Internal Communication in Libraries

Are We Organizations 2.0?

Raphaëlle Bats1 Centre Gabriel Naudé, ENSSIB, France

I : Background and Purposes

The sub-theme "Organizations 2.0" of BOBCATSSS 2012 offered me a perfect opportunity to question what may be the internal communication at the time of these new communication tools whose watchwords are participation, interaction, sociability. And because internal communication is definitely a matter of management, can we say that today in the library, the roles of directors and leaders are changing with these tools that claim to be equalitarian, transparent, to break boundaries, to spread the untold? For beginning and having the first step for answering that question, we therefore investigated whether there is a use of Web 2.0 tools in internal communication in French university libraries.

Our first issue was to define on which tools to focus our investigation. If one classify quite easily in the Web 2.0 some tools for their unquestionable collaborative social and interactive aspects, then such is the case of social networks, blogs, wikis and microblogging, nonetheless some tools arouse some questions. Thus, should we consider that the chat is a Web 2.0 tool? As William Latzko-Toth says "[a] brief overview of the origins of the chat allows us to observe the concomitant emergence of two distinct modes of articulation of the chat, a rather instrumental, self-centered and focused on efficiency -whose device type is instant messaging -and the other, more user-friendly and oriented toward sociability in a virtual place -on the model of the electronic forum." (Latzko-Toth, 2010, p74) 2 . The Web 2.0 quality of the chat is not obvious and that tool is quite ambivalent. In addition, the mix of genres within the Web 2.0 with media which are related to a form of written communication (blogs, wikis) and other rather related to an conversational communication (Facebook, Twitter) makes it difficult to classify all the media under the same banner for internal communication.

Our second issue was to define the internal communication we want to study. We decided to focus on direct and informal communication, which would take over an oral communication that is common between two offices in a hallway, at the coffee break or the cigarette break. But today where project management has taken all its importance, we find that "What most characterize the current period and that is often overlooked by management is that the main vector of cooperation is precisely the direct communication at work (not just the organizational framework and managerial action)." (Zarifian 2010, p 137) 3

The more projects we launch in an institution, the more unclear become the roles of people because of their tasks, the higher is the "risk of fragmenting the social complexity and the organization" (Zarifian 2010, p 138). The informal or direct communication becomes absolutely necessary, yet by necessity replaced by remote communication. As noted, however, there media are playing on a more or less synchronous communication, or on an informal conversational style and are almost finally relays of current and virtual direct communication that is no longer in the corridors.

II : Materials, Procedures and Equipment Used

For such reasons, we decided to ask our colleagues about the following four informal media: Facebook and Twitter whose Web 2.0 aspect is unquestionable, the chat whose aspect is ambivalent, and the texting communication whose aspect are obviously not Web 2.0 like. So we launched in November 2011 a survey of university libraries' directors. Its purpose was to see if these tools were used in internal communication to communicate with their management team, in what situations they were, what information to share and with what physical media (personal or professional). The survey was created on Lime Survey, hosted by Enssib, broadcasted via my own blog 4 , my Twitter account 5 , the mailing list of ADBU6 and finally mails to colleagues working in university libraries. 37% are texting with their teams (figure 1) to advice on contingency (33.33%), to give appointment (22.22%), to inform on their presence or absence (18.52%), to sort out easy problems (18.52%) and to share updated information (11.11%). Business phones are used less frequently (11.11%) than personal are (14.81%). There is some indiscriminate use of mobile phones and professionals to 11.11% of responses. Finally, this mode of communication is privileged when the person is out of the facility (29.63%), it should be noted, however, an indiscriminate use between the outside and the facility to 7.41% of the responses and use in the facility but out of the office for the same response rate. No library director or university library director uses Facebook to communicate with his team (figure 2). Only one director of university library uses Twitter to inform his/her team about the unexpected, to sort out easy problems and finally to share updated information (figure 3). However, he/she does not use it to give appointment or to give notice of his/her presence or absence. He/she uses either professional or personal tools for twittering (telephones, computers, tablets). Finally, this medium is used both inside and outside the institution. Only one director of university library uses the chat to inform his team about the unexpected, to give appointments, to give notice of his/her presence or absence, sort out easy problems (figure 4). However he/she does not use it for updating. He/she uses only this chat when in the facility but outside his/her office and uses only without distinction computers or tablets either professional or personal. However, he/she does not chat via his/her phone.

III : Findings

IV : Discussion

Given these initial results, we conclude easily that our university libraries are far from being Organizations 2.0. The importance of using texting shows that the problem is not relying in the use of a nomadic and fast media but in the use of media that can be considered Web 2.0. These media being no longer new and getting started being easy, the know-how to use them is widespread. The reason of their low use is to be looked else-where.

The rise and fall of some medias can explain a refusal to get involved. On the other hand, for some people, these tools are not that serious and are much more characterizing a trend, rather an adolescent communication. Such a feeling is hardly compatible with the seriousness expected of an internal communication. Finally, these media seems to require availability that the directors do not feel compatible with their responsibilities. The publicity of Medias 2.0 can also be an issue for the involvement in that kind of communication and the question of the "privassionnal" (private-professionnal) line has to be questioned.

But foremost, maybe the main obstacle to these tools is their participative and collaborative aspects. In the study by Pan 2011, on the use of a blog in internal communication, the authors note how the leadership is not to be taken by the one with the official rank of director but by the one who has the skills at hand to deal with the current task. "Since they possessed equal rank and complementary roles, they created a shared leadership environment where each librarian shifted between leader and follower based on the circumstances and required expertizes" (Pan et al. 2011, p.348). The top-down model of internal communication that emphasizes the constructivist aspect manipulation and control of employees and in which the workplace is not a place of dialogue and exchange, must evolve [START_REF] Morillon | Nomadisme du modèle marketing, quelle appropriation dans les recherches actions en communication organisationnelle[END_REF]). The 2.0 media could play the role of internal communication and push micro-business communities, towards a model animated with the aim of recreating a corporate culture. "The contemporary thought considers corporate culture is built from the experience, knowledge and ways of thinking developed and shared socially. It consists mainly of micro cultures that are strengthened within groups of employees. These are forms of social relations and informal modes of behavior which are dynamic and have unique characteristics." (Massiera 2007, p 9) 7 . The Web 2.0 media gave us possibility to be internal community managers. But it is true that the management team requires taking decisions. Is there not then a risk of confusion between the direction given by an expert (leadership) and decision chosen by the official direction (management)? Maybe the solution is in a hybrid governance, part of top-down management, part of basis management. Medias 2.0 seem to offer us the opportunity of such a hybridity which the first step to a library 2.0. (CEFRIO 2011).

Conclusion

Our investigation is far from being over and we must finish processing the information on the felt about these tools, compare this with the use of these tools in external communication and finally launch the second survey of university libraries' management team. The form will be fairly symmetrical as above but modified in some methodological points: first, the number of incomplete responses will be limited with clearer headings, then useful information to know the sample will be request: place, discipline, size of library and of the managed team and finally, some items will be distinguished to be treated more easily. In conclusion, we hope to present next year the continuation of this work and to propose the modified survey to other countries to establish a European map of our libraries as organizations 2.0 or not. 7 Translation Philippe Larochette, Enssib

  66% of academic libraries have responded. This satisfactory result shows a real interest in issues of internal communication. At the time of this writing, the questionnaire wassent only three weeks ago and no stimulus was made. It is therefore hoped to reach a 75% response rate after a stimulus. The colleagues who have still considered the question of the use of these media in external communication have given most of the incomplete responses. They have generally responded negatively, and this suggests that they would have also answered "no" to the question of the use of these media in internal communication. The 25.42% complete responses provide us with the following results:

Figure 1 :

 1 Figure 1: Are you texting with your team? (Survey November 2011)

Figure 2 :

 2 Figure 2: Are you using Facebook with your team? (Survey November 2011).

Figure 3 :

 3 Figure 3: Are you tweeting with your team? (Survey November 2011)

Figure 4 :

 4 Figure 4 : Are you chatting with your team? (Survey November 2011)

Table 1

 1

	: Survey Results
		% compared to the total number of	% compared to the number of
		responses (72)	French University Libraries (118)
	Incomplete answers	58	35,5
	Complete answers	41,6	25,42

Great thanks to Philippe Larochette for the translation and to Benoît Epron for the presentation during the Bobcatsss conference.

Translation by Philippe Larochette, Enssib

Translation by Philippe Larochette, Enssib

http://crieurspublics.blogspot.com

@knitandb : https://twitter.com/#!/knitandb

French Association of the Directors of University Libraries


Soil susceptibity mapping as a proxy for exploration

Hervé Théveniaut, Clarke Brendan

To cite this version:

Hervé Théveniaut, Clarke Brendan. Soil susceptibity mapping as a proxy for exploration. 34th International Geological Congress, Aug 2012, Brisbane, Australia. hal-00711187

Soil susceptibity mapping as a proxy for exploration

Hervé THEVENIAUT, Brendan CLARKE 1 BRGM, GEO/GSO, 3 avenue C. Guillemin, BP 36006, 45060 Orléans Cedex 2, France. h.theveniaut@brgm.fr 2 20B Rothesay Avenue, Craighall Park, Johannesburg 2196, PO Box 81356, Parkhurst, 2120, South Africa. brendanc@msagroupservices.com Within the framework of a Eu funded geological mapping program in Ghana, hand field magnetic susceptibility measurements have been performed to allow petrographical comparison between similar outcrop facies. This method allowed identifying varying lithologies of similar facies in north-western Ghana (Bole area). It completed geological observations, petrographical and geochemical analyses to facilitate geological mapping.

Another experiment was tested on a more weathered area in the southwestern zone of Bogoso marked by a more tropical climate. Susceptibility measurements revealed only the level of weathering. We therefore replaced such method by applying hand field susceptibility measurements on collected soil samples for soil geochemistry.

Around 3000 measurements were done on a 0.5° square map. Magnetic susceptibility signal was therefore used as a proxy for mapping and showed more consistency with radiometric images rather than aeromagnetic images. This method revealed a good agreement with petrographical, even though on weathered rocks, field observations. Comparison of these results with soil geochemical analyses also revealed good consistency with the main mineral anomalies offering the possibility to use such tool as a proxy for mineral exploration.


Hervé Theveniaut
email: h.theveniaut@brgm.fr

Claude Delor

P M Ndiaye

D P Diallo

E Dioh

Paleoproterozoic evolution of Senegal in the Birimian Framework

The whole of East-Senegal Birimian terrains have been investigated with a pluri-thematic approach combining airborne geophysics, field mapping, geochemical and isotopic data. Birimian Easternmost Paleoproterozoic terrains begins with the Mako Group of volcanics and metavolcanics, all assumed to have been emplaced at 2.20-2.18 Ga as a juvenile crust.

Reworking of this Eo-Rhyacian crust is recorded with evidence of melting processes and associated products. At the scale of the Mako Group, the Mesorhyacian Sandikounda-Soukouta granodioritic suite and coeval intermediate to acid volcanism (2.18-2.14 Ga) reflect the consumption of the Eorhyacian juvenile crust during early collision stages.

The breakup of Eo-Rhycian rocks, between 2.14 and 2.10 Ga has resulted in the formation of a main detrital basin that is now referred as the Dialé-Daléma Group. Main lithologies include silicoclastic deposits among which carbonate formations have been found. The upper part of this Group is characterized by the presence of acid to intermediate volcanics dated at ca. 2.1 Ga The Saraya granitic suite dated at 2.10-2.08 Ga, is mainly recorded in the DD Group with emplacement of the main Saraya batholith and peripheric plutons. It is characterized as a syntectonic magmatic pulse generated in a tectonic context dominated by strong senestral shearing and melting of silicoclastic sources. The specific emplacement of the more Mg-K Boboti magmatic suite is recorded between 2.08 and 2.06 on the easternmost Birimian areas, with evidence of high temperature magma.


Mohamed Bizi
email: m.bizi@brgm.fr

Stability and flocculation of nanosilica by conventional organic polymer

Keywords: Bridging flocculation, Coagulation, Nanoparticles, Nanotechnologies, Silica, Zeta potential

More than 2 000 000 tons of silica nanoparticles (NPs) are produced annually in the world to cover the needs of nanotechnologies. Inevitably, a quantity of NPs, will be in industrial discharges and domestic, or even in water resources. Share their high surface reactivity, these NPs may also carry with them through a specific adsorption of other toxic chemical pollutants inherent to the industrial sectors.

To preserve public health and the environment from this pollution, it is necessary to remedy the potential pollution. In this context, the main motivation of this work is to answer this environmental issue by proposing a scheme of remediation based on the use of a conventional treatment process. The process of elimination nanoparticles by coagulation / flocculation was selected for its simplicity and also for its universal use. The NPs of industrial silica S30R50 were used as support to develop the process.

The optimization of coagulation

/ flocculation, was greatly facilitated by the use of laser diffraction online. This technique allowed to follow the dynamic character of the treatment and to determine the size and the most relevant textural parameters (density, porosity and fractal dimension) of the flocs depending on the nature of the used reagents. The critical concentrations of different coagulants and flocculants used were determined by electrophoresis and turbidity. The ratio of their charge density / molecular weight has conditioned the quality of separation, the floc size and their texture. Excellent coagulation/flocculation performances are reached using organic reagents authorized by the Directorate General for Health of several countries. After optimization of the process, the size distributions are between 10 µm and 1 mm, with fractal dimensions (compactness) ranging from 2.3 to 2.5. The performances obtained show that the use of cationic polymers is a promising potential route to treat other types of NPs. The treatment proposed to reach a ratio of average diameters d Floc /d NP of 3500, and therefore it facilitates the elimination of these NPs agglomerated by filtration

Introduction

The current surge in nanotechnologies has been made possible by recent technological progress. They are already widely used in industry to synthesize new products with new properties, making it possible to satisfy the expectations of the consumer society. The nanomaterials on the market are therefore used in many fields, from electronics to medicine, including textiles and surface coatings. It is expected that NPs will soon be omnipresence in products used in every-day life, and this will entail a remarkable socio-economic revolution.

The factors that confer these materials with new properties and might present a risk are size, particle shape, form factor (ratio between extreme dimensions), size distribution, specific surface, chemical composition, surface charge, surface reactivity, stability, dispersion behaviour and crystallinity [START_REF] Oberdörster | Toxicology of ultrafine particles: in vivo studies[END_REF][START_REF] Banfield | Nanoparticles and the environment. Reviews in mineralogy and geochemistry[END_REF]. Particles are considered to be nanometric when one of their dimensions is between 1 and 100 nm.

The most common nanoparticles used for consumer products are metallic nano-oxides (SiO 2 , TiO 2 , ZnO, CeO 2 , Al 2 O 3 , etc.), gold, nano-silver and nano-clays. Silica, for example is used in tyres, paints, solar panels, sports equipment, cleaning products and dietary supplements. It is by far the most vastly produced. In France, it represents around 500,000 tonnes, or 2 times more than TiO 2 , the second type of NP manufactured.

Nevertheless, this enthusiasm for nanotechnological progress goes hand in hand with a growing awareness of the inherent environmental and toxic impacts. The nanometric size of nanoparticles makes them relatively mobile in the environment, bioavailable to living organisms, and therefore potentially toxic. Furthermore, their large specific surfaces and surface reactivity facilitates their bio-physico-chemical interaction with environmental components. Special attention must therefore be paid to the fate of nanomaterials when they are discharged into the environment, either accidentally or in the course of their normal use.

They will inevitably end up in industrial waste, then solid municipal waste, or even water resources. In the environment, NPs can disperse, aggregate, adsorb other soil pollutants or be absorbed by organisms depending on the media's physico-chemical properties.

At the present time, no monitoring is being done to take into account risks that might be caused by gaseous, solid or liquid waste containing NPs. However, in all industrialized countries, governments recommend the treatment of this waste at the source. For example, Article 191 concerning the environment in the consolidated version of the Treaty on European Union states, "Union policy on the environment shall aim at a high level of protection taking into account the diversity of situations in the various regions of the Union. It shall be based on the precautionary principle and on the principles that preventive action should be taken, that environmental damage should as a priority be rectified at source and that the polluter should pay."

In this context, and considering the quantities of silica produced and its various uses and methods of manufacturing, it is crucial that industrial waste rich in silica NPs be treated.

Treatment processes must also be developed and implemented at the source of effluents.

Silica NPs can also transport, by specific adsorption, other chemical pollutants inherent in the original industrial sectors. Their reactivity with pollutants is much greater than that of larger silica particles [START_REF] Yean | Effect of magnetic particle size on adsorption and desorption of arsenite and arsenate[END_REF]. The hydrated silanol groups at the surface of silica induce strong polarity and high surface free energy. Our aim is to reduce the risk of pollution by eliminating silica nanoparticles in water. We suggest using flocculationthe least-expensive solid/liquid separation method.

The basic material chosen for this study is a nanometric amorphous silica used by industry in catalysis, coating/paint, polishing and textiles [4,5]. Nanosilica is marketed as a pulp and meets the specifications of these industries. It is pure (>99 %), its particles are spherical, and they have an almost uniform size distribution.

In terms of pollution, the example most often cited is that of post-polishing effluents. The major contamination is metallic. During chemical mechanical polishing (CMP), around 10 12 at./cm² of metallic atoms are liberated [5]. In effluents, depending on mechanical, electric and physico-chemical properties, the silica NPs can be single or complexed with any pollutants present.

This paper is an introduction to all initiatives to treat effluents of industries using NPs, with and without contamination. Its aim is to evaluate the behaviour of NPs when subjected to solid/liquid separation by coagulation and flocculation. It addresses the key points of a future global environmental study:

-the basic characterization of this product; -the stability of this silica as a function of pH; -the methodology of treatment at the source of an effluent rich in silica NPs, which requires that suitable materials be identified.

The originality of this work resides in the treatment of a nanometric product widely used in industry, smaller than 100 nm, as a highly diluted suspension (0.1 g/L). The use of reagents that are currently certified and authorized by the Directorate General of Health is one of the strengths of this procedure.

Materials and methods

Material

The silica nanoparticle suspension used was supplied by the Clariant Corporation. It is marketed under the name "Klebosol 30R50". It is made up of spherical amorphous silica nanoparticles with an average diameter of 50 nm, according to Clariant, and is 30 % in solid concentration. The suspension is stabilized in an alkaline environment where total Na 2 O is less than 0.2 %. It has a pH of 8.7  0.1. "R" indicates antibacterial protection [4].

Methods used to characterize silica NPs

The NPs were diluted to 10 mg/L and observed directly with a Philips C200 Transmission Electron Microscope (TEM). Density and specific surface were determined on a sample that was freeze-dried and degassed at 110 °C to a residual vacuum of 2 Pa.

The density was determined by helium pycnometry using a MicroMeritics AccuPyc 1330.

The specific surface was measured by nitrogen adsorption using the BET method [START_REF] Brunauer | Adsorption of gases in multimolecular layers[END_REF] with a MicroMeritics ASAP 2010 adsorptometer for relative pressures between 0.02 and 0.2. The size of the nitrogen molecule at 77 °K is set at 0.162 nm².

The particle size distribution, zeta potential and treatment were done on a secondary suspension prepared from the stock solution with Milli-Q water (resistivity 18 M/cm) at a concentration of 0.1 g/L and an equilibrium pH of 6.1 0.1 at 20°C. The turbidity of this diluted suspension is 18 1 NTU (the suspension is almost transparent). It was measured with turbidity meter Turb 555 IR (= 860 nm).

Size distribution as a function of pH was determined with a Zetasizer Nano ZS (Malvern Instruments Ltd., UK). This apparatus determines the size by first measuring the Brownian motion of the particles in a sample using Dynamic Light Scattering (also know as Photon Correlation Spectroscopy or PCS). It does this by illuminating the particles with a laser and analysing the intensity fluctuations in the scattered light. The rate of the intensity fluctuation is used to calculate the size of particles. The relationship between the size of a particle and its speed due to Brownian motion is defined in the Stokes-Einstein equation (Eq.1). The particle size measured is the hydrodynamic diameter of the sphere that diffuses at the same speed as the particles being measured. The basic distribution obtained from a DLS measurement is intensity. All other distribution is generated from this.

i D kT  3 d H  (1)
Where d H is the average hydrodynamic diameter, D i is the average diffusion coefficient, k is the Boltzmann constant, T is the absolute temperature and  is the dynamic viscosity of the solvent.

For consistency when analysing data obtained before and after flocculation, size distributions are all given in volume.

The refractive index used for the determination of particle size is 1.467 (~1.47). This value was obtained from the linear relationship (Eq. 2) between the refractive index and the density of silica (silica polymorphs) with no chemical impurities [START_REF] Marler | On the relationship between refractive index and density for SiO 2 polymorphs[END_REF]. Measuring the refractive index at a wavelength of 632.8 nm by m-line spectroscopy on an amorphous silica substrate having a density of 2.203 g/cm 3 gives an index of 1.4702 [START_REF] Murillo | Elaboration, propriétés structurales, optiques et spectroscopiques de films sol-gel scintillants de Gd 2 O 3 et Lu 2 O 3 dopés Eu 3+[END_REF], which is almost identical to the calculated value.

999

. 0 047 . 1 189 . 0 2    R with n S  (2)
Where n is the refractive index,  S is the average density of the solid and R² is the coefficient of determination.

Electrokinetic potential (zeta potential) was measured with a Zetasizer IV (Malvern Instruments Ltd). The Zetasizer IV uses electrophoresis to determine this potential. The electrophoretic mobility is related to the zeta potential of the particles by the Henry equation [START_REF] Henry | [END_REF]. Knowledge of the sign and value of the zeta potential is important since the surface charge governs the stability or state of dispersion, the choice of the type of coagulant and/or flocculant to be used to obtain a good agglomeration and the reagent concentration. This parameter must, therefore, be determined as a function of pH.

  r f e        1 (3)                        3 1 2 1 1 3 2 r r f    (4) Ohshima's approximation [10]     r      exp 2 1 5 . 2 (5)             e and r f then r if 1 (6) Smoluchwski's formula        
Silica immersed in water acquires a pH-dependant surface charge. The extent and the sign of this surface charge depend on the H + and OH concentrations in the solution. The surface charge appears during immersion as silanol surface sites become hydrated [START_REF] Carman | Constitution of colloidal silica[END_REF][START_REF] Iler | Colloid chemistry of silica and silictes[END_REF]. They can then be ionized, depending on pH, as described by the following reactions:

SiOH +H + ⇋ SiOH 2 + (8) SiOH +OH -⇋ SiO - + H 2 O (9)
The solid can therefore be considered to be an ion exchanger whose exchange capacity is pHdependent. To these acid-base equilibria associated with the Si-OH surface sites, we must introduce reactions of the charged sites (SiOH ) introduced to control the pH [START_REF] Kent | Surfacecomplexation modeling of radionuclide adsorption in subsurface environments[END_REF].

SiOH 2 + + Cl -⇋ SiOH 2 + …Cl - (10) SiO
- + Na + ⇋ SiO - …Na + ( 11
)
This suite of equilibrium reactions leads to a given surface charge as well as to a distribution of charge farther from the interface.

This potential was measured at 20 °C and the pH was adjusted with HCl or NaOH.

Nanoseparation

Solid/liquid separation by coagulation and flocculation is done to provide clean water containing no NPs. The basic principle is to agglomerate the NPs, turning them into visible entities that can settle rapidly and/or be removed by classical filtration, which is already part of water treatment processes. We must, therefore, use non-toxic reagents that respect the environment and develop dense flocs larger than 10 µm, with low permeability and a fractal dimension of around 3. To do this, a well-targeted set of reagents was selected. Combinations of 4 organic coagulants and 3 flocculants supplied by SNF-FLOERGER were tested. The coagulants are in liquid form and the flocculants are powders. They were prepared at concentrations of 2g/L and 0.5g/L, respectively. Tables 1 and2 give their main characteristics. The best combination was determined by jar test with 6 identical reactors.

Each of these was equipped with 4 orthogonal baffles and a 5.1 x 5.1 mm square, singleblade, leaf-type, stainless steel agitator [START_REF] Bizi | Contribution of static light scattering to the textural characterization of large aggregates[END_REF]. The volume of the suspension in each reactor was 0.8L at a concentration of 0.1 g/L. Coagulation was done at 300 rpm (G =583 s -1 ) for 10 min, followed by flocculation at 100 rpm (G =133 s -1 ) for 5 min. The average gradient values applied were calculated using the power curve of these reactors [START_REF] Bizi | Contribution of static light scattering to the textural characterization of large aggregates[END_REF]. During conditioning, the contact between particles is caused by the differences in velocity gradients created in the suspensions by mechanical mixing. This is an orthokinetic mechanism. Under these conditions, perikinetic aggregation (particle collisions caused by Brownian motion) is insignificant.

In the nomenclature for coagulants and flocculants, the first two numbers indicate molecular mass, FL 4520 having a lower mass than FL4820. The proportion of active matter is indicated by the 2 last numbers. The charge density is expressed as a percentage of ionogenic group relative to all groups. When the exact information about charge density and molecular weight is not accessible for the commercially available materials, the approximate categories of high, medium and low will be used, as defined in table 2. M: standard molar mass not given. L: Linear.

Polyamines and PolyDADMACs are organic coagulants that may completely or partially replace the inorganic coagulants (aluminium sulphate, aluminium perchloride, ferric chloride, etc.). These substances are approved for drinking water in many country. For confidentiality reasons, SNF-FLOERGER does not provide the molecular weight of coagulants. These flocculants are used to treat drinking water, waste process water, municipal sewage and ores.

The solid/liquid separation method used here is based on the neutralization of the negative charge of the silica with the coagulant, followed by bridging flocculation.

The concentration needed to neutralize the charge of the silica was determined by testing with solutions having increasing cationic coagulant concentrations, after which the zeta potential and turbidity were measured. The optimum coagulation concentration (OCC) is the quantity of coagulant that results in zero zeta potential and maximum turbidity.

This was determined by observing the evolution of the electrophoretic mobility and turbidity of the suspension of NPs in the presence of increasing concentrations of coagulant. On an industrial treatment site, a turbidimeter can be used instead of a zeta potential meter. These are easy to use and very inexpensive.

The test with each coagulant was done for each concentration on 100 mL of NP suspension at 0.1 g/L, mixed with a magnetic stirrer at 500 rpm for 15 min in a 125 mL beaker with an internal diameter of 5 cm. Turbidity and electrophoretic mobility measurements were done on samples collected during mechanical mixing.

The optimum flocculant concentration (OFC) is estimated by jar testing. The experimental matrix investigated is made up of 4 coagulants and 3 flocculants selected. The three flocculants were tested for or each previously determined OCC. For each combination, conditioning was done at a velocity gradient of 583 s -1 for 10 min for coagulation and then at 133 s -1 for 5 min for flocculation. The same stirring rate was used in the 6 beakers of the jar test. The OFC was determined after stirring had been stopped by measuring the turbidity in the supernatant in the suspensions after 15 min of settling. It is the quantity of flocculant that results in the lowest turbidity.

Method used to characterize floc size and structure

After the optimum coagulant concentration for neutralization had been determined and the best flocculants had been selected by jar test, flocculation was optimized by measuring the particle size with a Malvern MasterSizer S laser granulometer. This apparatus was equipped for the study with a 1 L vessel with a tap in its bottom that enabled the drawing off of the suspension to the analysis cell. Circulation through this cell is done in a fully hydraulic open circuit with a flowrate controlled by the head and by the centrifugal pump at the outlet.

This reactor tank is also equipped with four orthogonal riffles and a single-blade sheet-type impeller (tangential-flow system). The impeller makes it possible to reach high velocity gradients for fairly low speeds while decreasing the turbulence heterogeneity in the stirred volume. This flocculation tank configuration reproduces quite well the hydrodynamic characteristics of an industrial flocculation box. The mean gradient values during the conditioning are calculated on the basis of its power curve [START_REF] Bizi | Contribution of static light scattering to the textural characterization of large aggregates[END_REF].

The granulometer's short optical bench with an analysis cell having a 2.4 mm optical path was used for sizes between 0.1 and 878 µm. For sizes between 4.2 and 3473 µm, the long bench was used with a specially manufactured cell having a 10 mm optical path. Optical data was exploited using the Fraunhofer optical model for diameters greater than 3.2 µm (5 0 ) and the Lorentz-Mie theory [START_REF] Van De Hulst | Light scattering by small particles[END_REF] for smaller particles. The refractive index for silica is 1.47 and the extinction index is 0.

The laser diffraction measurements also provide information on the average porosity, the average density and the average fractal dimension of the flocs according to the following equations [START_REF] Bizi | Contribution of static light scattering to the textural characterization of large aggregates[END_REF]:

S V S F C C       2 10 1 (12) F L F S F           ) 1 ( (13)
Where  F is the average floc porosity, C s is the solid concentration kg/m 3 ,  F is the average floc density kg/m 3 ,  s is the average solid density in kg/m 3 ,  L is the fluid density in kg/m 3 and C v is the volume concentration of the flocs measured by the granulometer in %.

For fractal aggregates, it can be shown that [START_REF] Kerker | The scattering of light and other electromagnetic radiation[END_REF][START_REF] Guinier | Small angle scattering of X rays[END_REF][START_REF] Bohren | Absorption and Scattering of Light by Small Particles[END_REF] the total scattered intensity will exhibit a power law dependency on the amplitude of the scattering vector q; i.e.

For R g << q << r 0 , I (q)  q -D F (14)

       2 sin 4 0 0   n q (15)
Where q is the amplitude of the scattering vector, R g is the radius gyration of the aggregate, r 0 is the primary particle radius and D F the mass fractal dimension. q is a function of the wavelength of the incident beam ( 0 =0.632 µm), the refractive index of dispersion medium and the scattering angle.

It is therefore possible to determine the mean fractal dimension of the aggregates from the curve of log(I(q)) versus log(q). Over the interval [R g , r 0 ], the curve then displays a linear segment with a slope equal to -D F .

Results and discussion

Morphological characterization of silica NPs

Various enlargements were made of the microscope images (Fig. 1). The analytical approach entailed characterizing the material at different scales in order to see granulometric details.

Minor magnification shows that the material is homogeneously distributed. Major magnification (x 50,000 to x 88,000) reveals the presence of several particles in groups of, at most, 2 or 3 particles. There are relatively few of these in the images studied. The strings of beads observed in a magnification x 20,000 very probably formed when the grids were dried. On all of the images studied, particles appear to be almost circular and, for the most part, between 50 and 80 nm in diameter. The largest size observed is about 190 nm. This corresponds to the Feret's diameter of 3 connected particles.

The density of this material measured by helium pycnometrie is 2.222 0.001 g/cm 3 and its BET specific surface is 45 2 m 2 /g.

Physico-chemical stability of silica NPs

To monitor the mobility of NPs in the environment, it is necessary to determine NPs stability boundary conditions as a function of pH and ionic strength. We therefore investigated, as a reference study, the behaviour of these NPs in terms of size and zeta potential as a function of pH with no salt added. The NPs were dispersed in MilliQ water at a concentration of 0.1 g/L (SiO 2 at 0.01 wt.%). The appearance of the prepared suspension is between opalescent and transparent. Its turbidity is 18  1 NTU and its natural pH is 6.1  0.1. The pH was then modified with HCl or NaOH. Measurements were done at 20 °C after one day of stirring.

Size distribution

The evolution of the hydrodynamic diameter (d H ) determined with NANOZS as a function of the suspension pH is given in figure 2. The particles i) aggregate for pH below 3, ii) are stable at  1 nm for pH between 3 and 9, iii) decrease in size from pH 9 to 11.

The increase in the mean diameter between pH 3 and 1.8 indicates an increasing agglomeration of particles fostered by the drop in pH. This monotonic increase also implies that the zero point of charge pH ZPC is certainly below pH 1.8. The flocculation yield in this acid pH interval hardly exceeds 30 %, a maximum value obtained for pH 1.8 (Fig. 2). At pH 1.8, the size is between 44 and 340 nm.

The decrease in size beyond pH 9 is due, to some extent, to the compression of the diffuse double layer and, to a large extent, to a partial solubility of the particles. These NPs that have a very small diameter and a high surface tension are therefore particularly sensitive to dissolution phenomena. This point corresponds perfectly to the beginning of silica solubilization [START_REF] Michard | Chemical balances in natural waters[END_REF].

The size of these NPs is between 100 and 44 nm for pH between 3 and 9. They have a stability range much broader than those of magnetite, CeO 2 or TiO 2 NPs [START_REF] Bizi | French National Research Agency Report[END_REF]. This great stability implies that the surface charge of this product is high within a rather broad pH range.

Zeta Potential

Figure 3 shows the evolution of nanosilica zeta potential in water as a function of suspension pH. For (r) Ohshima approximation is used (Eq. 4). The potential becomes increasingly negative with increasing pH.

In the acidic pH range, the zeta potential is linear with pH. Consequently, there is almost no complexation of charged sites with the Cl Since the silica surface charge is negative, the problem can be simplified by disregarding equations ( 8) and ( 10 The result obtained is therefore largely attributed to:

SiOH +OH -⇋ SiO - + H 2 O (9) SiO
- + Na + ⇋ SiO - …Na + (11)
Many authors have reported that the surface charge of silica is negative for a very wide range of pH values [START_REF] Bolt | Determination of the Charge Density of Silica Sols[END_REF]. It is also accepted that the structure of silica is open enough so that the coordination number of each surface atom can still increase [START_REF] Iler | The Chemistry of Silica : Solubility, Polymerization, Colloid and Surface Properties and Biochemistry of Silica[END_REF][START_REF] Prezzi | Alkali-silica reaction. Part 2: the effect of chemical additives[END_REF].

For pH values between 1 and 6, the zeta potential can be represented by a straight linear regression line that intersects the x-axis at pH 1.47 0.03 (=-14.68pH+21.55, R²=0.997).

This point is, by definition, the pH of zero point of charge (pH ZPC ) of this silica sample. This value is in agreement with literature data. The pH ZPC of quartz is 1.4 [START_REF] Cases | Point de charge nulle et structures des silicates[END_REF]. This point is defined as the pH value for which the surface of particles is globally neutral. In this case, the repulsive forces between the particles are too weak to oppose aggregation. The agglomeration threshold is set at pH 3 according to the particle size analyses (Fig. 2).

When pH increases, the state of the suspension goes progressively from maximum flocculation (=0 mV) to good stability, which it reaches in a strongly basic environment.

This state is well illustrated by the results of the particle size analysis as a function of pH figure 3.

The solubility of amorphous silica becomes significant at pH values above 9 [START_REF] Michard | Chemical balances in natural waters[END_REF]. This dissolution process forms silicate HSiO 3 ions that behave like an electrolyte, increasing the charge. Therefore, at high pH, the increase in the surface charge is due to both the addition of sodium hydroxide and silica dissolution.

Nanoseparation

Optimization of coagulant concentration

Before we can set up the solid/liquid separation process for a given physico-chemistry, we must determine the optimum concentrations of the reagents to be used. The first phase consists therefore in determining the optimum concentrations of coagulant and then of flocculant.

When coagulants are added, pH variations remain insignificant (less than 0.1 pH unit). The variations in electrophoretic mobility as a function of added amounts of cationic polymers correspond to the classic neutralization curves. Increasing the polymer concentration (Fig. 4) results in a decrease in the absolute value of the electrophoretic mobility, going through the isoelectric point, and then an increase of up to a horizontal asymptote located at an electrophoretic mobility lower than that of the uncoagulated product. In turbidity (Fig. 4), the function increases up to a given value, decreases forming secondary maxima, and then stabilizes, plateauing slightly above the initial turbidity. The isoelectric point and the maximum turbidity for each coagulant correspond to the optimum coagulation concentration.

The shape of these curves reflects the various coagulation states. The reactions can be broken down into three states:

-Simultaneous neutralization and bridging between the beginning and the isoelectric point (IEP) (maximum turbidity).

-A combination of 2 conditioning mechanisms between the IEP and the first plateau (turbidity between the first and last maxima). There is competition between neutralization/bridging and steric stabilization beyond the IEP. Steric stabilization increases with the coagulant concentration to the detriment of neutralization/bridging.

-Total steric neutralization corresponding to the individual neutralization of each particle.

This mechanism causes a redispersion of particles in solution as a result of a reversal of charge within the solution. The near-environment of a particle surface can then be entirely occupied by hydrophilic polymer chains that generate a repulsive hydration force. This is observed when the coagulant concentration is high enough so that all of the particles are rapidly covered.

The non-return to the initial turbidity after steric stabilization is due to the coating of the particles by the polymer and to the presence of free coagulant in solution. In this way, the value of the refractive index for the suspension is modified and, consequently, also that of the turbidity [START_REF] Gregory | Rates of flocculation of latex particles by cationic polymers[END_REF][START_REF] Gregory | Flocculation by polymers and polyelectrolytes[END_REF]. These configurations are represented by figure 5. The first state corresponds to the path from a to c1 and the last to a path from a to c2.

The transition from destabilization (IEP) to steric stabilization follows a competition between the increase in the number of individual coated nanoparticles and the decrease in the formation of aggregates.

The optimum concentration is the quantity of coagulant that does not adsorb uniformly on the entire surface of each particle and that produces electrically neutral aggregates (Fig. 5). Each active cluster of coagulant adsorbs on at least two particles and the neutrality of the electrical charge of each particle is ensured by at least 2 active clusters. The particles having surfaces with opposite charges can therefore touch, leading to the formation of an aggregate by neutralization of surfaces with opposite charges. The number of NPs per aggregate, its diameter and its texture depend on the nature of the coagulant and the applied hydrodynamic conditions. 17 Figure 6 shows the influence of the ratio of charge density to molar mass. Below the IEP and for high charge densities (FL2250 and FL2565), the adsorption curve is concave (rapid recovery) and the adsorption kinetics are rapid. Conversely, for low charge densities and high molar masses (FL4520 and FL4820), the adsorption curve is convex (slow recovery). These two behaviours correspond to two different adsorbed polymer conformations. The presence of long hooks and loops for 20 % cationicity, and a flat conformation for cationicities between 50 and 65 %. The molar mass associated with cationicity enables us to explain the behaviour of the 2 coagulants and these two last cationicities. For the same concentrations, the FL2250 coagulation performance is lower than that of FL2565. This is due to the difference in the length of the chains of these two coagulants. The free, non-adsorbed parts of the polymers are not the same size and therefore their agglomeration efficiency is different (Table 5).

The OCC of the polymers can therefore be optimized with reference to the molar mass and the cationic charge. The OCC obtained are given in Table 3. The lowest value is given by coagulant FL2565, which has the highest charge density. The OCC obtained decrease with the percentage of active matter and therefore the effective charge used for coagulation (Fig. 7).

Table 3 Optimum coagulant concentrations (OCC) at  0.1 (mg/g). Méthode FL2250 FL2565 FL4520 FL4820 Turbidimétrie Electrophorése It is difficult to predict, based on the physico-chemical characteristics of a suspension, which reagent will give the best results. Indeed, the efficiency of a flocculant depends on numerous, and in some cases contradictory, factors related mainly to the nature of the suspension to be treated, to the design and use of the installation and how the flocculant is used.

In order to optimize our search for the best reagent for the suspension studied, 8 flocculants were tested using the jar test. These polymers are all cationic, with different molar masses and concentrations (OFC) of between 2.8 and 3.12 mg/g. This last value was used for the study of floc texture in spite of the fact that it is in excess in the case of FO4990SH.

Coagulation and flocculation were done in the 1-liter reactor described above. The performance of this reactor is similar to those of industrial flocculation containers [START_REF] Bizi | Flocculation analysis and control system by laser diffractometry at industrial scale[END_REF].

Moreover, this one-dimensional reactor is energy efficient.

The coagulants were conditioned under a gradient of 583 s -1 for 10 min. This set of parameters was selected following a kinetic and hydrodynamic study that is not discussed in detail here. An example of the impact of the duration of conditioning on the mixing efficiency and on the fractal dimension is summarized below (Table 4). After 10 minutes, we observed a very compact population of aggregates having a very high fractal dimension and a very limited size distribution. 10 minutes is a turning point after which the size of microflocs and their fractal dimensions vary relatively little. After 10 minutes, the microflocs are more resistant than those obtained in less than 10 minutes and are similar to the microbeads obtained after 120 minutes. The performances of the 4 coagulants selected in terms of size and fractal dimension are given in table 5. FL2250, a polyamine with a low molar mass (Table 1), gave the poorest results. It aggregated the mineral particles much less well. The flocs obtained with this coagulant were weak (Fig. 8) [START_REF] Thouy | Structure Factors for Fractal Aggregates Built Off-Lattice with Tunable Fractal Dimension[END_REF], had a fractal dimension of 1.96 and a very broad size distribution, DSI = 37. Indeed, with short chains (low molar mass), the surfaces are isolated without causing a great formation of bridges between mineral surfaces. The performances of the other coagulants are similar, even identical for FL4520 and FL4820. The fractal dimensions of these 3 reagents are similar and represent very compact structures (Fig. 8). In light of these results, we chose to continue the coagulation/flocculation treatment only with FL2565 and FL4820.

Fig. 8 -Two-dimensional projections of typical three-dimensional aggregates of 4096 primary particles obtained for D F = 1.5 to 2.5 [START_REF] Thouy | Structure Factors for Fractal Aggregates Built Off-Lattice with Tunable Fractal Dimension[END_REF].

Flocculant performance

The main characteristics of the flocculants used are given in table 2. The coagulation required a rather rapid stirring rate in order to mix the suspension well and bring the various small entities (NPs/polymers) into contact. Flocculation, however, requires a relatively slow stirring rate in order to foster contact and the aggregation of the microflocs into larger flocs without breaking the flocs that have already formed.

The most relevant textural parameters are given in table 6. In terms of particle size distribution, the treatment used for the 3 combinations selected conditions the product in populations of large homogeneous, almost monomodal flocs (Fig. 9). The proportion of small flocs is almost insignificant compared to the central population. The smallest diameter observed in the 3 particle size analyses is about 4 µm, which is 47 times larger than the average diameter of the untreated product. Where t is the time, dmL is the average diameter measured by laser diffractometry, dx is the diameter corresponding to x% of cumulative undersize by volume (x=10, 50 or 90), DSI is the spread index expressed by the ratio (d90-d10)/(2d50), D F is the masse fractal dimension,  F is the average floc porosity,  F is the average floc density and  is the turbidity. The existence of a population of small flocs is related to the flocculation process. As flocculation proceeds, the formation of large flocs decreases, the number of particle collisions drops and, as a result, a certain number of microflocs are not aggregated. The shapes of the 3 distributions is similar (Fig. 9). This suggests that the floc formation conditions are identical and the observed differences in size range are a result of the nature of the reagent used. The smallest variation is observed with the FL2565/FO4550 combination, which also fosters the formation of the densest and most compact flocs (fig. 8). Table 6 shows that the density decreases rapidly as size increases, which indicates the formation of increasingly open structures characterized by an increasingly low fractal dimension. This shows that the average fractal dimension is a constant that reflects both the initial state of particle coagulation and the role and nature of the added flocculant. 6b). DLS particle size analyses done on these samples after sieving at 10 µm did not reveal the presence of NPs. The measured intensities are nil.

Concerning sedimentation, the size of the flocs and their size distribution, d10 in particular, govern most of the variation in the floc decantation rate. Literature references indicate that water flow through porous intra-floc space can also influence the decantation rate of the most porous, granular flocs that have sufficient permeability. For a given density and size, the sedimentation rate of a porous and permeable sphere is greater than that of a compact sphere.

Fluid circulation in the pores increases the velocity, under laminar flow and at the beginning of transient flow, for a porous sphere compared to a non-permeable sphere having the same size and average density [START_REF] Matsumoto | Settling velocity of a permeable model floc[END_REF].

This criterion, based solely on clarity, does not, by itself, enable us to select a combination. In the absence of measured decantation rate data, it is preferable not to make a selection, especially since this treatment will be part of a solid/liquid separation process that includes filtration.

Conclusion

The aim of this work was to contribute to the study of the stability of silica NPs (nanosilica)

and to the development of a methodology for their destabilization by coagulation-flocculation.

The aggregation process proposed here uses standard organic reagents and involves the characterization on line by laser diffractometry of the aggregates formed. The results obtained depend on the nature of the solid phase, the physico-chemical properties of the NP suspension, the nature of the aggregation reagents and the hydrodynamic conditions of stirring and mixing.

In an effort to attain good performance, we used cationic organic coagulants. These have advantages compared to common reagents like iron or aluminium salts. They are used in low concentrations and have a low impact on the pH of the suspension. Under fixed hydrodynamic and physico-chemical conditions, the nature of the coagulants chosen was a determining factor for the success and the optimization of the separation process. The ratio of their charge density to their molar mass governs the quality of the separation and the floc size and texture.

Aggregation was also fostered by the NPs' surface energy.

Reaching our objective was greatly facilitated by the use of laser diffractometry on line. This technique also enabled the determination of the porosity, density and fractal dimension of the flocs, although not the size distributions.

The performances obtained show that the use of cationic polymers is a promising process for treating other types of NPs. However, prior to industrial use, a hydrodynamic study of the process should be carried out in order to determine the impact of the process on floc aggregation and rupture phenomena and on their structure. Efforts must be made in this direction to better understand the relationship between structure and size, the consequences on floc cohesion and permeability and, lastly, on filtration.

Future work might involve the inclusion of this process in an industrial flowsheet entailing coagulation-flocculation and filtration.

( 7 )

 7 Hückel's formula (r) is the Henry correction factor. It depends on the size of the particles, their form factor and the ionic strength of the environment by taking into account the thickness of the diffuse layer (1/).

Fig. 1 -

 1 Fig. 1 -TEM image of S30R50.

Fig. 2 -

 2 Fig. 2 -Evolution of the average diameter as a function of pH and the Size distribution of S30R50 for the most significant pH values.

-counterions.

  An increase in the HCl concentration only reduces the negative charge. The contribution of the complexation with Na + is significant only beyond pH 9.

  ) concerning the formation of positive sites. For pH values greater than pH ZPC , therefore, the contributions of [SiO predominant. The surface charge  0 is the sum of these two terms.

Fig. 3 -

 3 Fig. 3 -Estimation of zeta potential based on H. Ohshima's approximation.

FL4820Fig. 4 -

 4 Fig. 4 -Influence of coagulant concentration on the electrophoretic mobility and on the turbidity of S30R50 nanoparticles.

Fig. 5 -

 5 Fig. 5 -Mode of action and conformation of organic coagulants with the particle surface.

Fig. 6 -

 6 Fig. 6 -Shape of the electrophoretic mobility curve concavities below the OCC.

Fig. 7 -

 7 Fig.7-Evolution of the OCC as a function of the percentage of the coagulant's active matter.3.3.2 Coagulation-Flocculation

  cationic charges. Their references are FO4115, FO4115SH, FO4190, FO4190SH, FO4990, FO4990SH, FO4550 and FO4800SH. The experimental protocol therefore included 4 coagulants and 8 flocculants. Each test involved coagulation followed by flocculation. The efficiency of the various reagents was evaluated in terms of supernatant clarity. The lowest turbidities were obtained with FO4190, FO4550 and FO4990SH with optimum flocculant

Fig. 9 -

 9 Fig. 9 -Size distribution after coagulation-flocculation.

Table 1

 1 Main characteristics of the cationic coagulants used.

	Parameter	FL2250	FL2565	FL4520	FL4820
	Composition	L. Polyamine	L.Polyamine	PolyDADMAC	PolyDADMAC
	Charge density	Very high	Very high	Very high	Very high
	Active content %	50	65	20	20
	Molecular weight	0.03.M	0.2.M	0.89.M	1.M
	Specific gravity	1.14	1.20	1.04	1.04
	Approximate Brookfield viscosity (cps)	25-35	1000-3000	200-500	1000-3000

Table 2

 2 Main characteristics of the flocculants used.

	Parameter

Table 5

 5

	Main size parameters after coagulation.
	Coagulant	d10	d50	d90	dmL	DSI	D F
		(µm)	(µm)	(µm)	(µm)
	S+FL2250	0.2	0.4	28.0	7.3	36.7	1.96
	S+FL2565	6.4	8.1	12.3	8.5	0.4	2.88
	S+FL4520	7.4	9.1	15.2	10.6	0.4	2.87
	S+FL4820	7.4	9.1	15.2	10.6	0.4	2.86
	Table 6a
	Turbidity and texture after coagulation and flocculation.
	Traitement		d10	d50	d90	DmL	(d90-d10)
			(µm)	(µm)	(µm)	(µm)	(µm)
	S+FL2565+FO4990SH		74	269	576	300	502
	S+FL2565+FO4550		36	92	203	107	167
	S+FL4820+FO9190		59	173	367	166	308

Table 6b

 6b Turbidity and texture after coagulation and flocculation.

	Traitement	 NTU		(g.cm -3 )  F	D F
	S+FL2565+FO4990SH	2	0.98	1.02	2.28
	S+FL2565+FO4550	1.5	0.94	1.07	2.51
	S+FL4820+FO9190	1.9	0.97	1.03	2.46

Acknowledements

The author is grateful to French National Research Agency for financial support (NANOSEP, ANR-08-ECOT-009). He would also like to thank SNF FLOERGER (France) for providing samples of the coagulants and flocculants used and AZ Electronic Materials for providing the nanosilica.


Khaldoun Saleh
email: ksaleh@laas.fr

Pierre-Henri Merrer

Olivier Llopis

Gilles Cibiel

Gilles Cibiel Millimeter

Millimeter Wave Generation Using Brillouin Scattering in a High Q Fiber Ring Resonator

Keywords: Millimeter-wave generation, microwave photonics, fiber ring resonator, Brillouin scattering, phase noise I

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INTRODUCTION

Extremely high frequency generation and distribution using optical techniques represent an interesting approach. These techniques are used in many applications, from telecommunications to radio-astronomy, and at distances that vary from a few meters (e.g inside a plane or a satellite) to a few kilometers (e.g. antenna networks) and even several tens of kilometers (e.g inter-laboratories clock comparison). Many millimeter-wave (mmw) sources carried using optics have been demonstrated. Among these, the method using the beat note of a dual frequency (or mode locked) laser, where two modes are sharing the same cavity and the same gain [START_REF] Pillet | Dual-frequency laser at 1.5 lm for optical distribution and generation of high-purity microwave signals[END_REF], and the one based on the heterodyning of two independent lasers [START_REF] Simonis | Optical generation, distribution, and control of microwaves using laser heterodyne[END_REF], have become quite popular, because they do not require an ultra high frequency modulator. Dual frequency lasers are particularly interesting to get high output power and high carrier to noise ratio (CNR) in the mmw range. Also, it benefits from the fact that the noise in the system affects each of the laser's two modes equally, which leads to a noise reduction in the radio frequency (RF) domain. However, either in the case of dual mode laser or of heterodyning two independent lasers, it is difficult to get a strong correlation between the two modes, and thus an efficient rejection of the laser phase noise which degrades the beat note, and thus the resulting RF signal. Contrarily to the above mentioned methods, frequency multiplication technique is quite easy to set up and only requires a Mach Zehnder modulator (MZM) [START_REF] Llopis | 50-60 GHz local oscillator transmission over fiber using optical frequency multiplication[END_REF]. With this approach, the optical harmonics generated by the MZM nonlinearity are strongly correlated so that the noise is equally distributed in the optical domain and thus cancelled in the RF domain. The only problem using this method is the harmonics low power levels, particularly in case of high order harmonics, which degrades the signal to noise ratio. It is thus interesting to find a way to amplify the different optical harmonics while preventing a gain competition between them. Fortunately, optical harmonics can be independently amplified thanks to the Brillouin selective sideband amplification concept (BSSA) [START_REF] Yao | Brillouin selective sideband amplification of microwave photonic signals[END_REF].

In this paper, we present a millimeter-wave signal generation setup based on the frequency multiplication approach using a MZM to generate high optical modulation harmonics, combined with a high optical quality factor (Q opt ) fiber ring resonator (FRR) in order to generate a selective Brillouin gain spectrum at each of these optical harmonics, thus independently amplifying them while maintaining a good close to the carrier phase noise of the mmw signals.

II. FIBER RING RESONATOR

The 20 meter long FRR used in the BSSA mm-wave signals generation (BSSA-SG) system is depicted in Fig. 1. It consists of two low loss directional couplers, linked with a single-mode polarization-maintaining (PM) optical fiber. Resonances occur if the total integrated phase shift of the incident laser carrier ( laser ~1.55 μm) around the resonator ring is an integer multiple of 2 rad. This resonator is thus characterized by a single transverse resonant frequency comb with a free spectral range (FSR) related to the fiber length L and its refractive index n: FSR = c /(n.L) (~ 10 MHz in our case). This resonator features a -3dB bandwidth of 65 kHz, thus an optical Q opt factor of 3x10 9 . This high Q opt factor leads Funding from ANR project "ORA" 2010 BLAN 0312 03 to a significant intra-cavity circulating power (P cavity /P in ~ 54). This will reduce the thresholds of many nonlinear optical effects, especially stimulated Brillouin scattering (SBS) [START_REF] Saleh | Optical scattering noise in high Q fiber ring resonators and its effect on optoelectronic oscillator phase noise[END_REF]. In optical fibers, many scattering phenomena may occur. Some of them are passive, like Fresnel reflections at the fiber end faces, and some others are active like Rayleigh backscattering, Brillouin and Raman scattering which feature two scattering modes each: spontaneous and stimulated scattering [START_REF]Nonlinear Fiber Optics[END_REF].

Theoretically predicted by L. Brillouin in 1922, SBS in optical fibers was firstly observed in 1964 and has been extensively studied since then [START_REF]Nonlinear Fiber Optics[END_REF]. It is caused by the interaction a light wave and an acoustic wave existing already at the optical medium thermal equilibrium. At a critical incident light wave power, called stimulated Brillouin scattering threshold (SBST), the interference between the Stokes wave and the laser carrier amplifies the acoustic wave in a process called electrostriction. Thus, the scattered wave will become more intense and reinforces the interference and so on. In optical fibers, the Brillouin backscattered Stokes wave is privileged and is frequency downshifted from that of the laser carrier by B , set by the nonlinear medium characteristics ( B = 10.87 GHz in our case). However, a very weak backscattered wave, called Anti-Stokes wave, and upshifted in frequency by B , can be also generated. When the Stokes wave power exceeds the medium SBST, it creates a second order backscattered Stokes wave downshifted in frequency from the first Stokes wave by B , and thus by 2 B from the laser carrier. The theoretical travelling directions inside the resonator and the spectral representation of the different scattering components at the resonator's second and third outputs are given in Fig. 1 and Fig. 2. The Brillouin gain bandwidth was less than 20 MHz in the PM fibers used to fabricate the FRR, so with a resonator FSR of 10 MHz, the generated Brillouin lines inside the resonator feature a single mode operation and automatically resonate, thus taking benefit of the resonator's power enhancement factor.

Even if the generation of the Brillouin scattering is known to be very harmful to optical links and optical systems like optoelectronic oscillators [START_REF] Saleh | Optical scattering noise in high Q fiber ring resonators and its effect on optoelectronic oscillator phase noise[END_REF], it can be useful in many other applications, such as low noise and ultra-narrow linewidth Brillouin lasers [START_REF] Jihong | Highly stable low-noise Brillouin fiber laser with ultranarrow spectral linewidth[END_REF] or in modulation depth enhancement of optically carried RF signals [START_REF] Norcia | Efficient single-mode Brillouin fiber laser for low-noise optical carrier reduction of microwave signals[END_REF]. Our aim here is to use the Brillouin effect generated at very low threshold inside the resonator, to selectively amplify the different optical modulation harmonics generated in the mmw range and thus generate high power and low phase noise mmw frequencies.

III. MMW SIGNALS GENERATION SETUP

The BSSA-SG system is illustrated in Fig 3 . We use a Koheras laser at 1.55μm wavelength with a 1 kHz linewidth. The optical carrier is stabilized to the FRR via a Pound-Drever -Hall loop [START_REF] Drever | Laser phase and frequency stabilization using an optical resonator[END_REF], then modulated via a 20Gbits/s EOspace MZM DC biased at V /2 in order to have a linear modulation and get high order upper and lower sidebands while keeping a high carrier power to be able to generate SBS in the FRR. Around V /2 , the MZM transfer function is odd, and only odd harmonics are generated: 1, 3, 5… [START_REF] Llopis | 50-60 GHz local oscillator transmission over fiber using optical frequency multiplication[END_REF]. Then, we use the Brillouin gain generated every 10.87 GHz multiple in the optical spectrum to amplify these harmonics. On the receiver side, we visualize the optical spectrum of the FRR third output on an Agilent HP 86142A optical spectrum analyzer (OSA) with 0.06 nm resolution and ±1 dB amplitude precision, and then send it to a 75 GHz U 2 T photodiode (PD). At the PD output, we visualize the RF spectrum on a 67 GHz Rohde&Schwarz electrical spectrum analyzer (ESA) and then analyze the signal phase noise using an Agilent E5052B signal source analyzer (SSA), which uses two equilibrated 50-85 GHz external mixers.

A. Optical Characterization

In order to optically characterize the BSSA-SG technique, the spectrum of a 4 dBm laser carrier at the resonator input and the spectrum of the resonator third output were visualized on the OSA. Results are depicted in Fig. 4. From figure 4, we can see that with a 4 dBm input laser carrier, at least the second order SBS Stokes wave could be generated, spaced by 21.742 GHz (0.176 nm) from the carrier. We call it free-running SBS. Now if a RF seed signal, having the same frequency than the second SBS line, is injected to the MZM with a high power level (20 dBm), the modulator will produce odd upper and lower sidebands (±21.742 GHz, ±65.226 GHz…) around the laser carrier. The higher the order of these harmonics is, the lower is their power. However, due to the Brillouin selective gain created by the carrier inside the resonator, especially Stokes lines gain, these harmonics will be amplified, and we will be able to measure even the tenth modulation harmonic, spaced by 108 GHz (0.88 nm) from the carrier, thanks to the BSSA process. Also, Brillouin scattering generation helps to increase the modulation depth [START_REF] Norcia | Efficient single-mode Brillouin fiber laser for low-noise optical carrier reduction of microwave signals[END_REF].

B. RF Characterization

The resulting beat note of the third output on a 75 GHz PD was observed on the ESA and results are presented in Fig. 5. The 4 dBm input carrier leads to a high RF power free-running Brillouin scattering wave at 21.74 GHz and a weaker one at 43.4 GHz frequency. However we can also find a 10.87 GHz component in the RF spectrum created by the beat note of the carrier wave, the second Stokes wave and the first Stokes wave backscattered part due to the Rayleigh scattering as already mentioned in Fig. 2.

When the laser carrier is modulated by the 21.74 GHz seed signal with a 20 dBm power level, the RF components at the resonator third output will be considerably amplified (odd harmonics) and we can especially notice the creation of a 65.2 GHz component with a -36 dBm power level (a 6 dB attenuator was used at the ESA input). The 10.8 GHz, 32.6 GHz and 54.32 GHz even harmonics exist because of the same reason mentioned in the paragraph above, also because of the non-perfect linear modulation of the MZM. In order to evaluate the power levels difference between the BSSA-SG method and the classical frequency multiplication method [START_REF] Llopis | 50-60 GHz local oscillator transmission over fiber using optical frequency multiplication[END_REF], the first and third harmonics power levels were measured versus the 21.7 GHz RF seed signal power. For the classical linear modulation method, the resonator was replaced by an attenuator to simulate its intrinsic and nonlinear losses to be in the same conditions as for the BSSA-SG method. Results are presented in figure 6. The measurements in figure 6 show clearly a real power gap between the two methods that increases with higher harmonic orders. A 15 dB gap at the third harmonic signal is obtained, demonstrating the gain efficiency of the BSSA-SG.

C. Noise Characterization

An important parameter to be characterized is the phase noise of the mmw signals generated via the BSSA-SG method. The phase noise spectrum of the Brillouin waves at 21.7 GHz and 65.2 GHz has been measured using the SSA. Fig. 7 shows the phase noise of the free-running Brillouin at 21.7 GHz, the synthesizer seed signal at the same frequency, and finally the phase noise of synchronized Brillouin wave via the BSSA-SG. The impact of BSSA-SG on the spectral purity of the different free-running Brillouin components can be easily noticed even when using the ESA only, (see Fig. 7 -upper right corner). Fig. 7 results clearly demonstrate that BSSA-SG method seems to not only amplify the desired harmonics but also it significantly reduces the Brillouin gain spectrum noise, so that Brillouin gain will get almost the spectral shape and purity of the seed signal through synchronization, and thus lead to a more stable amplification. Finally, the phase noise of the generated 65.2 GHz signal has been measured and compared to the original 21.7 GHz seed signal phase noise and to its theoretical phase noise after being multiplied by 3, (+20log(N) where N is the frequency multiplication factor), see Fig. 8. We can notice that the synchronized signal at 65.2 GHz features the same phase noise spectrum as if it was generated by the classical multiplication method, at least in the close to carrier noise range from 1 Hz till 600 Hz offset frequencies. The excess noise at frequencies from 600 Hz to 80 kHz seems to be generated by the PDH loop noise, the Rayleigh scattering noise of the different optical spectrum components and the Brillouin gain noise. The rapid decrease in the phase noise after the 40 kHz offset frequency is due to the optical resonator filtering effect. The PDH noise part can be reduced if a double PDH stabilization technique controlling the laser and the resonator at the same time is used, like in [START_REF] Gross | Tunable millimeter-wave frequency synthesis up to 100 GHz by dual-wavelength Brillouin fiber laser[END_REF] were interesting mmw signals generation system stability and accurate tunability were demonstrated. However, high order mmw signals generation with low phase noise is possible with our BSSA-SG method, where there is theoretically no limit in the generation of higher order Brillouin lines; The only limit will be at the receiver part, especially the photodiode bandwidth.

IV. CONCLUSION

Investigations have been performed on the generation of millimeter-wave signals using Brillouin selective sideband amplification process in a high Q fiber ring resonator. The synchronization of Brillouin lines has resulted in high spectral purity millimeter-wave signals generation up to 65 GHz, which is of great interest for many applications. The proposed technique allows a high signal to noise ratio and a low close to carrier phase noise.

Figure 1 .

 1 Figure 1. 20 meter long double directional coupler fiber ring resonator used to generate nonlinear optical effects (Brillouin scattering). Stokes and Anti-Stokes acronyms refer only to the Brillouin scattering in this scheme

Figure 2 .

 2 Figure 2. Theoretical optical spectrum at the second and the third outputs of the FRR, in the presence of the pump, its Rayleigh scattering and the first and second order Brillouin scattering lines and their own Rayleigh scattering lines

Figure 3 .

 3 Figure 3. BSSA-SG setup using a 20 meter long FRR; ISO: isolator; EDFA: erbium doped fiber amplifier; OSA: optical spectrum analyzer; PD: photodiode; PDH: Pound-Drever-Hall laser stabilization system; ESA: electrical spectrum analyzer; A: mmw amplifier; •••: optical and RF switches

Figure 4 .

 4 Figure 4. Optical spectrum of the laser carrier at the resonator input, of the resonator third output when Brillouin is in a free-running behavior and when modulating the laser carrier at 21.7 GHz with a 20 dBm RF seed signal

Figure 5 .

 5 Figure 5. RF spectrum of the resonator third output when Brillouin is in a freerunning behavior and when modulating the laser carrier at 21.7 GHz with a 20 dBm RF seed signal. A 6dB attenuator was used at the ESA input

Figure 6 .

 6 Figure 6. RF output power levels of the first and third harmonics versus the RF 21.7 GHz seed signal power, when using the classical frequency multiplication method and when BSSA-SG technique is used

Figure 7 .

 7 Figure 7. Phase noise of the free running Brillouin wave at 21.7 GHz, the synthesizer seed signal at the same frequency, and the synchronized Brillouin wave via the BSSA-SG method. In the upper right corner, the free-running Brillouin spectral purity enhancement was visible on the ESA after being synchronized by the seed signal (ESA: 100 kHz span, 30 Hz RBW and VBW)

Figure 8 .

 8 Figure 8. Phase noise of the synthesizer seed signal at 21.7 GHz, the synthesizer phase noise multiplied to 65.2 GHz and the generated 65.2 GHz signal via BSSA-SG method


Khaldoun Saleh
email: ksaleh@laas.fr

Pierre-Henri Merrer

Olivier Llopis

Gilles Cibiel

Investigations on Noise Processes in Optical Resonator Based Microwave Oscillators

Keywords: optoelectronic oscillators, microwave photonics, fiber ring resonators, whispering gallery mode resonators, phase noise I

Optoelectronic oscillators based on high Q optical resonators are presented in this paper. These oscillators use a Pound-Drever-Hall laser stabilization technique and two different types of resonators: fiber ring and monocrystalline disk resonators. Noise processes in the oscillators are discussed, particularly the influence of the laser noise conversion and nonlinear optical scattering noise. A modeling approach using CAD software is also proposed.

INTRODUCTION

Microwave oscillators based on optical frequency references have become quite common, at least the ones based on fiber optics spools which have been studied since 1994 [START_REF] Yao | Progress in the optoelectronic oscillator -a ten year anniversary review[END_REF]. These optoelectronic oscillators (OEOs) take benefit of the ultra-low losses in silica fibers, and thus of the large delay provided by long fibers in the kilometer range. This large delay is equivalent to a high microwave quality factor (Q RF ), and Q factors higher than 10 6 can be reached at an application frequency of 10 GHz. However, these delay line OEOs suffer from different drawbacks which are the fiber spool size, making the system hard to stabilize in temperature, and the spurious modes generation. Many approaches have been proposed to solve these problems, but they still quite complex and the system remains bulky.

An alternative solution instead of using delay lines in OEOs, is the use of optical resonators [START_REF] Maleki | New schemes for improved opto-electronic oscillator[END_REF], [START_REF] Savchenkov | Optical resonators with ten million finesse[END_REF]. Optical quality factors (Q opt ) as high as 10 8 to 10 11 may be obtained with different types of optical resonators: fiber ring resonators (FRRs), monocrystalline disks, silica spheres or toroids, Fabry-Perot ultra stable cavities… Using these optical resonators, the equivalent microwave quality factor is linked to the optical quality factor by the relation below:

opt RF opt RF f f Q Q × = (1)
where f RF and f opt are respectively the microwave (RF) and the optical frequencies.

From [START_REF] Yao | Progress in the optoelectronic oscillator -a ten year anniversary review[END_REF] we can see that interestingly, and unlike microwave resonators, the equivalent Q RFs of these optical resonators increase while increasing the RF application frequency f RF . As an example, a Q opt factor of 10 9 , at 1.55 µm wavelength (~ 200 THz), results in an equivalent Q RF factor of 10 5 at 20 GHz. This is lower than the equivalent Q RF factor of a long delay line but still particularly interesting if compared to the Q RF factor of conventional microwave resonators, taking also into account the reduction in system size if we replace the delay line by a resonant device.

A special case of resonant or regenerative OEOs is the coupled OEO (COEO) [START_REF] Matsko | Theory of coupled optoelectronic microwave oscillator I: expectation values[END_REF], in which a microwave oscillator is coupled to an optical oscillator. Like the resonator approach, the COEO allows a reduction in the fiber length, while keeping high performances. The advantage of the COEO relies in the fact that the laser and the resonator are the same device. However, system size and Q opt factor could be better in passive resonator based OEOs, if problems of noise conversion and laser stabilization can be efficiently resolved.

In this paper, noise processes in OEOs based on either FRRs or tridimensional monocrystalline resonators are discussed. All these OEOs use the same system to stabilize the laser onto the resonator: a Pound Drever Hall (PDH) technique [START_REF] Drever | Laser phase and frequency stabilization using an optical resonator[END_REF]. Some noise processes are studied theoretically, especially those related to the laser amplitude (AM) and frequency (FM) noise conversion, thanks to a system design approach developed on Agilent ADS microwave software. Experimental results are also provided.

II. RESONATOR BASED OPTELECTRONIC OSCILLATOR

The OEOs described in this paper are based on ultra-high Q opt optical resonators featuring a comb of resonances with microwave spacing called free spectral range (FSR). The resonator FSR must be a sub-multiple of the application frequency. In this case, the beat note between two or three optical modes of the resonator will be used in the microwave domain. Before setting up the filtering of the microwave signal, it is necessary to stabilize the laser carrier on one of the modes of the resonator. The extreme Q opt factors of these resonators make them very sensitive to the incident light power. When the light wave is resonant inside the resonator, the circulating intracavity power can be as high as 54 times the incident light power, depending on the resonator Q opt factor. This induces a strong thermal effect [START_REF] Carmon | Dynamical thermal behavior and thermal self-stability of microcavities[END_REF], which shifts the optical resonance and the resonator is no more coupled to the laser unless a feedback system is used to maintain the laser at the resonance frequency. Also, the high circulating intra-cavity power can lead to the generation of many nonlinear optical effects inside the resonator, as we will see later in section IV.

Many feedback approaches can be used to stabilize the laser to the resonance frequency. First, using whispering gallery modes (WGM) disks or sphere resonators, one can take benefit of a natural counter-rotating wave inside the resonator to optically lock the laser to the resonator [START_REF] Maleki | On the Development of Photonic RF Oscillators and Resonant Electro-Optic Modulators for Advanced RF Front-End Applications[END_REF]. Of course, this requires an accurate control of the resonator-laser distance. A self-thermal lock can be also realized in some cases, depending on the thermal expansion parameters of the resonator, but such a lock process is not reliable enough for all applications. The approach we have chosen, the PDH technique, is based on an electrical feedback to the laser: the phase transition at the resonance is converted into an error signal and fed-back to control the laser frequency. This approach is very reliable in time and it can be applied to any laser having a linewidth smaller than the resonance linewidth and on which a frequency control parameter is available.

The OEO system is depicted in Fig. 1. The laser is first locked to the resonator thanks to a PDH low frequency (LF) loop and then the microwave oscillation is started thanks to a high frequency (HF) loop. The HF loop includes a RF amplifier, a phase shifter and, in the case of FRR, a mode selection filter, because we use a 20 meter long FRR that features a 10 MHz FSR. This is not the case of the WGM disk resonator, which is of millimeter size and thus its resonant comb features a FSR higher than 12 GHz. For OEOs based on WGM resonators, the microwave filter is thus useless.

III. FIBER RING AND WGM OPTICAL RESONATORS

The above OEO system has been firstly set up with a FRR [START_REF] Merrer | High-Q Optical Resonators for Stabilization of High Spectral Purity Microwave Oscillators[END_REF]. The resonator is realized with two low loss fibered directional couplers with low coupling factors (about 1%) linked with an optical fiber of a few meters, Fig. 2. As an example, we have been able to obtain a Q opt factor of 5.1x10 9 with a 20 meter long FRR. It is a relatively small device (planar device) featuring an equivalent Q RF factor of 5.1x10 5 at 20 GHz, which is above conventional microwave resonators Q RF factors. This FRR's Q opt factor is very similar to Qs of WGM disk resonators, and the first goal in using this fibered resonator was to set up an OEO system which would be compatible with WGM resonators in order to study them accurately. However, the performances of the FRR are already very interesting. Also, it is much easier than WGM resonators to set up, thanks to the well-established technology of fibered directional couplers.

The other types of resonators we have studied are WGM silica spheres and calcium fluoride CaF 2 polished disk resonators, Fig. 2. These resonators are coupled to the laser thanks to tapered fibers and a Nano-scale positioning system. This coupling system is very efficient, but it remains a laboratory experiment system. We have obtained Q opt factors in the range of 10 8 both on silica spheres and CaF 2 disks. Q opt as high as 10 11 have already been demonstrated with CaF 2 disks [START_REF] Savchenkov | Optical resonators with ten million finesse[END_REF].

IV. NOISE IN A RESONATOR BASED OEO

Unlike microwave oscillators, in which phase noise is dominated by RF amplifiers noise, the phase noise in OEOs is generally dominated by noise processes occurring in the optical part of the system. This is even more true for resonator based OEOs, in which the required correlation between the laser and the resonance frequency may induce specific noise processes. Also, the resonator ultra-high Q opt factor may lead to an induced nonlinear optical scattering noise inside the resonator, converted into microwave phase noise in the OEO setup.

Two types of laser noise conversion processes are particularly important: the laser AM and FM noise conversion. Because the photodiode performs amplitude detection, it is obvious that the laser AM noise may have an influence on the microwave phase noise. Also, this is generally the parameter which determines the signal to noise ratio (unless there are too much losses through the resonator) and thus the OEO phase noise far from the carrier. However, for most applications, the close to the carrier phase noise performance (1 Hz to 10 kHz) is the most critical parameter. At these offset frequencies, a 1/f like frequency noise is observed.

To determine the ratio of laser AM and FM noise conversion into RF phase noise, a modeling approach has been set up using Agilent ADS microwave software. This approach takes benefit of the harmonic balance technique provided by ADS to describe the nonlinear signal and noise conversion processes occurring between the laser frequency (~200 THz), the microwave frequency and the DC. Because ADS does not include models for optical devices, we have developed our own models, which are either based on equivalent circuit descriptions or on mathematical black box descriptions. As an example, the laser is described with a classical frequency source with its FM noise, and an amplitude modulator is added to model the laser AM noise. Fig. 3 depicts the model used for the resonator. In this case, a FRR was modeled and described using modified models of ideal lines and coupled lines of ADS. The resonant comb, the FSR and the Q opt factor are accurately described with this approach on any of the four ports of this resonator and simulation results fit very well with our experimental measurements data. One of the advantages of such ADS resonator model is the capability of easily simulating very complex scheme based on multiple optical resonators. For our OEO application and noise investigations, an interesting study which can be performed on ADS is on the way the optical modes are translated into electrical resonances in a system including: laser + modulator + optical resonator + photodiode. If a classical Mach-Zehnder linear modulation is used (V bias = V /2 ), the modulated laser carrier features two optical sidebands which simultaneously go through two lateral modes of the resonator. This process gives birth to a unique microwave mode at the photodiode output, which results from the two optical modulation sidebands and the laser carrier folded one onto the other. If the laser is perfectly centered on one of the modes, and the two lateral sidebands are identical, then a microwave mode identical to the optical modes of the comb (same 3 dB bandwidth and phase slope) is observed in the microwave domain. However, if the laser is not perfectly centered, the phase slope of the microwave signal (and thus the Q RF factor) is reduced, as it can be seen from the simulation results in Fig. 4. Moreover, if the laser is not at the center of the resonance, the system becomes sensitive to laser frequency fluctuations, and thus it is able to convert the laser phase noise into electrical phase and amplitude noise. This simulation demonstrates how important is the laser lock and the ability to control this locking process. Such a possibility is well provided by the Pound-Drever-Hall approach.

Another problem in these systems relies on the starting up of optical nonlinear processes inside the resonator due to the high circulating intra-cavity power. This will also degrade the microwave phase noise. The two main processes to be considered are Rayleigh and Brillouin scatterings. We have experimentally found that the stimulated Brillouin scattering (SBS) process occurs at relatively low input power in these resonators, at least in the case of FRR [START_REF] Saleh | Optical scattering noise in high Q fiber ring resonators and its effect on optoelectronic oscillator phase noise[END_REF], depending on its Q opt factor. Once this process starts, a Brillouin (back-reflected) Stokes wave downshifted in frequency from the laser carrier by about 10.8 GHz (for silica fibers) can be observed. Using a 20m long FRR, and because of the high circulating intra-cavity power, we have been able to detect the generation of the seventh order Brillouin line at 10 dBm of optical input laser power, Fig. 5. This parasitic signals mix either inside the resonator (they modulate the amplitude of the main signal) or at the photodiode level with the main signal, thus increasing the RF phase noise, especially close to the carrier. The Brillouin scattering generation also leads to nonlinear losses inside the resonator which will be added to the resonator intrinsic loss. After being generated, above the SBS threshold, the Brillouin scattering converts any additional laser power injected above this threshold to its own power and generates other Brillouin lines (Fig. 5). This will cause laser carrier depletion, and thus it leads to the degradation of the noise to carrier ratio of the optical link. Fig. 6 shows the DC detection of the photodiode at the resonator third output using an oscilloscope, where we can clearly notice the saturation in the detected signal while the laser frequency is scanning a resonance line of the resonator and when its injected power inside the resonator starts to be above the SBS threshold.

Therefore, a good performance close to the carrier can only be obtained at low optical input power, unless a specific set up can reduce the onset of these processes, while maintaining a high Q opt . This could be possible if optical fibers of different materials are used together (different Brillouin gain frequencies, thus a reduced global Brillouin gain), or if the fiber material is locally changed (thermally or mechanically), and also when changing the fiber structure (e.g. increasing its core diameter…). V. OEO PHASE NOISE MEASUREMENTS Fig. 7 depicts the measured phase noise of a 10.2 GHz OEO realized with a FRR featuring a Q opt factor of 3.5x10 9 (equivalent Q RF = 1.8x10 5 ) [START_REF] Saleh | Optical scattering noise in high Q fiber ring resonators and its effect on optoelectronic oscillator phase noise[END_REF], and of a 12.5 GHz OEO realized with a CaF 2 disk resonator featuring a Q opt factor of 1.4x10 8 (equivalent Q RF = 9x10 3 ). Compared to microwave oscillators having same Q RF factors, these two oscillators feature a higher phase noise. This is due to the optical noise contribution which is still not completely optimized in spite of taking into account the remarks of paragraph IV. The peaks in the phase noise of the CaF 2 disk OEO may come from mechanical perturbations in the coupling using tapered fibers. Work is in progress to reduce these contributions, particularly in the case of the FRR in which solutions exists to remove some of the nonlinear optical effects. In the case of the disk resonator, attempts to improve the phase noise will be first based on an improvement of the resonator Q opt factor.

VI. CONCLUSION

Noise in optoelectronic oscillators based on fiber ring and whispering gallery modes resonators has been studied in this paper. It has been confirmed through theoretical and experimental studies that the phase noise in these OEOs is generally dominated by noise processes occurring in the optical part of the system. In resonator based OEOs, a correlation between the laser and the resonator frequency is required and a specific laser AM and FM noise conversion processes may be induced if this condition is not respected. Also, the high optical Q factors of these resonators can lead to the generation of some nonlinear optical scattering effects at low laser input optical power. Working at low enough optical power is mandatory in order to avoid this noise type and to get a good OEO phase noise. Further investigations include the design of new high Q optical resonators, immunized against nonlinear optical effects.

Figure 1 .

 1 Figure 1. OEO setup based on a PDH loop to stabilize the laser and a HF loop to maintain the microwave oscillation; PDH: Pound Drever Hall, MZM: Mach-Zehnder modulator.

Figure 2 .

 2 Figure 2. A 20m long fiber ring resonator (left) and a 5.5 mm whispering gallery modes CaF2 resonator (right).

Figure 3 .

 3 Figure 3. FRR model using ADS, and S21 amplitude simulation results.

Figure 4 .

 4 Figure 4. S21 RF amplitude and phase responses through modulator + optical resonator + photodiode; Experimental and ADS simulation results. Case of a laser perfectly centered on the mode (red curve) and of a shift between the laser frequency and the resonator frequency (blue and green curves).

Power

  1549,48 1549,63 1549,78 1549,93 1550,08 1550,23 1550,38 1550,53 Brillouin scattering lines generation inside a 20m long fiber ring resonator with a Qopt factor of 3.5x10 9 .

Figure 6 .

 6 Figure 6. Visible laser carrier saturation, due to the Brillouin scattering generation, by measuring the photodiode DC voltage at the resonator third output, while the laser frequency is scanning a resonance line.

Figure 7 .

 7 Figure 7. Phase noise of OEOs realized with a CaF2 resonator (12.5 GHz) and a 20 meter long fiber ring resonator (10.2 GHz). Measurements are performed with an Agilent E5052 B signal source analyzer.

ACKNOWLEDGMENT

This study is part of a French National Research Agency (ANR) project ORA (2010 BLAN 0312 03).