Sabri Khssibi
email: sabri.khssibi@irit.frhanen.idoudi

Hanen Idoudi

Adrien Van Den Bossche

Thierry Val

Leila Azzouz Saidane
email: leila.saidane@ensi.rnu.tn

Presentation and analysis of a new technology for low-power wireless sensor network

Keywords: ANT, 802.15.4, BLE, WSN, MAC protocol

The tremendous and rapid development in sensors technology allowed their application in various fields requiring monitoring, such as, transportations, rare species surveillance, agriculture, military activities, medical field, etc. Due to their intrinsic constraints and limitations, several dedicated MAC protocols have been designed for wireless sensor networks and whose main objectives are bandwidth optimization while keeping very low energy consumption. One of the newest proposals is ANT which is emerging as a widely used MAC protocol for wellness and sports sensor devices. In this paper, we give a comprehensive overview of ANT/ANT+ and a comparison between ANT and two established standards: Bluetooth Low Energy (BLE) and 802.15.4/4a. We detail also some practical experiments we conducted to evaluate some characteristics of ANT.

INTRODUCTION

Wireless Sensor Networks (WSNs) have been proposed for many applications requiring the collection and aggregation of environmental data detected in a certain area of perception. We can mention some typical applications: the monitoring of vehicle movements in hostile area [START_REF] He | Energy-Efficient Surveillance Systems Using Wireless Sensor Networks[END_REF], the observation of the lives of rare species [START_REF] Mainwaring | Wireless Sensor Networks for Habitat Monitoring[END_REF], the monitoring of the structure of infrastructure [START_REF] Xu | A wireless sensor network for structural monitoring[END_REF] [4], medical assistance [START_REF]Wireless Medical Sensor Networks[END_REF], etc. Several researches are directed to design new MAC protocols adapted to the characteristics of wireless sensor networks. To this end, several MAC protocols [6] [START_REF] Polastre | Versatile Low Power Media Access for Wireless Sensor Networks[END_REF] [8] [START_REF] Ye | Medium Access Control With Coor-dinated Adaptive Sleeping for Wireless Sensor Networks, Networking[END_REF] have been proposed in the literature to optimize access to the wireless medium. In recent years, we have witnessed a major expansion of the ANT (Advanced and adaptive Network Technology) [10] protocol and its extension ANT+. These protocols are considered by the industrial community as a well suited architecture to the monitoring applications in sports and medical domains, where it is necessary to use wireless sensor networks.

ANT is a communication protocol with ultra low power consumption. It maximizes battery lifetime and provides the use of many channels. It has a very good theoretical baud rate which attends 1Mbps, making this protocol more suitable for Wireless Personal Area Networks with low bandwidth (LR-WPAN). ANT+ adds network management layers which enables interoperability, defines data structure, provides definition of node profile and manages network keys.

In this paper, we propose to present a theoretical overview of ANT and ANT+ and some practical tests conducted with real material. This paper is organized as follows: In the beginning, we present the basic principles of ANT protocol and ANT+. Then, we present a comparison between ANT, BLE [24] [25] [START_REF]Bluetooth low energy[END_REF] [27] [START_REF]Bluetooth low energy wireless technology backgrounder[END_REF] and 802.15.4/4a. Next, we present a practical study of ANT. In the end, a conclusion comes to take stock of our study and discusses the prospects for research on which we move.

PRESENTATION OF ANT

ANT is a protocol designed for wireless personal area networks (WPAN) with low power consumption, low processing power and low baud rate. The small size of the ANT protocol stacks allows the integration into components such as: PDAs, watches, phones, Smartphone, etc. It operates in the 2.4GHz ISM (Industrial, Scientific and Medical radio bands) band and allows for a flow baud rate of 1Mbps with transmission duration less or equal than to 150 microseconds / frame for 8bytes of data.

ANT Node

ANT defines two types of nodes. The first type is the master node. It is the initiator of communication, the responsible of controlling the channels and the transmitter of data (the primary transmitter). Its window of reception is used to provide the co-existence of many masters in the same network with the same frequency and to receive data from slaves or other masters (Figure 2).

The slave node, the second type of node, is the primary receiver of a frame from the Master and responsible of synchronization with the master (Figure 2 (a)).

In ANT protocol, a node can act as a master and a slave at the same time with different nodes. In Figure 2 (b), we have three nodes where the node 1 is a master of node 2 (slave in this case) and the node 2 is the master of the node 3 (slave).

ANT channels

Parameters

The ANT protocol uses 2.4 GHz bandwidth and divides it into 125 channels of width equal to 1 MHz and a baud rate of up to 1 Mbps. In order to create a connection between two nodes, they must have the same channel configuration. Then the slave needs to know several parameters we cite here after [START_REF]ANT Message Protocol and Usage, Application notes[END_REF].

a-Network

ANT can set up several private and public networks. In order to establish a communication between two nodes, they must be in the same network, which enables a network service that can be shared with multiple source nodes. On the other hand, we can establish a private network to ensure confidentiality and restrict access. ANT node can participate in several networks since the channels can be assigned independently to multiple networks. This parameter contains two information: Network number and Network key.

Network number is coded on 8 bits and varies between 0 and a maximum value fixed during the implementation of ANT. The default value of the network number is 0.

The Network Key is coded on 8 bits and configured by the application. Each network must have a network key. The key and the network number allow the deployment of networks with a varying level of security and access control.

Initially, the default network number is equal to 0 with a public network key and no rule for the use of the network. b-Frequency RF (Radio Frequency) It represents the frequency where the network operates. For example, if Frequency RF is equal to 66, then the network is operating at 2466 MHz.

In ANT protocol a channel must operate on a single frequency among the existing. The RF frequency is coded on 8 bits and varies between 0 and 124.

The Frequency RF value represents the offset from the 2.4 GHz by 1 MHz increment.

c-Channel ID

This is the most important information for the channel. The higher layers are responsible for the specification of this parameter. The value of Channel ID is coded on 4 bytes and contains the following information:

• Transmission type: 8 bits, it presents the type of transmission • Device Type: 8 bits, this field is used to differentiate between different types of nodes in the network, which allows participating nodes to know the different classes of connected nodes, and hence they can decode the information received. If the device type is equal to 0, the receiving node can connect to multiple types of nodes.

• Device Number: 16 bits, supposed to be unique in the network.

Table 1. Transmission types and characteristics

Forward direction Reverse direction

Broadcast

-Send the data in each time period.

-The data are not acknowledged.

-If the higher layer does not send new data, ANT retransmits the last data received by the HC layer.

-The frames are sent only once.

-Send at the end of the period of transmission of the master.

-Frames sent by this type of communication are never acknowledged.

Acknowledged

-The master may decide to send a frame with the request of acknowledgement during the step of establishing a two-way connection.

-The HC layer can choose to send all data frames with a request of acknowledgement or it mixes the broadcast transmission and data transmission with acknowledgment.

-Communication by request of acknowledgment of data uses more bandwidth and consumes more energy.

-This type of transmission is important for critical data.

-There is no automatic retransmission of data packets without acknowledgment.

-If the ANT protocol doesn't have a new data in the interval time, the last frame is retransmitted.

-The slave may send a frame to be acknowledged by the master at the end of the master transmission period during the stage of establishing a two way connection.

-There is no automatic retransmission of data packets without acknowledgment.

Burst

-This mechanism is used by the master to transmit a large amount of data to the slave.

-The burst transmission begins in the transmission period and it is expected to send a set of frames that must be acknowledged by the slave.

-All lost frames are automatically retransmitted.

-The transmission time is not limited -Data rate is up to 20kbps.

-The channel that uses this type of transmission has priority over all other channels Data can be sent to the master by the burst transmission in the same manner described in the master.

d-Channel type

This parameter defines the type of transmission that will occur in the channel. It is coded on 8 bits and can define eight types of communication.

e-Channel period

This is the basic frequency used by the master for transmission of data. By default, this parameter represents the interval time between two successive transmissions of data transmission with broadcast transmission (Figure 3). The frequency of data frames in a channel varies between 0.5Hz and 200Hz and the default frequency is equal to 4Hz. The channel period is coded on 16 bits. The data type field determines the type of communication taking place between the participants of this channel and it is fixed by the higher layers. Communication consists generally of two levels [START_REF]ANT Message Protocol and Usage, Application notes[END_REF] (Table 1):

• Manage the direction (Figure 4)

o Forward direction (from the master to the slave) o Reverse direction (from the slave to the master)

• Specification of type of communication o Broadcast o Acknowledge o Burst
ANT does not provide an algorithm to ensure the QoS in the network, but it defines only the acknowledgement packet. This packet must be transmitted by the slave node when it receives a frame that requires an acknowledgement. This ACK is used only to inform the master that the frame was transmitted successfully. ANT does not retransmit the unacknowledged frame.

Different methods of channels management

ANT defines three different ways to use the channel: Independent channels, Shared channels and Channels scan.

In the independent channels, the channel has one master and one slave. The node can have a different role in another channel. The node can support a limited number of independent channels. The shared and scan channels are used when an ANT node must receive data from multiple sources. In the channel scan mode, the slave node is on receiving state all the time, for this reason it can receive the data from multiple masters at any time. The radio is always in the continuous scan mode, so the ANT node cannot open other channels.

Establishment of a channel

If two nodes want to communicate, they must undergo the following process: First, the master sets the type of network, the frequency, the message rate and the channel ID. Secondly, it establishes the channel by transmitting the channel ID with the data in a particular time interval (channel period). ANT channel will be maintained indefinitely at the given time interval and frame baud rate. The higher layers of the master will eventually provide new data to the ANT protocol for continuous transmission. Thirdly, the slave opens its channel to search for a specific master or to search a subset of masters (the type of research depending on the configuration of slave channel). When the slave receives the first message, it selects the type of network, operating frequency, and frame baud rate of the master. With this information it can synchronize with the master and begin receive data [START_REF]ANT Channel Search and Background Scanning Channel[END_REF][21] [START_REF]Proximity search[END_REF].

In ANT, after the synchronization step, in the ideal case, we don't have a transmission failure if the slave node is in the transmission ranges of the master nodes. If the slave node is connected to many master nodes, it switches between channels to receive the information.

Device pairing

Pairing action consists of establishing a relationship between two nodes that wish to communicate together (master and slave). This relationship may be permanent, semi-permanent or transitory.

It consists of a slave device acquiring the unique channel ID of the master device. In the case of a permanent pairing, the slave node must keep the identity of the master in the permanent or nonvolatile memory. This ID is used to open a channel with this ID in all subsequent communication sessions. In semi-permanent relationship, the pairing lasts as long as the channel is maintained [START_REF]ANT Device Pairing[END_REF][21].

PRESENTATION OF ANT+

ANT+ is an enhancement of ANT protocol by adding the interoperability function and defining the data structure, channel parameters and the network keys in order to enable the communication with others ANT+ products. A managed network, ANT+ simplifies the collect, transmission and tracking of health information.

ANT+ allows shared access to the channel; it manages the definitions of node profiles and adds it to the managed networks in order to know the needs of the participant nodes.

ANT+ is used in any application including wireless sensor monitoring in sport, wellness or home health such as: temperature sensor, heart rate monitor, speed and distance monitors, bicycle power, blood pressure, etc.

The Figure 5 presents the layers defined by ANT+. The use of ANT+ and ANT together offers an Ultra low power wireless technology solution and enables the interoperability between nodes (Figure 5). In 802.15.4/4a a node can be an FFD or RFD, the RFD nodes will be connected to an FFD node. In the other hand, an FFD node can be a coordinator or a router for other nodes and can be connected to all types of nodes in the network. In ANT we have two different nodes: a simple node (sensor) and a central node. Simple nodes collect the information and send it to the central node where it will be conserved.

COMPARISON BETWEEN ANT AND OTHER PROTOCOLS

BLE is not compatible with classical version of Bluetooth. But, a node can implement a dual mode to be able to communicate with BLE or classic Bluetooth nodes.

Finally, ANT can be used for transmission of data with small size. 802.15.4/4a can be used for the transmission of big size of data and it allows us to allocate time slots and use TDMA to transmit the data (generally used for QoS application).

PERFORMANCE STUDY

In this section, we will present some radio measurements of ANT protocol. Our goal is to understand how ANT transmits messages and uses the bandwidth and to verify if ANT offers the same theoretical baud rate with burst transmission rate. For this reason, we used two ANT USB keys and two spectrum analysers (WiSpy [START_REF]WiSpy : Spectrum Analysis[END_REF] and a classical HP tool) to observe the power on the physical wireless medium and the frequency of the signal transmitted by ANT USB. The WiSpy has a intersting functionnality for our performance study: it represents temporal medium energy density. This functionnality enables us to view medium activity, especialy in burst mode.

ANT USB is a computer dongle used to receive, store, analyze and display data transmitted by another ANT USB or other devices like ANT sensor and watch.

There are two ANT USB generations, USB1 and USB2. The first generation, USB 1, is replaced by the second generation and it is no longer used. The USB 1 and USB 2 have the same hardware. The difference between the two generations is in the software application only. Where, the new software offers better functionality and performance. In our tests, we used the second generation USB2.

Synchronization

The transmission of beacon periodically

The transmission of the parameters of synchronization in all transmitted packets By the master (AFH)

Mode of transmission

We These USB sticks will work in the 2466MHz frequency, the frequency of transmission is equal to 4 Hz.

We have configured the ANT USB to use the 2466MHz frequency to transmit data with a transmission frequency equal to 4 Hz, these values are the default values of the ANT product.

We have transmitted 1000Kbytes of data with burst transmission. Our goal is to test and verify the correct functionality of ANT protocol.

The Figures 6 and 7 will help us to find the center frequency and the spectrum large that are used by the node. The Figure 6 represents the signal transmitted by the ANT USB and detected by the oscilloscope. This spectrum is periodic and shows the effect of this transmission in the networks. The device uses the full bandwidth from 2464 to 2468MHz frequencies to transmit the data and we have a peak in 2466MHz, so ANT USB uses a bandwidth with 1 MHz of width and a center frequency equal to 2466MHz. In Figure 7, we note the existence of points with different colors. These colors represent the power level on every spectrum portion generated by the transmitter during the message's broadcast. As you note, the frames are sent on 2466MHz (center frequency) presented with red color and when the points are moving away from the center, the transmission power decreases. The variation of transmission power appears in Figure 7 by the change of the colors.

The transmission of data has taken some time. This delay made us deduce the baud rate and compare it with the theoretical value.

ANT protocol took 7min and 29seconds to transmit a payload of 1000Kbytes, which means it transmitted 20568bits per second. This result is the same presented in the theoretical study and USB sticks characteristic. We have used a single channel and since ANT allows the use of multiple channels, we decided to test this property and look at the effect of the use of four channels which have the following frequencies:

• Channel 0: 2420MHz • Channel 1: 2440MHz • Channel 2: 2460MHz • Channel 3: 2480MHz
We note in Figure 8 that the transmission is not performed on all channels, we only have signal in 2 channels (channel 0 and channel 3).

Then we deduce that ANT can't transmit in many different channels at the same time. This is because the channel period is not very large and the time of transmission of one frame is equal to 150microseconds. Now, we will test the possibility of transmission over 8 channels with the same frequency.

In Figure 9, we can see the effect of using 8 channels in the same time. The transmission is occurred between 2464 and 2468MHz and the center frequency is 2466MHz.

Hence, we can deduce that ANT allows the transmission over multiple channels in one condition: all channels will be configured to transmit at the same frequency as shown in Figure 9. We, also, note that the results shown by Figure 9 are close to that presented by Figure 7 but here we don't use burst transmission, we use broadcast transmission instead. In addition, in the Figure 7 we note that the transmission is occurs in different frequencies in the interval [2464MHz, 2468MHz]. This variation of frequencies permits to avoid the collision. The points represent the transmission and the reception periods. In this section, we have presented some practical test of ANT protocol realized with the use of two ANT USBs. When we use burst transmission ANT uses all the bandwidth and stops other transmission.

In the second test, we have many transmissions in the same bandwidth, despite we haven't interference. This is explained by the fact that ANT protocol allows a single channel to be divided into hundred of timeslots to ensure the co-existence of many transmission in the same frequency and the use of an adaptive isochronous network technology which provides the ability for each node to have a free time slot within the used bandwidth. Also, ANT protocol is used for the transmission of low data quantities, which limits its use to some monitoring applications only.

CONCLUSION

In this paper, we presented a new emerging protocol for wireless sensor networks which is at early stage of development and improvement. Yet, it is already widely used in sports and health monitoring field.

At first, we made a general presentation of the ANT protocol. Then, we presented the enhancement and the new functionality added by ANT+. Next we compared ANT with BLE and 802.15.4/4a, and we deduced that ANT can be used only for application where we don't have a large amount of data collected and do not require QoS. Finally, we presented some practical tests we conducted with real material, where we compared the theoretical study with real analysis of ANT protocol. In our future work, we will perform more advanced testing with this protocol with an ANT Development Kit [START_REF]kit de developpement : ANTAP2DK1 (Nordic p/n nRF24AP2-DK1), Dy-nastream Innovations Inc[END_REF], so we can properly confirm the theoretical study of ANT and ANT+.

  ANT provides a management of Physical, Data link, Network and Transport OSI layers (Fig 1). It's a very compact stack requiring minim material resources.

Figure 1 .

 1 Figure 1. Correspondence between the ANT model and the OSI model

Figure 2 .

 2 Figure 2. Different roles of a node

Figure 3 .

 3 Figure 3. Channel transmission

Figure 4 .

 4 Figure 4. Channel communication direction

Figure 5 .

 5 Figure 5. Layer model of ANT/ANT+[START_REF]ULP -advantage ANT[END_REF]

Figure 6 .

 6 Figure 6. Spectrum analysis by the HP tool during the transmission of 1000Kbytes

Figure 7 .

 7 Figure 7. Spectrum analysis by the WiSpy during the transmission of 1000Kbytes

Figure 8 .

 8 Figure 8. Result of the multi-channels tests

Figure 9 .

 9 Figure 9. Result of the transmission in 8 channels in the same frequency

Table 2 presents

 2 a comparison between 802.15.4/4a, Bluetooth Low Energy (BLE) and ANT protocol. We note that 802.15.4a have a transmission rate greater than that of ANT, BLE and 802.15.4. The range of transmission of 802.15.4/4a is greater than that of ANT and BLE. The transmission range and rate of ANT and BLE are equal.

Table 2 .

 2 Comparison between ANT and 802.15.4/4a

		802.15.4	802.15.4a	ANT	BLE
	Frequency band	3 frequency: 868, 915 2400MHz and	3 frequency: and high band Sub-Ghz, low band	2400MHz	2400MHz
			-16 with
	Channel numbers	27	UWB -14 with chirp	8 channels	40
			signal
	Max Packet
	Play load		100	8	20
	(bytes)
					10m and other
	Range (meters)		100	30	ranges depending on
					application
	Min configuration	Transceiver	Transmit only or transceiver	Transceiver
				We have two types
				of node: central
				node (for collecting
	Node Type	A node can be: FFD (Full Function Device) or RFD (Reduce Function Device)	the information from simple nodes ) and simple node (transmit the detected	Single mode (BLE) or dual mode (Bluetooth & BLE)
				information to the
				central
				node)
	Battery life	6 months	Up to 3 years	1 year


Nicolas Noé

François Gaudaire

Mame Diarra

Bousso Lo-Ndiaye

Pierre Combeau

Toward a stand-alone monitoring system for mobile telephony base stations exposure using simulations and smartphones crowdsourcing

Toward a stand-alone monitoring system for mobile telephony base stations exposure using simulations and smartphones crowdsourcing N. Noé (1) , F. Gaudaire (1) , M. Diarra Bousso Lô-Ndiaye* (1) and P. Combeau (2) (1) Centre Scientifique et Technique du Bâtiment, division éclairage et électromagnétisme,

(2) XLIM Institute, UMR CNRS 7252, SIC department, Futuroscope, France

Monitoring of people electromagnetic waves exposure to mobile telephony base stations is of interest for local communities, in order to communicate towards inhabitants or to enforce local exposure rules. This could be achieved with measurements but they quickly become outdated due to the ever changing network. Furthermore this could be very expensive for a large number of measurement spots. On the other hand numerical simulation gives accurate results but need precise antenna description (location, power, radiation diagram, \dots).

Unfortunately such precise information is not publicly available. Nevertheless nowadays most terminals are smartphones that give access to information (received signal strength, location with GPS) that allow them to be used as cheap, low-quality sensors.

In this paper we first introduce numerical simulation of electric field generated by base station antennas anywhere in urban environment, and discuss about the essential parameters do describe exposure level. Second we describe useful information for exposure that can be gathered from smartphones. As expected the collected information is sparse (signal strength from current cell only and in 2G cases neigboring cells) and inaccurate (low definition and saturation of the signal strength value, time lag in value change, GPS uncertainty).

Nevertheless we demonstrate in an almost open area that it can be correlated very well to simulation results. Third we lay the foundation for a future autonomous monitoring system. Antenna parameters are initialized with (inaccurate) publicly available data, either from official organizations or from web databases and an initial simulation is performed. Then antenna parameters are tuned to maximize correlation with the signal strength measurements. To this day only a proof of concept with artificially generated signal strength data exists. It is expected that the mass effect of collected data through crowdsourcing will compensate the low quality of the real data.

Figure 1 :

 1 Figure 1: Comparison between phone received signal strength and simulation


Patrick Paillet

Elena Man-Estier

Peggy Bonnet-Jacquement

Unpublished Magdalenian art from Pont d'Ambon (Bourdeilles, Dordogne, France)

Keywords: art mobilier, Magdalénien, Pont d'Ambon, supports osseux, art figuratif Portable art, Magdalenian, Pont d'Ambon, Bone materials, Figurative. art

Une révision systématique et méthodique des collections fauniques provenant du site de Pont d'Ambon (fouilles G. Célérier), réalisée dans le cadre du Projet Collectif de Recherche « Peuplements et cultures à la fin du Tardiglaciaire dans le Nord du Périgord », dirigé par P. Paillet, a permis la découverte de trois objets d'art mobilier en contexte magdalénien supérieur, localisés dans le site du point de vue archéostratigraphique (couche 5, carré J8). Il s'agit des premières oeuvres d'art découvertes dans les niveaux magdaléniens de Pont d'Ambon, fouillés seulement sur 1 m. Sous forme d'une prise de date, les auteurs proposent une première et brève lecture de ces pièces et en révèlent l'originalité et les spécificités techniques et stylistiques.

Introduction

The Collective Research Project entitled "settlements and cultures at the end of the Tardiglacial in north Perigord", directed by P. Paillet, aims to characterize the cultural transition from the upper Magdalenian to the Azilian/Laborian between the Dronne and Tardoire Basins, within the Charente boundaries. This research focuses on several sites, such as the habitat sites of Rochereil, Pont d'Ambon, La Peyzie, or the painted caves of La Mairie (Teyjat) or Fronsac (Vieux-Mareuil).

As part of this research, we conducted fieldwork (test pits, excavations, surveys…) and undertook a systematic review of the early collections.

For the site of Pont d'Ambon, we studied the faunal remains issued from the G. Célérier excavations (1970Célérier excavations ( to 1987)). These collections are curated at the National Prehistory Museum and are mostly from the Laborian (layer 2) and Azilian levels (layers 3 and 4) of the rock shelter. We identified numerous engraved bone fragments, some of which clearly recall the Laborian style (Paillet, Man-Estier, submitted and accepted). A detailed publication will be devoted to these pieces.

(1) Muséum national d'Histoire naturelle, département de Préhistoire -UMR 7194 Histoire naturelle de l'Homme préhistoriquepaillet@mnhn.fr (2) Centre national de Préhistoire, Ministère de la Culture et de la In 1987, G. Célérier conducted a test pit in the levels underlying "middle layer 4", or ""median 4", attributed to the final upper Magdalenian (lower layers 4, 5 and 6). The exploration of these layers was made possible by the artificial lowering of the level of the Dronne. For practical reasons, the test pit was limited to a single square metre (square J8) [START_REF] Célérier | Pont d'Ambon[END_REF].

In spite of this limited extension (fig. 1), G. Célérier identified the presence of three thin successive human occupation levels from a "final stage of the upper Magdalenian" (Célérier 1991, p. 11 andCélérier 1998, p. 237). The levels are made up of expanses or beds of quartzite pebbles, often reddened by fire and shattered, coated in combustion residues and separated by sterile sandy layers [START_REF] Célérier G | L'abri sous roche de Pont d'Ambon à Bourdeilles (Dordogne) : l'industrie osseuse et la parure[END_REF]. The lithic industry is abundant and contains many fine backed bladelets in beige flint and burins. Several micro-borers and Laugerie-Basse points, mainly in local Santonian flint, complete the range of lithic tools. These levels also contain an ample bone industry and G. Célérier notes that it is almost exclusively made on reindeer antler and that the rods were extracted using the parallel double groove technique. He also mentions several tools destined to work soft materials (awls, lissoirs, perforated needles), as well as some rare bilaterally barbed harpoons (fig. 2) and a pendant imitating a perforated red deer canine [START_REF] Célérier G | L'abri sous roche de Pont d'Ambon à Bourdeilles (Dordogne) : l'industrie osseuse et la parure[END_REF] (fig. 3). The abundant consumed fauna is mainly made up of reindeer remains. The presence of several fish, mainly Salmonids, is noteworthy. No objects of art have been mentioned in previous publications related to these levels.

The transition between the Magdalenian and the Azilian is located in the same sedimentary context. In contrast, G. Célérier points out the brutal passage between "lower layer 4" and "middle layer 4", where the red deer and the rabbit are exploited rather than the reindeer, where the bone industry disappears and where the lithic industry contains more end scrapers and less burins and backed bladelets.

Objects of art in the fauna

The systematic review of the faunal series from the Magdalenian levels from square J5 led to the identification of several bone tool elements (perforated needles and lissoirs or polishers), as well as three fragments of engraved bone. These are all from layer 5 (square J8). Piece n° 1 (Inventory number PCR -PDA61) (fig. 4) Length: 44 mm; Max. width: 13 mm; Thickness: 3 mm It is a bone blade broken into two pieces. The exact nature of the bone could not be identified but it may be a hemi-mandible fragment (probable remnants of dental sockets on the lower side). The bone bears a head and neckline of an incomplete animal facing towards the left.

We think that this animal represents a reindeer. We can identify the ear, which is slightly stretched upwards and towards the rear. As the antlers are absent, due to the fact that the piece is broken, it is not possible to attribute a genus or species to the animal with certainty.

The eye is striking due to the formal technique adopted. It is drawn without a pupil, by a diamond extended by a lachrymal caruncle and is framed by two fine lines that evoke the fur of the orbital projection. Fur lines can be observed in front of the ear and along the cervical and dorsal contour.

The style of this representation conforms to realist middle and upper Magdalenian iconography.

The precision of the line and the depiction of anatomical details are exceptional.

Piece n° 2 (Inventory number PCR -PDA62) (fig. 5) Length: 24 mm; Max. width: 14 mm; Thickness: 1 mm The second piece is a fragment of flat bone (probably a scapula), broken into two parts. The bone bears traces of burning which seem to be anterior to the engraving.

The represented figure is a red deer protome facing left. The engraving is cut off at the neckline by the break. The head is well proportioned. The eye, the nostrils and the mouth are absent. The ear is suggested and the antlers can be seen clearly. The layout, the way they are represented and the number of tines are consistent with those of real animals. It is possible to identify the basal tine, the top tine and perhaps the central tine. Some of the outlines are double lines and appear to represent both antlers in perspective. At the edge of the bone, we can see the rest of the stave (stave B).

The neckline is robust. A curved line underlines the back of the cheek. The fur on the neck is illustrated by a series of very fine interconnected lines.

The originality of this representation resides in its dimensions. The red deer measures 1.4 cm from the top of the tine to the base of the neckline and is less than 1 cm wide. This is one of the smallest known representations in the corpus of Paleolithic portable art. It is a miniature which can be compared to certain upper Magdalenian portable objects of art from Bourrouilla Cave at Arancou (Pyrénées-Atlantiques) [START_REF] Chauchat C. (dir.) | -L'habitat Magdalénien de la grotte Bourrouilla à Arancou (Pyrénées Atlantiques)[END_REF][START_REF] Aurière | Art mobilier inédit du gisement de Bourouilla à Arancou : données techno-stylistiques et chrono-culturelles[END_REF]). The contour line (less than 1 mm wide) was observed with a stereomicroscope and was etched with the same tool, in a continuous and single gesture, without going back over the line. The marks of the tool used for the wide flat-bottomed line are perfectly preserved with a very clear "barcode" effect [START_REF] Fritz C | -La gravure dans l'art mobilier magdalénien. Du geste à la représentation[END_REF]. This representation illustrates exceptional engraving skills, in both the dexterity of the gesture and the skilled use of the tool and technique. It nonetheless raises questions concerning practical engraving aspects. The macroscopic observation and more detailed microwear analysis will bring to light the exact engraving modalities of these lines and identify the type of tool used by the artist among the panoply of lithic tools known at the site (Fritz 1999).

Piece n° 3 (Inventory number PCR -PDA50) (fig. 6) Length: 21 mm; Max. width: 8.5 mm; Thickness: 2 mm The last object is a fragment of burnt bone decorated with two superposed sequences of small curved lines shaped like nested accents. It depicts a simple geometric pattern which is quite frequent in upper and final Magdalenian art.

Figure 4 -Engraved bone with a reindeer head(?) (PDA61). Photo and drawing E. Man-Estier.

Cultural and symbolic relations

The site of Pont d'Ambon is located several hundred metres from the small cave of Rochereil (Grand-Brassac) and less than two kilometres from the cliffs of La Peyzie (Lisle), which contain several habitats identified by P.-E. Jude. These sites are all ascribed to the upper Magdalenian. The corpus of portable art from Rochereil is among the most abundant collections known for this period [START_REF]-La Grotte de Rochereil. Station magdalénienne et azilienne[END_REF][START_REF] Paillet | Men and cultures at the end of the late Ice age in the north of Perigord : continuities and ruptures[END_REF][START_REF] Man-Estier | Rochereil et l'art magdalénien de la fin du Tardiglaciaire dans le Nord du Périgord (Dordogne, France)[END_REF]. At La Peyzie, several works of art have been documented but are not issued from a well-defined stratigraphic context (Paillet in press). In many respects, the two Magdalenian figurative representations from Pont d'Ambron are comparable to them. They have similar stylistic characteristics and the fur is depicted in a similar way. These details are part of a wider graphic tradition known throughout the Perigordian upper Magdalenian. However, the red deer protome also recalls several exceptionally small pieces from contemporaneous sites in the Pyrenees (La Vache, Bourrouilla). These objects raise the question of middle and long distance relations between populations and the role of the sites of Pont-d'Ambon, Rochereil and La Peyzie in an extended cultural territory.

Provisional conclusions

The two figurative representations identified on these small fragmented bones have clear formal and esthetic qualities, in different stylistic and expressive modes. The discovery of these rare decorated objects in the Magdalenian context of Pont d'Ambron is fundamental for the analysis of the site and the presumed links with the two neighbouring and allegedly contemporaneous sites of Rochereil (Grand-Brassac) and La Peyzie (Lisle). According to G. Célérier, the site of Pont d'Ambon does not present any decisive criteria indicating that this site was a meeting place due to the absence of portable art [START_REF] Célérier G | Á propos de trois habitats magdaléniens de la vallée de la Dronne et la notion de site de rassemblement[END_REF]. The three objects presented here do not represent firm evidence of a contradictory viewpoint, given the general paucity of the Magdalenian levels from Pont d'Ambon, which were only excavated over one square metre, compared to those of Rochereil, which are characterized by abundant objects of art. But the presence of three engraved bones enables us to clarify the picture and to establish links between the three neighbouring sites, links which were widespread during the Epipaleolithic sequence. Furthermore, these partial data attest to the probable abundance of the Magdalenian occupations from Pont d'Ambon, which are unfortunately inaccessible below the level of the water table and the present day Dronne under normal flow rate conditions. Lastly, these discoveries also prove that reviewing collections, even recent series, always entails surprises.

Figure 2 -

 2 Figure 2 -Bilaterally-barbed decorated harpoon.

Figure 3 -

 3 Figure 3 -Perforated and incised deer canine.

Figure 5 -

 5 Figure 5 -Engraved bone with a deer protomé (PDA62). Picture and drawing P. Paillet.

Figure 6 -

 6 Figure 6 -Engraved bone with small curved lines (PDA50). Photo P. Paillet.

  Communication et UMR 5199 PACEAelena.man-estier@culture.gouv.fr (3) Musée national de Préhistoire, Ministère de la Culture et de la Communication et UMR5199 PACEApeggy.jacquement@culture.gouv.fr

		Signature numérique de
	Millan	Millan Brun Anne-Lise DN : cn=Millan Brun
	Brun	Anne-Lise, o=UMR 7194, ou=Bibliotheque, email=biph@mnhn.fr,
	Anne-Lise	c=FR Date : 2015.04.01 16:14:14 +02'00'


Yohann Brelet
email: yohann.brelet@ipcms.unistra.fr

Amélie Jarnac
email: amelie.jarnac@fysik.lth.se

Jérôme Carbonnel
email: jerome.carbonnel@ensta-paristech.fr

Yves-Bernard André
email: yves-bernard.andre@ensta-paristech.fr

André Mysyrowicz
email: andre.mysyrowicz@ensta-paristech.fr

Aurélien Houard
email: aurelien.houard@ensta-paristech.fr

Dominique Fattaccioli
email: dominique.fattaccioli@intradef.gouv.fr

Régine Guillermin
email: guillermin@lma.cnrs-mrs.fr

Jean-Pierre Sessarego
email: sessarego@lma.cnrs-mrs.fr

Underwater acoustic signals induced by intense ultrashort laser pulse

Keywords: numbers: 43.30.Lz, 43.25.Zx, 43.35.Ud, 43.30.Xm

Acoustic signals generated in water by terawatt (TW) laser pulses undergoing filamentation are studied. The acoustic signal has a very broad spectrum, spanning from 0.1 to 10 MHz, and is confined in the plane perpendicular to the laser direction. Such source appears to be promising for the development of remote laser based acoustic applications.

Investigation of energy deposition in water from ultrashort laser pulses has attracted considerable interest in the last decade in view of potential applications ranging from laser surgery [START_REF] Plamann | Ultrashort pulse laser surgery of the cornea and the sclera[END_REF][START_REF] Vogel | Femtosecond-Laser-Induced Nanocavitation in Water: Implications for Optical Breakdown Threshold and Cell Surgery[END_REF] , to triggering of high voltage water switches [START_REF] Woodworth | Water Switching at 1.6 MV[END_REF] , or remote generation of acoustic sources [START_REF] Jones | Remote Underwater Ultrashort Pulse Laser Acoustic Source[END_REF][START_REF]Bubble Dynamics & Shock Waves[END_REF][START_REF] Blackmon | Experimental demonstration of multiple pulse nonlinear optoacoustic signal generation and control[END_REF] . It has been recognized early on that an intense laser pulse focused in a transparent liquid can heat or ionize the medium, leading to the emission of an acoustic transient [START_REF] Vogel | Acoustic transient generation by laser-produced cavitation bubbles near solid boundaries[END_REF][START_REF] Egerev | In search of a noncontact underwater acoustic source[END_REF] . A laser-based method offers advantages in standoff underwater acoustics, in comparison with traditional sources consisting of arrays of hydro-acoustic transducers or sonars [START_REF] Sreeja | Dynamics of tightly focused femtosecond laser pulses in water[END_REF][START_REF] Helle | Formation and propagation of meter-scale laser filaments in water[END_REF] . The first experiments were carried out with CO 2 , Neodymium glass and ruby laser sources, with pulse durations longer than 100 ns. In this case, the laser induces a slow heating of the medium followed by a thermal expansion and emission of an acoustic wave [START_REF] Chotiros | Nonlinear Optoacoustic Underwater Sound Source[END_REF][START_REF] Tang | Dynamic thermal expansion under transient laser-pulse heating[END_REF] . Later, intense nanosecond pulses appeared to be more efficient, since they can easily generate optical breakdown in water through multiphoton and impact ionization [START_REF] Noack | Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficients, and energy density[END_REF] . After the rapid heating of the ionized volume, an explosive expansion occurs, yielding the emission of a shock wave [START_REF] Vogel | Energy balance of optical breakdown in water at nanosecond to femtosecond time scales[END_REF][START_REF] Potemkin | Laser control of filament-induced shock wave in water[END_REF] . Thus, fast lasers provide several orders of magnitude improvement in the conversion efficiency of the photon to acoustic energy if compared with the slow laser heating scheme [START_REF] Jones | Remote Intense Laser Acoustic Source[END_REF] . With pulse durations in the sub-picosecond range, the ionization process being very fast, one expects the generation of a very broad acoustic wave. In the present paper we experimentally report in situ space-time properties of the acoustical signal generated by a focused terawatt picosecond laser pulse in water. Several focusing geometries have been explored, under controlled laboratory conditions. The spectrum and directivity of the source were characterized, revealing a very broad emission ranging from 0.1 to 10 MHz and a sharp directivity in elevation with respect to the laser beam axis. The properties of this acoustic source makes it particularly promising for sonar and imaging applications.

The laser used in the experiment is a mobile multi terawatt CPA (chirped pulse amplification) laser sytem (ENSTAmobile). It delivers transform-limited 50 fs pulses at 800 nm with energy of up to 290 mJ per pulse at a repetition rate of 10 Hz. The laser beam (diameter FWHM ~ 35 mm) was focused in water by convex lenses with focal lengths of f = 200 and 500 mm, and crossed the air-water interface at normal incidence (see Fig. 1). The distance h between the lens and the water surface was varied between 40 and 380 mm. The laser pulse was temporally stretched up to 1 ps by misalignment of the compressor stage of the chirped pulse amplifier to avoid damages on optical lenses, yielding a maximum peak power of 290 GW. Two hydrophones were used to monitor the underwater acoustic signal. A high frequency hydrophone (HF) Precision Acoustics 1.0 mm needle with a detection range 1 MHz -10 MHz and a sensitivity of -241.4 dB ref 1V/µPa at 3 MHz. A low frequency hydrophone (LF) Reson TC4035 detecting between 50 kHz and 800 kHz, with a sensitivity of -215 dB ref 1V/µPa. A preamplification gain of +20 dB was applied to the hydrophone signals. The LF and HF hydrophones were installed at distances r larger than 80 cm and 30 cm from the laser axis respectively. Thus, both hydrophones were in the acoustic far field, determined as r  100 where λ is the acoustic wavelength defined by  =  water / F us , where F us is the ultrasound frequency and  water the speed of sound in water with  water ≈ 1487 m/s at T = 21.6°C. They could be moved longitudinally and collinearly with respect to the laser propagation axis using a motorized platform. The experimental setup is sketched in Fig. 1. The pool with dimension  13×3×2 m was filled with freshwater, at room temperature (T  21.6°C).

Figures 2(a) and (b) present typical temporal waveforms measured by the hydrophones, when the laser pulse was focused in water with a lens f = 200 mm placed 40 mm above the water surface. The position z of the hydrophones was adjusted to obtain the highest acoustic signal in the far field. The measured electric signals present an asymmetric N-shape [START_REF] Beyer | Nonlinear acoustics[END_REF] revealing a steep positive pressure peaks followed by a negative pressure. The peak amplitude of this pressure wave in the far-field was found to decrease as 1/r, as shown in Fig. 3. Moreover, a signal-to-noise ratio (SNR) of + 40 dB, for the HF hydrophone placed at r  31 cm and + 25 dB for the LF hydrophone at r  80 cm have been deduced. The corresponding spectra for LF and HF hydrophones are plotted in Fig. 2(c). In both cases, the temporal signal has been deconvoluted from the hydrophone response and corrected for the preamplification gain. The spectrum of the acoustic signal is particularly broad, covering almost 10 octaves (precluding the band 0.8-1 MHz which is not covered). The equivalent pressure level of the signal at 1 m lies between 130 and 160 dB ref 1 µPa at 1 m over the range 60 kHz-6 MHz.

To get closer to undersea conditions, we injected small particles of kaolinite with a radius of a few tens of µm into water around the laser beam focal plane. The recorded signals exhibited a significant enhancement of the acoustic peak amplitude (up to +20 dB). Therefore one would expect that in a real undersea environment containing a large amount of impurities, the laser generated signals would also be stronger.

The dependence of the acoustic signal on elevation z has been studied with laser pulses of 290 mJ and duration of 1 ps focused by a lens f = 200 mm at h = 40 mm. A scan with 10 mm steps was performed along the z direction, in the plane containing the laser propagation axis, with z = 0 defined as the air-water interface. Taking into account the refraction of the beam at the air/water interface this height corresponds to geometrical focus positions z ≈ 213 mm. The shortest time-of-flight (ToF) is observed around z = 220 mm, close to the estimated geometrical focus of the laser beam. A similar behaviour is also observed with the LF hydrophone. Analogous results were obtained at different heights h, with a maximum acoustic signal always obtained when the detector position in z was close to the geometric focus of the laser pulse [START_REF] Plamann | Ultrashort pulse laser surgery of the cornea and the sclera[END_REF] .

The directivity of the optoacoustic source in the far-field was measured by recording signals in the (x,z) and (x,y) planes. Figure 4(a) displays the directivity diagrams in the vertical plane (x,z) for three ultrasonic frequencies. The diagrams present a main lobe enclosed within less than 2 = 10°, where  is the angle formed between the positions z of the acoustic source and that of the hydrophone along the Ox axis (see Fig. 1). The opening angle of the lobe experiences a small decrease as frequency increases. The observed slight disymetry with respect to the angle 0° might by explained by an imperfect alignment with respect to the laser axis. We have determined that the acoustic source possesses a rotational symmetry in the plane (x,y). One then obtains the 3D emission diagram, as shown in Fig. 4(b), here for F us = 2 MHz. The acoustic signal is null along the laser beam axis and maximal in its equatorial plane. This quasi 2-dimensional emission pattern is responsible for the 1/r law of the pressure signal that we measured (see Fig. 3). To explain this feature, we note that the incident laser power exceeds by orders of magnitude the threshold power for filamentation. In this case, one expect the formation, close to the geometric focus, of superfilaments with elongated plasma column and densities exceeding by order of magnitude the plasma density found in a single filament [START_REF] Point | Superfilamentation in air[END_REF] . Such a high density plasma column corresponds to a cylindric source responsible for the observed acoustic pattern in the far field. Note that shockwaves with a similar cylindrical shape were observed in ref. 15 in the vicinity of millimeter scale filaments produced in water.

In conclusion, we have demonstrated that focused ultrashort pulses with TW peak power can generate an optoacoustic source in water. Time of flight measurements reveal that it is localized close to the laser geometrical focus. Several characteristics of this optoacoustic source have also been derived, such as an interesting broad spectrum spanning at least from 0.1 to 10 MHz, with a pressure level of 160 dB ref 1 µPa at 1 m for 1 MHz and a sharp directivity in the plane perpendicular to the laser propagation axis. This optoacoustic source may find applications in acoustic communications, or acoustic imaging.

Captions and figures lists

FIG. 1 (FIG. 3 (FIG. 4 (

 134 FIG. 1 (Color online). Experimental setup in the oceanic tank facility of Laboratoire de Mécanique et Acoustique.

A secundary acoustic source generated at the air/water surface was also detected when the geometric focus of the lens gets closer to the interface (i.e. for h large).

Acknowledgments

This project has been supported by the French Direction Générale de l'Armement (grant n° 066003600470750). The authors thank Laboratoire de Mécanique et Acoustique staff for technical assistance.


Keywords: Vertical Cavity Surface-Emitting Lasers, Atomic Clocks, Metrology

The availability of small atomic clocks should greatly improve the mobility and robustness of, for example, satellite positioning system and high bitrate communication networks. In this context, coherent population trapping (CPT) is an interesting technique for the development of compact atomic references. It is based on the coupling of the two hyperfine ground states of an alkali atom, through excitation to a common atomic level, by two phase-coherent laser fields. We propose an innovating laser source for the production of such bifrequency field based on the dual-frequency and dual-polarization operation of an optically-pumped vertical external-cavity semiconductor laser (OP-VECSEL). Laser noise contributions to clock performance have been evaluated and results in an estimated clock frequency stability of 2.7 x 10 -12 over a second limited by laser intensity noise. Stability level below 3 x 10 -13 over one second is reasonably reachable with small changes in clock working conditions or laser set-up.

INTRODUCTION

Microwave photonics is an emerging field which studies the generation, distribution, processing and analysis of microwave signals carried on optical frequency carriers, using the advantages of photonics technologies [START_REF] Yao | A Tutorial on Microwave Photonics[END_REF][START_REF] Marpaung | Integrated microwave photonics[END_REF]. It enables access to high-frequency signals generation [START_REF] Czarny | THz-dualfrequency Yb3+:KGd(WO4)2 laser for continuous wave THz generation through photomixing[END_REF] and processing [START_REF] Tonda-Goldstein | Optical signal processing in Radar systems[END_REF], without the state-of-the-art electronics and also to long range transmission of microwave signals through optical fiber links [START_REF] Narbonneau | High resolution frequency standard dissemination via optical fiber metropolitan network[END_REF]. Firstly developed for defense applications, microwave photonics spreads to a large number of civil applications such as cellular, wireless, and satellite communications and medical imaging [START_REF] Marpaung | Integrated microwave photonics[END_REF]. It is also used in metrology, in the development of frequency standards and inertial captors. Here we are interested in the realization of compact and stable atomic clocks using the coherent population trapping phenomenon in which the radiofrequency (RF) probe frequency is optically carried [START_REF] Vanier | Atomic clocks based on coherent population trapping: a review[END_REF]. It requires a high purity, optically carried, microwave signal as well as low-noise properties for the laser source (intensity and frequency fluctuations).

The common solutions for the generation of an optically carried microwave signal are sideband generation by microwave modulation of a single laser diode, either internally through injection current or externally through an electro-optic modulator [START_REF] Vanier | Atomic clocks based on coherent population trapping: a review[END_REF], and optical phase-locking of two independent single mode lasers [START_REF] Fan | Optical generation of a mHz-linewidth microwave signal using semiconductor lasers and a discriminator-aided phase-locked loop[END_REF]. Research on more simple design has also been investigated with development of dual-frequency laser source. As they share the same thermic and mechanic fluctuations, laser modes are intrinsically strongly phase coherent. Dual frequency emission of solid state lasers has been demonstrated with Nd:YAG and Yb:KGW crystals respectively with a frequency difference in the GHz [START_REF] Le Gouët | Dual-frequency single-axis laser using a lead lanthanum zirconate tantalate (PLZT) birefringent etalon for millimeter wave generation: beyond the standard limit of tunability[END_REF] and THz range [START_REF] Czarny | THz-dualfrequency Yb3+:KGd(WO4)2 laser for continuous wave THz generation through photomixing[END_REF]. A similar configuration has been recently demonstrated with an optically-pumped vertical external cavity surface emitting laser (OP-VECSEL) at 1 µm [START_REF] Baili | Twopolarization two-frequency operation in a class-A semiconductor laser[END_REF].

We demonstrate here the dual frequency operation of an OP-VECSEL emitting at the Cs D2 line (𝜆 = 852 nm) with a frequency difference tunable to the Cs ground state splitting of 9.2 GHz, and noise properties compatible with population trapping of Cs atoms. OP-VECSEL presents many advantages: first, emission wavelength can be tuned at the desired wavelength thanks to a careful design of the semiconductor structures. Output power in the watt range has been obtained with AlGaAs-based devices. Then, with centimeter long cavity and an excited-carrier lifetime of 1 ns, OP-VECSEL lasers exhibit a class-A dynamical behavior and are therefore relaxation oscillations free. OP-VECSEL relative intensity noise (RIN) is thus very low on a wide spectral range [START_REF] Baili | Shot-noiselimited operation of a monomode highcavity-finesse semiconductor laser for microwave photonics applications[END_REF]. Finally, single frequency operation of optically-pumped semiconductor lasers with high power has been demonstrated, with narrow spectral linewidth of 100 kHz [START_REF] Kaspar | Semiconductor disk laser at 2.05 µm wavelength with <100 kHz linewidth at 1 W output power[END_REF]. (28-30 January 2014 -Paris)

The CPT phenomenon and its use in CPT-Ramsey atomic clocks is explained in section II. The next section details the dual-frequency laser design; tunability of the frequency difference between the modes is described. Section IV presents the laser characterization under free-running mode and section V details the stabilization set-up of the laser emission on the Cs three-level system. Finally section VI is dedicated to the measurements of noise properties of the dualfrequency laser, which are then used in section VII to evaluate the laser noise contribution to the clock frequency stability.

CPT-RAMSEY ATOMIC CLOCK

Atomic clocks are based on the interrogation of a reference atomic transition by a macroscopic local oscillator (LO) which frequency is locked onto the stable atomic reference, usually in the radiofrequency (RF) range. In CPT-atomic clocks, a 3-level excitation scheme is used, meaning the LO frequency is optically carried using an optical phase-lock-loop to convert the electrical signal to an optical signal [START_REF] Seeds | Microwave Photonics[END_REF]. This technology enables the development of miniature atomic clocks with very low level of frequency fluctuations [START_REF] Knappe | A microfabricated atomic clock[END_REF]. Such levels of frequency stability in compact housing make possible to integrate atomic clocks in demanding applications as satellite positioning and synchronization of high bit rate communication networks.

CPT phenomenon occurs when two atomic ground states are coupled using a two-frequency coherent laser fields resonant with a common excited state. When the optical frequency difference is equal to the ground state splitting (the so-called clock transition), the atoms are pumped in a coherent superposition of both ground states -called dark state -which does not interact with the incident light (Fig. 1) . At resonance, the light absorption and the fluorescence spectrum exhibit a strong decrease over a narrow spectral linewidth corresponding to the CPT-resonance. This linewidth is related to the coherence lifetime of the ground states. Narrower linewidths can be reached by combining CPT with Ramsey interrogation [START_REF] Vanier | Atomic clocks based on coherent population trapping: a review[END_REF]: it consists, after pumping a group of atoms into the dark state, to let them evolve freely and then excite again those atoms with the resonant 2-frequency optical field. This last pulse induces the Ramsey fringes and is used in the same time for detection by monitoring the fluorescence light or the transmitted power through the atoms. The corresponding signal is used to generate the error signal in order to correct long-term frequency drifts of the local oscillator. Among alkali-metal atoms used for CPT, cesium atoms have been chosen since 1967 as a frequency etalon to define the second. Its ground state splitting is exactly 9.192 631 770 GHz and it can be either pumped at 894 nm (D1 line) or 852 nm (D2 line) (Fig. 1). CPT-Ramsey atomic clocks using cesium atoms have reached very good frequency stability of 3.2 × 10 -13 at 1 second [14] limited by LO frequency noise, through Dick effect [START_REF] Dick | Local oscillator induced instabilities in trapped ion frequency standards[END_REF].

DESIGN OF THE DUAL-FREQUENCY OP-VECSEL

The optically-pumped VECSEL design has many advantages: it enables the possibility of adding free space intracavity elements while using specially designed semiconductor structure emitting at the targeted wavelength. For this work, we take advantage of our previous work on the design of AlGaAs semiconductor active chips at 852 nm, which have demonstrated up to 300 mW at the Cs D2 line [START_REF] Cocquelin | Tunable single-frequency operation of a diode-pumped vertical external-cavity laser at the cesium D2 line[END_REF].

Semiconductor structure

The semiconductor chip has been carefully designed to provide light emission at 852 nm and to tolerate optical losses of about 2%, which are introduced by intra-cavity elements (cf 3.2). This conventional multilayer active structure has been grown with metal-organic chemical-vapor deposition on a 350 µm-thick GaAs substrate.

The 30λ/4 active cavity is composed of seven 8nm-thick GaAs quantum wells (QW) embedded in pump-absorbing Al 0.225 Ga 0.775 As barriers, absorbing up to 90% of the internal pump intensity in a single pass. QWs are placed at the antinodes of the optical standing wave created inside the active cavity. Two 30-nm thick Al 0.39 Ga 0.61 As layers create potential barriers on each side of the active cavity, for the carrier confinement. Finally, a 50 nm-thick InGaP capping layer protects the cavity from Al-oxidation. The 32.5 pairs of quarter wavelength-thick AlAs/Al 0.225 Ga 0.775 As in DBR provide a 80-nm large high reflectivity pass band centered at 850 nm, with R > 99.94% at 852 nm (Fig. 2) [START_REF] Camargo | Tunable high-purity microwave signal generation from a dualfrequency VECSEL at 852 nm[END_REF]. (28-30 January 2014 -Paris)

Laser cavity

The laser cavity is formed by the semiconductor chip and a R = 15 mm concave output coupler, transmitting 0.5 % at 850 nm. The pump source is a broad-area laser diode emitting at 670 nm, coupled into a 100 µm diameter, NA = 0.22, multimode fiber. This source delivers up to 1 W at the fiber end. The pump beam is focused on the semiconductor chip with two doublets of f 1 = 25 mm and f 2 = 19 mm under a 50° angle, yielding a 70 µm by 110 µm-elliptical spot on the semiconductor structure.

The dual-polarization emission is obtained by introducing a birefringent element in the laser cavity, which controls the anisotropy inside the cavity and results in the emission of two crosspolarized lines (Fig. 3). We use a 500 µm-thick antireflection coated YVO 4 plate cut at 45° to its optic axis, which induces a spatial separation d of 50 µm between the extraordinary and ordinary beams in the structure in the longer axis of the pump ellipse. This spatial separation reduces the coupling between them to C ~ 10%, which ensures a stable dual-polarization frequency emission [START_REF] Pal | Measurement of the coupling constant in a two-frequency VECSEL[END_REF]; nevertheless the spatial separation is small enough to maintain a good overlap between the pump beam and the two laser spots. Finally, the single frequency operation at each polarization, as well as the wavelength coarse tunability, are obtained using a 50 μm-thick (𝐹𝑆𝑅 !"#$%& = 2 THz) uncoated silica etalon. Fine tuning of the laser wavelength is obtained using a piezo transducer glued on the output coupler.

To control the laser frequency difference, a 5 % MgO-doped stoichiometric lithium tantalate (SLT) crystal is placed inside the cavity. Its high transparency at 852 nm limits the intra-cavity losses. Both thermo-optic (T.O.) and electro-optic (E.O.) properties of the MgO:SLT enable a broad tunability of the cavity birefringence. The crystal axes are oriented to limit the ordinary-polarized mode frequency dependency with the SLT applied voltage. With all intra-cavity elements, the 𝐹𝑆𝑅 of the laser cavity is 𝐹𝑆𝑅 !"# = 12 GHz, higher than the targeted frequency difference ∆𝜈 ! = 9.192 GHz, and corresponding to an optical cavity length 𝐿 !"# = 12.5 mm.

The laser cavity design has focused on compactness as well as high mechanical and thermal stability (Fig. 4). Pump optics, semiconductor chip and intra-cavity elements are integrated in a compact 90 mm × 90 mm × 40 mm casing. This limits mechanical and acoustic vibrations as well as air temperature fluctuations inside the external cavity. The temperature of the whole set-up is stabilized to 24°C. The semiconductor chip temperature is controlled at 16°C using a Peltier element.

Frequency difference tunability

The birefringence introduced in the cavity generates two cavities with slightly different lengths, one per polarization (Fig. 5). Therefore it produces two combs of cross-polarized longitudinal modes, in which only two modes distanced by ∆𝜈 are selected by the Fabry-Perot etalon. For two consecutive modes, the laser beatnote frequency, defined as ∆𝜈 = 𝜈 !"# -𝜈 !"# , is given by the formula:

6 th International Symposium On Optronics In Defence and Security (28-30 January 2014 -Paris)

∆𝜈 = 𝐹𝑆𝑅 !"# !∆! !
where ∆𝐿 = 𝐿 !"# !"# -𝐿 !"# !"# corresponds to the optical path difference due to birefringence over one round inside the cavity, and is defined modulo 𝜆/2. Thus ∆𝜈 is tunable over one 𝐹𝑆𝑅 !"# of the cavity equal to 12 GHz. ∆𝐿 is calculated from the contributions of both YVO 4 and SLT crystals, taking into account three main effects: thermal expansion, thermo-optic and electro-optic effects.

∆𝐿 !"! ! 𝑉, 𝑇 = ∆𝑛 !"! ! 𝑇 ×𝐿 !"! ! 𝑇 ∆𝐿 !"# 𝑉, 𝑇 = ∆𝑛 !"# !.!. 𝑇 + ∆𝑛 !"# !.!. (𝑉) ×𝐿 !"# (𝑇)
The birefringence variation of SLT with the applied transverse voltage, follows the relationship:

∆𝑛 !"# !.!. 𝑉 = 𝑉 𝑒 𝑛 ! ! 2 𝑟 !! - 𝑛 ! ! 2 𝑟 !"
where e is the distance between the two electrodes used to apply a voltage 𝑉 on the crystal and equal to 2 mm, 𝑛 ! and 𝑛 ! are the refraction indexes for the extraordinary and ordinary polarizations, 𝑟 !! and 𝑟 !" are the electro-optic coefficients along the axes x and z, respectively, where x is the axis on which the voltage is applied and z is along the beam propagation.

Temperature variations affect the birefringence in both crystals (YVO 4 and SLT) through thickness dilatation and thermo-optic effects. Contribution of thermal changes on birefringence can be calculated with the following relationship (valid for both crystals):

𝜕(∆𝐿) 𝜕𝑇 = 𝜕𝐿 𝜕𝑇 𝑛 ! -𝑛 ! + 𝐿( 𝜕𝑛 ! 𝜕𝑇 - 𝜕𝑛 ! 𝜕𝑇 )
We introduce the thermal expansion coefficient 𝛼 = From those values, we compute the sensitivity of the frequency difference 𝛥𝜈 to temperature and E.O. applied voltage of, respectively, 1.41 GHz/K at 25°C and 1.56 MHz/V. Thus temperature allows a coarse tunability of the frequency difference to the targeted value of 9.192 GHz. Experimentally the sensibility coefficients are 1.4 GHz/K and 1.3 MHz/V, in good agreement with the theoretical values.

LASER CHARACTERIZATION

First of all, the laser is characterized without intracavity elements. The laser output power reaches 83 mW at 855 nm in a multimode spectrum, and the laser threshold is obtained at 0. The optical spectrum of the dual-frequency laser around 852.1 nm is measured with a Fourier transform optical spectrum analyzer with a resolution of 2 pm (Fig. 7). The beatnote frequency is evidenced by mixing the cross-polarized modes with a polarizer oriented at 45° of their axes, and coupling the beam into a fiber-coupled fast photodiode followed by two low-noise RF amplifiers (Gain = 22 dB each) and a RF amplifier. The generated beatnote frequency is around 9.2 GHz with a spectral linewidth at -3 dB below 600 kHz on a time scale of 300 ms, measured with a resolution bandwidth of 100 kHz (Fig. 9).

LASER STABILIZATION

Under free-running conditions, the laser performance is not compatible with the interrogation of Cs atoms in a CPT-based atomic clock, which requires a high-purity optically-carried microwave signal. For the dual-frequency laser to be actually used on a Cs-atomic clock, the laser emission has to be further stabilized. In this section we detail the stabilization of the ordinary-polarized laser line onto a hyperfine Cs atomic transition, and the concurrent locking of the frequency difference onto a RF oscillator.

At the output of the laser, the two cross-polarized modes are separated by a polarization beam splitter. The laser is protected from any optical feedback with two -30 dB optical Faraday isolators (one per polarization). A fraction (0.5 mW) of the ordinary-polarized power is injected into a saturated absorption set-up for its stabilization on a Cs atomic transition at 852.1 nm. Finally, both beams are recombined with the same polarization axis in order measure the beatnote frequency and lock it on the RF frequency reference (Fig. 8).

Optical frequency stabilization at Cs transition

The laser frequency of the ordinary polarized beam is locked onto a Doppler-free transition (F = 4 towards F' = 4'/5') of the Cs D2 line using a pumpprobe saturated absorption technique [START_REF] Koslova | Caractérisation d une horloge à piégeage cohérent de population dans une vapeur thermique de Cs. Principaux effets pouvant affecter la stabilité de fréquence a moyen-long terme[END_REF], as shown in Fig. 8. An acousto-optic crystal is used to modulate the so-called pump beam at 100 kHz to generate an error signal 𝜖 ! . This method avoids the direct modulation of the pump diode current, which would simultaneously introduce a modulation of the laser power.

The error signal is integrated and the correction is made by a low-frequency two-integration stages servo loop on the piezo-electric transducer glued to the output coupler. We measured a sensitivity coefficient of the optical frequency to the error signal of 12 MHz/V.

Frequency difference stabilization

The frequency difference between the two laser modes (the so-called beatnote frequency) is locked onto a local oscillator (LO), which generates a stable RF reference at the frequency 𝜈 !" , using an (28-30 January 2014 -Paris) optical phase-lock loop described in this section. After recombining the beams and superimposed their polarization axes, the two laser frequencies are mixed on a fast GaAs photodiode. The subsequent beatnote signal is amplified and mixed with the RF reference to generate an error signal 𝜖 ! proportional to (Δ𝜈 -𝜈 !" ). The error signal is then amplified by a high-bandwidth proportionalintegrator corrector and applied to the intracavity electro-optic crystal to compensate for the frequency-difference fluctuations. Fig. 9 compares the beatnote spectra of the freerunning laser and of the laser when the frequency difference Δ𝜈 is locked to the RF reference at 9.2 GHz. The servo loop bandwidth is about 1 MHz which depends on the proportional gain as well as on the electro-optic crystal response. The signalto-noise ratio, measured between maximum of the peak and the minimum close the frequency carrier, is 55 dB. The two servo-loops -of the absolute frequency difference on a Cs atomic transition and of the frequency difference on the RF local oscillator -operate together for 30 minutes under laboratory conditions. Better working conditions with acoustic isolation of the set-up is being implemented to achieve a longer operating time for the stabilized laser.

LASER NOISE AND DYNAMICS

The noise properties of the stabilized laser emission are investigated in order to evaluate the contribution of the dual frequency OP-VECSEL to the performance of a CPT-Ramsey atomic clock.

We study three main noise sources: laser frequency noise, beatnote phase noise and laser intensity noise.

Laser frequency noise

The laser frequency noise reveals the fluctuations of the absolute optical frequency as compared to the Cs transition. It affects the atomic clock by reducing the interaction between Cs atoms and the laser beams. To quantify this frequency noise, we measure the power spectral density of the error signal 𝜖 ! with a Fast Fourier Transform analyzer, and normalized it by the sensitivity coefficient of the set-up (12 MHz/V). When the optical frequency locking is activated, we observed a (in-loop) noise level below detection noise floor, meaning we reach a 60 dB frequency noise reduction at 1 Hz. The low-frequency technical noise is suppressed on a bandwidth of 600 Hz, which is limited by the piezo transducer resonance (Fig. 10). In order to have a higher stabilization bandwidth, we investigate establishing an additional feedback loop to the pump injected current.

Beatnote phase noise

The local oscillator (LO) which provides the RF interrogation signal is a key element in an atomic frequency reference. In CPT atomic clocks, the LO frequency is optically carried for the atom interrogation process. Conversion from electrical to optical domain is obtained by locking the laser frequency difference ∆𝜈 to the LO frequency. This conversion may add some noise, originating from the LO oscillator and the laser itself, on the beatnote spectral purity. To characterize the laser additive phase noise (or residual phase noise), we use the set-up presented in Fig. 11 which rejects the LO noise as a common source and measures only the laser additive phase noise. Fig. 12 shows the additive phase noise under free running operation and locked operation (for a frequency difference ∆𝜈 locked at the LO reference frequency of 9.6 GHz). A level of -105 dBrad²/Hz on the 100 Hz -5 kHz frequency range is measured, below the LO standard phase noise, leading to a 100 dB noise reduction of the beatnote phase noise at 100 Hz, compared to the free running operation. At frequencies above 5 kHz, the noise level reaches -90 dBrad²/Hz up to 1 MHz which corresponds to the optical phase-lock loop bandwidth. For higher frequencies a 1/𝑓 ! slope is observed which is typical of the behaviour of such lasers under free-running conditions [START_REF] De | Phase Noise of the Radio Frequency (RF) Beatnote Generated by a Dual-Frequency VECSEL[END_REF].

Laser intensity noise

The relative intensity noise (RIN), which is converted into a frequency noise in the phase-lock loop, has been the object of a specific study.

A white noise floor of -110 dB/Hz for each polarization has been measured directly at the laser output. Polarization resolved measurements show no difference of the RIN behaviour between the two modes. Moreover, the two frequencystabilization servo-loops do not disturb the RIN level (Fig. 13).

The laser intensity noise is limited by the pump intensity noise with a gain factor of +5 dB [START_REF] Baili | Experimental Investigation and Analytical Modeling of Excess Intensity Noise in Semiconductor Class-A Lasers[END_REF]. We have verified that the RIN of the pump diode is not limited by its injected current noise, and we suspect the mode partition noise resulting from the competition between laser modes to be the main limiting factor of the pump source RIN [START_REF] Dolev | Linear and nonlinear optical properties of MgO:LiTaO3[END_REF]. A lower RIN of our 2-frequency laser should thus be achievable by using a single-mode pump source. High power tapered laser diodes at 670 nm with quasi-single mode emission have been demonstrated [START_REF] Sumpf | Nearly diffraction-limited tapered lasers at 675 nm with 1-W output power and conversion efficiens above 30%[END_REF], and are considered as good candidates.

EVALUATION OF CLOCK FREQUENCY STABILITY

In this section, we evaluate the laser noise contribution to the atomic clock performance and therefore the ultimate clock frequency stability reachable with a CPT-Ramsey atomic clock using our dual frequency laser source.

The atomic clock set-up is described in Fig. The clock frequency 𝜈(𝑡) is defined as the following [START_REF] Koslova | Caractérisation d une horloge à piégeage cohérent de population dans une vapeur thermique de Cs. Principaux effets pouvant affecter la stabilité de fréquence a moyen-long terme[END_REF]:

𝜈 𝑡 = 𝜈 ! 1 + 𝜀 + 𝑦 𝑡
where 𝜈 ! is the ground-state splitting, 𝜀 the inaccuracy caused by deterministic effects, and 𝑦(𝑡) the frequency stability which corresponds to the relative frequency fluctuations of the clock signal measured on a duration time 𝜏. To characterize the frequency stability of the signal 𝜈(𝑡), Allan variance is commonly used and is defined as:

(6) (7)
6 th International Symposium On Optronics In Defence and Security (28-30 January 2014 -Paris)

𝜎 ! ! 𝜏 = 1 2 𝑦 !!! -𝑦 ! !
where 𝑦 ! is the average value of 𝑦(𝑡) on a time interval 𝑡 ! ; 𝑡 !!! of duration 𝜏. 𝜎 ! 𝜏 is given by the quadratic average of three contributions: the laser intensity noise (IN), the laser frequency noise (FN) and the beatnote phase noise amplified by the Dick effect. The clock frequency is sensitive to the laser frequency fluctuations (FN) during the pumping time 𝜏 ! of the Cs atoms. A laser frequency variation from the Cs optical transition reduces the interaction between light and atoms. Thus it induces a fluctuation of the number of atoms trapped into the dark-state, converted into amplitude noise on signal 𝑆(𝑡) (Fig. 14). The calculated sensitivity bandwidth is about 700 Hz under usual operating conditions.

Finally, the Dick effect arises from the lack of information on the probe frequency during the pumping of the Cs atoms, equivalent to a dead time during which the LO noise is not probed and then not corrected [START_REF] Dick | Local oscillator induced instabilities in trapped ion frequency standards[END_REF]. It can be described by the down-conversion of the LO frequency noise at Fourier frequencies higher than the interrogation frequency. The LO frequency noise originates from its intrinsic noise and the laser beatnote frequency noise, i.e. the beatnote phase noise evaluated previously. The LO intrinsic noise will not be considered here, as we are only interested here in the noise added by the bifrequency laser source. The Allan variances, calculated for each contribution, are grouped in table 1. White noise assumption is made to simplify calculations. From these calculations, we estimate a clock stability of 𝜎 ! 𝜏 = 2.7 x 10 --12 𝜏 !!/! , limited by the laser intensity noise. In order to reach better clock performance, the clock set-up should be adapted. An increase of detection time from 25 µs to 125 µs could reduce the Allan variance to 8.7 x 10 -13 𝜏 !!/! . However, it may reduce the atomic signal and also decrease the Dick effect [START_REF] Danet | Dick effect in a pulsed atomic clock using coherent population trapping (under review process)[END_REF]. Thus as a second step, a study of the improvements in terms of total signal to noise ratio will be undertaken. The clock sensibility to the laser RIN might also be reduced by monitoring the laser beam power in front of the atomic cell and normalizing the CPT signal. With such a normalization, a three-fold reduction of the contribution of the laser RIN to the Allan variance has been demonstrated for RIN floor level of -110 dB/Hz [START_REF] Danet | Compact atomic clock prototype based on coherent population (28-30 January 2014 -Paris) (under review process)[END_REF]. Alternatively we may add a power stabilization loop of the pump laser or use a singlemode tapered laser diode as a pump source (cf 6.3).

Once intensity noise contribution will be reduced below the Dick limit, we hope to achieve a total dual-frequency laser contribution to clock frequency stability below 3 x 10 -13 𝜏 !!/! by a careful optimization of the beatnote servo-loop gain in order to obtain a flat phase noise level of -105 dBrad²/Hz on the whole 1 MHz bandwidth.

CONCLUSION

The dual-frequency emission of an opticallypumped VECSEL has been demonstrated at 852 nm with a frequency difference of 9.2 GHz. Stabilized operation of the laser with both servoloops activated has been demonstrated. Under this working operation, the laser noise properties have been carefully investigated. Numerical evaluations based on measurements of the frequency noise, the intensity noise and the beatnote phase noise, demonstrate that a clock frequency stability of 2.7 x 10

-12 on 1 s may be achieved, limited by the intensity noise contribution. Assuming that we reduce the laser intensity noise contribution by changing either the clock or the laser set-up, the laser contribution to clock frequency stability would be limited by the Dick effect and could be reduced below 3 x 10 -13 , paving the way for future compact atomic clocks with 1.10

-13 frequency stability level.

Figure 1 .

 1 Figure 1. Three-level system of Cs atoms used for CPT.

Figure 2 .

 2 Figure 2. Multilayer structure index profile with intracavity electric field intensity. Multilayer structure was designed and fabricated at the Laboratoire de Photoniques et de Nanostructures.

Figure 3 .

 3 Figure 3. Dual frequency laser cavity.

Figure 4 .

 4 Figure 4. Dual frequency laser prototype. Mechanical design was realized at the Observatoire de Paris.

Figure 5 .

 5 Figure 5. Longitudinal mode selection in the dualfrequency laser.

= 6 𝛼 ∥ = 8 .44 x 10 - 6 Table 1 .

 681061 K -1 and the thermo-optic coefficients 𝛽 ! , 𝛽 ! = ∑𝑎 ! 𝑇 ! in K -Material parameters of YVO4 crystal at 25°C by Ter-Gabrielyan & al.

  25 W of incident pump power (Fig 6). Using the Fabry-Perot etalon with a FSR of 2 THz, the laser operates in single mode emission with a wavelength tunability of almost 5 nm. With all intracavity elements, the laser output power decreases to 26 mW at 852.1 nm corresponding to 13 mW per polarization. The laser threshold increases to 0.35 W due to the additional optical losses induced by the cavity elements. The fine tunability of the cross-polarized laser lines is achieved with the rotation of the Fabry-Perot etalon and the adjustment of the cavity length. Proper adjustments of the cavity and pump alignments allows to force the laser emission on two adjacent longitudinal modes on orthogonal polarizations, with a frequency difference ∆𝜈 below the free-Symposium On Optronics In Defence and Security (28-30 January 2014 -Paris) spectral range of the cavity.

Figure 6 .

 6 Figure 6. Laser power characterization for different cavity configurations. Black: without any intracavity elements. Red: with all intracavity elements, for single frequency emission at 852.1 nm. Green: with all intracavity elements, for bifrequency emission at 852.1 nm.

Figure 7 .

 7 Figure 7. Optical spectrum of the dual frequency laser with a resolution of 2 pm. Peaks are separated by 26 pm corresponding to approximately 9 GHz at 852 nm.

Figure 8 .

 8 Figure 8. Stabilization set-up. EO: electro-optic crystal, PZT: piezo-electric transducer, PBS: polarization beam splitter, BS: beam splitter, AOM: acousto-optic modulator, OSA: optical spectrum analyser, ESA: electrical spectrum analyzer.

Figure 9 .

 9 Figure 9. Beatnote frequency spectrum in free-running operation (RBW = 100 kHz) and in lock operation (RBW = 10 kHz), at 9.2 GHz. Noise is rejected 1 MHz away from the carrier frequency.

Figure 10 .

 10 Figure 10. Power spectrum density of the frequency noise of the ordinary polarized mode, under free-running operation and under locked operation.

Figure 11 .

 11 Figure 11. Additive phase noise measurements set-up. LO: Local oscillator.

Figure 12 .

 12 Figure 12. Power spectrum density of the beatnote phase noise due to the laser contribution under freerunning operation and under locked operation (LO frequency: 9.6 GHz) compared to the standard phase noise of the LO.

Figure 13 .

 13 Figure 13. Spectral density of the laser relative intensity noise for each polarization, and of the pump relative intensity noise. Measurements reveal a gain transfer factor of +5 dB from pump RIN to laser RIN.

  14. The two cross-polarized laser modes, stabilized on Cs transition lines (852 nm and with a frequency difference of ∆𝜈 = 9.2 GHz), illuminate a cell full of Cs atoms. An acousto-optic modulator is used for temporal pulse shaping. The clock sequence of duration 𝑇 ! = 6 ms is composed of a first pumping pulse 𝜏 ! = 2 ms, a free evolution time 𝑇 ! = 4 ms and finally a very short detection pulse 𝜏 ! = 25 µs, during which the transmitted power through the cell is measured with a photodiode.

Figure 14 .

 14 Figure 14. General set-up for a CPT-Ramsey atomic clock using Cs atoms trapped in a cell.

  𝜎 ! ! 𝜏 = 𝜎 !/!" The major contribution of the laser power fluctuations (IN) is on the amplitude noise of the detected signal 𝑆(𝑡) which is converted into an additional clock frequency noise through the LO lock loop. Since the signal 𝑆(𝑡) is measured during a time 𝜏 ! = 25 µs, the atomic clock is sensitive to the laser intensity noise on a bandwidth of 1/ 𝜏 ! = 40 kHz.

Table 2 .

 2

Material parameters of SLT crystal doped with MgO at 25°C by

Dolev & al. [20]

.

Table 3 .

 3 Calculations of Allan variance for each laser noise contributions

	Parameter	Max Noise Level	Allan Variance 𝜎 ! 𝜏
	Laser intensity	-110 dB/Hz	2.7 x 10	-12 𝜏 !!/!
	noise
	Laser	3 x 10	9 Hz²/Hz
	frequency	(equivalent white	4.2 x 10	-14 𝜏 !!/!
	noise	noise level)
	Beatnote phase noise	-90 dBrad²/Hz	2,7 x 10	-13 𝜏 !!/!