Timing Jitter in an Otical Soliton Source Based on a Gain-Switched Semiconductor Laser Jorge. A. Pinto, Tiago N. G. Maia, A. Nolasco Pinto and ui S. ibeiro Instituto de Telecomunicações, Pólo de Aveiro, Camus Santiago, Portugal Abstract In this aer the outut timing jitter of a soliton source, based on the gain-switching technique of a semiconductor laser, is analyzed. A laboratorial timing jitter measurement, at the laser outut, is initially erformed, followed by the identification of its origins. After characterizing the laser noise and the electrical signal, used to ulsate the laser, a numerical model is develoed in order to be used in the simulation. The numerical results exhibit good agreement with laboratorial ones. I. INTODUCTION In high eed otical communication systems a technique based in solitons roagation can be used in order to comensate simultaneously the diersion and the self-hase modulation non-linear effect. In transmission systems based on solitons several limitations arise when we intend to increase the bit rate. One of such limitations is the temral uncertainty of the ulses arrival time, usually called timing jitter. As the tolerance of a system to the varying arrival time of the ulses is limited, the timing jitter can be directly related with the system error robability. In this work we will focus our attention in the jitter introduced by the soliton source when it is used a technique based on the gain-switching of a semiconductor laser. First of all it is characterized the otical soliton emitter used in this study. The laboratorial results of the timing jitter measurements at the outut of the semiconductor laser are then resented and analyzed. An analytical model, which relates the timing jitter with the ontaneous emission rocess is then deicted and used in the SCOE[] simulation environment. The study makes clear the outut timing jitter origins in a soliton emitter based on a semiconductor laser gain-switching technique. II. OPTICAL SOLITON EMITTE The soliton emitter used on this study is based on a distributed feedback laser (DFB) with an electrical bandwidth of 0 GHz, emitting on the 550 nm window. In order to obtain short otical ulses one can oerate the laser in the modelocked or gain-switching regime []. In our soliton source, the DFB laser is oerated in the gain-switching regime. This regime consists in the fast commutation of the laser from a lower to a higher density of carriers [3]. When the laser drive current is below threshold both carrier and hoton density have low values. After the current commutation the carrier density increases raidly, whereas the hoton density increases slowly due to ontaneous emission. At a level above threshold, where the stimulated emission dominates, the otical gain in the laser cavity becomes larger and the hoton density raidly increases causing laser saturation and the aearance of relaxation oscillations. If the current commutes to a level below threshold before the second relaxation oscillation, as it is shown in figure, a sequence of narrow otical ulses can be roduced. Fig. Evolution of the hoton and carrier number when the drive current forces the laser to commute before the second relaxation oscillation. The direct modulation of the DFB laser using a,5 GHz clock signal generates otical ulses with a full width half maximum (FWHM) of 33 s. The diagram of the soliton emitter can be found in the figure. Instituto de Telecomunicações, Pólo de Aveiro. Instituto de Telecomunicações, Pólo de Aveiro, Deartamento de Electrónica e Telecomunicações da Universidade de Aveiro Fig. - Diagram of the soliton emitter. The soliton source is achieved through direct modulation of a DFB laser. A shortcoming of the gain-switching technique is that otical ulses are considerably chired. The chir is intrinsic
to the rocess of direct modulation of the semiconductor laser and is due to fluctuations in the refractive index of the laser cavity induced by the carrier density variations. A 0,6 nm bandwidth Fabry-Perot otical filter is used in order to reduce the mentioned chir, while the coding section of the emitter is erformed by a Mach-Zehnder modulator. The Erbium doed fibre amlifier (EDFA) adjusts the ulses eak wer. The EDFA is succeeded by a,6 nm band ass otical filter which removes the ontaneous emission noise, added by the EDFA, that is not in the signal ectral band. Laboratory measurements showed that the devices in the soliton emitter that follow the semiconductor laser have negligible contribution to the overall timing jitter, therefore, our jitter analysis is focused into the laser outut. III MEASUEMENT OF JITTE AT THE SEMICONDUCTO LASE OUTPUT The test set used to measure the jitter resent at the laser outut is deicted in figure 3. otical detectors and the remaining was made in a back-toback configuration. One of the detectors was a direct detection PIN, model HP830C, while the other was an amlified PIN model HP98A. The clock generator used was a HP708B. The results are shown in figure 5. 7s 6s 5s s 3s s s 0s Clock HP98A HP830C 3 5 6 7 8 9 0 Fig.5 - Three sets of 0 jitter measurements made in laboratory. The average in each set of 0 measurements of the jitter standard deviation is 5,75 s for the HP830C, 6,33 s for the HP98A detector and,8 s for the signal Clock. IV JITTE CAUSES A - The Electrical Clock Signal Fig.3 - Test Set for jitter measurements on the soliton source outut. An oscilloscoe, model HP50B, was used to obtain an histogram of the time where the electrical ulse detected crosses the imsed threshold (figure ) Fig. - Photograh of an histogram of a temral rtion of an eye diagram obtained on the oscilloscoe. The signal being analyzed is the clock signal. Three sets of 0 measurements each were made to determine an average for the jitter standard deviation. The first two sets of measurements were done with two different available The first contribution to the outut jitter comes from the electrical signal that modulates the laser, since it comes from a non-ideal clock generator. If we assume that the frequency noise is white and gaussian with null average, which means to consider a Lorentzian ectral lineshae, then the hase drift in seconds has a variance of [] φ π ν, () where ν is the linewidth full half maximum of the clock ectral density. The time deviation can be related with the hase drift by π φ T t where T is the clock eriod. Assuming equals T and using () then the standard deviation timing jitter is given by exression (3). ν T π 3 () t (3) By inection of the signal on a ectral analyzer, model HP8563A, we have found that ν is 0 Hz, and by using exression (3), we have concluded that the jitter roduced by the clock generator (signal Clock ) is negligible, as it falls below a few fentoseconds. B The Laser Noise The dynamics of a semiconductor laser can be modelled by the following rate equations []: dn( dt I( N( g( + qva fn( ()
d ΓβsN( Γg ( + + dt dφ( αh Γgo[ N( Nt] + fφ( dt fs( (5) (6) where and N( are the hoton and carrier density, reectively, φ( is the electric field hase, I( is the drive current, g( is the ontaneous emission gain and g 0 is its sloe constant, n and are the carrier lifetime and hoton lifetime reectively, Γ is the mode confinement factor, β s is the ontaneous emission factor, q is the electron charge, V a is the active layer volume, α H is the linewidth enhancement factor, N t is the carrier density at tranarency, and ƒ n, ƒ s and ƒ φ are the Langevin forces that reresent the noise. The laser noise is deendent on the ontaneous emission factor, β s. Since the ontaneous emission rocess is reonsible for the intensity noise, we have decided to measure the relative intensity noise (IN), which is defined by the ratio between the laser noise wer density and the otical signal wer, in order to determine the ontaneous emission factor, β s. The ontaneous emission rate,, as it was defined in [5], can be related to the ectral wer density (one-sided) of the IN by the exression (7). IN ( f ) / f sin ( ω F) ( ( α H ( jω ) + ) S ω ω + γ + n α sin (ω H( jω ) cos ( ω F) H( jω ) ) F) If the minimum IN is measured after a few meters of fibre, it is reasonable to consider the diersion arameter, F, null. Hence we can simlify (7) and end u with (8). ω γn ( H ( j ) ) + IN ( f ) / f ω S (7) (8) Considering the small signal transfer function, H(jω), obtained by (), (5) and (6) [], and relacing it in (8) we obtain (9). IN ( f ) / f * S ( ω * r ω ) + ( ωγr) ( ω + γn ) were the values of the γ r (daming carrier factor), γ r (daming factor of the angular relaxation oscillating frequency), and ω r (angular relaxation oscillating frequency), are given by the exressions (0), () and () reectively []. γn gs + + εs γr gs ε ( + ) + + εs g (9) (0) () gs ε + ( + εs) g () Finally, is related to the ontaneous emission factor, β s, by exression (3) []. βsn n (3) If we substitute the steady-state value of the carrier density (N), the ontaneous emission factor can be described by (). β s q + I 0 q S q () With exression () it is ssible to calculate the ontaneous emission factor, from the IN ectral density, used to determine the ontaneous emission rate arameter, see exression (9), and the other laser arameters. Those laser arameters were extracted during EMITON roject, as resented in [6]. Our aroach to IN measurement, was divided in two stes. The first ste consisted on finding the maximum of the noise wer, when the laser is driven by a direct current just above the threshold, in order to obtain better laser noise measurement accuracy. This maximum was found in the vicinity of 5 GHz. The maximum noise level is extremely low and demands for alternative methods, as averaging measurement, and the use of an otical receiver with stamlification. The number of averages taken was 00, and the otical receiver used, one HP98A, makes the recetor reonsivity equivalent to 50 A/W. Figure 7 shows a hotograh of the averaged ectrum of the laser noise Fig.6 - Photograh of the ectral averaged measurements of the laser noise. A second ste is required to determine the carrier continuous wave (CCW) wer. This CCW wer was found to be 5 dbm. The maximum value of IN obtained was - db/hz, which occurs at a frequency of 5,5 GHz. The β s was calculated by means of exression (9) and exression (), using a least minimum square fitting method with 0 ints around the maximum noise value. The value obtained was 3,58x0-5.
C Other contributions to the timing jitter The oscilloscoe used to erform the histograms measurements also introduced some error in the measurement rocess. As exlained before, see section IV-A, the jitter of the Clock signal is in the order of fentoseconds, negligible for this study, therefore it is assumed to be without jitter. In section III, see figure 5, the signal Clock jitter measurement gives a value of,8 s, which can be interreted as an oscilloscoe systematic error. There is no correlation between the oscilloscoe uncertainty and the laser noise, so the value of the timing jitter at the laser outut can be determined by means of exression (5). real (5) Measured Oscilloscoe Considering the laboratory jitter measurement, 5,75 s, and taking into consideration the oscilloscoe measurement error,,8 s, we obtain the value of 5,5 s for the timing jitter standard deviation at the laser outut. The additive noise introduced in the system by the otical detector also increases the timing jitter at the decision time. As the two otical detectors used have different noise levels and frequency reonse, they introduced different levels of jitter, as seen in figure 5. The electrical noise introduced by the HP830C is less than 3 A /Hz according to the device data-sheet. Performing another simulation considering only the thermal noise in the detector we obtain a standard deviation timing jitter value in the order of 76 fs, which is negligible comared with the turn-on timing jitter of the laser, as we have seen in the revious aragrah. In order to analyse the jitter contribution due to the other comnents of the soliton emitter, see figure, we erformed a jitter measurement at the Mach-Zehnder outut, obtaining the value of 5,6 s, which confirms the negligible contribution of coding stage of the emitter. The booster noise is artially filtered by a band ass otical filter (BPF), introducing a negligible contribution in terms of timing jitter measured at the soliton emitter outut. D Drive current against laser outut timing jitter Laboratorial research measurements were made to find out the relationshi between the laser bias current and the laser outut timing jitter. The increase of the bias current reduces the timing jitter standard deviation, as shown in figure 7. 6 Jitter(x0 - ) 5.5 5.5 5.0 6.0 7.0 8.0 9.0 0.0.0.0 Bias Current (ma) Fig. 7 Evolution of the timing jitter when the laser drive current increases. However, the increasing of the bias current induces the aearance of the second relaxation oscillation that will increase the width of the otical ulse, as shown in figure 8. Fig. 8 Evolution of the otical ulse with the increasing of the laser drive current. This roves that the laser outut timing jitter can be directly controlled by the laser bias current, but by increasing the bias one degrades the shae of the otical ulse, which is a significant system erformance factor. V THEOY The fluctuations in laser turn-on time delay are a direct result of the stochastic nature of ontaneous emission [7]. The outut of the laser is searated into two distinct regimes, deending un the hotons number in the active region. In the low number, stochastic regime, the evolution of the hoton density is a random rocess. In higher hotons number, deterministic regime, the evolution can be modelled by deterministic laser rate equations. In this way, we lit the oeration of the laser into two regimes: a deterministic regime in which the Langevin noise terms can be negligible and a stochastic regime in which, because of the low hoton number, the laser is never saturated, so the nonlinear gain saturation term can be ignored in (), (5), (6) and the Langevin terms are significant. Whether or not a laser enters the stochastic regime and the duration it ends in this regime is strongly influenced by the bias current value. As the laser is modulated, its behavior alternates between the stochastic and deterministic regime. The work resented in [7], showed that the error rate floors will not be simulated unless it is included the stochastic turnon rocess in the laser model. If the stochastic turn-on rocess is included, the robability density function (PDF) for the delay time, td, between the current ulse and the resulting outut light ulse, is no longer a deterministic time, but a continuous robability density function. That is why the model of the laser must include the imact of ontaneous emission on the ulses. VI. SIMULATION ESULTS To simulate the systematic error found on laboratory a model for the Clock signal was develoed. The choice of encasulating the effect of the systematic error caused by the
oscilloscoe within the Clock model is justified by saying that the contributions of uncorrelated jitters are commutative. The model imlementation is obtained by adding gaussian noise and distorting the timeline, by means of simle signalrocessing techniques, of the samled signal Clock obtained exerimentally. It can be described in the mathematical form of exression (6). G(F(t+φ(t,))+n( (6) F( is the samled Clock, found on laboratory, t\t, where T is the average eriod, the oerator \ stands for integer division, φ and n are normal distribution variables. The overall result of this model is very close to the actual waveform. The values for jitter on the clock model were made equal to the uncertainty of the oscilloscoe (,8 s). When inecting the ectral comnents of the signal Clock we have also taken into account the noise-level resent. This white noise is reonsible for a noise wer of 3.9 dbm considering the 0 GHz of the oscilloscoe bandwidth. This wer correonds to a variance of 0µW. This variance, was modeled as a gaussian distribution noise source, n( in exression (6). The PIN model was numerically imlemented through an ideal otical wer detector considering the quantum noise by adding a random Poisson rocess generator. Since the actual PIN, used in the laboratory, has limited bandwidth, a low ass filter was added to the numerical model. Fig. 9 - The two solitons: Simulation vs. Laboratory suerimsed. We erformed the simulation of the soliton emitter, considering the value for β s, and we obtained numerically a standard deviation timing jitter value of,9 s, that comares with the value of 5,5 s obtained in the laboratory measurements. From this results we can conclude that the laser noise is the most relevant factor in terms of timing jitter in our soliton emitter. The waveform obtained by simulation resents a very high visual likelihood to the detected ulses on laboratory, as shown on figure 9. VII. CONCLUSION The timing jitter roduced by the otical soliton emitter can have a significant imact on the reective communication system erformance. In our emitter, based on a semiconductor laser oerating in a gain-switching mode, the main contribution to the jitter is due to the laser noise. The numerical results obtained by simulation exhibit good agreement with laboratorial ones. The jitter found exerimentally is 5,5 s, which is clearly above the systematic error of the oscilloscoe,,8 s, and it is in agreement with numerical results,,9 s. The timing jitter roduced by this tye of soliton emitter cannot be comensated by additional comnents in the system. However, it can be artially controlled by an aroriated choice of the laser bias current. VIII ACKNOWLEDGMENT We like to acknowledge Victor Abreu and Ana Monica for their revious studies. IX EFEENCES []. F. S. ibeiro, C. J. F. Lourenço and L. F. B. ibeiro, "Project and Analysis of otical communication systems with SCOE", in Proc nd International Conference on Otical Fiber Submarine Telecommunications Systems Subotic 93, 9 March Aril 993, Versailles - France. [] A. Nolasco Pinto, P. S. André, J. L. Pinto, F. da ocha, Short otical ulses generation by gain-switching of a DFB laser diode, Confetele'99, Sesimbra, Portugal, Livro de esumos 8, Abril 999. [3] Armando N. Pinto, Análise e Otimização de Sistemas de Comunicação Óticos Baseados em Solitões, Universidade de Aveiro, 999. [] ui ibeiro, Simulação, Análise e Otimização de Sistemas FSK Óticos, Universidade de Aveiro, 996. [5] K. Peterman e J. Wang, Small Signal Analysis for Diersive Otical Fiber Communication Systems, J. of Lightwave Technol., vol. 0, No,. 96-00, 99. [6] Equations Parameters, Proceedings of SPIE, n.º 357,. P. S. André, A. Nolasco Pinto, J. L. Pinto and J. Ferreira da ocha, Extraction of Laser ate -6, 999. [7] Tom Stehens, Kerry Hinton, Trevor Anderson and Bruce Clarke, Laser turn-on delay and chir noise effects in Gb/s intensity-modulated direct-detection systems, J. of Lightwave Technol., vol. 3, No,. 666-67, 995.