V Roncin

G Girault

M Gay

L Bramerie

J C Simon

Abstract-T This paper presents a theoretical and experimental investigation of optical signal regeneration properties of a non-linear optical loop mirror using a semiconductor optical amplifier as the active element (SOA-NOLM). While this device has been extensively studied for optical time division demultiplexing (OTDM) and wavelength conversion applications, our proposed approach, based on a reflective configuration, has not yet been investigated, particularly in the light of signal regeneration. The impact on the transfer function shape of different parameters, like SOA position in the interferometer and SOA input optical powers, are numerically studied to appreciate the regenerative capabilities of the device. Regenerative performances in association with a dual stage of SOA to create a 3R regenerator which preserves the data polarity and the wavelength are experimentally assessed. Thanks to this complete regenerative function, a 100.000 km error free transmission has experimentally been achieved at 10 Gb/s in a recirculating loop. The evolution of Bit Error Rate for multiple pass into the regenerator and the polarization insensitivity demonstration to input data are presented.

Index

Terms-Optical communication, Optical Interferometry, Optical Signal Processing, Semiconductor Optical Amplifier, Optical Regeneration.

I. INTRODUCTION

ptical signal processing is now possible at high bit rate (up to 40 Gb/s) and could be an alternative way to allelectronic signal processing in high-capacity optical core networks. Signal regeneration is an attractive way in long haul optical data transmission. Indeed,, the signal undergoes several well-known impairments along propagation, like fiber attenuation and distortions due to chromatic dispersion and nonlinear effects, or the addition of noise due to EDFA. As a consequence, the signal must be regenerated before excessive degradation, in order to increase the transmission distance.

We can distinguish three schemes for optical regeneration.

The simplest one, called 1R (first R for Repeater), consists in a simple signal amplification. The 2R regeneration, for "Reshaping Repeater", allows the reduction of optical noise and the increase of optical data extinction ratio by use of an optical function with a fast nonlinear transmission. Finally, the 3R regeneration, for "Retiming Reshaping Repeater", is a complete regeneration for On-Off Keying (OOK) modulation signals including an optical clock extracted from input signal, which is then modulated by the data. The principle of the 3R regeneration is described in Fig. 1. Degraded input data modulate a high-speed nonlinear optical gate which is able to reduce optical noise on data and transmitting an optical clock synchronised with the input data rhythm. Therefore, the jitter and the optical noise are both reduced. In order to achieve a complete regeneration, the useful nonlinear optical gate has to yield an S-shaped transfer function as shown on Fig. 1. Thus, thanks to its two nonlinearities, it reduces amplitude noise of the digital signal as well on symbols "1" as on symbols "0" [START_REF] Simon | All-optical regeneration techniques[END_REF], [START_REF] Ohman | Noise and regeneration in semiconductor waveguides with saturable gain and absorption Quantum Electronics[END_REF].

Furthermore, the higher its slope, the more the extinction ratio of regenerated data. Several all-optical functions have already been studied as nonlinear optical gates for regeneration. Some of them using Self Phase Modulation (SPM) in a fibre associated with filter [START_REF] Mamyshev | All-optical data regeneration based on self-phase modulation effect[END_REF], [START_REF] Brindel | Experimental demonstration of new regeneration scheme for 40 Gb/s dispersion-managed long-haul transmissions[END_REF], or a nonlinear interferometers [START_REF] Seguineau | Experimental demonstration of simple NOLM-based 2r regenerator for 42.66 Gb/s WDM long-haul transmissions[END_REF], have been associated with synchronous modulation technique [START_REF] Raybon | 40 Gb/s pseudo-linear transmission over one million kilometres[END_REF].

SOA -NOLM in Reflective Configuration for

Optical Regeneration in High Bit Rate Transmission Systems

V. Roncin, G. Girault, M. Gay, L. Bramerie and J. C. Simon O Thus, other highly reliable nonlinear components like Semiconductor Optical Amplifiers (SOA) have are very attractive. Actually, SOA have several advantages: compactness, possible polarization insensitivity, also low input power required for Cross Gain Modulation (XGM) or Cross Phase Modulation (XPM) operation. Thanks to their fast dynamic gain and their phase-amplitude coupling, SOA-based interferometers have been strongly studied achieving interesting results for optical regeneration [START_REF] Zuqing Zhu | 10 000-hop cascaded in-line all-optical 3R regeneration to achieve 1 250 000-km 10-Gb/s transmission[END_REF], [START_REF] Lavigne | Full validation of an optical 3R regenerator at 20 Gb/s[END_REF] and signal processing at high bit rate [START_REF] Wolfson | 40-Gb/s all-optical wavelength conversion, regeneration, and demultiplexing in an SOA-based all-active Mach-Zehnder interferometer Photonics Technology Letters[END_REF].

The Nonlinear Optical Loop Mirror (NOLM) is potentially a stable interferometer because the two delayed paths are in the same fiber. Therefore the fiber lengths, in which the copropagative and contra-propagative fields propagate, are changing simultaneously, consequently reducing the phase difference noise (provided that the fiber is not too long). Its association with a semiconductor optical amplifier as the nonlinear element has often been proposed for all optical processing like demultiplexing in Optical Time Domain multiplexing (OTDM) context [START_REF] Sokoloff | A terahertz optical asymmetric demultiplexer (TOAD) Photonics Technology Letters[END_REF], [START_REF] Ueno | All-Optical signal processing for over 100 Gb/s optical TDM networks[END_REF],It has also been studied, to a less extent, for optical regeneration applications [START_REF] Phillips | Simultaneous demultiplexing, data regeneration, and clock recovery with a single semiconductor optical amplifier based nonlinear-optical loop mirror[END_REF].

The SOA-NOLM is commonly used in transmission configuration which corresponds to "off-state" interferometer when no phase difference is applied between the two paths. In this paper we present a study of the SOA-NOLM in a reflective wavelength conversion configuration, which corresponds in this case to the "on-state" of the interferometer when no phase difference is applied between the two paths. The purpose of the proposed study is to evaluate the performance of this reflective configuration in the optical regeneration context.

In a first part, we describe the SOA-NOLM principle and we recall the main equations used in our numerical investigations. In a second part, we numerically study the transmission function of the interferometer in reflective configuration when the gain imbalance varies. In a third part we experimentally study and assess the low input polarization sensitivity of the SOA-NOLM. Finally we present the system assessment of a regeneration scheme combining this reflective SOA-NOLM wavelength converter, with a two-stage SOA wavelength converter

II. SOA-NOLM BASIC EQUATIONS

The NOLM is an interferometer based on the Sagnac's loop set-up including a nonlinear device into its arm. As previously mentioned, the two waves which interfere propagate in the same length of fibres what confers to them lower sensibility to surrounding fluctuations (temperature and pressure) than other two waves interferometers like Mach-Zehnder and Michelson interferometers. Then, the phase response of this optical interferometer is obtained thanks to a phase-amplitude coupling into the nonlinear element. In the case of SOA-NOLM, the nonlinear element is an SOA in cross gain modulation configuration [START_REF] Olsson | Extinction ratio improvement using the nonlinear optical loop mirror Photonics Technology Letters[END_REF]. Many previous works also studied the capability of the NOLM for signal regeneration [START_REF] Jinno | All optical signal regularizing/regeneration using a nonlinear fiber Sagnac interferometer switch with signal-clock walk-off Lightwave Technology[END_REF]. In Fig. 2, we present the SOA-NOLM operating principle. The input signal (E i ) is a continuous or a pulsed probe which is injected through a 3dB coupler and then divided into two coand counter-propagating fields. The modulated pump signal (E m ), which is injected in the interferometer thanks to another 3dB coupler, corresponds to degraded data in the case of regeneration. It directly modulates the gain and as a consequence, the phase of the SOA thanks to the phaseamplitude coupling factor in semiconductor structures.

From the previous SOA-NOLM principles we then propose the basic matrix of the SOA-NOLM including well-know NOLM equations and amplitude modulation in the SOA [START_REF] Eiselt | semiconductor laser amplifier in a loop mirror Lightwave Technology[END_REF]. The evolution of the reflected and transmitted fields E r and E t are defined as regard to the NOLM input theoretical 3dB coupling factor K, the SOA gain modulations induced by the co-and counter-optical powers g co (t) and g counter (t), and the corresponding non linear co-and counter-propagative optical phases co (t) , conter (t) also in the SOA :

(1)

We deduce from it the power relations of the SOA-NOLM used in the numerical analysis. Moreover we simplify them by introducing the gain difference and the corresponding phase difference in the non linear interferometer:

And we give the expression of the reflected and transmitted optical power output of the SOA-NOLM:

(2)

The phase-amplitude coupling in the SOA is obtained thanks to the following relation with H the Henry factor in semiconductor structures.

The gain modulation is caused by the input optical power P in such as h the internal gain integrated through the SOA length can be expressed in a dynamic approach [START_REF] Agrawal | Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers Quantum Electronics[END_REF] with P sat the saturation power:

(3)
The numerical values for each parameter used in the numerical study are summed-up in the following table. All the results of the SOA-NOLM numerical simulation in a static approach are obtained thanks to the stationary solutions of Eq. 3. We then use the following simplified expression in order to describe the static gain which only depends on the injected optical power and G0 the small signal gain of the SOA [START_REF] Desurvire | Amplification of spontaneous emission in erbium-doped single-mode fibers Lightwave Technology[END_REF]:

We can deduce the transfer function of the SOA-NOLM from its contrast C. We also introduce the extinction ratio parameter ER of the SOA-NOLM output signal which is often used in digital transmission studies to evaluate the quality of a digital signal. In our study, it allows to describe both static and dynamic behaviour I noise is the optical noise intensity generated by the SOA in the interferometer, which limits the contrast of the modulation. I max and I min are deduced from Eq. ( 2).

In fig. 3, the contrast of the SOA-NOLM output power is plotted, respectively for configuration in transmission (It) and reflection (Ir) The maximum of contrast is obtained for each configuration with a phase difference of φ SOA = π. For the reflective power Ir, the theoretical maximum is about 13 dB and 30 dB for the configuration in transmission (It). For the theoretical result, it is important to note that the optical spontaneous emission continuous power P opt noise is -30 dBm.

So the SOA-NOLM in reflection configuration presents a lower output contrast but a higher robustness to signal degradation and external instabilities, which often are the main problem of optical functions based on interferometer. Indeed we observe that the slope of the reflected contrast presents firstly, two saturation zones allowing to reduce, the noise fluctuations on "1" and "0" levels and secondly, a real "S" shape which is required for multi-pass optical regeneration.

III. NUMERICAL STUDY OF THE SOA-NOLM IN REFLECTIVE

CONFIGURATION

In this study we introduce the static transfer function which represents the evolution of the probe power versus the input pump power. This function f sat is determined in the case of continuous probe (P probe ) and pump (P pump ). We use the following expression:

For the temporal analysis of the optical function, we introduce the dynamic transfer function, f dyn , which is obtained with a modulated pump signal defined temporally. The function gives us the relation between the input power P in and the output probe contrast, C out defined from [START_REF] Agrawal | Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers Quantum Electronics[END_REF]. In the following expression, f dyn is obtained from the equations of the dynamic gain.

Hereafter, we study and compared the transfer functions of the SOA-NOLM in the static and dynamic approach. Then, we numerically check that both approaches lead to similar results and that the SOA-NOLM dynamic transfer function using G SOA = 1, corresponds to the static transfer function of a single SOA.

Moreover, in this study we define, two different origins which can generate a gain difference in the SOA-NOLM:

The first one is linked to the static approach and corresponds to the small-signal gain difference of the copropagative probe and the counter-propagative one. We talk about the static gain difference G SOA-static , caused principally by imbalanced losses in the set-up, between the co and the counter-propagating optical ways.

The second one is the instantaneous gain difference caused by the position of the SOA in the NOLM being able to cause a temporal delay, already mentioned, between the co and counter-propagating optical ways.

In the following paragraph, we use the previously described equations to study the SOA-NOLM transfer function.

A. Study of the static transfer function

In that case, the pump and the probe are continuous waves. Consequently, there are no phase changes generated by the position of the SOA in the NOLM. Thus the only phase difference is caused by the static gain difference between the co-and counter-propagating gains induced by the loss imbalance of the set-up. This effect can be understood if the co and counter injected probe powers are themselves imbalanced. Therefore, a modification of the saturation power is introduced for the co and contra optical gains in the SOA. This generates then a static gain difference.

We theoretically study the transfer function by using the following parameters: a continuous probe P probe = -5 dBm, a linewidth enhancement factor = 7 [START_REF] Lee | Measurement of the carrier lifetime and linewidth enhancement factor of semiconductor optical amplifiers using their optical modulation responses Optical Engineering[END_REF] and a bias current of 300 mA for the SOA. Considering a classical parabolic gain evolution with the wavelength, we do not consider any gain dependency, in our study, induced by the wavelength shift between the pump and the probe.

The SOA-NOLM equations are given for a coupling coefficient of the input 3 dB coupler of 0.45. We change the value of G SOA-static , the static gain difference between co and counter propagative fields, in the range of 1.6 to 2.6 dB in order to describe the inflection of the transfer function. This parameter includes the loss imbalance of the set-up. The range of G SOA-static is chosen in order to lead to a sufficient SOA-NOLM static transfer function transformation and a modification of its slope while remaining in a realistic configuration. It is important to note that this static phase difference does not induce any temporal distortion on the output pulses. This point is important in the case of multi-pass into the SOA-NOLM.

Theoretical results are presented on the Fig 4 . For this unbalanced configuration, we clearly observe a slope increase for the static transfer function of the SOA-NOLM with the increase of G SOA-static and as compared to the SOA alone. Therefore, the best transfer function for optical regeneration is observed for a value of 2.4 dB for G SOA-static . Moreover, we observe a contrast of the SOA-NOLM higher than 9 dB for an optical input power of about 5 dBm. In the following paragraph we study the impact of the SOA position in the NOLM in a dynamic configuration. Non linearity and contrast of the SOA-NOLM transfer function will then be studied.

B. Study of the dynamic transfer function

In this part we theoretically study the influence of the position of the SOA in the SOA-NOLM architecture. This configuration introduces a temporal imbalance which is wellknown in optical switching application because it allows to open a temporal window corresponding to the delay on the arrival of the probe pulses into the SOA [START_REF] Prucnal | Unbalanced TOAD for optical data and clock separation in self-clocked transparent OTDM networks Photonics Technology Letters[END_REF]. It is then possible to create a temporal gain difference in the SOA, previously call G SOA-dynamic . In the previously proposed Tab. 1, we have presented all the physical values computed for theoretical simulation of SOA and SOA-NOLM. The obtained results have been successfully compared with another quantitative model [START_REF] Ginovart | Gain recovery dynamics in semiconductor optical amplifier Optics Communications[END_REF] with 20 ps pulses-width at 10 GHz.

For the numerical simulation, the optical input is an RZ 10 Gb/s signal with 20 ps pulse-width. The extinction ratio of the signal is 25 dB. The SOA bias current is 300 mA and the input power of the continuous probe is -10 dBm. The signal is presented in Fig. 5. On the other hand, we present the temporal distortions caused by the delay in the SOA-NOLM. The results of the simulation are presented on Fig. 6 (b).

In fig 6-(a), we show the modification of the transfer function of the SOA-NOLM according to the delay linked to the position of the SOA, which modifies the G SOA-dynamic and thus the SOA . We observe that, for a delay of 0 ps, the transfer function of the SOA-NOLM and the SOA are the same. For other values, an instantaneous phase difference is generated leading to the modification of the slope of the transfer function. Thus the more important the delay is, the more the dynamic transfer function slope increases.

The steepest transfer function is obtained for a delay value of 40 ps. Therefore, for an input extinction ratio of 25 dB, the output extinction ratio is more than 15 dB and the "S" shape is clearly demonstrated, despite the extinction ratio degradation. This result shows that the delay allows to shape the DTF in order to increase the regenerative capacity of the SOA-NOLM in a reflective scheme. However, we can not disconnect the transfer function to the signal quality and particularly to the temporal distortions induced on the optical signal. It is the reason why we limit the delay to 40 ps at a bit rate of 10 Gb/s. For higher delays, the distortions are not compatible with 3R applications anymore. This point is clearly shown in Figure 6-(b). These traces present the temporal response of the SOA-NOLM with an input data signal corresponding to a RZ 50% at 10 Gb/s, with a binary sequence of [0 1 0]. We observe that the SOA-NOLM response is similar to the SOA gain compression if the delay is 0 ps. For other values of delays, the compression is increased but temporal distortions appear. So, the higher the delay is, the more important the distortions are, which can lead to dramatic patterning effects in a real transmission system. In the experimental part we have tried to increase the value for the delay, and also to minimize the distortion on the SOA-NOLM output modulation.

IV. EXPERIMENTAL RESULTS

We have theoretically shown that a SOA-NOLM in reflective configuration is a suitable optical function for all-optical regeneration at 10 Gb/s. We are now going to experimentally study its ability to regenerate signals. In a first paragraph, we show that the function is polarization insensitive and in another one, we evaluate its qualities as a regenerator in a system environment. The experimental set up of the polarization maintaining SOA-NOLM is made up with an optical fibre is presented on Fig.

.

An optical circulator (OC) allows to collect the reflected signal. The port "1" of the circulator is connected to the probe input, the port "2" to the SOA-NOLM and the port "3" allows to extract the output reflected signal from the SOA-NOLM. This circulator is followed by an optical filter (OF) for rejecting the pump signal. The optical distance L between the SOA and the middle of the fiber loop is adjusted with an optical delay line (ODL). The SOA has been designed by Alcatel CIT for 10 Gb/s applications. Its small-signal gain is up to 30 dB and centred around 1550 nm. The laser is packaged in a module to ensure the efficiency of the coupling into the fibres. This coupling is free-space mounted for maintaining the optical polarization in the set-up.

A. Polarization sensitivity analysis

The polarization insensitivity of a device is a fundamental property for an optical function in a transmission system environment [START_REF] Vinegoni | The statistics of polarization-dependent loss in a recirculating loop Lightwave Technology[END_REF]. Indeed, optical polarization of telecommunication signals at the entrance of an optical function is a random parameter which changes continuously. The characteristic parameter generally used for the polarization sensitivity estimation of a device is the Polarization Dependant Loss (PDL). For active functions like optical amplifiers, the Polarization Dependant Gain (PDG), which corresponds to the amplification gain sensitivity induced by the input signal polarization, is used. The PDG is defined as the difference, in decibel, between the two transfer functions obtained with a linear polarized signal, according to the two main axes of the device. These axes are commonly called TE and TM corresponding to the TE and TM main propagative modes in the SOA waveguide [START_REF] Dorren | Nonlinear polarization rotation in semiconductor optical amplifiers: theory and application to all-optical flip-flop memories Quantum Electronics[END_REF]. Then it is possible to plot the two gain functions of the amplifier, respectively called G TE_dB and G TM_dB . Thus, the PDG is calculated thanks to the following expression:

dB TE_dB TM_dB PDG = G -G (1)
In our configuration, the PDG of the SOA and the SOA-NOLM (in reflected configuration) are thus obtained considering the gain G co_dB measured for the co-propagative field and I r_dB , the reflected intensity at the output of the SOA-NOLM.

The experimental set up used to measure the polarization sensitivity of the devices is described on Fig. 8. In order to alternatively impose the TE or TM polarizations of the pump we have used a polarization controller to adjust the state of polarization in front of a variable polarizer (VP). We ensure that the polarization is stable the power level after the VP is a maximum. The linear polarization at the SOA input is checked, before each measurement, thanks to a polarimeter (Profile PAT 9000). Each measurement has been made several times and the measurement error has been assessed to 0.3 dB. This value corresponds to the PDL of the set up without DUT (Device Under Test). Also in Fig. 8, we present the two DUT with the port (1) for the pump, the port (2) for the probe and the port (3) for the output. The SOA in the NOLM is used in cross-gain modulation with high pump power levels. Therefore, the SOA PDG must be compared to SOA-NOLM PDG in this configuration. The results are presented in Fig. 9-(a) for the SOA alone and in Fig. 9-(b) for the SOA-NOLM.

For a better comprehension of the set-up, we notice that the SOA-NOLM has been built in Polarization Maintaining Fibres and that the probe is linearly polarized thanks to a polarized optical source. The probe polarization is preserved in all the interferometer and particularly at each side of the SOA. For the pump polarization, we choose the VP position to reach the TM or the TE linear polarization corresponding to a maximum and a minimum of the small-signal gain. The other polarization cases correspond to a combination of TE and TM polarizations.

The curves shown on Fig. 9 allow experimentally to deduce the PDG of each device by subtracting the square and dot curves. We thus obtained an experimental PDG equalled to 0.5 dB for the SOA as well as the SOA-NOLM, whatever the pump power. So the SOA and the SOA-NOLM are totally polarization insensitive in this case of operating. Further investigations should be necessary to clearly explain the polarization insensitivity of the SOA. This result has been obtained with a probe signal at 1557 nm and a pump signal at 1552 nm. However, we can note that the polarization insensitivity of the SOA-NOLM is directly linked to the SOA polarization insensitivity in the studied pump-probe configuration.

So we experimentally demonstrate that the SOA-NOLM is potentially polarization independent in wavelength-conversion, which is a necessary condition for 3R regeneration application in a system application.

B. Regeneration Performance in system

As previously shown in the numerical analysis, the SOA-NOLM has a nonlinear transfer function, suitable for regenerative applications. We have also experimentally shown the polarization insensitivity of the SOA-NOLM, when made of PM fibre, in cross-gain modulation and reflective configuration.

In this part, we propose to demonstrate the optical regeneration capability of the SOA-NOLM in a system experiment which necessarily preserves the wavelength and the data polarity [START_REF] Bramerie | Performance of a polarization insensitive 3R optical regenerator based on a new SOA-NOLM architecture[END_REF].

Therefore, we use a second wavelength-converter and also data polarity inverter which has been proposed hereafter to increase the output extinction-ratio without particular regenerative properties: the Dual-Stage of SOA (DS-SOA) [START_REF] Simon | Two-stage wavelength converter with improved extinction ratio[END_REF]. The main advantage of the DS-SOA is to increase the extinction ratio twice, in decibel, as compared to a single SOA.

The complete set-up used for the 3R optical regenerator experiment, is presented in Fig 10 . The input signal is a 10 Gb/s data, with RZ 50% format, at 1 =1552 nm. The second optical signal is a linearly polarized continuous laser, at diagram inset of Fig. 10.

The SOA-NOLM output data signal is amplified and next injected into each SOA of the DS-SOA to modulate simultaneously their gains. The optical clock used for the 3R configuration is obtained with a commercial optoelectronic clock recovery. The electrical signal modulates a continuous laser at 1 =1552 nm, through an optical modulator. It is injected as a probe signal in both SOA, to be modulated twice by cross-gain modulation (XGM). The measurement has been succeeded by reducing the power of the input data and then measuring the output regenerated data with a sampling oscilloscope. The S-shape is clearly shown and an extinction ratio of 10 dB for the input signal (input power) corresponds to an output extinction ratio of more than 14 dB. This extinction ratio improvement combining to the "S" shape ensure a full 3R regeneration.

In the transmission system experiment, we used an optical power for data signal with the level of symbols "0" lower than -12 dBm, and level of symbols "1" higher than -3 dBm. This configuration ensures an efficient operating of the regenerative function of the SOA-NOLM. Therefore, the optical noise on symbols "0" and symbols "1" is reduced. Concerning the retiming process, which corresponds to an efficient timing jitter reduction, the recovered optical clock has been chosen to be narrower than the timing window of the regenerated data.

The best way to validate a regenerator is to test it in a transmission link [START_REF] Gay | 2R and 3R optical regeneration: from device to system characterization[END_REF]. So we test the efficiency of the regeneration function composed by the SOA-NOLM in a recirculation loop. This experimental set-up allows to do multiple pass into the regenerator and then, to accumulate the effect of regeneration, and also to observe and quantify its efficiency.

The experimental set up of the recirculation loop is represented on Fig. 11-(a). The loop is composed of two 50 km Non-Zero Dispersion Shifted Fiber (NZDSF) spans, with chromatic dispersion of 4ps/nm/km. The fiber link dispersion is compensated (DCF).

Losses are compensated by Erbium Doped Fibre Amplifiers (EDFA) and counter-propagating Raman pumping ensuring a low noise accumulation line. The transmitter consists of a 2 15 -1 pseudo-random bit sequence combined with a logical gate which produces an RZ electrical signal. This signal modulates the optical 1552 nm source thanks to a LiNbO 3 modulator which produces a 50 ps full width at half maximum signal. The signal is injected into the recirculating loop thanks to an Acousto-Optic Modulators (AOM).

A polarization scrambler (polarization modulation frequency ~ 1 MHz) is placed in front of the regenerator in order to take polarization effects into account and to check the stability of the device versus polarization fluctuations and highlight the polarization insensitivity of the 3R regenerator.

With the previously described set up, without regenerator, a maximal transmission of 2000 km has been achieved. When including in the loop the 3R device composed by the SOA-NOLM followed by the DS-SOA, an error free transmission of 100 000 km, corresponding to 1000 laps of 100 km, has been achieved. This result has been obtained for an OSNR (Optical Signal to Noise Ratio) in the loop, at the input of the 3R regenerator, of 33 dB / 0.1 nm.

Then in order to do BER (Bit Error Rate) measurements, noise is artificially included in the loop, using an Amplified Spontaneous Emission source (ASE). This allows degrading the OSNR in front of the regenerator which is necessary to measure a BER in regenerated signal experiments [START_REF] Kuebart | 40 Gb/s transmission over 80 000 km dispersion shifted fibre using compact opto-electronic-3R regeneration[END_REF]. The evolution of the BER versus the number of laps in the loop, which corresponds to the transmission length, can thus be plotted. The results are reported on Fig. 11-(b). The empty and full symbols respectively correspond to tranmissions without and with the 3R regenerator. The curve with square symbols has been obtained with an OSNR of 24 dB in front of the regenerator and the curve with triangles with an OSNR of 21 dB.

These curves show that the tranmission length is significantly improved when including the 3R regenerator in the loop. Moreover a transmission with a BER of 10 -8 is obtained with an OSNR of 24 dB measured in front of the regenerator. With an OSNR of 21 dB a transmission with a BER of 10 -4 is achieved which is a good performance considering the possibility of using a FEC (Forward Error Correcting Code). We can note that the shape of the regenerated curve corresponds to the classical shape preview for 3R regenerated transmission with optimal regenerator.

We can finally note that all these measurements have been achieved thanks to the high stability of the proposed regenerator, widely studied and commented in the article.

Fig. 1 :

 1 Fig. 1: 3R regeneration principle with nonlinear optical gate characterized by its nonlinear transfer function.

Fig. 2 :

 2 Fig. 2: SOA-NOLM operating principle. The SOA is the nonlinear element allowing to convert the input data signal into the transmitted or reflected output data signals

1 :

 1 Physical values used for the numerical simulation of the SOA

Fig. 3 :

 3 Fig. 3: Theoretical SOA-NOLM contrast evolution for the two considered configurations. Effect of the differential phase shift SOA corresponding to the co-and counter-propagative probe phase difference.

Fig 4 :

 4 Fig 4: Theoretical comparison between the static transfer function of the lonely SOA and the SOA-NOLM. Improvement of the nonlinear shape for the SOA-NOLM, induced by the static co/counter gain difference GSOA-static

Fig. 5 :

 5 Fig. 5: Signal characteristics for the simulation with injected data (ER=25 dB) on the left and reflected probe (modulated by the pump) on the right. The delay used for the simulation, introduced by the SOA position in the SOA-NOLM is 15 ps On the one hand, we deduce the Dynamic Transfer Function (DTF) from the dynamic contrast of the reflected output of the SOA-NOLM. The characteristics of the signals used for the simulation are presented in Fig. 5. The critical parameters are the optical input power of the input data Pin and the output probe contrast C out . We then deduce the DTF by varying the optical input power, and this for different delays caused by the position of the SOA in the interferometer. The results are reported in Fig. 6 (a).

Fig 6 :

 6 Fig 6 : (a) Theoretical dynamic transfer function of the SOA-NOLM for different delay between co and counter probe. (b) Theoretical temporal response of the SOA-NOLM for an input [0 1 0] sequence for the same delays in the SOA-NOLM Input signal is a 20 ps RZ at 10 Gb/s.

Fig. 7 :

 7 Fig. 7: Scheme of the SOA-NOLM experimental set up in using the reflective port.

Fig. 8 :

 8 Fig.8: Experimental set-ups for polarization sensitivity analysis of a DUT in pump-probe configuration: DUT#1 is a single SOA and DUT#2 is the SOA-NOLM in reflection scheme. "A" is an optical Amplifier, "VA" a Variable Attenuator, "OF" a bandpass Optical Filter for OSNR improvement, "PC" a Polarization Controller and "VP" a Variable linear Polarizer.

Fig. 9 :

 9 Fig. 9: Experimental transfer functions of the single SOA (a) and the SOA-NOLM (b) in pump / probe configuration. These results allow the calculation of the polarization dependant gain (PDG) of each device.

Fig. 10 :

 10 Fig. 10: 3R regenerator scheme with "A" for EDFA and "CR" for optoelectronic Clock Recovery, "CK" for optical clock. The curve in inset is the dynamic transfer function of the complete regenerator obtained from data extinction ratio measurement with a sampling oscilloscope We have experimentally measured the transfer function of the complete 3R regenerator. The curve is plotted in the inset of Fig 10.The measurement has been succeeded by reducing the power of the input data and then measuring the output regenerated data with a sampling oscilloscope. The S-shape is clearly shown and an extinction ratio of 10 dB for the input signal (input power) corresponds to an output extinction ratio of more than 14 dB. This extinction ratio improvement combining to the "S" shape ensure a full 3R regeneration.In the transmission system experiment, we used an optical power for data signal with the level of symbols "0" lower than -12 dBm, and level of symbols "1" higher than -3 dBm. This configuration ensures an efficient operating of the regenerative function of the SOA-NOLM. Therefore, the optical noise on symbols "0" and symbols "1" is reduced. Concerning the

=1557 nm, which is injected into the SOA-NOLM. The polarization of the continuous laser is collinear to the TM axis of the SOA. The reflected output signal is converted at the wavelength 2 and data polarity inverted, as shown in the eye

journal and conference papers including some 25 invited presentations, 10 patents, and 3 book chapters. He has contributed to European research programs (RACE 1027, ESPRIT 3 MOSAIC and ACTS KEOPS). He is recipient of the Fabry-de Grammont award from the French Optical Society.

This work was supported in part by the "Ministère de la recherche", the "Région Bretagne" and the European Founding for the Regional Development (FEDER).

V. CONCLUSION

In this work, we studied, in an original configuration, a classical optical function often used for optical signal processing: the SOA-NOLM in a reflective scheme. The interferometer used in this configuration is a wavelength converter which changes the data polarity. In this complete article, we demonstrated experimentally that the SOA-NOLM is very stable, thanks to its intrinsic properties linked to its singular construction: one single arm and one unique SOA, which is in this configuration, polarization insensitive. We then used its capability of nonlinear transmission and its properties for optical regeneration operation. We theoretically studied its transfer function and highlighted two different ways to increase its slope, as it is required in the optical regeneration theory. We shew the results obtained by changing dynamically and statically the phase difference between the co and counterpropagative fields in the interferometer, thanks to the phaseamplitude coupling in the SOA. Finally, we tested this function experimentally by showing in a first paragraph its optical polarization insensitivity and consequently, in a second part its capability to work in an data transmission environment. So we present the result of a 3R regenerated transmission of 100 000 km, without detecting any error.

VI. ACKNOWLEDGMENT

The authors would like to thank all the team "Fonctions Optiques pour les Télécommunication" for the fruitful discussions. This work has been supported by the European Found for Regional Development FEDER; the "Ministère de la recherche" and the "Region Bretagne".


V Roncin

S Fève

A Millaud

R Cramer

J-C Simon

Y Jaouën

High-sensitive Optical Pulse-Shape Characterization using a Beating-Contrast-Measurement Technique

Ultrahigh-speed optical transmission technology, such as optical time domain multiplexing or optical signal processing is a key point for increasing the communication capacity. The system performances are strongly related to pulse properties. We present an original method dedicated to short pulse-shape characterization with high repetition rate using standard optical telecommunications equipments. Its principle is based on temporal measurement of the contrast produced by the beating of two delayed optical pulses in a high-bandwidth photodetector. This technique returns firstly reliable informations on the pulse-shape, such as pulsewidth, shape and pedestal. Simulation and experimental results evaluate the high-sensitivity and the high-resolution of the technique allowing the measurement of pulse extinction ratio up to 20 dB with typical timing resolution of about 100 fs. The compatibility of the technique with high repetition rate pulse measurement offers an efficient tool for short pulse analysis.

Introduction

Optical short-pulse characterization is a fundamental goal in physics for short phenomena characterization [START_REF] Bucksbaum | The future of attosecond spectroscopy[END_REF] as well in the area of high capacity optical communication engineering based on Optical Time Domain Multiplexing (OTDM) technology [START_REF] Weber | Ultrahigh-speed OTDM-transmission technology[END_REF]. In this last application, the pulse train which has to carry out optical data is build from interleaving of several optical short pulse train delayed in order to increase the repetition rate. The most important points in optical pulse characterization are the pulsewidth, commonly defined as the full width at half maximum (FWHM), shape and pedestal. Particularly in the OTDM context, significant pulse pedestals can lead, to great instability caused by inter-pulse interference [START_REF] Saruwatari | All-optical signal processing for terabit/second optical transmission[END_REF]. Specific solutions have been proposed for pulse-shape control in order to measure extinction ration improvement [START_REF] Smith | Pulse shaping, compression, and pedestal suppression employing a nonlinear-optical loop mirror[END_REF] or pulse pedestal reduction [START_REF] Gosset | Extinction ratio improvement and wavelength conversion based on four-wave mixing in a semiconductor optical amplifier[END_REF]. On the other hand different techniques for optical pulse characterization have been developed for the shape monitoring, the pulse energy and the effects induced by its interaction with material. Non-linear autocorrelators [START_REF] Sala | CW autocorrelation measurements of picosecond laser pulses[END_REF] which are commonly used for ultra-short pulse measurement, are not able neither to give real pulse-shape nor to evaluate precisely the pulse duration because of the shape hypothesis made for the deconvolution. However the temporal pulsewidth is obtained with a low precision of about 20% if the initial hypothesis is a Gaussian or a hyperbolic secant shape. Note that the obtained trace obtained is necessary symmetrical which is leading to a lack of information on the pulse pedestal. Other methods for time analysis with high repetition rate has been proposed in the 90's years such as streak camera [START_REF] Prade | A simple method for the determination of the intensity and phase of ultrashort optical pulses[END_REF] and optical sampling [START_REF] Ohta | Highly sensitive optical sampling system with 100 GHz bandwidth[END_REF]. Different approaches have been investigated as all optical sampling using SOA [START_REF] Jiang | Sampling pulses with semiconductor optical amplifiers[END_REF] or fiber-based parametric amplification [START_REF] Li | 300-Gb/s eyediagram measurement by optical sampling using fiber-based parametric amplification[END_REF]. Optical sampling with repetition rate up 640 GHz [START_REF] Yamada | 640-Gb/s OTDM signal measurement with high-resolution optical sampling system using wavelength-tunable soliton pulses[END_REF] has been obtained. Combining time and frequency resolved measurement, many interesting techniques have been investigated allowing to give instantaneous phase information as well-known Frequency resolved Optical Gating (FROG) [START_REF] Trebino | Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating[END_REF] and other derived methods [START_REF] Walmsley | Characterization of the electric field of ultrashort optical pulses[END_REF], [START_REF] Dorrer | Simultaneous temporal characterization of telecommunication optical pulses and modulators by use of spectrograms[END_REF], [START_REF] Gosset | Phase and amplitude characterization of a 40-GHz self-pulsating DBR laser based on autocorrelation analysis[END_REF]. Based on spectrum modulation and Fourier analysis, these different approaches are extensively studied for pulsed source shaping [START_REF] Shank | Compression of femtosecond optical pulses[END_REF], [START_REF] Nibbering | Spectral determination of the amplitude and the phase of intense ultrashort optical pulses[END_REF] and for chirp management in optical communication [START_REF] Suzuki | Simultaneous compensation of laser chirp, kerr effect, anddispersion in 10Gb/s long-haul transmission systems[END_REF].

We present in this article an extensive analysis of our original approach for pulse characterization based on homodyne Beating Contrast Measurement (BCM) technique. This method required only low-bandwidth photodetector, compared to pulse bandwidth and a conventional electrical sampling oscilloscope [START_REF] Roncin | Optical short pulse characterization by interferometric contrast measurement method[END_REF]. Two pulse trains from a same laser source are decorrelated using optical fiber section in order to avoid optical interference, precisely delayed and afterwards recombined in the photodetector. By controlling the delay between the pulses and measuring the contrast of the beating detected we realize the pulse-shape measurement. The theoritical limitations of the BCM technique have been investigated through numerical modelling. Experimental results allow the validation of the measurement technique using pulse-shape characterization of two different pulse sources. The first one is based on electrical commutation in semiconductor laser (Q-Switched laser) producing weakly coherent laser emission with highly chirped pulses. The other source is based on fiber-doped-mode-locked laser (Mode-Lock laser) producing greater coherent pulse emission with low chirp.

Principles of BCM technique

The method is described thanks to the set-up presented in Figure 1. The incoming pulse train is separated onto the arms of the fiber-based Mach-Zehnder interferometer. The field in the path (1) is decorrelated as compared to the field in the path (2) assuming that the decorrelation fiber section is designed in order to avoid interference in the output 3 dB coupler. This operation is fundamental in the technique because the two optical pulses in interaction in the photodetector has to be decorrelated in order to avoid a coherent beating and to cover all the values of phase difference between the pulses and then to obtain the entire contrast of the beating. This point is critical because the technique is based, as it will be described analytically in the following of the article, on the measurement of the beating contrast. thus, the instantaneous phase-difference between the pulses has to be a random parameter which only depends on the phase fluctuations induced by the interferometer environment. It is the reason why, the ab- solute state of phase of the pulses in interaction in the detector must be different. So, using an electrical sampling oscilloscope it is possible to observe the accumulation of all the values of the electrical phase-difference in the range [0,2π]. For a long time acquisition using histogram measurement, the whole description of beating amplitude contrast is possible. A photodetector with a cut-off frequency greater than the repetition frequency of the pulse train is used to describe the beating contrast for each value of the delay between the two pulses.

In order to make a rigorous description of the BCM technique, we present in Figure 2 a simulation of its principle. According to the set-up previously described, we introduced a pulse-train of 10 ps pulsewidth (left column). The beating is firstly shown at the output of the interferometer using an infinite (ideal) bandwidth detector (center column). Finally, the beating is observed using a 10 GHz detector (right column) directly plugged on a high bandwidth sampling oscilloscope. This simulation is presented for three different delays: τ = 20, 10 and 0 ps. For these different delays we show that closer are the pulses and higher is the contrast of the beating. So, it is then possible to measure the contrast of the beating for different delays between the two separated pulses (τ). Experimentally, we measure the beating contrast in a histogram window using the histogram function of the sampling oscilloscope. The simulation which takes into account the photodetector bandwidth limitation is clearly shown on the curves on the right of Figure 2. By measuring the minimum and maximum value of the beating, it is possible to determine the contrast. Finally, we deduce thanks to the appropriate hypothesis, the shape of the pulse versus the delay between the pulses. In the following part, we propose an analytical description of the technique, in order to study the performances and the limitations of the BCM technique.

Phase description

In this part, we introduce the formalisme used hereafter for the optical phase description in the modelisation approach. We also suggest a discussion about the validity of the analytical description if the phase of the pulse is linear or nonlinear. We define an expression of the phase of the optical pulse by the introduction of the chirp contribution:

φ pulse (t) = φ init + φ chirp (t)
Where φ init is the initial phase of the pulse defined arbitrarily at the pulse beginning. And φ chirp is the instantaneous phase in the pulse which depends on the type of the process of generation of the optical pulse. For example, a mode-locking or a gainswitching process are not producing the same phase evolution in the pulse. Then, the chirp may be consider as linear or non-linear.

The decorrelation process is described with the delay time T which is given for T = n * L/c, with c the velocity of light in vacuum, n the propagation index and L the length of the decorrelation fiber. This process imposes that, for a delay higher than the optical source coherency time, φ init-1 for the path (1) and φ init-2 for the path (2), are supposed independent and correspond to a random phase.

Then, in the BCM technique, the measurement is achieved thanks to the variation of the contrast produced by the beating of the two pulses in the photodetector. Then, the discrete changing of the delay between the pulses is defined by τ. Then, one of the two pulses is taken as a reference and the other is shifted by τ as compared to the reference in order to obtain the expression of the phase for each pulses. Moreover, the chirp expression is identical for each pulses. We give the expression of the phase of the pulses (1) and (2):

φ pulse-1 (t) = φ init-1 + φ Chirp (t) φ pulse-2 (t + τ) = φ init-2 + φ Chirp (t + τ) + φ T
Therefore, we will consider in the nest part the expression of the beating in the photodetector. So, we introduce the phase difference between the pulses during the measurement process. In order to study the impact of the phase on the beating expression we suggest two hypothesis for the chirp expression:

• The chirp is linear and its expression is simply obtain thanks to a constant C corresponding to the chirp evolution into the pulse as well:φ Chirp-L (t) = C * t

• The chirp is nonlinear and its analytical expression φ Chirp-NL (t) is not the purpose of this article

The phase difference is then suggested for these two previous hypothesis.

-For a linear chirp it is possible to express the phases as following:

φ pulse-1 (t) = φ init-1 +C * t φ pulse-2 (t + τ) = φ init-2 +C * (t + τ) + φ T = φ init-2 +C * t +C * τ + φ T
We obtain the expression of the phase difference:

∆φ (τ) = φ (2) pulse (t + τ) -φ (1) pulse (t) = ∆φ 0 +C * τ With ∆φ 0 = φ init-2 -φ init-1 + φ T that
may be considered as independent to t and τ. For a correct decorrelation operation, its value is randomized and moving slowly as regard to eventual fluctuations introduced in the experimental set-up.

-For a nonlinear chirp, the expression of the phases is more complicated and depends on the pulse generation process:

∆φ (τ) = ∆φ 0 + ∆φ chirp-NL (τ)
With ∆φ chirp-NL is a nonlinear fonction which depends on the delay τ. Considering these expressions, we will base further hypothesis of the measurement analytical description, on the linearity or not of the pulse phase.

Analytical description

E 1 (t, 0) is the reference pulse train which is propagated in the optical path ( 1) and E 2 (t, τ) the delayed pulse train in the optical path 2. The beating of the two optical pulses is produced into the photodetector. The time reference of the beating is given by the pulse field E 1 which is not delayed (τ = 0). We note that the decorrelation is not introduced in the analytical model because the delay is fix for the measurement. The intensity of the beating into the photodetector is then given by the expression [START_REF] Bucksbaum | The future of attosecond spectroscopy[END_REF].

I(t, τ) = E 1 (t) * E 1 * (t) + E 2 (t + τ) * E 2 * (t + τ) + 2 E 1 (t) * E 1 * (t) * E 2 (t + τ) * E 2 * (t + τ) cos [∆φ (τ)] (1)
Several hypothesis may be considered:

-The contrast measurement is complete as soon as ∆φ (τ) has described the range [0,2π].

-The limited photodetector bandwidth modifies the electrical response of the beating. In order to get the more sensitive measurement, the intensity of the contrast has to correspond to the beating between only two pulses. Consequently, for an optical pulse train of N GHz, the bandwidth of the detector must be close to the repetition rate of the pulse train. For a bandwidth lower than N, the analytical expression of the beating intensity would be more complicated because several pulses have to be taken into account in the analytical expression of the filtering.

The extrema of the beating amplitude are then expressed: For ∆φ (t, τ) = 0 (2kπ),

I max (t, τ) = E i (t, 0) E * i (t, 0) + E j (t, τ) E * j (t, τ) + 2 E i (t, 0) E * i (t, 0) E j (t, τ) E * j (t, τ) (2)
For ∆φ (t, τ) = (2k + 1)π, In order to determine the contrast of the beating, it is important to measure I min (t) and I max (t). The Histogram routine of the sampling oscilloscope allows this measurement from the information on the width and the voltage values of the histogram. Several considerations have to be done: For a narrow histogram width, we consider the variable t as a constant in the expressions 2 and 3. Moreover, t is equal to zero at the top of the pulse. Then, if the position of the histogram window is the same all along the contrast measurement: -The vari-ables t and τ are constant for each measurement -The variable t could be equal to zero and then neglected in the following expressions of the beating contrast C at the maximum of intensity of the reference pulse becomes.

I min (t, τ) = E i (t, 0) E * i (t, 0) + E j (t, τ) E * j (t, τ) -2 E i (t, 0) E * i (t, 0) E j (t, τ) E * j (t, τ) (3)
C(τ) = I max (τ) -I min (τ) I max (τ) + I min (τ) = 2 E i E * i E j (τ).E * 2 (τ) E i E * i + E j (τ) E * j (τ) (4)
The pulse shape I j (τ) is directly related to the intensity ratio R(τ) between the two pulses in the histogram window as:

R(τ) = E j (τ) E * j (τ) E i E * i 1 = I j (τ) I i (5)
Finally, the relation between the beating contrast C(τ) and the pulse intensity R(τ).

R(τ) = 1 C(τ) - 1 C 2 (τ) -1 1 2 2 (6)
By this way, we can determine the shape of I 2 with the resolution corresponding to the Optical Delay Line precision.

Bandwidth photodetector limitations

The dependency on the photodetector bandwidth of the BCM technique has been studied. The beating response depends intrinsecally to the detector response h(t). The formalism used for this study is expressed as following:

I F (t, τ) = I(t, τ) * h(t) = + T H 2 - T H 2 I(t, τ) h(u -t) du (7)
In order to simplify the expression of the beating detected with a limited bandwidth photodetector, we consider the following hypothesis :

-The contrast measurement is determined using a histogram window bounded by [T H /2; T H /2].

-We consider that the position of the window coincides with the top of the reference pulse and this, for each measurement. In a realistic approach, the histogram window width is variable and must be adjusted in order to optimize the measurement. We will discuss this point at the end of this section.

-We consider that for each value of delay τ, the histogram is completed within the acquisition time T A . This time is necessary for covering all the values of the phase difference between the pulses and produce a statistical histogram that make use for the contrast measurement.

-For the contrast measurements, we only consider the convolution of the beating in the selected histogram window T H . In the histogram window, the temporal response of filter h(t) can be considered as a constant in order to simplify the expression of the convolution product which is contained in the global constant K = T A × T H . For example, a 100 ps photodiode response which corresponds to a 10 GHz bandwidth (B = 10 GHz) should be simplified by a constant if the measurement in realized in the histogram time window of few picoseconds. The condition for this hypothesis is that:

T H << 1/B.
According to the distributivity of the convolution product and the temporal integration between the boundaries determined by the measurement time window, we give the expression of the three different terms. We notice that I i is the reference and does not depends on the delay τ:

So, the expression of the intensity is composed of three terms A 1 , A 2 and A 1,2 :

I F (τ) = + T A 2 - T A 2 I F (t, τ) dt = A 1 (τ) + A 2 (τ) + A 1,2 (τ) (8)
A 1 (τ) = + T A 2 - T A 2 [I i (t) * h(t)] dt = + T A 2 - T A 2 + T H 2 - T H 2 I i (t) h(u -t) du dt = K I i (τ) (9)
A 2 (τ) = + T A 2 - T A 2 [I j (t, τ) * h(t)] dt = + T A 2 - T A 2 + T H 2 - T H 2 I j (t, τ) h(u -t) du dt = K I j (τ) (10)
A 1,2 (τ) = + T A 2 - T A 2 2 I i (t) I j (t, τ) cos ∆φ i = j chirp (t) * h(t) dt = K 2 I 1 I 2 (τ) cos ∆φ i = j chirp (t) (11)
Also, the following expressions give the extrema of the filtered beating, deduced from Equations ( 2) and (3) with a distribution of the phase difference between 0 and 2π:

I max F (τ) = K[ I 1 + I 2 (τ) + 2 I 1 I 2 (τ) ] I min F (τ) = K[ I 1 + I 2 (τ) -2 I 1 I 2 (τ) ] (12)
Therefore, we are able to write the expression of the beating contrast with an ideal detector. We show that the filtering effect is, according to the hypothesis, negligible:

C F (τ) = I max F (τ) -I min F (τ) I max F (τ) + I min F (τ) = 2K 2 I 1 I 2 (τ) 2K { I 1 + I 2 (τ) } C F (τ) = C(τ) (13)
Thus, thanks to the model hypothesis, the filtered beating contrast must be theoretically considered equal to the ideal beating contrast. According to this result, we neglect in the BCM measurement the filtering effect generated by the photodetector. Thus, the use of a low filter bandwidth allows the use of a wider histogram window. This point is really important because in the reality, larger is the histogram window is large and higher is the number of hits and faster is the measurement is fast. This discussion has been taken into account in the following of the study. The histogram window is fixed at 5 ps for all the simulations and experimental measurements. The second point is that the detector bandwidth has to be higher than the repetition rate in order to maximize the contrast and then enhance the sensitivity of the measurement. This condition is one of the limitations of the measurement. In the following part, we have done several simulations thanks to the theoretical model in order to estimate the benefits and the limitations of the technique.

Modelling results

The BCM technique modelling has been computed using the analytical expressions presented in the previous part. We present here different results obtained thanks to the equation 13 which takes into account the realistic photodetector response. Most of the parameters which have been introduced in the computation are extracted from the experimental part of the study.

Three studies have been done:

• Impact of the bandwidth on the pulsewidth measurement

• Measurement of pulse pedestals and impact of the bandwidth on it

• Influence of the noise (optical and/or electrical noise) on the measurement of the pulse extinction ratio

In order to validate the simulation approach, we present qualitative results obtained using the simulation. In Figure 3, we show the theoretical pulse to be characterized (continuous line). The input pulse has an hyperbolic secant shape with 4.5 ps FWHM. The dash curve is the theoretical response of a 50 GHz bandwidth photodetector. That provides a 12.5 ps pulse. The dot and dash curve shows the pulse trace obtained using the BCM technique which produces a 4.5 ps FWHM. The photodetector simulated for the BCM technique is 20 GHz bandwidth corresponding to a 2 nd order Butterworth filter function for h(t). The width of the histogram window is 5 ps and the delay between the incident pulses is a fraction of the incident pulse-width. The sampling rate of the delay is chosen in order to optimize the time of calculation and the measurement resolution. Moreover, we introduce a variable additional noise in the simulation in order to analyze the sensitivity of the technique to the signal to noise ratio (SNR) on the input signal. in these conditions, we observe in one hand, that the method is really efficient and on the other hand, that the hypothesis done in the theoretical part are confirmed. In the following of the study, we present several results allowing us to determine the performances expected with the BCM technique.

Pulsewidth analysis

In this part we present the theoretical study concerning the pulsewidth measurement using the BCM technique. We test the calculation with different pulsewidths from 100 fs to 50 ps. We also modify the detector bandwidth used for the simulation in order to determine the most suitable one according to the previous hypothesis. Results are shown in Figure 4. The curve with down triangles corresponds to the 20 GHz bandwidth and is very close to the continuous line which represents the real pulsewidth. The result with this bandwidth gives very reliable results because each calculated pulsewidths are included in the range corresponding +/-20% of the true width. On the other hand, the infinite bandwidth does not give the best result because the corresponding temporal response is lower than the histogram width. This critical parameter leads us to choose the histogram window width in order to keep a flat response of the detector in the window and then to avoid nonlinearities in the measurement. We clearly observe on the simulation results that the bandwidth parameter introduces important variations on the pulsewidth measurement. This behaviour is linked to the approximation made on the photodetector response that imposes h(t) as a constant. Moreover we show that the 10 GHz photodetector gives us the most reliable pulsewidth measurement.

Another consequence linked to the histogram window width, is the speed of the measurement which will be increased experimentally by a wider histogram window. This point is also important for the choice of this parameter especially for the experimental part.

In the next part, we focus our study on the measurement of the pulse shape obtained using the BCM technique and especially on the detection of the pedestals which are not detectable using classical methods as direct photo-detection and autocorrelation.

Pulse shape analysis

We present a study on the capability of the BCM technique to pedestal detection. So we simulate two pedestals on each side of the pulse in order to determine the best configuration allowing the measurement of the pedestals position and amplitude. Results are shown in Figure 5. The incident pulse is composed of three 4.5 ps width hyperbolic secants separated by 15 ps from the central peak. The repetition frequency of the pulse train is still 10 GHz. The ratio between the pedestals and the normalized central peak is 7 dB for the right peak and 12 dB for the left peak. We simulate the BCM technique for different photodetector bandwidths. The first observation concerns the pulsewidth which is not correctly determined in presence of pedestals. The second observation concerns the pedestal position which is determined with the BCM technique. The third observation concerns the influence of the photodetector bandwidth on the pedestal measurement efficiency. By the way, we simulate the technique for 5, 10, 30 and 50 GHz photodetector bandwidths. We show clearly that higher is the bandwidth, more efficient is the measurement. The first conclusion is that the technique allows pedestal detection. The second conclusion is that the contrast of the pedestal obtained using the BCM technique is reduced as compared to the incident pulse. For this analyse, we use two criteria in Figure 5, based on the peak and background intensities values:

• the contrast C = I peak -I background / I background ,

• the Extinction Ratio ER = I peak#1 -I background / I peak#2 -I background .

For the 50 GHz bandwidth configuration, the contrast of the pulses (central peak and pedestals) is divided by two as compared to the incident pulse, which is the best result obtained with the simulation. On the other hand, the extinction ratio is not modified as compared to the incident pulse. So this interesting result shows that, with a suitable calibration, the BCM technique allows a realistic measurement of pulse pedestals.

In the following part, we focus our study on the theoretical sensitivity of the technique to optical and/or electrical noise in excess introduced in the measurement process.

Noise influence in the BCM technique

Optical and electronic noises are considered as the main limitations in the photodetection process. Beatings between optical noise and signal are generated into the photodetector. Electronic resulting noise is proportional to the noise spectral density in the band B. In order to study the influence of the noise in the BCM technique, we simulated an additive white noise in a band B equal to 5 nm. The corresponding Signal to Noise Ratio (SNR) is expressed in dB/5 nm. The signal is still a pulse train at 10 GHz of repetition frequency with a 4.5 ps pulsewidth. The extinction ratio of the pulse train which is defined as the ratio between the maximum of the pulse and the background of the signal is fixed to 20 dB. The results are shown in Figure 6. We present the extinction ratio in a logarithm scale in order to observe precisely the performance of the BCM technique to determine the extinction ratio. So, we changed the SNR of the pulse train from 31.4 dB, which correspond to a noiseless signal, to 8.4 dB which corresponds to a degraded signal. The first observation is that the extinction ratio of the pulse train determined using the BCM technique is very close to the true value if the SNR is high. For example, the extinction ratio measured with a SNR of 31.4 dB is higher than 19 dB. We show that the reduction of the SNR generate a degradation of the extinction ratio measured using the BCM technique. The second observation is that the noise is transmitted through the BCM technique with a shape fluctuation corresponding to the sampling rate of the measurement (sampling rate of the delay line). Also, the BCM technique is really sensitive to noise so, its minimisation is necessary for the method optimisation. decorrelation fiber depends on the repetition rate of the optical source. The purpose of the measurement is the production of a beating between two decorrelated incident pulses. The decorrelation fiber length corresponds to a multiple of the repetition rate. The length also depends on the type of the pulse source, especially, on its coherency. The all fibered motorized ODL has a typical resolution of 10 fs allowing to control precisely the delay between the pulses. The pre-amplified photodetector module has a bandwidth B o = 20 GHz. The sampling oscilloscope has an electrical bandwidth limited to 40 GHz. The equivalent bandwidth is then close to 20 GHz. According to the equations 11 and 12, the contrast C F (τ) of the beating is experimentally measured using the histogram function of a CSA 803 sampling oscilloscope from Tektronix, Inc. This measurement gives the statistical distribution of the beating voltage in the controlled measurement time window. A time window of T H = 5 ps is used in order to obtain a flat signal for the histogram measurement and then to confirm the hypothesis developed in the simulation part:(T H << 1/B). The duration of the histogram measurement is about 5 seconds in order to store a great number of samples with all values for the phase difference between the two pulses. Then, we measure the mean value, the maximum and the minimum at 3σ of the distribution corresponding to the routine for >99% of shots. This experimental process allows the measurement of the contrast C F and then the obtaining of the ratio between the pulse shape and the reference R. For the calculation, we take into account the loss of the set-up and the ratio between the two pulse train. This calibration is necessary to optimize the BCM technique.

Using a stable experimental set-up and an optimized routine for the calculation, we present in the following part experimental results of the BCM technique with two different pulsed sources in order to validate the technique.

Results and comparison with autocorrelation trace

In this section, we wish to definitely validate the BCM technique using a comparison between results with a reliable characterization technique of optical pulses. So, each optical pulse source is first characterized using an autocorrelator FR-103MN from Femtochrome. Each result obtained with the BCM technique is auto-convoluated mathematically in order to be compared with the experimental autocorrelation trace.

BCM validation using gain-switched pulse source

The first optical source is a 10 GHz internally modulated DFB laser from Alcatel OPTO+ [START_REF] Bouchoule | Barrier strain influence on the high-speed properties ofcompressively strained InGaAsP multiquantum-well laser structures[END_REF]. The bias polarization current is 25 mA in order to generate a dynamic carrier response above 10 GHz. The 10 GHz electrical clock modulation is 16 dBm in order to obtain the shortest optical pulse of 23 ps at 10 GHz, characterized using a 45 GHz photodetector. The pulses generated by the laser are highly chirped by the internal current modulation. They are then compressed in 800 m of 29 ps/nm/km dispersion compensation fiber (DCF) in order to obtain the shorter pulses [START_REF] Chusseau | 250-fs optical pulse generation by simultaneous soliton compression and shaping in a nonlinear optical loop mirror including a weak attenuation[END_REF]. An optimal pulse compression is then achieved. In Figure 7 (a), we present the results obtained using the BCM technique. We show firstly the measured beating contrast with a measurement resolution close to 1 ps. The calculation of the shape gives a pulsewidth of 6.3 ps with a symmetrical shape and an extinction ratio up to 20 dB. The pulse train is characterized using the autocorrelator. The autocorrelation trace which is shown in Figure 7 (b), gives a convoluted width of 8.3 ps. We compared the result with the BCM result convoluated in Figure 7 (b). We show firstly that the two traces are almost the same. Secondly, the pulsewidth deducted from the autocorrelation trace deconvoluated with a Gaussian shape give a value for the pulsewidth of 5.8 ps which is very close to the BCM result. This repeatable experimental result shows that the BCM technique is validated for optical pulses with a compensated nonlinear chirp, generated by a Qswitched laser.

BCM validation using mode-locked pulse source

The second optical source is a commercial erbium-doped fiber-based mode-lock Laser from Pritel,Inc [START_REF] Barnett | High-power erbium-doped fiber laser mode locked by a semiconductor saturable absorber[END_REF] with 20 MHz of repetition frequency. The shortest optical pulses was obtained using an output 5 nm bandpass filter, centred at 1549 nm with a pump current of 150 mA. The constructor vouches for the Fourier transform limit condition of these optical pulses. The experimental characterizations are presented in Figure 8.

The BCM measurement is achieved with a high time resolution of 100 fs allowing a precise characterization of short pulses shown in Figure 8 (a). We observe that the shape is not symmetrical and it does not look like a Gaussian shape. The pulsewidth measurement obtained using the BCM technique is 1.1 ps and the extinction ratio is higher than 20 dB. The auto-convolution of the trace gives a width of 4.4 ps. The comparison with the autocorrelation trace is shown in Figure 8 (b). The autocorrelation trace gives a 4.2 ps pulsewidth. We observe that the two results are very close. This result validates once again the efficiency of the BCM technique for a non-chirped optical source. An important point to be discussed is the reliability of the autocorrelator. In this experimental result, we found that the pulse shape is not Gaussian-like. With a Gaussian shape hypothesis, the deconvolution of the autocorrelation trace gives a pulsewidth value of 2.9 ps which is really far from the BCM technique result, while the auto-convoluated traces are very close. We understand with this result that the BCM technique does not depends on the initial pulse shape.

Benefits and limitations of the BCM technique

The method allows reliable pulse-width and pulse-shape measurement of short optical pulses with at least 100 fs of resolution. The asymmetry of the pulse shape is conserved. The contrast and the extinction ration of the pulse and the pedestals are obtained with a simple calibration of the experiment which depends principally on the photodetection block. The linear chirp of the optical pulses does not introduce any distortion on the measurement. Even if several parameters impose some limitations to the BCM technique, a suitable analysis of the experimental set-up must lead to an optimization of the measurement and give reliable results according to the pulse source type.

Conclusion

Ultra-short optical pulses characterization using BCM technique offers wide new possibilities in terms of pulsewidth, contrast and pedestal extinction ratio measurements with high resolution. Simulation and experimental results have been presented in this study in order to validate and determine the limits of the technique. BCM measurement provides higher bandwidth than traditional photodetection, higher resolution than optical sampling equipment and more realist results than autocorrelators. The technique uses commercial and standard optoelectronic devices specifically suitable for 10 GHz optical communication applications. The validation of the technique has been successfully done with optical sources used for 40 Gb/s and 160 Gb/s OTDM application and then, using a standard 20 Gb/s photodetector.

Figure 1 :

 1 Photodetector

Figure 2 :

 2 Figure2: Simulation of the BCM technique for different values of the delay τ between the two successive pulses. On the left figures, we show the incident pulses. On the middle figures, we show the beating of the pulses in an ideal photodetector with an infinite bandwidth. On the right figure, we show the beating in a 10 GHz bandwidth photodetector. We also observe the histogram window allowing the histogram measurement in order to measure the contrast of the beating.

Figure 3 :

 3 Figure3: Comparison of the BCM technique with direct detection using a 50 GHz bandwidth photodetector. The pulse to measure is 4.5 ps (continuous line), the detected pulse is 12.5 ps (dash line) and the pulse measure using BCM technique is 4.5 ps (dash and dot line).

Figure 4 :

 4 Figure 4: Analyse of the efficiency of the BCM technique for the pulsewidth estimation. Results of the BCM are compared for different photodetector bandwidths: 10 GHz, (diamonds), 20 GHz (down triangles), 50 GHz (circles) and infinite bandwidth (squares). The dashed line gives the real width of the pulse.

Figure 5 :

 5 Figure 5: Pedestal measurement using the BCM technique. Results of measurement for different photodetector bandwidths are compared to the incident pulse shape: 5 GHz (dashed line), 10 GHz (dotted line), 30 GHz (dash-dotted line) and 50 GHz (dash-dotdotted line).

4 20

 20 Experimental results and measurement validation 4.1 Experimental set-upThe experimental set-up of the BCM technique has been already shown in Figure1. For the experimental validation of the technique, we use a Mach-Zehnder interferometer composed of two single mode fibers (SMF) and 3 dB couplers. The length of the -

Figure 6 :

 6 Figure 6: Simulation of the BCM technique in presence of noise in the processus. The signal to noise ratio values are expressed in decibel for a signal bandwidth of 5 nm.

Figure 7 :

 7 Figure 7: First pulsed source characterization: figure (a) presents the experimental results of the beating contrast and the calculated pulse shape; figure (b) shows the comparison between the autocorrelation trace and the auto-convolution trace of the shape obtained with the BCM technique.

Figure 8 :

 8 Figure 8: Second pulsed source characterization : figure (a) present the experimental results of the beating contrast and the calculated pulse shape; figure (b) shows the comparison between the autocorelation trace and the auto-convolution of the shape obtained with the BCM technique.

Acknowledgments

This work was supported by the Ministère de la Recherche, the Région Bretagne and the European funding FEDER. The authors are especially grateful to Dr Blin for sharing his expertise and fruitful discussions on this new characterization method. We also want to thank Dr Joindot for its valuable assistance.


V Roncin

J Poëtte

J-F Hayau

P Besnard

J-C Simon

F Van Dijk

A Shen

G-H Duan

Experimental investigation of relaxation oscillations resonance in mode-locked Fabry-Perot semiconductor lasers

We propose in this communication an experimental study of the relaxation oscillations behavior in mode-locked lasers. The semiconductor self-pulsating laser diode is composed by two gain sections, without saturable absorber. It is made of bulk structure and designed for optical telecommunication applications. This specific device allows two different regimes of optical modulation: the first one corresponds to the resonance of the relaxation oscillations and the second one, to the mode-locking regime at FSR value. This singular behavior leads us to characterize the self-pulsations which are coexisting in the laser and to describe two regimes of output modulation: the first one appears thanks to the resonance of the oscillation relaxation and the other one corresponds to the FSR of the Fabry-Perot laser at 40 GHz.

INTRODUCTION

Recent advances in semiconductor lasers sources propose new devices allowing to generate high-frequency optical pulsed sources compatible with optical communications requirements. This type of lasers is based on passive mode-locking at the frequency imposed by the laser geometry [START_REF] Pham | Self-pulsation in two-section DFB semiconductor lasers and its synchronization to an external signal[END_REF] and particularly imposed by the length of the cavity. The telecommunication applications such as high bit-rate optical transmitter demand very stable and high spectral purity mode-locked lasers based on self-pulsation process [START_REF] Bobbert | Compact 40 GHz RZ-transmitter design applying self-pulsating lasers[END_REF] . Other specific applications such as all-optical regeneration [START_REF] Simon | All-optical regeneration[END_REF] impose specific optical injection properties for the all-optical clock recovery stage at high frequencies above 40 GHz [START_REF] Sartorius | All-optical clock recovery module based on self-pulsating DFB laser[END_REF][START_REF] Roncin | Multidata-rate system performance of a 40-GHz all-optical clock recovery based on a quantum-dot Fabry ŰPerot laser[END_REF] . This all-optical telecommunication context require high performances without electrical modulation neither external feedback. One of the most studied self-pulsating lasers is designed using multi-sections allowing the combination of optical properties such as phase control and wavelength tuneability [START_REF] Duan | Self-pulsation in multielectrode distributed feedback lasers[END_REF] . Recently, it has been proposed a simple Fabry-Perot semiconductor laser offering high-speed optical performances characterized by short pulses generation compatible with telecommunication applications [START_REF] Gosset | Subpicosecond pulse generation at 134 GHz using a quantum-dash-based Fabry-Perot laser emitting at 1.56 µm[END_REF][START_REF] Lavigne | Polarization-insensitive low timing jitter and highly optical noise tolerant all-optical 40-GHz clock recovery using a bulk and a quantum-dots-based self-pulsating laser cascade[END_REF] . The principle of the self-pulsating process is partially described in the literature [START_REF] Radziunas | Modeling self-pulsating DFB lasers with an integrated phase tuning section[END_REF] but without a clear explanation of the mode-locking starting. Furthermore, classical references on passive mode-locking process in lasers [START_REF] Siegman | Simple analytic expression for AM and FM mode-locked in homogeneous lasers[END_REF] and particularly in semiconductor lasers [START_REF] Haus | Theory of mode locking with a slow saturable absorber[END_REF] describe it in one hand thanks to the saturable absorption allowing a passive phase selection of the optical modes, and on the other hand, thanks to an internal modulation or perturbation at the harmonic frequency of the Free Spectral range (FSR) [START_REF]Mode-locking of lasers[END_REF][START_REF] Jones | Dynamics of monolithic passively mode-locked semiconductor lasers[END_REF] . Thus, the origin of the self-pulsation in multimode semiconductor lasers without saturable absorber is usually attributed to nonlinear mechanisms of interaction similar to wave-mixing between the optical modes in the gain region. We propose in this paper a pure experimental study of the self-pulsating semiconductor lasers starting and the behavior of the relaxation oscillations. We described firstly the self-pulsating laser provided in the frame-work of the French research program ROTOR and particularly their dynamic properties at 42 GHz. Spectral and time domain analysis of the output optical modulation is observed at the relaxation frequency and at the FSR frequency. Then, we propose a study of the coexistence of both type of modulations induced by two different process observed simultaneously in the laser.

SELF-PULSATING LASER CHARACTERISATION

The laser studied in the following experimental report is a Fabry-Perot Bulk semiconductor laser with a length of about 970 µm emitting over a bandwidth of 10 nm at 3 dB centered at 1.6 µm [START_REF] Van Dijk | Highly stable sub-picosecond pulse generation at 41GHz in a two-gain-section bulk active layer Fabry-Perot laser[END_REF] . The ridge waveguide, which is 1.3 µm wide over two gain sections, is buried with bulk p-doped InP. The two sections are electrically isolated from the others by ion implantation of the inter-electrode regions. The principal section designated at S 1 corresponds to about 90% of the laser length. The secondary section is 10% of the laser length and will be called in the following S 2. Firstly we realized the basic characterisation of the laser output power with a laser threshold I L th corresponding to a couple of current values equal to 18 mA in the S 1 and 0 mA in the S 2: {I 1 , I 2 } = {18, 0}. The self-pulsating threshold I SP th has been measured at about 4-times I L th corresponding to a value of 73 mA. We observed that it is necessary to polarize the S 2 in order to induce self-pulsations. Nevertheless, the current in the S 2 does not modify the laser threshold when it is higher than 4 mA. Let's stress that the S 2 does not behave as a saturable absorber because it is definitely a gain section, identical to the S 1. Figure 2 shows the classical autocorrelation trace of the optical pulse-train with a deconvoluted value of 5.5 ps for the pulsewidth and a repetition rate around 25 ps corresponding to a frequency of about 40 GHz. This value is close to the value of the FSR of the Fabry-Perot cavity. This temporal trace was obtained without any optical bandwidth filtering of the laser spectrum. Moreover we have been able to obtain shorter pulsewidth by using narrowband optical filters. The filter allows the chirp influence to be reduced and the pulsewidth to be close to the Fourier Transform limit. This point implies that the mode-locking of the optical modes present a chirp according to the wideness of the spectrum. In this paper, we propose a characterization of the self-pulsation process. This measurement is obtained thanks to an electrical spectrum analyzer. The relaxation frequency evolution is directly measured in the band of the electrical spectrum analyzer corresponding to a frequency limitation at 8 GHz. Besides, the self-pulsation modulation at 42.2 GHz is too high for our equipment. So we resolved this by using a specific frequency converter which transposes the high frequency in the the band of the analyzer. The narrowest electrical linewidth obtained with our device is presented in figure 2, when the laser is self-pulsating. The width of about 100 KHz corresponds to a very high spectral purity of the optical modulation at 42.2 GHz. This result is obtained for the couple of current values in the S 1 and S 2 {100, 40}. Figure 2 gives the evolution of the linewidth at a fixed current in the principal gain section S 1 when a variable current is injected in the gain section S 2. It shows clearly that the linewidth is varying within 2 orders of magnitude and that is very sensitive to the current value. The high threshold observed for the self-pulsation as compared to the low laser threshold allows the laser relaxation frequency resonance to be studied, in the range of current for S 1: [I L th ,I SP th ]. In the following part using both the electrical spectrum analyzer and a real-time oscilloscope the resonance of the relaxation oscillations, which is leading to a deep optical modulation, are analyzed by using an electrical spectrum analyzer and a high-bandwidth oscilloscope.

HIGH RESONANCE OF THE RELAXATION OS-CILLATIONS

Frequency and Time domain observation

This section is devoted to the analysis in the time and spectral domain of the resonance induced by the carrier relaxation. Former works have already proposed numerical studies and experimental observations of oscillation resonance due to carrier relaxation in semiconductor lasers [START_REF] Vahala | Observation of relaxation resonance effects in the field spectrum of semiconductor lasers[END_REF][START_REF] Ovadia | Low-frequency relative intensity noise in self-pulsating ridge-waveguide quantum-well lasers[END_REF] or due to optical feedback in coupled cavity [START_REF] Tager | High-frequency oscillations and self-mode locking in short external-cavity laser diodes[END_REF]. This phenomena leads to an output self-pulsation allowing to generate an optical modulation enhanced by a resonance effect. In our laser, an important optical modulation at the characteristic relaxation frequency is observed both in the time domain using a real time oscilloscope with a wide bandwidth up to 4 GHz and simultaneously in the frequency domain using an electrical spectrum analyzer. The observations of the phenomena are plotted in figure 3.1. The curves on the left hand figure presents the peak of resonance at f relax and the harmonics. The curves on the right hand figure present the corresponding modulation observed in the time domain. We show the evolution of the phenomena by increasing the current in S 1 for a fixed current in S 2 equal to few milliamps. The modulation observed in the time domain appears for I S1 ≈ 40 mA, under the self-pulsation threshold I SP th , and disappears as soon as I S1 is reaching the I SP th value. Besides, the relaxation frequency is moving with the injected current in S 1 in accordance with the behavior proper to semiconductor bulk lasers [START_REF] Poette | Highly-sensitive measurement technique of relative intensity noise and laser characterization[END_REF] .

Optical domain observation

The characterization of the resonance is made thanks to an optical spectrum analysis with 10 pm of resolution and high sensitivity equipment. Figure 3.2 shows the optical spectrum of the laser under the self-pulsating threshold at the maximum of optical power. A modulation of the Fabry-Perot modes is clearly observed. The experimental measurement of the modulation gives a value close to the relaxation frequency. The limited accuracy of the equipment does not allow a precise measurement of the frequency in the optical spectral domain. On the other hand, it is possible to observe that the over-modulation seems to be disymmetrical with regard to the Fabry-Perot peaks.

In figure ??, the optical spectrum of the laser is given, at the same wavelength, above the self-pulsating threshold. Regarding to the symmetry of the modulation lines with the Fabry-Perot modes we deduce that they are in phase with the modulation at the relaxation frequency. These results allow us to understand the phase correlation process at the FSR frequency. Such as it has been proposed in the laser theory of mode-locking without saturable absorption [START_REF] Vahala | Semiclassical theory of noise in semiconductor laserspart II[END_REF], the gain modulation at a harmonic frequency of the FSR leads to lock in phase the optical modes. Thus, the quality of the mode-locking is enhanced thanks to the nonlinearities in the laser [START_REF] Renaudier | Phase correlation between longitudinal modes in semiconductor self-pulsating DBR lasers[END_REF] and the estimation of the phase correlation is deduced from phase noise measurement [START_REF] Tsuchida | Wideband phase-noise measurement of mode-locked laser pulses by a demodulation technique[END_REF]. In the following section we propose an additional result allowing to synthesize the coexisting of the two modulations in the lasers and to describe the transfer of power between relaxation oscillation and self-pulsation at the FSR.

THE SELF-PULSATION AT THE FSR

We propose hereafter to synthesize the experimental observations by plotting the power evolution of the relaxation oscillations resonance and comparing it with the evolution of the self-pulsation modulation. We change the peak powers of the modulations by varying the drive current in S 1 with a fixed current of 2 mA in S 2. The results are presented in figure 4. Two different regimes are clearly observed: the first one corresponds to a current I 1 under I SP th equal to 73 mA and the second one to the above I SP th . These two regimes are both characterized by the presence of a strong optical modulation: in the first one, at the relaxation frequency and in the second one, at the FSR frequency. In the first range of current, the resonance of the relaxation oscillations is increasing until a saturation which is then stopped in close to the Self-pulsation threshold I SP th . Thanks to this comparison, we show that when the self-pulsation at the FSR reaches a sufficient value, the modulation at the relaxation frequency decreases. Thus, when the self-pulsation regime starts, the relaxation oscillations disappear. Nevertheless this singular optical modulation transfer does not allow further hypothesis about a possible correlation between the two self-pulsation regimes.

CONCLUSION

We reported an experimental investigation of the self-pulsating process in a Fabry-Perot laser made of bulk semiconductor structure. The high resonance of the relaxation oscillations under the mode-locking threshold and the birth of the self-pulsation regime at the FSR frequency are experimentally observed. The particularly high self-pulsation threshold at the FSR frequency, equal to 4-times the laser threshold, allow us a fine comparison between the two coexisting regimes of output modulations. We particularly propose results on an hypothetical transfer of modulation from relaxation oscillation to self-pulsation.

acknowledgments

This work has been supported by the "Région Bretagne" and the "Ministére de la recherche" in the framework of the research programs DisTO and ROTOR. Foton is also supported by the European Found for Regional Development (FEDER). The authors want to specially thanks all the projects partners for fruitful discussions.

Figure 1 :

 1 Figure 1: Autocorrelation trace when the laser is self-pulsating at 40 GHz: the deconvulated pulsewidth is 5.5 ps.

Figure 2 :Figure 3 :

 23 Figure 2: Electrical bandwidth of the self-pulsation. The narrowest modulation is about 100 KHz at a frequency of 42.2 GHz for the couple of current {100, 40}.

Figure 4 :

 4 Figure 4: Frequency and time domain experimental analysis of the resonance of the relaxation oscillations and its harmonics in the self-pulsating Fabry-Perot laser. The increase of the current in the S 1 is changing the magnitude of the modulation. The current in the secondary gain S 2 is fixed to 2 mA.

Figure 5 :Figure 6 :

 56 Figure 5: Optical spectrum observation of the Fabry-Perot modes under the selfpulsation threshold I SP th . I 1 = 72 mA and I 2 = 2 mA. The modulation is observed on the spectrum thanks to the 10 pm of resolution for the optical spectrum analyzer