ABSTRACT

The heat pump for simultaneous heating and cooling (HPS) carries out space heating, space cooling and hot water production for small office and residential buildings. It works under heating, cooling and simultaneous modes to produce hot and chilled water according to the thermal demand of the building. A subcooler connected to a water tank is placed after the condenser to recover some energy by subcooling of the refrigerant during a heating mode. The water loop at a higher temperature than ambient air is used subsequently as a source for a water evaporator. Average winter performance is improved compared to a standard reversible heat pump (HP). The air evaporator is defrosted by a two-phase thermosiphon without stopping the heat production. The operation of the HPS is modelled using TRNSYS software. The model is validated using results of an experimental study carried out on a HPS prototype working with R407C. Annual simulations of the HPS coupled to a hotel are run in order to evaluate annual performance and energy consumption of the system. The results are compared to the ones of a standard reversible HP. Depending on the scenario, savings in electric energy consumption and annual performance improvement can reach respectively 55% and 19%.

Keywords: heat pump, simultaneous heating and cooling, defrosting

INTRODUCTION

In developed countries, commercial and residential buildings account for around 40% of national energy consumption and 25% of greenhouse gas emissions. This is the sector in which savings have to be made in priority. Thermal performance of buildings is thus continuously improving thanks to thermal regulations. Besides, comfort requirements demand more and more energy. Whilst domestic hot water (DHW) demands increase continuously, a demand for cooling appears or rises to compensate internal heat gains caused by more and more household electrical equipment. A more insulated thermal envelope implies also that new buildings need less energy for heating and more for cooling. Therefore thermal needs of new buildings are more balanced between heating and cooling over the year.

During winter, energy is demanded exclusively for space heating and DHW production. Between winter and summer, some buildings can demand simultaneously cooling in rooms facing south and heating in rooms facing north. During summer, energy is needed for DHW production and space cooling at the same time. An answer to a dual energy demand is the heat pump, since it supplies simultaneously a heating capacity at the condenser and a cooling capacity at the evaporator. Annex 48 of the ECBCS programme (Energy Conservation in and Community Systems) of the IEA (International Energy Agency) deals with this topic [START_REF] Stabat | IEA ECBCS Annex 48 Subtask 1: Analysis of heating and cooling demands and equipment performances[END_REF]. The annex first highlights that some buildings actually present simultaneous or slightly delayed heating and cooling needs and then proposes solutions to satisfy these needs using heat pumping technology.

This study presents the model of a heat pump that can satisfy fluctuating needs, simultaneous or not, in heating and cooling. This heat pump is named HPS (Heat Pump for Simultaneous heating and cooling) and can be installed in hotels where DHW demands are high and glassfronted buildings where simultaneous needs in space heating and space cooling are more frequent. The first objective is to produce, as often as possible, heat and cold using the same energy input at the compressor. The second objective is to limit the performance loss of airsource heat pumps during winter due to low air temperatures and frosting [START_REF] Liu | Frosting of heat pump with recovery facility[END_REF]. A previous publication on the modelling and simulation of the HPS using HFC or CO 2 as a working fluid was carried out [START_REF] Byrne | Design and simulation of a heat pump for simultaneous heating and cooling using HFC or CO 2 as a working fluid[END_REF]. In the present study focusing only on R407C, the models chosen are not highly-efficient ones (like in the previous publication) but real ones, validated by experimental data. Two other articles were published on the HPS prototype description and the experimental study (Byrne et al., 2011a and2011b).

The most recent modelling techniques are reviewed by [START_REF] Ding | Recent developments in simulation techniques for vapour-compression refrigeration systems[END_REF]. This article states that the compressor model should precisely calculate input power, refrigerant mass flow rate and discharge temperature and that multi-node heat exchanger models divided into zones are accurate enough for dynamic modelling of refrigeration systems. Numerous publications can be found in the literature on more or less detailed compressor modelling [START_REF] Blunier | A new analytical and dynamical model of a scroll compressor with experimental validation[END_REF]) [START_REF] Cuevas | Testing and modelling of a variable speed scroll compressor[END_REF] [START_REF] Cuevas | Characterization of a scroll compressor under extended operating conditions[END_REF] [START_REF] Duprez | Modelling of reciprocating and scroll compressors[END_REF]) [START_REF] Duprez | Modeling of scroll compressors -Improvements[END_REF]) (Negrao et al. 2011) [START_REF] Tseng | Family design of scroll compressors with optimization[END_REF] (Winandy et al. 2002) (Winandy and Lebrun, 2002) [START_REF] Sun | Simulation research on scroll refrigeration compressor with external cooling[END_REF]. Heat exchanger modelling methods can be found in the ASHRAE Handbook Fundamentals [START_REF] Ashrae | ASHRAE Handbook Fundamentals[END_REF]. [START_REF] Bourke | Energy consumption modelling of air source electric heat pump water heaters[END_REF] coupled an air-source heat pump water heater to domestic hot water consumptions using TRNSYS software (Solar Energy Laboratory, 2000). [START_REF] Kinab | Reversible heat pump model for seasonal performance optimization[END_REF] also used this software to model and simulate a reversible heat pump including detailed compressor, heat exchangers and frosting/defrosting model. In this article, the components of the HPS model are programmed in FORTRAN and adapted to the draft of TRNSYS models. They are assembled to form a global model of heat pump in the TRNSYS Simulation Studio and coupled to models of water tanks, themselves coupled to a building model. The heat pump model is validated by results of experiments carried out on a R407C HPS prototype. Finally, annual simulations are run using three weather data files to evaluate the performance of a HPS, which is compared to the one of a standard reversible heat pump.

HPS CONCEPT

Refrigeration circuit

The HPS prototype (figure 1) produces hot and chilled water using plate heat exchangers. Performance verification of this prototype can be found in a previous publication (Byrne et al. 2011a).

Compressor

Water evaporator

Air heat exchanger

Subcooler

T hot gas

Figure 1: HPS refrigerant circuit

A balancing air coil (figure 2) works either as a condenser for heat rejection in a cooling mode or as an evaporator for heat suction in a heating mode, using two separate and alternated circuits of refrigerant. The air evaporator and the air condenser are never used at the same time. These functions have been assembled in the same three-fluid air coil (air, high pressure refrigerant and low pressure refrigerant) in order to decrease the finned surface area compared to separate air condenser and evaporator. When the tubes of the air evaporator are used, the surface of the fins near the tubes of the air condenser is also used for the air evaporator and vice versa. A plate heat exchanger is placed after the water condenser to recover the subcooling energy of the refrigerant in the cold water tank. This amount of energy is a short-time heat storage that will be used subsequently to carry out the evaporation on a water source during winter sequences.

Depending on the mode of operation, the electric components (compressor, fan and electronic valves named Evr) are managed automatically by a programmable controller or by an action of the operator on the control computer. The thermostatic expansion valves are named TEV1 (connected to the water evaporator) and TEV2 (connected to the air evaporator). Non-return valves named Nrv1 and Nrv2 are placed at the outlets of the air and water condensers to avoid refrigerant trapping in the condensers. Table 1 shows the general specifications of the components of the prototype.

Air flow

Evaporator inlets

Condenser outlet

Evaporator outlet Condenser inlet

High pressure control

As pressures and temperatures are linked during condensation, a high pressure control system ensures that condensation is completed in the condenser (and does not finish in the subcooler).

Moreover it is able to control the condensation temperature and thus the heating capacity. A special liquid receiver is placed on the liquid line. It is connected to the compressor discharge line and the inlet of the air evaporator by copper tubes of smaller diameter on which electronic on-off valves are placed (EvrHP and EvrLP in figure 1). The high pressure control system indirectly controls the volume of liquid in the receiver. The volume of liquid in the different condensers depends on the mode. If the high pressure is below the set point, the electronic valve EvrHP is opened by the controller. The receiver is filled up with gas coming from the compressor discharge line at a pressure higher than the pressure in the receiver until the set pressure is reached. The gas entering the receiver drives the liquid towards the evaporator. The non-return valve closes because pressure becomes higher at its outlet than at its inlet. The subcooling heat exchanger and the bottom part of the water condenser are filled up with more liquid until the appropriate level of liquid is reached. If however the chosen mode is the cooling mode, the condenser becomes the air heat exchanger. The set point for pressure is then the lowest possible. The pressure is reduced by driving the vapour out of the top part of the receiver towards the inlet of the air evaporator. The refrigerant in a liquid phase is sucked out of the water condenser and the subcooler and enters the receiver. The operation of the control system depends upon a special liquid receiver being designed sufficiently high and narrow with the main objective to enhance temperature stratification and to limit as much as possible thermal transfer between the gas and the liquid. When the gas is injected, part of it condenses. When gas is rejected to the low pressure, part of the liquid evaporates. Although these phenomena can reduce the efficiency of the liquid variation process in the receiver, it stabilizes the control system. The receiver is also thermally insulated to reduce the heat transfer towards the ambience.

Operating modes

Three operating modes can be run.

-The simultaneous mode produces hot and cold water using the water condenser and the water evaporator (electronic valves Evr1 and Evr3 are open).

-The heating mode produces hot water using the water condenser, the air evaporator (electronic valves Evr2 and Evr3 are open) and also uses the subcooler to store the subcooling energy in the cold water tank.

-The cooling mode only produces cold water using the water evaporator and the air condenser (electronic valves Evr1 and Evr4 are open).

The variables used to activate the mode of operation are the temperatures of water entering the water condenser and the water evaporator. Every simulation time step, the values are compared to set points using on/off differential controllers with hysteresis. The controllers deliver a signal at 1 if heating and/or cooling is needed. The corresponding operating mode, heating only, cooling only or simultaneous mode is consequently activated.

Summer sequence

During summer, the needs are usually higher in cooling than in heating. Some needs in heating can be observed for DHW production. The sequence alternates between cooling and simultaneous modes depending on the water temperatures.

Classic winter sequence

During winter, the sequence alternates between heating and simultaneous modes. The cold water tank is used as a short-time heat storage. The sequence begins by the heating mode engaging the water condenser, the air evaporator and the subcooler. The hot water tank is heated by water circulating through the condenser. Meanwhile, the cold water tank is heated, usually from 5 to 15°C, by the refrigerant subcooling energy. Then the HPS switches to the simultaneous mode and uses energy stored in the cold water tank as a heat source for the water evaporator. The cold water tank temperature decreases from 15 to 5°C.

In the simultaneous mode, the evaporating temperature is higher than in the heating mode from the moment that ambient air is colder than the short-time heat storage tank.

Therefore, using the simultaneous mode for a time during the winter sequence enables to produce hot water continuously with improved average system performance compared to standard air-source heat pumps. Besides, in the simultaneous mode, the air evaporator is not used for evaporation and can be defrosted using a two-phase thermosiphon.

Winter sequence with defrosting

In the heating mode, under cold outside air temperatures, the fins of the air evaporator get frosted. Before frost thickness becomes critical, the cold tank temperature rises to 15°C and the simultaneous mode is switched on by the controller. In this mode, the air coil is inactive and automatically defrosted by a two-phase thermosiphon formed between the two evaporators. Evaporation is carried out using the water source at a higher temperature than ambient air. Inside the air coil, the inner surface temperature of the tubes is at a low temperature because of the frost layer that has grown on the fins during the heating mode (previously running). Refrigerant in a vapour phase surrounding the low temperature surface condenses and flows down to the water evaporator by gravity. The condensation energy is transferred to the frost layer which actually melts. In addition to the regular flow of vapour generated at the evaporator and sucked by the compressor, a supplementary flow of vapour is created by the pressure difference. This amount of vapour flows to the condenser of the thermosiphon to occupy the volume difference created by condensation of the refrigerant. The phenomenon ends when the temperature and pressure differences disappear, thus when the evaporator is completely defrosted. A major advantage of this sequence is to carry out defrosting without stopping the heat production. Frost thickness can thus be minimized and mean convection heat transfer coefficients at the air evaporator can be maximized. The average heat pump efficiency under frosting conditions is improved compared to standard airsource heat pumps that use hot gas or reversed cycle defrosting methods [START_REF] Brand | Comparison between hot-gas bypass defrosting and reverse-cycle defrosting methods on an air-to-water heat pump[END_REF]. This defrosting method was tested in laboratory. Methods and results can be found in a previous publication (Byrne et al. 2011b).

MODELLING

Simulation tool

The numerical study is carried out under the TRNSYS environment. The scheme of the simulation model is shown in figure 3. The heat pump model and the building are linked by a system for thermal energy storage and distribution composed of water tanks, a tap water temperature calculator, a consumption profile generator and an auxiliary heater. The simulation time step is 5 minutes.

A preliminary study is made to calculate the steady state thermal capacities and electric power of the HPS, for each mode and for a wide range of water and air temperatures (paragraph 4.4).

Every component of the machine is a homemade model programmed in FORTRAN. The refrigeration device is modelled as the connection of the different components using the input and output variables. These simulations result in tables of thermal capacities and electric power depending on source temperatures (appendixes 1 and 2).

In the final simulation model, these tables are read by type42a "conditioning equipment with 3 independent variables" (shown in figure 3) available in the TRNSYS model library. The 3 independent variables are the heat source temperature, the heat sink temperature and the operating mode. The operating mode is given by the regulation model depending on the water tank temperatures. TRNBuild is used to obtain a multizone building model. The output variables are the heating and cooling demands. The DHW demand is given by a consumption profile provided by the French organization CSTB for an implementation in the TRNSYS model library.

Building description

A hotel of 45 bedrooms is modelled. Figure 4 shows a 3D-view of the building on which it can be noticed that the reception area outside wall is fully glazed and that the dining room has an outside wall oriented towards the West. Thermal zones, wall materials, glazed surfaces, solar protections and ventilation, occupancy and lighting schedules are defined using the building module of TRNSYS in accordance with the French thermal regulation RT 2005. The model calculates the thermal need of the hotel in heating and cooling. Energy for domestic hot water production is given by the water consumption depending on a daily profile, multiplied by the specific heat of water and the temperature difference between the set temperature of 50°C and the cold water network temperature. This simulation is run using the weather data file of three sites with different climates: Rennes (mild oceanic climate), Brussels (colder oceanic climate) and Marseille (Mediterranean).

Control strategy

In the final simulations using the environment described in paragraph 4.1, the regulation model defines the operating mode depending on the water temperatures. The cold water set point for temperature is 9°C with upper and lower dead bands of 2°C as shown in figure 5.

The set point temperature for hot water is given by the heating curve presented in figure 6.

The differential is ± 2.5°C. For example, at an ambient temperature of 0°C, the control signal that indicates a need in heating switches from 0 to 1 when the temperature of hot water entering the water condenser falls under 37.5°C and turns back to 0 when 42.5°C is reached.

The DHW production control signal switches from 0 to 1 when the water temperature falls under 47.5°C and turns back to 0 when it reaches 52.5°C. The standard heat pump does not produce DHW because this production is incompatible with cooling during the summer. In this case DHW production is carried out by a separate electric heater. A frosting model is applied to the standard reversible heat pump. This model calculates the frost thickness depending on the air mass flow rate, temperature and humidity. A clock launches a defrosting phase every 45 minutes if ambient temperature is below 7°C. During a time step of 5 minutes, the cycle is reversed and the defrosting energy is provided by a condensation at the air heat exchanger. The defrosting energy is given by the frost mass and the latent heat of fusion. The corresponding cooling energy is provided by the hot water tank for space heating. This strategy simulates a break in the heat production and induces a loss of performance compared to a HPS. Thanks to the two-phase thermosiphon, defrosting of the HPS is carried out during a simultaneous mode. Therefore the frosting model is not applied to the HPS model.

Detailed heat pump

Three models corresponding to three operating modes (heating, cooling and simultaneous modes) were defined to calculate the steady state heating and cooling capacities and electric power. Pressure drops and heat losses to the environment are assumed negligible in heat exchangers.

The detailed heat pump modelling can be schemed following figure 7. The models of compressor and heat exchangers are assembled depending on the operating mode. The dotted lines represent the fact that the subcooler is used only in the heating mode. Input temperatures are in grey (T hsi : heat sink temperature; T hso : heat source temperature, T cw : cold water temperature). Water and air mass flow rates are constants. The outputs are temperatures of hot or cold water production and electric power, cooling (subscript c), subcooling (subscript sc) and heating (subscript h) capacities. A module standing for the high pressure control system calculates the high pressure in function of the inlet heat sink temperature.

T hsi T hso T cw HP T hsi c Q & W & h Q & sc Q &

Compressor

The compressor model calculates the mass flow rate and the compression work knowing the input and output pressures (Equations 1 to 6) and using the Refprop database (2002). The volumetric efficiency (Equation 1) is calculated using a constant polytropic exponent of 1.076 for R407C. This value has been calculated using experimental results obtained in our laboratory on a Copeland ZB38KCE scroll compressor. A brief sensitivity analysis showed that a variation of ± 0.1 of the polytropic exponent value would provoke a variation of the heating COP inferior to 1.4% on a range of pressure ratios from 1.5 to 5. Equation 1 comes from the theory of piston compressors. Thus the "relative clearance volume" c becomes a "fictitious relative clearance volume" for scroll compressors. In this study, parameter c is used as a fitting variable so that the modelling corresponds to the experiments.

The output pressure is assumed to be calculated by the high pressure control system in accordance with the hot water inlet temperature. The compressor efficiency for R407C is calculated using a correlation based on curve-fitted results of experiments carried out in our laboratory on the Copeland ZB38KCE compressor (Equation 2). The compressor efficiency was calculated using equation 6 knowing the enthalpy at suction and discharge of the compressor for a series of 97 experimental points. The average discrepancy between the model of equation 2 and the experimental points is 6% (maximum value 14%). Finally, the discharge temperature is calculated thanks to the Refprop database for the outlet values of enthalpy (Equation 6) and high pressure.

        -       ⋅ - = 1 1 1 n vol LP HP c η (1)       ⋅ - ⋅ = BP HP comp 0565 . 0 exp 9962 . 0 η (2) s vol V m ⋅ ⋅ = η ρ & (3) ( ) i ideal o carnot h h m W - ⋅ = - & & (4) comp Carnot W W η & & = (5) comp i ideal o i o h h h h η - + = - (6)

Heat exchangers

The heat exchangers models use the Log Mean Temperature Difference (LMTD) method. The heat transfer coefficients and the steady state capacities are calculated using the geometrical characteristics of existing heat exchangers (Table 1), the McAdams correlations described in the ASHRAE Handbook Fundamentals (2001) for sensible heat transfers and condensation and the [START_REF] Tran | Small Circular and Rectangular-Channel Boiling with Two Refrigerants[END_REF] correlation for boiling heat transfer in the evaporator (Equations 7 to 9). The heating and cooling capacities are deduced from the heat transfer coefficients.

( )

4 0 3 0 2 5 10 4 8 . v l . l We Bo . -         ⋅ ⋅ ⋅ = ρ ρ α (7) v h G S Q Bo ∆ ⋅ ⋅ = & (8) σ ρ ⋅ ⋅ = l l d G We 2 (9)
The heat exchange surface of condensers and evaporators are divided into zones. Each zone is related to a fraction of the total surface of the exchanger. The evaporator has a two-phase zone for evaporation and a single-phase zone for superheating. The condenser has a single-phase zone for desuperheating, a two-phase zone for condensation and another single-phase zone for subcooling. The fundamental equations used on the zone i are presented hereunder. Equation 10 corresponds to the heat transfer between the two fluids. Equations 11 and 12 give the heat flux on the refrigerant ("r" as subscript) side and on the source side ("s" as subscript).

i i i i LMTD S U Q ⋅ ⋅ = & (10) ( ) i r r i h m Q ∆ ⋅ = & & (11) ( ) i s s s i T Cp m Q ∆ ⋅ ⋅ = & & (12)
In both heat exchangers models, the iterative calculation progresses from zone to zone from one end of the exchanger to the other. In the beginning, on each zone, outlet temperatures are set at the inlet values. Then, the calculations use the inlet and outlet temperatures and the structural parameters of the heat exchanger (hydraulic diameter, plate thickness) to determine the heat transfer coefficients, the new outlet temperatures and the heating or cooling capacity. The outlet variables of a zone are the inlet variables of the next zone. Once the calculation has reached the last zone, it starts again in the other way to the first zone. The whole calculation is iterated until the outlet temperatures of the refrigerant and the other fluid (water or air) have converged for the entire heat exchanger.

The low pressure adapts so that temperatures fit to a correct operation of the evaporator. In other words, the superheating has to correspond to the set value (4 K). The algorithm modifies the low pressure until convergence is achieved.

The subcooler is modelled as a condenser having only a liquid phase zone.

SIMULATION RESULTS

Model validation

The compressor model carried out using Trnsys software was fit to experimental results by adjusting parameter c of equation 1. Figure 8 shows a good agreement between experimental and modelled values of mass flow rate. The uncertainty of this calculation is estimated at ± 7 %. Figure 9 shows the comparison of electric power in a heating mode, depending on the source temperature, for two hot water inlet temperature T hw-in at the condenser, between our model of heat pump ("model"), the model from the manufacturer ("man") and the experimental results ("exp"). Agreement is considered satisfactory as the experimental results and the manufacturer's model results are within the uncertainty bars of 5% applied to the homemade model. Nevertheless some improvement can still be achieved with more model development. Indeed, at a hot water temperature of 30 °C, the model is systematically underestimating the experimental values.

Tables of performance

For each mode, tables of input power and thermal capacities were built using the detailed heat pump models (appendixes 1 and 2). They gather the results of heating and cooling capacities and electric power for different heat source and heat sink temperatures. These tables were obtained by running the detailed heat pump models with variable source temperatures. A couple of source temperatures was set at the inlet of two heat exchangers depending on the mode of operation and the calculation was run until convergence was achieved. Then another calculation started with a second couple of source temperatures and so on over the whole range of heat source and heat sink temperatures.

Appendixes 1 and 2 show the electric power and the cooling, subcooling and heating capacities provided respectively by the HPS and a standard heat pump, on the range from -15 to 15 °C for heat source temperatures and from 25 to 50 °C for heat sink temperatures.

Cooling and simultaneous modes only work under heat source temperatures from 5 to 15 °C, as the heat source is pure water. The cooling mode results are the electric power and the cooling capacity. The simultaneous mode provides also a heating capacity. In the heating mode, the results are the electric power and the heating and subcooling capacities. For a better comparison, the results are divided by the nominal heating capacity in the heating mode (T hso = 5 °C and T hsi = 35 °C) and multiplied by a factor 10.

The main tendencies of appendixes 1 and 2 are reported in figures 11 and 12. Independently on the mode, when the heat sink temperature decreases, the values of electric power decrease and the values of capacities increase, so COPs increase. When the heat source temperature decreases, thermal capacities also decrease whereas electric power follows a more complex trend. Indeed electric power is function of the pressure ratio and also of the low pressure. Electric power tends to decrease with the low pressure but tends to increase with a higher pressure ratio. Both trends result in a curve having a maximum for a heat source temperature around 0 °C. The HPS and the standard HP have the same values of electric powers and thermal capacities in the cooling mode because the devices are equivalent. When comparing the heating mode values, a difference due to the subcooler appears. A subcooling capacity is provided with the HPS and this increases the total heat production compared to the standard HP. The evaporator of the HPS (which is the same that the one of the standard HP) has to produce more cooling energy to compensate the increase in heat production. The evaporating pressure slightly decreases so that the temperature difference and the cooling capacity increase. Whereas there is not much difference between heating capacities, the low pressure of the HPS and the electric power are lower than that of the standard heat pump (figure 13).

Figure 13: Evolution of heating capacity and power input of HPS and standard heat pump models depending on the heat sink temperature for a heat source temperature of 5 °C (extract of appendix 1 and 2)

Building consumptions

The building annual consumptions are calculated over a representative year of each site (figure 14). Space heating and space cooling needs vary in opposite ways from the hotter to the colder climates: Marseille, Rennes and Brussels. The needs in DHW production are very high because the hotel is considered a 100 % occupied every day of the year. The needs vary scarcely with the cold water network temperature.

Heating and cooling system behaviour

System sizing

In accordance with the building needs depending on the climate, the systems were sized according to the French recommendations from COSTIC (Centre d'Etudes et de Formation, Génie Climatique, Equipement Technique du Bâtiment) and AFPAC (Association Française pour les Pompes A Chaleur). The HPSs and the standard HPs were sized to provide 80 % of the space heating needs at the base temperature. The electric auxiliary heater power corresponds to 40 % of these needs. The colder the climate during winter, the more powerful the heat pumps. In table 2, the heating capacity corresponds to 80 % of the needs given by simulation at the base temperature. The nominal heating capacity is the interpolation of the values of appendixes 1 and 2 to fit to the base temperature value. The sizing factor is the ratio between the heating capacity and the nominal heating capacity at T base . This factor is applied to every value of the tables of performance (Appendixes 1 and 2) during the annual simulations. In the intention of providing a fair comparison between the three climates, the sizing procedure is based on space heating. It applies well to sites where the predominant needs are in space heating. In Marseille the needs are higher in cooling and DHW production so the sizing procedure underestimates the power of heat pumps that should be installed in this site. If heat pumps were sized according to the needs in DHW and/or cooling, the electricity consumption of the auxiliary heater for DHW production would be reduced and globally, the improvement brought by the HPS compared to the standard HP would slightly increase.

Electricity consumptions

Figure 15 shows the annual electricity consumptions resulting of the simulations run with the weather data files of Rennes, Marseille and Brussels. With the HPS, the electricity savings are of course tremendous (more than 50 %) because DHW production is predominant in the energy balance and because the HPS produces an important part of that energy with a favourable COP. In the case of the standard HP, the DHW production is carried out by an electric heater. This means that when simultaneous needs in heating and cooling are important, having a device that can carry out both at the same time is very profitable. The total electricity consumption varies only slightly with the climate because what is not used for heating (in Marseille compared to Brussels for example) is consumed for cooling.

Figure 15: Electricity consumptions of the heat pumps and their backups depending on the site

Figure 16 shows the annual electricity consumptions of the HPS and the standard HP depending on the mode of operation. This decomposition presents electricity consumptions in heating and cooling modes in good correspondence with the building's needs in space heating and space cooling for both machines plus DHW production for the HPS. It reveals also that the simultaneous mode stands for a little part of the total electricity consumed by the HPS. However the simultaneous mode consumption corresponds to between 4.7% and 6.5% of the heat pump electricity consumption, it influences quite significantly the performance factors which are analysed in the next section.

Performance factors

Table 3 and figure 17 show the results of the following performance factors:

-the annual heat pump COP defined as the total useful thermal energy produced by the heat pump (only) divided by the total electric energy consumed by the heat pump (only); -the annual system COP defined as the total useful thermal energy produced by the heat pump and the electric backups divided by the total electric energy consumed by the heat pump and the electric backups;

-the Carnot COP is the average of Carnot COPs calculated every time step weighted by the thermal energy produced during each time step;

-the exergetic efficiency is also the average exergetic efficiency weighted by the thermal energy.

Table 3 shows a clear tendency concerning the performance of the HPS compared to a standard heat pump. The annual COP is improved by 6% in Marseille, 13% in Rennes and up to 19% in Brussels. This site is the coldest of the three. Thus the system takes more benefit from the winter alternated sequence of the HPS. Carnot COP and exergetic efficiency, which are theoretical performance factors based on source temperatures, record also the highest improvement in Brussels. This means that the HPS works on average with a lower difference between source temperatures and converts better electric energy into thermal energy. In the different modes, Carnot COP and exergy efficiency calculations take into account only the heat source and the heat sink involved. Figure 17 presents the average coefficients of performance depending on the mode of operation per type of machine and per site. The first column corresponds to the heat pump performance without the auxiliaries. The following column shows the COP in a heating mode. The HPSs heating COPs are higher than the ones of standard HPs. This is due to the lower electric power of the HPS available in the tables of performance. On the contrary, cooling COPs are similar for both machines. The COP in the simultaneous mode is much higher in Marseille than in Rennes and Brussels. In Marseille the simultaneous mode is used in majority for cooling and DHW production whereas in the other sites, this mode is run in majority during winter sequences. In the first case, the heating and cooling capacities are useful energies that count in the COP calculation. During winter sequences, the cooling energy is not useful. Therefore it is not taken into account.

Table3: Performance factors of heat pumps depending on the site

Figure 17: Coefficients of performance of heat pumps depending on the operating mode

CONCLUSION

A Heat Pump for Simultaneous heating and cooling has been designed in the aim of heating and cooling small office and residential buildings and also producing domestic hot water.

Running costs and greenhouse gas emissions can be diminished by using the same electric energy to produce hot and chilled water simultaneously. This machine also proposes an answer to reduce the performance loss of air-to-water heat pumps under low ambient temperatures and especially during defrosting sequences by alternation between an air evaporator and a water evaporator. Especially, it increases the average performance in heating and liberates the air evaporator to carry out defrosting without stopping the heat production.

A model has been developed under the TRNSYS environment to assess the performance improvement of a HPS compared to a standard reversible air-to-water heat pump. The model was fitted and validated by the results of experiments run on a 15 kW heating capacity HPS prototype. Simulations were run with three different weather data files: Rennes, Marseille and Brussels. However the model can still be improved, namely in terms of sizing procedure, it results in a fair comparison between the HPS and a standard HP. The colder climate (Brussels) took more benefit from the winter alternated sequence for performance improvement and defrosting. In that case, the HPS outperformed the standard reversible airto-water heat pump by 19% in terms of COP. The simultaneous mode played a significant role in the performance improvement in spite of the low part of electricity consumed in this mode compared to the other modes of operation. In buildings where simultaneous needs appear in a sufficient proportion like in the case described in this paper, it looks obvious to resort to heat pumps with heat recovery such as the HPS.

Appendix 1: Table of input power and thermal capacities (kW) of the HPS having a 10 kW heating capacity for T hso = 5 °C and T hsi = 35 °C in a heating mode

c Q & sc Q & h Q & W & c Q & sc Q & h Q & W & c Q & sc Q & h Q & W & c Q & sc Q & h Q & W & c Q & sc Q & h Q & W & c Q & sc Q & h Q & W & c Q & sc Q & h Q & Appendix 2:
W & c Q & sc Q & h Q & W & c Q & sc Q & h Q & W & c Q & sc Q & h Q & W & c Q & sc Q & h Q & W & c Q & sc Q & h Q & W & c Q & sc Q & h Q & W & c Q & sc Q & h Q &

Figure 2 :

 2 Figure 2: Schematic side view of the three-fluid air heat exchanger

Figure 3 :

 3 Figure 3: Scheme of the simulation model of the heat pump coupled to the building

Figure 4 :

 4 Figure 4: 3D-view of the building

Figure 5 :

 5 Figure 5: Control signal for cooling needs

Figure 6 :

 6 Figure 6: Set temperature for hot water depending on ambient temperature

Figure 7 :

 7 Figure 7: Scheme of the detailed heat pump modelling

Figure 8 :

 8 Figure 8: Comparison of experimental and modelled values of mass flow rate The Trnsys model is validated in terms of electric power and thermal capacities using experimental data and results from Selection Software 7 from Emerson Copeland (2008).Figure9shows the comparison of electric power in a heating mode, depending on the source temperature, for two hot water inlet temperature T hw-in at the condenser, between our model of heat pump ("model"), the model from the manufacturer ("man") and the experimental results ("exp"). Agreement is considered satisfactory as the experimental results and the manufacturer's model results are within the uncertainty bars of 5% applied to the homemade model. Nevertheless some improvement can still be achieved with more model development. Indeed, at a hot water temperature of 30 °C, the model is systematically underestimating the experimental values.

Figure 9 :Figure 10 :

 910 Figure 9: Comparison of electric power between models and experiments depending on source temperatureFigure10shows the comparison of heating capacities in a heating mode. Good agreement is achieved. As in figure9, the uncertainty bars represent ± 5 %. The other modes have been checked and validated with an uncertainty of 5 % in the more frequent source temperature range. For extreme conditions, the model is validated with an uncertainty of 10 %.

Figure 11 :

 11 Figure 11: Evolution of power input and thermal capacities of HPS model depending on the heat source temperature for a heat sink temperature of 35 °C (extract of appendix 1)

Figure 14 :

 14 Figure 14: Needs in domestic hot water production, space heating and space cooling depending on the climate.

Figure 16 :

 16 Figure 16: Electricity consumptions of the heat pumps depending on the operating mode

Table 1 :

 1 Specifications of HPS components

	Component	Specification
	Compressor	Swept volume: 14.5 m³/h
	Brand: Copeland	Nominal cooling capacity
	Type: Scroll	(Tev = 0°C / Tcd = 40°C):
	Ref: ZB38KCE-TFD	11.5 kW
	Water heat exchangers	Type: plate heat exchanger
	condenser	50 plates, 2.45 m²
	evaporator	34 plates, 0.8 m²
	subcooler	14 plates, 0.16 m²
	Air heat exchangers	Type: finned tubes, 68 m²
		6 rows of 30 tubes
		(l = 750 mm , Ø = 10 mm)
	Working fluid	R407C

Table 2 :

 2 Sizing of the HPSs and standard HPs depending on the climate

	Site	Heat pump	T base (°C)	Needs at T base (kW)	Nominal heating capacity at T base (kW)	Heating capacity at T base (kW)	Sizing factor	Auxiliary heating power (kW)
	Rennes	HPS Standard HP	-4	38.11	7.07 7.1	30.49	4.31 4.29	15.24
	Marseille	HPS Standard HP	-5	28.11	6.83 6.85	22.49	3.29 3.28	11.24
	Brussels	HPS Standard HP	-8	52.6	6.19 6.24	42.08	6.8 6.74	21.04

Table of

 of

	7,61 7,42 7,22 7,03 6,85 6,71	2,14 2,39 2,65 2,92 3,19 3,49	8,97 8,77 8,53 8,30 8,08 7,86	2,18 2,46 2,74 3,02 3,31 3,61	10,46 10,23 10,00 9,73 9,47 9,21	9,65 9,29 8,88 8,42 7,91 7,36	1,99 2,21 2,44 2,67 2,89 3,12 2,18 2,50 2,82 3,13 3,44 3,75	12,07 11,86 11,59 11,30 11,01 10,71	11,50 10,98 10,45 9,91 9,36 8,81	1,97 2,25 2,53 2,82 3,12 3,42 2,10 2,46 2,82 3,18 3,54 3,89	13,85 13,59 13,30 12,99 12,67 12,35	13,63 12,92 12,28 11,71 11,21 10,77	1,88 2,17 2,47 2,79 3,13 3,48 1,98 2,38 2,78 3,17 3,56 3,96	corresponding standard heat pump	and thermal capacities (kW) of the	input power


Jean Maysonnave

Nathan Jukam
email: nathan.jukam@rub.de

M Shahrizan

M Ibrahim

Rakchanok Rungsawang

Kenneth Maussang

Julien Madéo

Perrick Cavalié

Paul Dean

Suraj P Khanna

D Paul Steenson

Edmund H Linfield

A Giles Davies

Sukhdeep S Dhillon

Jérôme Tignon

Measuring the sampling coherence of a terahertz quantum cascade laser

Keywords:

The emission of a quantum cascade laser can be synchronized to the repetition rate of a femtosecond laser through the use of coherent injection seeding. This synchronization defines a sampling coherence between the terahertz laser emission and the femtosecond laser which enables coherent field detection. In this letter the sampling coherence is measured in the time-domain through the use of coherent and incoherent detection. For large seed amplitudes the emission is synchronized, while for small seed amplitudes the emission is non-synchronized. For intermediate seed amplitudes the emission exhibits a partial sampling coherence that is time-dependent.

©2012 Optical Society of America

Introduction

A femtosecond laser pulse can measure (or sample) the phase-resolved value of a terahertz (THz) electric field by using techniques such as photo-conductive sampling [START_REF] Auston | Picosecond optoelectronic detection, sampling, and correlation measurements in amorphous semiconductors[END_REF][START_REF] Exter | High brightness beams characterized with an ultra-fast detector[END_REF], electro-optic detection [START_REF] Valdmanis | Picosecond electro-optic sampling system[END_REF][START_REF] Nahata | A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling[END_REF], and air-plasma sampling [START_REF] Dai | Detection of broadband terahertz waves with a laser induce plasma in gases[END_REF]. The sampling of THz fields with femtosecond pulses is often referred to as coherent detection in the literature [START_REF] Auston | Coherent time-domain far-infrared spectroscopy[END_REF], and depends on the absence of timing jitter (i.e. prefect synchronization between the THz pulses and the femtosecond pulses). If the femtosecond and THz pulses are synchronized with respect to each other, a large number of sampling events can be summed coherently without adding different phase values. Time-resolved measurements of the THz fields can be achieved by changing the delay time between the femtosecond and the THz pulse with an optical delay line. By transforming the field into the frequency domain, the spectral amplitude and phase can be recovered. As a result THz time-domain spectroscopy (TDS) is a widely used technique to investigate phenomena at THz frequencies [START_REF] Schmuttenmaer | Exploring dynamics in the far-infrared with terahertz spectroscopy[END_REF].

In contrast, if the THz pulses are not synchronized with the femtosecond laser, successive femtosecond pulses will sample different parts of the successive THz pulses, and the sum of a large number of sampling events will approach zero. The standard deviation of nonsynchronous sampling events can be significant; this can enable frequency information to be retrieved [START_REF] Gaal | Measuring the optical frequencies in the 0-40 THz range with non-synchronized electro-optic sampling[END_REF]. And if the THz field and signal are strong enough, single shot phase-resolved measurements can also be made [START_REF] Jiang | Single-shot spatiotemporal terahertz field imaging[END_REF]. However, in typical experimental arrangements, a large number of sampling events takes place, and this prevents phase-resolved detection of nonsynchronized THz signals. The inability to detect non-synchronized radiation can be an advantage when a strong background signal must be removed [START_REF] Cheville | Far-infrared terahertz time-domain spectroscopy of flames[END_REF]. For example coherent THz detection can be used to probe the gain [START_REF] Kröll | Phase-resolved measurements of stimulated emission in a laser[END_REF][START_REF] Jukam | Investigation of spectral gain narrowing in quantum cascade lasers using terahertz time domain spectroscopy[END_REF][START_REF] Burghoff | A terahertz pulse emitter monolithically integrated with a quantum cascade laser[END_REF] of THz quantum cascade lasers (QCLs) [START_REF] Williams | Terahertz quantum cascade lasers[END_REF] without detecting the non-synchronized laser emission of the QCL.

Sampling coherence can be defined as the correlation (i.e. synchronization) between the THz pulse and the sampling femtosecond pulses which permits coherent detection.

Traditionally THz sources have exhibited either complete sampling coherence (e.g. THz femtosecond based sources) or incomplete sampling coherence (e.g. thermal sources). However, recently, THz QCLs were synchronized to femtosecond lasers using coherent injection seeding [START_REF] Oustinov | Phase seeding of a quantum cascade laser[END_REF] and a feedback stabilization/injection locking scheme [START_REF] Barbieri | Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis[END_REF]. This enabled coherent detection of the phase-resolved emission from a QCL in the time domain and presents the possibility of using QCLs as sources for THz TDS. Although QCLs are sources of bright, narrow-band THz radiation, QCLs can also be designed with ultra-large gain bandwidths [START_REF] Scalari | Broadband THz lasing from a photon-phonon quantum cascade structure[END_REF] and mode-locked for short pulse formation [START_REF] Barbieri | Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis[END_REF][START_REF] Wang | Modelocked pulses from mid-infrared quantum cascade lasers[END_REF]. However, in contrast to other THz sources QCLs may exhibit partial sampling coherence, in addition to complete and incomplete sampling coherence. If QCLs are to realize their full potential as synchronized THz sources, diagnostic measurements of the sampling coherence must be developed preferably in the time-domain.

In this letter, we measure the degree of sampling coherence between a QCL and a femtosecond laser. (The femtosecond laser triggers coherent THz pulses that injection seed the QCL.) The sampling coherence is measured by using electro-optic sampling in two different configuration geometries to record the synchronized THz field component and the envelope of the instantaneous THz intensity (which includes both synchronized and nonsynchronized components). This permits the sampling coherence to be measured on picosecond time scales.

Synchronized field measurements in the quarter wave geometry

The QCL is based on a bound-to-continuum design with a single plasmon waveguide (length 2.85mm) that shows laser action at 2.5THz. All measurements are taken at 10K. THz seed pulses are generated by illuminating an inter-digitated photoconductive antenna [START_REF] Dreyhaupt | High-intensity terahertz radiation from a microstructure large-area photoconductor[END_REF] with femtosecond laser pulses. An RF pulse is produced by illuminating a fast photodetector with a portion of the femtosecond laser beam. The RF pulses are subsequently amplified with a GaN power amplifier (with a nominal bandwidth of 20MHz-6GHz, and a saturation power of 10W) before they are sent to the QCL. The THz seed pulse is coupled into the QCL cavity while an RF electrical pulse drives the QCL bias above threshold as shown in fig. 1(a). This places the QCL in a transitory state where the gain can be greater than the losses and large amplification can occur [START_REF] Jukam | Terahertz amplifier based on gain switching in a quantum cascade laser[END_REF]. Both the QCL spontaneous emission and the injected THz seed pulse are amplified until the internal THz field is strong enough to saturate the QCL gain and clamp it to the total losses. Since the THz seed is phase-locked to the femtosecond laser, emission originating from the THz seed is synchronized and can be detected in the quarter-wave geometry. In contrast emission originating from amplified spontaneous emission (ASE) in the QCL has a random phase, and cannot be detected in the quarter-wave geometry since it is not synchronized to the femtosecond laser.

The synchronized field measured in the quarter-wave geometry [START_REF] Nahata | A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling[END_REF] is shown in fig. 1(c). The THz seed pulses undergo multiple passes through the QCL cavity, which correspond to reflections of the THz pulse at the ends of the cavity. Initially the pulses are amplified as the RF pulse turns on the QCL. After ~150ps the amplitude of the THz output pulses (at the cavity round-trip time of ~70ps) are more or less constant, and remains so for ~400ps which corresponds to the duration of the RF pulse as shown in fig. 1(b). (Besides the primary seed pulse at ~0ps which occur at the round-trip time, secondary seed pulses arises from reflections in the photoconductive antenna substrate. Without the secondary seed pulses the QCL emission would only consist of the primary pulses separated by the round-trip time [START_REF] Maysonnave | Integrated injection seeded THz source and amplifier for time-domain spectroscopy[END_REF].)

Figure 1d shows the amplitude of the fourth, fifth, sixth and seventh THz pulses as a function of the antenna bias voltage, which is proportional to the amplitude of the THz input pulse [START_REF] Oustinov | Phase seeding of a quantum cascade laser[END_REF]. The amplitude of the THz output pulse saturates as the amplitude of the input THz seed pulse increases. This implies that the amplified seed pulse (generated with an antenna bias of 4.0V) in fig. 1(c) saturates the QCL gain, and indicates any non-synchronized field component in fig. 1(c) is small at the fourth, fifth, sixth, and seventh round-trip times.

However, at other times between the round trip pulses such as 341.5ps, which is shown in fig.

1(e), no synchronized field is present. Incoherent measurements of the intensity-envelope in the cross-polarizer geometry are then necessary to determine if a non-synchronized field component is present.

Fig. 1 a) RF pulses bias the QCL along with a quasi-DC bias added with a bias tee (BT). THz seed pulses (generated from a photoconductive antenna [PC]) are coupled into a facet of the QCL. The output from the opposite facet is focused onto a ZnTe crystal for electro-optic detection, which takes place in either a quarter-wave geometry with a λ/4 wave-plate and Wollaston prism (W), or a cross-polarizer geometry with an analyzer (A). The detection geometry can be changed by moving a mirror on a translation stage. b) The RF pulse measured with a pick-off tee (PT). The zero position is approximate and cannot be calibrated with the zero position of the femtosecond delay line. c) The synchronized THz field of the injection seeded QCL measured in the quarter-wave geometry. A quasi-DC bias of (1.91V, 70 A/cm 2 ) is applied to the QCL, which is significantly less than the threshold bias (3.21V, 125 A/cm 2 ) and the maximum QCL power bias (3.63V, 157 A/cm 2 ). A 6W RF pulse, which experiences a significant reflection from the impedance mismatch of the QCL, drives the QCL above threshold to roughly the maximum QCL power bias. The photoconductive antenna is biased at 4V. d) Maximum peak-to-peak (p-p) THz field of the fourth, fifth, sixth, and seventh round-trip pulses in c) as a function of the THz antenna bias voltage, which is proportional to the seed amplitude). e) A portion of part c, for which the synchronized THz field approaches zero.

Measurement of the total emission of the QCL in the cross polarizer geometry

Electro-optic sampling in the cross-polarizer geometry has an intensity response that can be used to measure the power emission of a non-synchronized QCL [START_REF] Rungsawang | Intensity detection of quantum cascade laser radiation using electro-optic sampling[END_REF][START_REF] Darmo | Quasi phase-matched terahertz detector[END_REF]. However detection in the cross-polarizer geometry also contains a strong amplitude response that is typically much greater than the intensity response [START_REF] Jiang | Electro-optic sampling near the zero-transmission point[END_REF]. In this work the coherent response is completely removed from the cross polarizer signal by using a fast scan and antenna modulation technique described in the Appendix. This allows the instantaneous intensityenvelope of the QCL emission to be measured even in the presence of a strong synchronized THz field which would normally dominate the signal of the cross-polarizer measurement. When the RF pulse is applied in the absence of the THz seed in fig. 2

Measuring the sampling coherence in the time-domain

For coherent detection in the quarter-wave geometry the sampled field, E s (τ), can be expressed as the cross-correlation between the envelope of the femtosecond laser power, P t τ , and the actual THz electric field, E THz (t) as

  = ≈     ∑ ∫ (1)
In eq. ( 1) τ is the time delay introduced by the optical delay line, t is the laboratory time, T is the period of the femtosecond pulses, fs J is average integrated energy of each laser pulse, n is an integer, and L is the number of femtosecond pulses in the measurement, which is typically a very large number. If the duration of the laser pulse is much less than the period of the THz wave, the laser pulses can be approximated as a train of dirac delta functions. Eq. ( 1) assumes ideal electro-optic sampling and does not take account of phase matching, absorption, or any frequency dependence of the electro-optic coefficient. If the THz field is not correlated with the femtosecond pulse the sampled THz field will go to zero as the number of samples (L) increases. Coherent detection in the quarter wave geometry is thus not only a measure of the THz field strength, but also a measure of the mutual correlation between the QCL and the femtosecond laser, which is the sampling coherence. Sampling coherence is a distinct concept from temporal coherence, since temporal coherence is determined by the self-correlation ( )

THz THz E (t-τ)E (t)dt

∫

of the THz field. The degree of sampling coherence, γ s (τ), can be defined as the ratio of the envelope function of the sampled field to the envelope function of the actual field. (Note that if the sampling coherence were defined in terms of the fields, γ s (τ) would oscillate with the phase of the THz frequency.) If γ τ 1 the femtosecond laser and THz radiation are perfectly synchronized, while if γ τ 0 there is no synchronization between the THz emission and the femtosecond laser.

The sampling coherence depends on the amplitude of the injected seed pulse as shown in fig. 3. For the smallest THz seed pulse, shown in fig. 3(a) and (e), the QCL emission is predominantly non-synchronized, γ s ~ 0. Here the amplitude of the seed pulse is significantly less than the RMS of the spontaneous emission, and the majority of QCL emission arises from ASE. The amplified THz pulses are proportional to the input pulse. This linear amplification regime corresponds to the lowest seed amplitudes (or THz antenna biases) of the saturation curve in fig. 1(d). For larger THz seed pulses, the QCL emission exhibits partial sampling coherence, as shown in fig. 3(b) and(c). THz sources are often assumed to be either completely synchronized (γ s = 1) or non-synchronized (γ s = 0) with respect to the femtosecond laser, but fig. 3(f) and (g) show that this is not always true. In addition the sampling coherence is maximized for delay times that correspond to an integer number of round-trips of the seed pulse. This demonstrates that partial sampling coherence cannot be completely characterized by integrated time-average measurements of the synchronized and non-synchronized power. For the largest THz seed amplitude, shown in fig. 3(d) and (h), the QCL emission is predominately synchronized with the femtosecond laser, except for times where the total emission is very small. This is the injection seeding regime where the amplitude of the seed pulse is significantly greater than the RMS field of the spontaneous emission. In this regime the THz seed initiates lasing and saturates the QCL gain. In fig. 3(d), 98% of the integrated THz power is synchronized with the femtosecond laser, which indicates the majority of the QCL power originates from the amplified seed pulse. Fig. 3 a-d) Blue curves are the Mean square (MS) synchronized field-envelope. Red curves are the total (synchronized and non-synchronized) MS field-envelope. The green curves are the MS non-synchronized field-envelope and are found by subtracting the MS field-envelope (blue curve) from the total MS field-envelope (red curve). The THz seed pulses are generated with photo-conductive antenna biases of a) 0.05V, b) 0.2V, c) 0.8V, and d) 4.0V. The amplitude of a THz seed pulse is proportional to the antenna bias. e-h) The degree of sampling coherence as a function of time for the corresponding curves in a-d). For all curves a quasi-DC bias of 1.91V (70 A/cm 2 ) is applied to the QCL along with 6W of RF power.

Conclusion

Techniques are being developed to phase-lock THz QCLs for coherent detection, since such phase-locked QCL sources could have a major impact on far-infrared spectroscopy. However coherent detection is incapable of detecting non-synchronized radiation and the measured synchronized field may not be representative of the actual field. Although the degree of synchronization, i.e. the sampling coherence, of QCLs can be characterized with average power measurements, this assumes the sampling coherence is constant in time. In the present work the sampling coherence of an injection seeded QCL was characterized on picosecond time scales. Electro-optic sampling in the cross-polarizer geometry enabled measurements of the instantaneous power emitted from the QCL. The sampling coherence was found to be time dependent, illustrating the importance of time-resolved measurements. Besides verifying whether QCLs exhibit complete sampling coherence for all times, time-resolved measurements of the sampling coherence could be used to investigate phase-locking and synchronization processes in QCLs. For example the response of the sampling coherence to an incoherent pump which de-synchronizes the QCL could be studied in the time domain.

Appendix: Coherent and incoherent detection in the quarter-wave and cross-polarizer geometries

The THz field, E THz (τ), induces a small birefringence, Γ(τ), between the principal axes of the electro-optic crystal, which is transferred to the polarization state of the femtosecond sampling beam. The birefringence is proportional to the THz field, E THz (τ) = ηΓ(τ), where η is a constant that depends on the crystal's length, electro-optic coefficient, index, and orientation. This neglects absorption, phase-matching effects, and the frequency dependence of the electro-optic coefficient. However the ZnTe crystal used in the present study is thin enough (200µm) so that these effects can be neglected [START_REF] Gallot | Measurement of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of THz radiation[END_REF]. The strength of the electro-optic signal, EO λ/4 (τ), in the quarter-wave geometry is

( ) ( ) ( ) ( ) o o o 4 EO t P sin P P E . τ τ τ THz λ η = Γ ∝ Γ =     (2)
In eq. ( 2) P o is power of the femtosecond sampling beam, and the small angle approximation is used. In the cross-polarizer geometry the strength of the detected electro-optic signal is

( ) ( ) ( ) ( ) { } 2 2 2 cross o o o THz o THz EO P sin P E τ 2 τ E τ . t η η    ∝ Γ  = Γ + Γ + (3)
In eq. ( 3) Γ o is the optical bias attributed to a residual birefringence in the ZnTe [START_REF] Jiang | Electro-optic sampling near the zero-transmission point[END_REF]. Terms that do not depend on Γ(τ) are neglected, since the THz field is modulated for lock-in detection. In contrast to the quarter-wave geometry, the cross-polarizer signal contains two terms; an amplitude response, 2ηΓ o E THz (τ), and a square-intensity response, η 2 E 2 THz (τ). If only non-synchronized radiation is present, the varying phase will cause the amplitude term to average to zero. The cross-polarizer signal will then measure the mean square (MS) of the THz field-envelope, and can be used to measure the emitted power from a non-synchronized QCL [START_REF] Rungsawang | Intensity detection of quantum cascade laser radiation using electro-optic sampling[END_REF][START_REF] Darmo | Quasi phase-matched terahertz detector[END_REF]. For synchronized radiation the amplitude response will often dominate since typically 2Γ o >> Γ(τ). As a result electro-optic detection in the cross-polarizer geometry can be used as an alternative to the quarter-wave geometry for coherent detection [START_REF] Jiang | Electro-optic sampling near the zero-transmission point[END_REF]. By using the following described techniques, electro-optic sampling in the cross-polarizer geometry can function as an incoherent detector which is only sensitive to the total MS fieldenvelope. An antenna modulation technique can be applied to remove the amplitude response in the cross polarizer geometry. Applying an opposite voltage to the THz generating antenna creates an identical THz seed pulse with an opposite sign. The sign of the amplitude component can then be modulated without changing the value of the square-intensity component in eq. [START_REF] Valdmanis | Picosecond electro-optic sampling system[END_REF]. In theory this should enable lock-in detection to remove the amplitude response, and only measure the square response. In practice this reduces the amplitude response by a factor of ~200. To eliminate the residual amplitude component and the oscillation component of the square-intensity response a fast scan technique is employed. The optical delay line is scanned at a relatively fast speed of ~1ps/second (delay time/laboratory time) while using a long time constant (1 second) with a 24dB/octave roll-off filter. This averages out the residual sinusoidal oscillations. The fast-scan technique works since the slowly varying envelope approximation is valid for the QCL emission, i.e. changes in the pulse-envelope take place on a longer time scale than the field oscillations. Although the fast scan technique shifts the signal to later times (the data is shifted by ~4ps), measurements at shorter and longer time constants show the shape of the MS-field envelope is not affected. The antenna modulation and fast scan techniques permit electro-optic sampling in the cross polarizer geometry to only detect the MS field-envelope.

The signal response of the separate detectors used for the cross-polarizer and quarterwave geometry is calibrated using the data in fig. 2(a) and (b). When laser action is initiated by spontaneous emission in fig. 2(a), no laser emission occurs before 200ps. Any emission before 200ps arises from the THz seed and can be used to calibrate the cross-polarizer and quarter-wave geometry detector response.

Fig. 2

 2 Fig.2The mean square (MS) field-envelope of the total emission (synchronized and nonsynchronized) of the QCL measured in the cross-polarizer geometry in the absence of a THz seed pulse a) and with a THz seed pulse b). For part b) an antenna bias of 4.0V is used to generate the seed. c) The square of the phase-resolved synchronized field measured in the quarter-wave geometry, with a 4.0V THz antenna bias. The time scale is too large to discern the individual field oscillations. (The MS field envelope is half the maximum value of the squared field.) For all graphs the RF power is 6W, and the quasi-DC bias is 1.91V-70 A/cm 2 .

  (a); lasing action is initiated by ASE; all phase information is lost; and only the mean square of the envelope of the field (MS field-envelope) is constant from pulse to pulse. The shape of the MS fieldenvelope when the QCL is seeded, which is shown in fig 2(b), is considerably different from when the QCL is not seeded. In fig.2(b) laser action is initiated by the THz seed pulse, and QCL emission begins at a significantly earlier time due to the large amplitude of the initial seed pulse. In contrast to the non-seeded emission in fig.2(a), the seeded emission in fig.2(b) consists of several peaks separated by the round-trip time. The maximum field of the seeded emission is 2.6 times larger than that of the non-seeded emission. The peaks of the synchronized field in fig.2(c), which are obtained from the data in fig.1(c), correspond perfectly with peaks of the MS field-envelope in fig.2(b) which indicates that a significant portion of the QCL emission is synchronized to the femtosecond laser.

Acknowledgements This work was supported by ANR projects "HI-TEQ" (ANR-09-NANO-017) and "THINQE-PINQE" (ANR-09-NANO-007) (France); ERC Advanced Grant projects NOTES, TOSCA, and EPSRC (UK); the Royal Society; and the Wolfson Foundation. MSMI acknowledges support from the MARA Agency, Government of Malaysia.


K Saleh
email: ksaleh@laas.fr

P H Merrer

O Llopis

Gilles Cibiel

Optoelectronic Oscillator Based on Fiber Ring Resonator: Overall System Optimization and Phase Noise Reduction

Theoretical and experimental optimization studies are presented in this paper, where the aim is to improve the phase noise of an optoelectronic oscillator based on a passive fiber ring resonator. Our experimental results demonstrate a significant reduction in the phase noise of the final optimized system, which is also compared to the best existing oscillator of the same type, an active cavity based coupled optoelectronic oscillator.

I.

INTRODUCTION

Optoelectronic oscillators (OEOs) are usually based on optical delay lines in order to generate high spectral purity microwave signals above 10 GHz. However, these systems are bulky (few-km-long optical fibres) [START_REF] Eliyahu | Low phase noise and spurious level in multiloop opto-electronic oscillators[END_REF], their thermal stabilization is difficult and they produce spurious modes which need bulky and complex systems to be reduced [START_REF] Okusaga | Spurious mode reduction in dual injectionlocked optoelectronic oscillators[END_REF]. The design of compact and high performances oscillators is linked to the investigation of new resonators. In classical microwave resonators field, the quality factors (Q RF ) decrease at high frequencies. This limits their efficiency to build high purity sources in the millimetre wave range. The best microwave resonators performance in terms of quality factor are today obtained using whispering gallery modes (WGM) sapphire crystal cylindrical resonators, with unloaded quality factors that can reach 2x10 5 at 10 GHz frequency.

An alternative optical solution, other than delay lines, is the use of optical resonators, featuring ultra-high optical quality factors (Q Opt > 10 9 ) and relatively low dimensions. WGM optical resonances in disk or sphere resonators may lead to such Q factors [START_REF] Savchenkov | Kilohertz optical resonances in dielectric crystal cavities[END_REF]. However, the use of these tridimensional shape resonators in a system is delicate, because of the mechanical difficulty in setting up a reliable coupling with a light source. Another approach is to take benefit of low loss proprieties of optical fibers technology to realize high Q Opt fiber ring resonators (FRRs). In the FRR case, the microwave signal is carried to the optical domain using a laser signal (λ laser ~1.55µm) via optical amplitude modulation, and the laser must be stabilized to an optical resonance. These FRRs are compact (few meters long), easy to fabricate and to use.

In this paper, a 10 GHz OEO based on a passive FRR is theoretically and experimentally studied to reduce its phase noise. First we give a brief description on the FRR and the OEO based on. Optimization studies are then detailed in the other parts of the paper. Finally, noise results of an optimized 100m FRR based OEO are discussed and compared to the best existing and commercialized OEO of the same type: a 330m cavity based coupled optoelectronic oscillator (COEO) [START_REF] Eliyahu | Modulation response (S21) of the coupled opto-electronic oscillator[END_REF].

II. OPTOELECTRONIC OSCILLATOR BASED ON A FIBER RING RESONATOR

A. Fiber Ring Resonator

The optical FRR is depicted in Fig. 1. It is realized using two symmetrical and low loss directional couplers, linked with single-mode polarization-maintaining (PM) optical fibers. The total length of our first FRR realization was 10 meters. Resonances occur in the resonator if the total integrated phase shift of the incident laser wave around the resonator ring is an integer multiple of 2π radian. This resonator is thus characterized by a single transverse resonant frequency comb Funding from ANR project "ORA" 2010 BLAN 0312 03 with a free spectral range (FSR) related to the fiber length (L) and its refractive index (n) by:

L n c FSR ⋅ = (1)
where c is the speed of light in free space.

The quality factor in this resonator depends on the couplers coupling factors and the overall losses in the resonator architecture (couplers excess loss, splices losses…). One of the advantages of this resonator is that its optical resonance 3dB bandwidth is maintained when used in the microwave domain. The equivalent Q RF factor is linked to the Q Opt factor and is directly proportional to the microwave application frequency f RF . This relation is given below:

Opt RF Opt RF v f Q Q ⋅ = (2)
where ν Opt is the laser optical frequency (193 THz).

From the relation above, it is clear that the resonator Q RF increases with the RF application frequency for a fixed optical frequency. Thus, to reach quality factors higher than those obtained in microwave resonators, Q Opt should be higher than 10 9 because of the frequency ratio between f RF and ν Opt , which is about 10 -4 for a laser carrier at 1.55 µm wavelength (around 193 THz) and a microwave signal around 20 GHz. Also, the resonator Q Opt factor is equivalent to a long optical delay line. This being said, the photons inside the resonator will encounter an optical delay (τ) as if they were travelling into a given equivalent optical fiber length in singlepass geometry. This equivalent length is given by:

Opt Opt eq f n c Q L . . . π = (3)
Thus, a resonator with a Q Opt of 3.5x10 9 (Q factor achieved with our second realization of a 20m FRR and accurately measured using the method described in [START_REF] Merrer | High-Q Optical Resonators for Stabilization of High Spectral Purity Microwave Oscillators[END_REF]), is equivalent to a 1180 meter long optical delay line. This high Q Opt leads to a significant circulating power inside the cavity [START_REF] Zhang | Direct-coupling single-mode fiber ring resonator[END_REF], (P Cavity /P Input ~ 54), which in turn reduces the thresholds of many nonlinear optical effects, as we will see later.

All these characteristics make the FRR interesting to be studied, especially when included in an OEO setup. We have thus theoretically and experimentally studied its behavior and then the OEO based on this FRR in order to get high performance, compact and low phase noise OEO.

B. Optoelectronic Oscillator

Our 10 GHz OEO based on a FRR, is presented in Fig. 2. It includes a Koheras laser with a very narrow linewidth (~ 1 kHz), a Mach-Zehnder modulator (MZM), a FRR, eventually an optical fibered EDFA amplifier and a fast photodiode (PD) -Discovery DCS30S. The laser frequency is then stabilized on one of the ring resonances using a low frequency Pound-Drever-Hall (PDH) feedback loop [START_REF] Drever | Laser phase and frequency stabilization using an optical resonator[END_REF]. The microwave oscillation is then maintained by another high frequency loop including two RF amplifiers, a phase shifter and a RF filter in order to get a single mode oscillation. In this PDH scheme, the laser carrier is phase modulated with a large modulation index at an RF frequency (ν G , from a signal generator) by means of an electro-optic modulator (EOM). The beam passes through the resonator and the transmitted beam is sent to the same PD of the oscillation loop. The amplitude of the PD output voltage at ν G depends on the detuning between the laser frequency and the optical resonance. This voltage signal passes through a low-pass filter to reduce its noise and eliminate unwanted higher modulation harmonics. It is then amplified and sent to an electrical mixer to be mixed with a fraction of the RF signal (ν G ) used to drive the modulator. The mixer output represents an error signal proportional to the frequency detuning between the laser and the optical resonance. This error signal is then sent to a proportional-integral-derivative controller (PID) in order to drive the laser piezoelectric actuator (PZT) and adjust its wavelength. Through our experimental studies, we have found that it is very important to accurately adjust the PDH loop parameters, because the OEO phase noise can be severely affected, as we will see in section III-1-a. Also, the PDH loop bandwidth seems to be a very critical parameter, because if it is reduced (especially the PID input and output filters), it can considerably degrade the OEO phase noise, (see the green and orange curves in Fig. 10).

III. OEO OPTIMIZATION STUDIES

A. 10m FRR with PM Fibers

Our first OEO realization was based on a 10m FRR. We used optical PM fibers to maintain the polarization of the carrier inside the resonator and prevent the deformation of the optical resonance response in the RF domain. However, the coupling factor (κ) in this 10m long FRR has not been optimized, (particularly the couplers excess loss was very high). The optical carrier to noise ratio at the resonator output was thus degraded. This directly affects the white frequency noise and the phase noise floor in the oscillator phase noise spectrum.

A Q Opt of 2x10 8 (Q RF of 1x10 4 at f RF = 10 GHz) has been obtained. This resulted in a high phase noise level for the OEO, (see the red curve in Fig. 9). To be able to get a better phase noise, the resonator Q Opt must be increased. This cannot be done unless if the coupling factor is optimized and losses are reduced. Thus, a new optimized 20m long FRR has been designed.

B. 20m Long FRR with an Optimized Coupling

The OEO white frequency noise contribution is directly linked to the optical noise to carrier ratio (NCR) and inversely proportional to the resonator quality factor as shown in the relation below:

( ) ( ) NCR f Q f f L m Opt Opt m log 10 . . 2 . 2 log 20 ⋅ + ⋅ = (4)
where f m is the noise modulation frequency (offset frequency).

From this relation, it is clear that to reduce this noise contribution part we have to increase the quality factor and reduce the NCR. However, these two parameters depend directly on the coupling factor, but change differently. A high Q Opt needs a low κ, but the NCR needs a high κ to be reduced. Thus, the white frequency noise contribution has been evaluated versus κ and an optimized coupling factor of 1% has been finally found to design a new 20m long FRR. The detailed study can be found in [START_REF] Bouchier | Theoretical and experimental study of the phase noise of optoelectronic oscillators based on high quality factor optical resonators[END_REF].

Using this 20m FRR we have first measured a Q Opt of 5.1x10 9 (Q RF of 2.5x10 5 at f RF = 10 GHz); The Q Opt has then degraded to 3.5x10 9 due to the extremely high intra-cavity power inside the resonator (10 mW at the resonator input means approximately a 540 mW inside the resonator at the resonance, which is higher than the couplers power limit (around 300 mW)). However, despite this very high Q Opt factor, the phase noise results obtained were far from theoretical expectations; (see the violet curve in Fig. 9). Consequently, different noise conversion processes have been suspected and studied. Also, nonlinear optical effects generation inside the resonator (because of its high Q Opt ) have been the field of many studies.

1) Laser Amplitude and Frequency Noise Conversions: a) Laser Frequency Noise Conversion to RF Amplitude and Phase Noise:

The laser frequency (FM) noise effects on the RF phase (PM) noise of delay line based OEOs have been already investigated in [START_REF] Volyanskiy | Contribution of Laser Frequency and Power Fluctuations to the Microwave Phase Noise of Optoelectronic Oscillators[END_REF]. It has been found that this noise conversion process comes essentially from chromatic dispersion in the optical delay line. However, our FRR based OEO is a more complex system, and in order to evaluate the laser FM noise conversion trough the resonator, we had to use a dedicated simulation approach. To this purpose, we have developed a model of the resonator on a microwave simulation software, ADS (Agilent). This model has been experimentally validated and then implemented in a global OEO model using the same software. The global OEO model includes the laser, the MZM, the resonator, the PD, the RF filter and the RF phase shifter…The modeling of the resonator using ADS will be detailed in a future publication. The OEO open loop response has been simulated by first stabilizing the laser carrier at the optical resonance center, and then by stabilizing the carrier to one of the resonance edges (right or left). The stabilization at the edges results in a deformation of the RF amplitude response (a splitted resonance) and a Q RF factor degradation. Also the RF phase transition response at the resonance frequency becomes less sharp, with two phase transitions corresponding to the two splitted resonances. These results have been validated experimentally by changing the PDH loop stabilization setpoint in order to stabilize the laser frequency on one of the resonance edges, (see Fig. 4).

These results confirm that the laser FM noise can be converted to RF AM and PM noise trough the FRR, especially if the resonator is not well stabilized to the resonance center. This means that the PDH loop is a critical parameter that must be carefully adjusted to prevent this kind of noise conversion in the OEO oscillation loop.

b) Laser AM Noise Conversion to RF AM and PM Noise:

It is well known that laser AM noise, called relative intensity noise (RIN), is one of the limiting factors of signals transmissions via optical links. This power fluctuation noise increases the link noise and degrades its NCR. Also, the baseband RIN can be up-converted to RF AM and PM noise via optical link nonlinearities, especially via the PD nonlinearities as it has been reported in delay line OEOs in [START_REF] Eliyahu | RF Amplitude and Phase-Noise Reduction of an Optical Link and an Opto-Electronic Oscillator[END_REF]. In our case, we have experimentally studied the PD nonlinear behavior versus the received optical power. The laser carrier was modulated at 10 GHz (the OEO frequency) via the MZM. The 10 GHz signal comes from a calibrated vector network analyzer (VNA) working in a CW mode. The amplitude and phase responses of the S 21 parameter were accurately measured (average = 1000) while changing the received optical power by using an optical variable attenuator just before the PD (the MZM nonlinearities were thus discarded). The results are presented in Fig. 5. The results of Fig. 5 reveal the presence of a reduced slope in the S 21 amplitude response (near PD saturation) and interestingly, two zero slopes in the S 21 phase response. Theoretically, one has to push the PD into saturation in order to reduce both RIN to AM and RIN to PM noise conversions. However, a 25 mW optical power is hard to get at the end of the OEO open loop optical link. Knowing that the RIN to PM noise conversion affects much more our OEO phase noise than the RIN to AM noise conversion, and that a 7 mW optical power at the optical link end is possible, we have chosen to work at this optical power in our new system based on a 100m FRR. In the 20m FRR based OEO, a 7 mW optical power was far from being achieved. In fact, the laser carrier saturates when passing through the FRR because of the generation of nonlinear optical effects inside the resonator, due to its very high Q Opt . These nonlinear optical effects, essentially stimulated Rayleigh (STRS) and Brillouin scatterings (SBS), were mostly the cause of the phase noise degradation in the OEO based on the 20m FRR.

2) Nonlinear Optical Effects Generation in the 20m FRR and Degradation of the OEO Phase Noise:

Due to its very high Q Opt (3.5x10 9 , after the Q Opt degradation as mentioned before), the 20m FRR is equivalent to a 1180 m delay line. Thus, the thresholds of many nonlinear optical effects will be reduced in the 20m FRR and will be close to those of a 1180 m long optical fiber. Also, if we add the fact that at resonance, the circulating power inside the resonator is approximately 54 times higher than the input power, we can conclude that the threshold will be also divided by 54. This has been experimentally observed by measuring the power of the different components in the optical spectrum at the second and third outputs of the resonator, versus the input optical power. We used an Agilent HP 86142A optical spectrum analyzer (OSA; with 0.06 nm resolution and ±1 dB amplitude precision). These measurements have revealed the presence of other optical components than the laser carrier: the Rayleigh and the Brillouin scattering waves at the resonator's second output, as they are both essentially backscattered (see Fig. 1). Optical power measurement results for both 20m FRR and the new 100m FRR are depicted in Fig. 6. In optical fibers, the Brillouin scattering is caused by the interaction between a light wave and an acoustic wave existing already at the optical medium thermal equilibrium. This interaction creates a scattered wave called Stokes wave; in this case we are in the spontaneous Brillouin scattering regime. In optical fibers, the backward scattered Stokes wave is privileged and is frequency downshifted from that of the incident pump light by an amount v B set by the nonlinear medium characteristics (v B ~ 11 GHz in silica fibers, [START_REF]Nonlinear Fiber Optics[END_REF]). However, a very weak and also backscattered wave called anti-Stokes wave but up-shifted in frequency by v B , can be also generated. At a critical incident light wave power, called stimulated Brillouin scattering threshold (SBST), the interference between the Stokes wave and the incident light wave amplifies the acoustic wave in a process called electrostriction. Thus, the scattered wave becomes more intense and reinforces the interference and so on; we are now in the stimulated regime. When the Stokes power exceeds the medium SBST, it creates a second order Stokes wave downshifted in frequency from the first Stokes wave by v B , and thus by 2v B from the incident light wave.

The Rayleigh and Brillouin scattering and their effects and use have been intensively studied in literature [START_REF]Nonlinear Fiber Optics[END_REF][START_REF] Zhu | Experimental study on stimulated Rayleigh scattering in optical fibers[END_REF][START_REF] Okusaga | Optical scattering induced noise in RF-photonic systems[END_REF]. Their contribution to optical links noise degradation and also to phase noise degradation in delay line based OEOs have been well explained in [START_REF] Okusaga | Optical scattering induced noise in RF-photonic systems[END_REF]. From Fig. 6, we can see that for the 20m FRR, and at an input power level as low as -10 dBm, the first Brillouin Stokes wave appears and its power starts to increase rapidly by converting the optical carrier power, making the carrier saturates. Also, the Rayleigh scattering power increases with the laser input power but remains constant after the Brillouin scattering process starts to be stimulated. Such a Rayleigh-Brillouin scattering behavior has been already thoroughly studied in single-pass geometry optical fibers [START_REF] Zhu | Experimental study on stimulated Rayleigh scattering in optical fibers[END_REF][START_REF] Okusaga | Optical scattering induced noise in RF-photonic systems[END_REF]. The saturation of the optical carrier prevents the PD from working at its optimal optical power and degrades the NCR of the optical link (see section III-B-1-b). Also, both Rayleigh and Brillouin scatterings introduce optical parasitic signals (higher order Brillouin Stokes and anti-Stokes waves, and their own Rayleigh waves) and noise which mixes with the OEO RF signal and degrades its phase noise.

We have experimentally studied the effect of these nonlinear optical phenomena on the OEO phase noise by reducing the input optical power, thus limiting the Brillouin scattering generation. The detailed study can be found in [START_REF] Saleh | Optical scattering noise in high Q fiber ring resonators and its effect on optoelectronic oscillator phase noise[END_REF]. We have found that a better close to carrier OEO phase noise can be obtained when the optical power is decreased, and a relatively good phase noise result has been obtained at -10 dBm input optical power (below the first SBST), (see the blue curve in Fig. 9). However, the phase noise shape was unusual. Some of the possible causes of this phase noise shape are the Rayleigh scattering, the spontaneous Brillouin scattering and the PD noise conversions.

C. 100m Long Immunized FRR

Knowing that a low optical power prevents optimal AM and PM responses of the PD and also degrades the OEO NCR, we have searched for a way to suppress the Brillouin scattering induced in the resonator and reduce the Rayleigh scattering, while maintaining a high optical quality factor.

The Brillouin scattering power depends essentially on the effective interaction length with the optical and acoustic waves in the optical fiber [START_REF]Nonlinear Fiber Optics[END_REF].The fact that photons circulates many times inside the 20m long FRR, due to its high Q Opt (high delay τ), as if it was a long delay line, increases the virtual interaction length (~1180m) between the spontaneous Brillouin scattering and the optical and acoustic waves. Thus, the spontaneous Brillouin scattering will be intensified all along this virtual optical fiber and becomes stimulated. Then it also creates other higher order SBS waves with their own Rayleigh scattering waves. One of the severe consequences is the optical carrier depletion due to these phenomena. Now, if a low loss isolator is inserted inside the resonator, it will completely prevent the SBS from building-up inside the resonator, due to the fact that virtually we will have a number (N) of isolators, equals to the photons laps number inside the resonator. These virtual isolators will be spaced by the loop length L, thus, the SBST inside the resonator will be reduced to be the SBST of the real resonator length L and not the SBST of its equivalent length L eq . Also the presence of the isolator will efficiently reduce the Rayleigh scattering.

Unfortunately, and despite the fact that the SBS will be suppressed and the STRS will be reduced, the isolator losses will be also multiplied by the number of turns N. So the Q Opt will be reduced unless if we optimize the resonator on different parameters (length, coupling factor, architecture, loss…) in order to compensate the isolator loss and get a satisfying quality factor and transmission loss, and finally a good phase noise result once the device is included in an OEO setup.

This optimization study has been performed using the FRR model over ADS, while always respecting the section III-B couplers optimization study. Using ADS, we have found that an optimized coupling factor of 8% in a 100m long FRR, while taking the resonator overall losses into account, must lead to a 92 kHz FWHM, thus a Q Opt of 2x10 9 (Q RF of 2.5x10 5 at f RF = 10 GHz), with a FSR of 2 MHz, a 4 dB optical transmission loss and a 22.5 dB rejection. Also, we have added an inline polarizer at the resonator input port in order to completely eliminate a possible two polarization states of the optical carrier at the input port, because PM fibers only maintain these states of polarization and do not ensure one state polarization behavior. The 100m immunized FRR (IFRR) architecture is depicted in Fig. 7. Using equation (4), we can expect a phase noise level of -134 dBc/Hz at 10 kHz offset frequency, (see dashed curve in Fig. 10). But if we add the phase noise contribution of the optical amplifier and the RF amplifiers used in the OEO setup, we can expect a -128 dBc/Hz phase noise level at 10 kHz offset frequency, (see blue curve in Fig. 10). Once the resonator has been realized, almost all experimental results were at expectations (Q Opt , rejection, FSR, transmission loss), (see Fig. 8). These characteristics were accurately measured using the VNA method described in [START_REF] Merrer | High-Q Optical Resonators for Stabilization of High Spectral Purity Microwave Oscillators[END_REF]. Also the SBS was completely suppressed, no carrier saturation has been observed (the carrier power at the resonator output increases linearly with a slope equal to 1) and the STRS was reduced (near 40 dB rejection), (see Fig. 6).

Finally, the 100m IFRR resonator has been included in the OEO experimental setup and a considerably reduced OEO phase noise has been measured, with a level of -128 dBc/Hz at 10 kHz offset frequency, and a -150 dBc/Hz noise floor, (see the green curve in Fig. 9).

IV. 100M IFRR PHASE NOISE RESULTS DISCUSSIONS AND COMPARAISION WITH THE COUPLED OEO RESULTS

The results obtained with the 100m IFRR are very interesting if compared with the 330m active-cavity based OEO, also known as coupled optoelectronic oscillator (COEO), currently commercialized by OEwaves [START_REF] Eliyahu | Modulation response (S21) of the coupled opto-electronic oscillator[END_REF]; see Fig. 10. Also, we can expect to get an even better result than the one presented in Fig. 10, if RF amplifiers contribution to the phase noise could be reduced, PDH loop is accurately adjusted and a low AM and FM noise laser is used.

CONCLUSION

We have presented theoretical and experimental studies performed in the aim to reduce the phase noise of a passive fiber ring resonator based optoelectronic oscillator (OEO). A phase noise level of -128 dBc/Hz at 10 kHz offset frequency has been measured in a 100m long passive-cavity based OEO. This result is close to the one obtained in a 330m active-cavity based coupled OEO. Improvement is still possible if the laser and RF amplifiers noise can be reduced.

Figure 1 .

 1 Figure 1. Double directional coupler fiber ring resonator, and the generation of nonlinear optical effects inside the 20m FRR.

Figure 2 .

 2 Figure 2. Optoelectronic oscillator based on an a fiber ring resonatorC. Laser Pound-Drever-Hall Stabilization LoopThe experimental setup for the PDH loop, used to stabilize the laser frequency to one of the resonator's resonances, is presented in Fig.3.

Figure 3 .

 3 Figure 3. PDH laser stabilization loop. EOM: electro-optic modulator; PID: proportional-integral-derivative controller.

Figure 4 .

 4 Figure 4. Experimental RF amplitude and phase responses of the resonance, deformed when the laser is stabilized at one of the resonance edge.

Figure 5 .

 5 Figure 5. Dicovery PD DCS30S S21 RF amplitude and phase responses versus received optical power.

Figure 6 .

 6 Figure 6. Power of the different optical components at the 20m and the 100m FRRs outputs versus the laser carrier optical power at the input. Rayleigh and Brillouin scatterings were measured at the FRRs second output.

Figure 7 .

 7 Figure 7. New 100m long immunized FRR.

Figure 8 .

 8 Figure 8. RF transmission characteristics of the 100m IFRR.

Figure 9 .

 9 Figure 9. Different phase noise results obtained through the different noise studies made to improve the phase noise of a FRR based OEO.Measurements are performed with an Agilent E5052 B signal source analyzer.

Figure 10 .

 10 Figure 10. 100m passive IFRR based OEO phase noise calculation and comparison with OEwaves 330m active-cavity based COEO. The effect of the PDH bandwidth reduction on the OEO phase noise is also presented.