the optical power in the measurement channel, we observe transients on the measured phase. Time constants of the order of 10 µs are measured, in agreement with the time dependence expected for the heating of the junction in contact with the InP substrate. Not only the applied bias appears to control the phase vs amplitude dependence, and hence the value of the optical power for which the AM-to-PM cancels, but it also controls the amplitude of the transient behaviour. In Sect. VII we show that optical demodulation of the microwave signal allows rejection, by several orders of magnitude, of AM-to-PM coupling in the photodetector.

These points are important for applications in which the phase has to be measured with high accuracy while the optical power is varied by significant factors at short time scales. They are particularly critical in recent developments in high accuracy absolute laser ranging [START_REF] Phung | A two-mode interference measurement for nanometer accuracy absolute ranging[END_REF] where a beam carrying a 20 GHz modulation has to be measured, both in phase and amplitude, with an accuracy of 10 -4 radian, and 5 10 -5 , respectively. The difficulty arises from the variations of the amplitude of the optical 20 GHz signal, associated with the ranging measurement sequence [START_REF] Phung | A two-mode interference measurement for nanometer accuracy absolute ranging[END_REF]. These large variations (from -to +50%) at the microsecond time scale give rise to spurious phase shifts well above the required accuracy for the phase measurement. The present work results from the need to understand, characterize, and finally reduce the AM-to-PM related phase systematic error and noise in the ranging measurement.

II. EXPERIMENTAL METHOD

The beat-note of two narrow-bandwidth fibre lasers at 1.55 µm (Fig. 1), phase-locked to a frequency offset of 20.00 GHz [START_REF] Fatome | Multiple four-wave mixing in optical fibers: 1.5-3.4-THz femtosecond pulse sources and real-time monitoring of a 20-GHz picosecond source[END_REF], is used to generate the optical signal. The optical power is kept constant in the reference channel. The reference and measurement 20 GHz For the measurement of the static AM-to-PM coupling in the measurement channel, the signal generator applies a slow (3 Hz) triangular signal to drive the power of the 160 MHz (fixed frequency) signal applied to the AOM (acousto-optic modulator). We first tried to use an integrated Mach-Zehnder electro-optic modulator (MZEOM) to drive the optical power, but, due to a slight coupling between transmission and transmitted polarization, changing the transmission of the MZEOM clearly resulted in phase offsets related to polarization-mode dispersion (PMD) in the polarizationmaintaining fibers of the MZEOM. No such coupling occurs between the diffraction efficiency in an AOM and the polarization of the diffracted beam, so that when an AOM is used to drive the optical power, PMD is not an issue.

As opposed to static measurements, transients are obtained after a gated signal drives the optical power from a low to a high value in less than a microsecond. The instantaneous response is followed by a delayed phase change of smaller amplitude.

The phase meter has been designed for high accuracy laser ranging with a microwave-modulated laser beam [START_REF] Phung | A two-mode interference measurement for nanometer accuracy absolute ranging[END_REF]. The two 20 MHz, intermediate frequency, sinusoidal signals are sampled during 10 µs using the two 245 MS/s, 14 bit analogue-to-digital converters of an FMC150 interface board. In separate measurements, we observe that the AM-to-PM coupling in the FMC150 board is less than 2x10 -3 radian (static) and 3x10 -5 radian (transient). Inside a Virtex-6 FPGA (field programmable gate array) the signals are then translated from 20 MHz to 0 Hz, low-pass filtered and decimated. The resulting complex values are used to compute the two amplitudes and the phase difference. Phase data obtained with noiseless 20 GHz optical signals show a resolution of 4 3.10radian, which improves as

1/ 2 t - ≈
with the integration time. Each set of elementary data is corrected for a cross-talk of about 10 -3 between the two measurement chains. The four cross-talk coefficients (two amplitudes and two phases) are determined in separate measurements. A new elementary data set is delivered every 15 µs, which allows us to study temporal evolution of the phase at time scales ranging from 10 µs to 1 s.

In refs [START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF], [START_REF] Taylor | Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes[END_REF], no time dependence was observed, except for the sampling oscilloscope subnanosecond records, showing the picosecond-scale temporal dynamics related to the charge carriers. In these works, measurements of the AM-to-PM coefficient were mainly done by the bridge method, that is by demodulating the optical microwave signal down to zero frequency [START_REF] Taylor | Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes[END_REF] or to intermediate frequency [START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF]. Then the AM-to-PM characteristics were recorded by measuring the RMS phase change while the optical power was modulated using an AOM, at low frequency (30 Hz, [START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF]) or at audio frequency (20 kHz, [START_REF] Taylor | Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes[END_REF]). In [START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF], the authors have looked for a change in the AM-to-PM coefficient when the modulation frequency is scanned from 10 Hz to 1 kHz, but did not observe any. Here we characterize two InGaAs commercial photodiodes. Table I gives some data provided by the manufacturers. Fig. 2 shows typical recordings of the measured phase as a function of the optical power Popt, with the two photodiodes. Contrary to results presented in [START_REF] Taylor | Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes[END_REF], [START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF], where all data presented are absolute values Φ , the phase difference values

mes ref ϕ ϕ Φ ≡ -
presented in this paper refer to the expression

( ) sin(2 20 ) mes ref t GHz π ϕ × -
for the microwave signal from the photodiode under test, and the reference photodiode, respectively. Phases are given in radian throughout the paper. Phase offsets are due to cable lengths and components.

To confirm that the observed effects originate in the photodiode and not in the measurement system, we have inserted a 14 dB attenuator between the photodiode Fig. 2. RF phase versus optical power for the two photodiodes. Bias voltage: 15 V (EM4), 4.1 V (New Focus). Each data point has been averaged over 100 elementary data. The measurement channel optical power is scanned at a frequency of 3Hz. One of the two recordings has been translated so that the phase offsets coincide. The cubic fits (see Table II) apply to the middle of the up and down curves. and the mixer. A 14 dB gain is added in the intermediate frequency amplifier, so that the size of the 20 MHz signal fed to the A-to-D converters is essentially the same. As expected due to the attenuation of the signal, we observe a slight increase of the noise, but the change in the phase data (black dashed line) shows that the contribution from the measurement system to the AM-to-PM coupling is negligible. The fact that the AM-to-PM effects are related only to the optical power that reaches the photodiode is confirmed in separate experiments where no AOM is used (and the power of the microwave modulated beam is constant), but an extra beam, provided by a diode laser is used to raise the power dissipated in the photodiode. Same results are obtained, particularly the behaviour observed in Fig. 4 and5, when the diode laser is switched ON or OFF. Unit radian/mW radian/mW 2 radian/mW 3 Coefficients of the cubic fit (y = ax + bx 2 +cx 3 + offset) of the phase-vs-power curves in Fig. 2, for the two photodetectors under test.

In [START_REF] Eliyahu | RF amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator[END_REF], figure 11 shows a power-to-phase coefficient of ≈ 4 10 -2 radian/mW which turns to zero and changes sign when the optical power reaches 9 ∼ 10mW, which is also the power at which the photodiode under test saturates. With the EM4 photodiode biased at 15V, we observe a similar behaviour, except that the small signal power-to-phase coefficient of 3.6x10 -3 radian/mW turns to zero at 2.3 mW optical power, whereas the photodiode shows no sign of saturation up to 6 mW. At 6mW the AM-to-PM slope reaches 0.076 -radian/mW ( 0.6 -ps/mW, if converted to a time delay). The New Focus photodetector shows a similar behaviour, although the coefficients of the cubic fit (see Table II) are about 3 times smaller than with the EM4 photodetector.

Although small compared to the overall phase variation, a hysteresis is clearly observable on Fig. 2: at the scan rate of 3 Hz, the "up" and "down" curves do not coincide. Sections V and VI will address more systematically the time dependence of the AM-to-PM coupling.

IV. THE RF PHASE VS APPLIED REVERSE BIAS

This study was not possible with the New Focus photodiode, which operates at a fixed value bias V of the bias voltage. With the EM4 photodiode the ( ) opt P Φ dependence has been plotted in Fig. 3 for different values of bias V . One remarkable effect of changing bias V is to continuously shift the optical power at which the AM-to-PM slope vanishes, from zero (at 13 V) to 5 mW (at 20 V). Thus, contrary to [START_REF] Eliyahu | RF amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator[END_REF], obtaining a zero amplitude-to-phase coefficient does not imply reaching saturation of the photodiode. As a temperature increase reduces carrier mobility [START_REF] Williams | Design considerations for high-current photodetectors[END_REF], the temperature transient that, due to the Joule heating, follows an increase of the optical power is expected to give rise to phase increase of the microwave signal. This is what is observed in Sections V and VI, on the microsecond and millisecond transients that follow a change in optical power.

V. DYNAMICS OF THE AM-TO-PM COUPLING AT THE MILLISECOND TIME SCALE

When the optical power is switched in less than 1 µs from low to high, both the EM4 and New Focus photo-detectors show -an immediate phase change, as expected from the very fast shielding of the bias electric field by the charge carriers in the junction [START_REF] Ivanov | Study of the excess noise associated with demodulation of ultra-short infrared pulses[END_REF][START_REF] Currie | Microwave phase retardation in saturated InGaAs photodetectors[END_REF][START_REF] Taylor | Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes[END_REF][START_REF] Kuhl | Influence of space charges on the impulse response of InGaAs metal-semiconductor-metal photodetectors[END_REF][START_REF] Fortier | Photonic microwave generation with high-power photodiodes[END_REF][START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF] -"slow" (millisecond) phase transients revealing the junction's thermal evolution.

Measurement system AM-to-PM coupling

A. EM4 photodetector

With the EM4 photodiode the transients (Fig. 4) cannot be accurately described by a single exponential. As shown in Fig. 5 where the time scale is logarithmic, a better fit is obtained with two exponential time constants. Note that in Fig. 5 data points before 50 µs are not accurate, as the data acquisition timing is not controlled to better than 15 µs. For quantitative data at the 10 µs time scale, see Section VI.

B. New Focus photodetector

When applying a fast power change to the New Focus photodetector, the same kind of overshoot is observed (Fig. 6), although with somewhat different values.

Contrary to the EM4 photodetector, the transients are well fitted by a single exponential of 45 ms time constant and amplitude 10 -3 radian (rising) and 1.6 10 -3 radian (falling optical power). Simulations in Section VI show that millisecond time scales can be found in the heating of a photodiode junction, depending on the geometry of the photodiode assembly.

VI. DYNAMICS OF THE AM-TO-PM COUPLING AT THE MICROSECOND TIME SCALE

Although phase and amplitude values are acquired every 15 µs, we have been able to observe, after a sudden change of the optical power, a transient behaviour at the 10 µs time scale, shown in Fig. 7. To allow accurate and reproducible synchronization, the amplitude of the 160 MHz signal fed to the AOM is driven, not by a signal generator (as shown in Fig. 1) but by the FPGA phase meter itself.

As in the case of the static AM-to-PM (Fig. 3), the value of the applied bias voltage allows to control the amplitude of the effect. This is illustrated in Fig. 8, where the amplitude 53 8 -Φ , defined as the difference between the phase data at 8 µs and 53 µs, is plotted against bias V .

The temporal behaviour of the phase at the microsecond time scale is similar with the two photodiodes, and is similar to the transient expected for the junction temperature after the change of the bias photo V I × dissipated power.

The finite element ANSYS software is used to simulate the temperature rise of the junction/substrate assembly (see the geometry in Fig. 9), assuming that the InP substrate, with diameter 450 µm and thickness A = 152 µm, is contacted with the photodiode junction, and with the photodetector case at ambient temperature. We assign the same thermal properties (conductibility and specific the junction and substrate, and calculate the temperature at different locations along the axis of the junction/substrate/heat sink assembly. We monitor the evolution of the temperature of the junction/ substrate contact, after the photocurrent photo I is switched on (with 500 ns rise time), for a duration of 550 µs, then switched off (with 500 ns fall time). The Joule dissipated power is assumed to be uniformly spread across the junction. A different mesh size is used in a sphere of 40 µm radius around the junction.

The software calculates the temperature with 1 µs time steps (smaller time steps are used for the first two microseconds). To account for the acquisition time sequence, we extract four temperature values, averaged over 10 µs time slots centred at 8, 23, 38 and 53 µs. From the exponential fit of the four data (Fig. 10) we obtain time constants of the order of 13 µs, in fair agreement with the experimental values.

Different checks have been done against possible problems with the convergence of the numerical calculations. A κ 68 Jm -1 K -1 is the thermal conductivity of InP [START_REF] Adachi | Physical properties of III-V semiconductor compounds InP, InAs, GaAs, GaP, InGaAs, and InGaAsP[END_REF], and

/ 2 a d =
is the radius of the junction. This formula holds on the cylindrical symmetry axis of the junction and substrate, assuming that the 450 µm substrate diameter is infinite as compared to the 32 µm junction diameter, and neglecting the 1 µm step size of the junction (see Fig. 9) and the dependence of κ with temperature [START_REF] Adachi | Physical properties of III-V semiconductor compounds InP, InAs, GaAs, GaP, InGaAs, and InGaAsP[END_REF]. When the 32 µm diameter junction is heated by a photocurrent of 6 mA under 15 V (heat load 112 W/mm 2 ), the three sets of data agree to better than 0.5 K, to be compared with the 25 K maximum temperature rise (see Table III). Other checks, based on energy conservation, also give confidence in the accuracy of the transient analysis calculations. 9), material conductivity 68 Wm -1 K -1 and specific heat 0.31 Jg -1 K -1 . Heat load 112 Wmm -2 , corresponding to a Joule power of (6 mA)x(15 V). Note the x5 factor for the right scale. * 'Constant κ': the ANSYS software solves the heat equations assuming that the conductivity κ is constant at 68 Wm -1 K -1 . 'Variable κ': the conductivity is assumed to vary with temperature according to

1.55 0 0 ( ) ( )( / ) T T T T κ κ = [16].
The results depend weakly on the geometry of the junction/substrate assembly, for instance in a change from 450 to 2000 µm of the substrate diameter. Changing the substrate thickness from 152 µm to 500 µm or 1 mm does not change the temperature rise in the first 300 µs. However, calculations show (Fig. 11) that thick substrates give rise to a heating at long time scales (milliseconds). As they have the same sign as the microsecond transients, one can speculate whether the slow transients presented in Section V are also due to thermal effects, depending on the thickness of the substrate or other element in the photodetector assembly. Lack of precise data from the manufacturers prevents from a quantitative modelling.

VII. WAYS TO REDUCE THE AM-TO-PM EFFECT

First, let us recall that correcting for AM-to-PM coupling can be done by numerical treatment of the data. This is a complexification of the data processing, but works quite well with static AM-to-PM, as it can be measured accurately beforehand. In the high accuracy range meter setup [START_REF] Phung | A two-mode interference measurement for nanometer accuracy absolute ranging[END_REF], raw measurements are severely affected by AM-to-PM coupling, which, if uncorrected for, gives rise to systematic deviations of 0.007 radian in the phase measurements for optical power variations of 0.35 mW. This appears on Fig. 13-a, where the power that reaches the photodiode changes due the variation of an interference effect. We have been able to correct for static AM-to-PM coupling to better than 3 %. For the transient effect, however, correcting the data using an exponential time dependence is not as accurate: residuals are of the order of 15 % of the systematic errors associated to the transient effect, and could not be completely eliminated in the ranging data of [START_REF] Phung | A two-mode interference measurement for nanometer accuracy absolute ranging[END_REF]. The residual errors and noise give rise to path length measurements which are shifted by +1 or -1 optical wavelength, as manifest on Fig. 6-b of [START_REF] Phung | A two-mode interference measurement for nanometer accuracy absolute ranging[END_REF]: 25% of the ranging measurements are wrong by ±1.5 µm, despite numerical correction of the data.

Thus it is important to look for ways to reduce AM-to-PM coupling, and designs for highly linear photodiodes [START_REF] Taylor | Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes[END_REF][START_REF] Fortier | Photonic microwave generation with high-power photodiodes[END_REF] have already brought significant improvement in AM-to-PM coupling in high signal strength photonic microwave generation.

Our approach follows a different idea. One has to keep in mind that, although it is called "amplitude to phase coupling", the consequence of the optical power reaching the photodiode is a time lag in the carriers generated in the junction, -at picosecond time scales in Fig. 1 of [START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF] and Fig. 5 of [START_REF] Taylor | Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes[END_REF], where pulsed lasers are used, -or at the tens to hundreds of femtoseconds in our case, corresponding to phase shifts in the milliradian to tens of milliradians.

For this reason, two different situations are to be considered, depending on the detection scheme.

If the detection scheme involves microwave to intermediate frequency conversion using a mixer at the output of the high bandwidth photodiode, then a modification of the detection set-up allows to reduce the amplitude-to-phase coupling by the ratio of the microwave and intermediate frequencies, which is a large factor. As put forward and demonstrated in [START_REF] Kim | Attosecond-precision ultrafast photonics[END_REF] in the context of optoelectronic phase lock loops, the modification consists in removing the mixer and using an intensity modulator before the photodiode (Fig. 12) to achieve the frequency transposition on the optical signal. Then the time shift remains the same (if the power reaching the photodetector is the same) but the detected modulation is at intermediate frequency. Hence the phase change is smaller by a factor which is the microwave to intermediate frequency ratio, in our case, 20GHz/20MHz = 1000. We have checked that this detection scheme allows to strongly reduce AM-to-PM effects on the setup of the range meter presented in [START_REF] Phung | A two-mode interference measurement for nanometer accuracy absolute ranging[END_REF], using the same EM4 EM169 photodiodes, with the same bias voltage. With optical demodulation, AM-to-PM coupling in the measurement photodiode was too small to be measurable. As shown on Fig. 13-b, systematic distortion of the signal was still observable, but at a level of 8×10 -4 radian for a power variation of 4.1 mW. This is a reduction by almost an order of magnitude, although the power variation is larger by an order of magnitude, as compared to Fig. 13-a. The residual phase systematic in Fig. 13-b is attributed to static AM-to-PM coupling in the intermediate frequency amplifier (blue triangle on Fig. 12) of the measurement chain, or in the data acquisition. More specifically, transient AM-to-PM coupling which was ≈ 3×10 -3 radian in [START_REF] Phung | A two-mode interference measurement for nanometer accuracy absolute ranging[END_REF], was reduced to less than 5×10 -5 radian (despite the 10 times larger optical power change), a level for which systematic correction for transient AM-to-PM is no longer required for the ranging measurements. An unexpected consequence of using optical demodulation is a lower electrical cross-talk between the reference and measurement chains (-80 dB) than with the setup of Fig. 1 (-60 dB). We believe that this is due to the absence of direct electrical link between the two measurement chains. These results confirm that the set-up of [START_REF] Phung | A two-mode interference measurement for nanometer accuracy absolute ranging[END_REF], with the addition of optical demodulation, is capable of high accuracy phase and amplitude measurements, as systematic errors associated with the detection chains are under control.

(a) Fig. 13: Plot of the systematic error on the phase measurement (corrected for electrical cross-talk, but uncorrected for AM-to-PM coupling), in conditions where the optical power undergoes large variations with time, due to some interference effect. Each data point is averaged over 320 elementary data. The photodiodes are the same in the two graphs, with the same 15V bias. In (a) the setup uses electrical demodulation to convert the signal from microwave to intermediate frequency. Measurement conditions are the same as in [START_REF] Phung | A two-mode interference measurement for nanometer accuracy absolute ranging[END_REF], Fig. 6-a. In (b) the setup uses optical demodulation. Residual phase modulation is attributed to AM-to-PM coupling in the intermediate frequency amplifier (right blue triangle in Fig. 12). Note that vertical scales are different in (a) and (b).

By contrast, when no transposition to intermediate frequencies is possible, reduction of AM-to-PM coupling has to take advantage of the dependence on the different parameters, particularly optical power and applied bias voltage. It has been shown in Sect. IV that scanning the applied bias voltage allows to find conditions where the slope of the static AM-to-PM coupling cancels, an observation that is connected to the observations, in [START_REF] Taylor | Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes[END_REF] and [START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF] of the influence of the applied bias when detecting mode-locked laser pulses. The transient AM-to-PM coupling can also be reduced by appropriate choice of the applied voltage, as shown in Sect. VI, Fig. 8. We have checked that a significant improvement can be obtained by switching the applied bias from 15 V to 7.5 V. We found that the systematic error associated with the static AM-to-PM coupling was reduced by a factor of 10. The transient AM-to-PM effect, however, was reduced by only a factor of 3: the improvement is real, but the residual transient AM-to-PM coupling, of the order of 3×10 -4 radian for a detected power of 0.5 mW was still too large for the goal of nanometric accuracy laser ranging [START_REF] Phung | A two-mode interference measurement for nanometer accuracy absolute ranging[END_REF]. This is why we implemented the optical demodulation, which proved successful, as described above.

VIII. SUMMARY

We present a quantitative investigation of the AM-to-PM characteristics of two commercial P-I-N InGaAs photodiodes, both as concerns the static and transient behaviours. The applied bias voltage appears to control the linear and quadratic coefficients of the stationary Φ vs opt P dependence, with the important consequence that one can adjust at will, through the applied bias voltage, the optical power at which the AM-to-PM slope cancels. Contrary to [START_REF] Eliyahu | RF amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator[END_REF], no close link is found between the zero-slope and the saturation optical power. The multiple zeroes, expected and observed in the case of femtosecond pulses [START_REF] Taylor | Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes[END_REF], [START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF], are not observed here. After a sudden change of the optical power, an immediate phase change occurs, followed by an opposite sign monotonous evolution of the phase at time scales between 10 µs and 1s. Qualitative agreement with results of numerical simulations suggests that the latter evolution involves the heating of the photodiode junction by the Joule dissipated power, and cooling by conduction through the InP substrate. Similar transients, known as "memory effects", have been reported in the context of the thermal management of power microwave amplifiers [18], but, to our knowledge, memory effects had not been reported previously for photodiodes. The transient effects we observe are typically an order of magnitude smaller than the static effects. This ratio is expected to be enhanced when detecting short pulses, such as in ref. [4, 5,

(b)

8]: for the same average optical power the peak power is considerably larger, which may explain why the AM-to-PM factors are larger, and why the transient effect has not been observed in [START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF].

Transient AM-to-PM takes place as soon as the detected optical power changes at microsecond time scales, or millisecond time scales as in "scintillation", the large intensity fluctuations that arise due to propagation over a long distance in a turbulent atmosphere. In the case where the photodiode receives, not only the microwave-modulated laser beam, but also another optical beam, we observe that any variation of the power of the latter will modulate the microwave detected phase. Both transient and static AM-to-PM effects depend on the applied bias voltage in a way which gives the opportunity to reduce the associated noise and systematics by operating at the appropriate bias voltage. Other ways to reduce the AM-to-PM effects, such as adapting the value of the optical power as suggested in [START_REF] Taylor | Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes[END_REF][START_REF] Zhang | Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation[END_REF][START_REF] Eliyahu | RF amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator[END_REF], or reducing the microwave frequency may conflict with the considered application. Finally, we have modified the detection set-up to replace electronic demodulation by optical demodulation using a Mach-Zehnder electrooptical intensity modulator, placed before the photodiode. Then, static and transient AM-to-PM effects in the photodiode are reduced by the ratio of the intermediate-to-microwave frequencies, that is, by a very large factor. The systematic errors quoted in the ranging data of [START_REF] Phung | A two-mode interference measurement for nanometer accuracy absolute ranging[END_REF] have been considerably reduced, which confirms the validity of this detection scheme for reducing AM-to-PM. These results are important with respect to low noise and high accuracy phase measurements of microwave optical signals.

  photodiode signals are converted to 20 MHz, intermediate frequency signals by two double balanced mixers (Miteq, model DM0520-LW1), then amplified in two Stanford SR445A amplifiers.

Fig. 1 .

 1 Fig. 1. Measurement set-up. L1, L2 : single-mode lasers, phase-locked to a frequency offset of 20.00 GHz. EDFA: 150 mW fibre optical amplifier. M : mixers. AOM : 160 MHz, double pass acousto-optic modulator, used to modulate optical power. Atten : fixed optical attenuator. Circ: optical circulator. Ref (meas) : high bandwidth photodiodes for the reference (measurement) signal. Phase + amplit.: signal data acquisition (during 10 µs, every 15 µs) followed by the calculation of the two amplitudes and relative phase.

Fig. 3 .

 3 Fig. 3. Static AM-to-PM characteristics at bias voltages of 12, 13, 14, 15, 16 and 20 V. EM4 photodiode. Data are not corrected for cross-talk.

Fig. 4 .

 4 Fig. 4. Phase transient after a sudden change of the optical power. EM4 photodetector biased at 15 V. One data (blue point) is plotted every 15 µs, and corresponds to the phase value over a 10 µs time slot, averaged over 100 successive 450 ms cycles. In yellow: fitting curves, see below.

Fig. 5 .

 5 Fig.5. Blue: phase transients with the EM4 photodetector (same data as Fig.4, with logarithmic time scale). Upper: rising; lower: falling optical power. In yellow: fitting curves with two exponential time constants. Dashed line, fitting curve with a single exponential. Data points before 50 µs are not reliable, due to the poorly controlled timing.

Fig. 6 :

 6 Fig. 6: Phase transient with the New Focus photodetector (blue points). In yellow: exponential fits (see text).

Fig. 7 .

 7 Fig. 7. Microsecond-scale transient behaviour of the phase after a sudden change of the optical power, for the two photodetectors under test. Data points are averaged over 4x10 5 samples. Inset: values of the parameters of the exponential fit: amplitude (radians) and time constant (µs). Residues of the fit (RMS values) are of 1.2% and 0.4% for the EM4 and New Focus photodiodes, respectively.

Fig. 8 .

 8 Fig. 8. Dependence of the amplitude of the short time (µs) transient behaviour of the phase, measured with the EM4 photodetector, as a function of the applied bias. The optical power is switched between 3.6 and 6.0 mW.

Fig. 9 :

 9 Fig.9: Geometry of the junction/substrate/heat sink assembly used for the simulations. Drawing is not to scale. The heat load is applied uniformly on the top side of the 1 µm thick cylinder that simulates the photodetector junction.

Fig. 10 :

 10 Fig. 10: results of the thermal transient simulation for the case of the EM4 photodiode, d = 32 µm, D = 450 µm, A = 152 µm (see geometry on Fig.9), material conductivity 68 Wm -1 K -1 and specific heat 0.31 Jg -1 K -1 . Heat load 112 Wmm -2 , corresponding to a Joule power of (6 mA)x(15 V). Note the x5 factor for the right scale.

Fig. 11 :

 11 Fig. 11: Influence of the substrate thickness (152, 500 and 1000 µm) on the time dependence of thermal transients of the photodiode junction. Calculated for junction diameter 32 µm and substrate diameter 450 µm. Time scale is logarithmic, as in Fig. 5.

Fig. 12 :

 12 Fig. 12: Detection set-up where optical demodulation replaces (on the measurement chain) electrical demodulation. Blue triangles: intermediate frequency amplifier.

ACKNOWLEDGMENT

We thank F. Bondu for comments and suggestions.