Pattern effects in time jitter of semiconductor lasersAdalberto Sapia, Paolo Spano, Claudio R. Mirasso, Pere Colet, and Maxi San Miguel Citation: Applied Physics Letters 61, 1748 (1992); doi: 10.1063/1.108415 View online: http://dx.doi.org/10.1063/1.108415 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/61/15?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Timing jitter reduction in modelocked semiconductor lasers with photon seeding Appl. Phys. Lett. 80, 1707 (2002); 10.1063/1.1459112 Parametric dependence of timing jitter in gainswitched semiconductor lasers Appl. Phys. Lett. 63, 3556 (1993); 10.1063/1.110095 Spectral measurement of timing jitter in gainswitched semiconductor lasers Appl. Phys. Lett. 60, 2451 (1992); 10.1063/1.106930 Theoretical analysis of timing jitter in gainswitched semiconductor lasers Appl. Phys. Lett. 55, 522 (1989); 10.1063/1.101866 Experimental observation of time jitter in semiconductor laser turnon Appl. Phys. Lett. 52, 2203 (1988); 10.1063/1.99533

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Pattern effects in time jitter of semiconductor lasers Adalberto Sapia and Paolo Spano Fondazione Ugo Bordoni-ISPT, Vie Europa 190, 00144 Roma, Italy

Claudio FL Mirasso, Pere Colet,a) and Maxi San Miguel Departament de Fisica, Universitat de les Illes Balears, E-07071, Palma de Mallorca, Spain

(Received 8 May 1992; accepted for publication 4 August 1992)

The effect of fast repetitive pulse modulation on the value of time jitter affecting the optical pulses emitted by semiconductor lasers is studied both experimentally and by numerical simulations. The results show that the modulation also induces pattern effects that increase the value of time jitter to non-negligible values for bias above threshold.

The increasing bit rate of optical transmission systems has stimulated in recent years the study of the time jitter properties in pulse modulated semiconductor lasers.’ The time jitter, which is defined as the standard deviation of the random delay between the emission of the optical pulses and the electrical exciting pulses, can represent, in fact, a limiting factor for the attainment of the highest bit rates.Z3

The random nature of the switch-on delay is due to the spontaneous emission process which triggers the emission of the optical pulses when the laser is gain switched.’ This means that when the laser is biased above threshold, the time jitter reduces to vanishing values4 because the spon- taneous emission is negligibly small with respect to the stimulated field. This conclusion, however, is valid .only when the optical pulses are separated more than a few ns as considered in Ref. 5, so that the laser can reach the steady- state condition, given by the bias current, before the emis- sion of the next pulse. It has recently been recognized6 that if the electrical pulses exciting the laser are closely spaced, as in high-speed communication systems, the value of time jitter also increases to appreciable values in the case of bias exceeding the threshold. This effect is induced by the re- laxation of both the density of photons and the excited carrier density which goes below threshold after the emis- sion of the optical pulse. If another electrical pulse is ap- plied after a time interval short enough with respect to the recovery time of the carriers (of the order of the ns), the laser starts from an effective condition which is below threshold, though the stationary bias is above threshold.

in this letter we report experimental measurements of the time jitter and a comparison with simulations of the laser dynamics based on the same model as in Ref. 6.

In order’to check the relaxation induced pattern effects on the value of time jitter we excited the laser by a se- quence of couples of electrical pulses. Any couple is spaced much more than any characteristic time involved in the laser dynamics while the two pulses of the couple are spaced much less than 1 ns. With this arrangement one can assume that any couple is independent of the previous one, so that the first optical pulse of the couple is emitted from

“)Present address: Georgia Institute of Technology, School of Physics, Atlanta, GA.

a condition really determined by the bias current. On the contrary, the second pulse starts from an effective condi- tion affected by the presence of the previous pulse and close to the effective condition present in high speed transmis- sion systems.

Theexperimental setup is shown in Fig. 1. A 75 ps full width half maximum electrical pulse with an amplitude of about C, = 30 mA, followed after a time to,= 75 ps by a second pulse with an amplitude C, = 25 mA and a rise time of 75 ps, is superimposed to a bias current and sent to a single mode i1/4 shifted distributed feedback laser emitting at 1.55 pm and having a threshold current of 16.5 mA. Although the actual values of the injected current can be affected by large errors because of the unknown impedance of the coupling circuit, a particular care was taken to main- tain between the two pulses the same level of current present before the first pulse by monitoring part of the electrical driving signal. A sampling oscilloscope is used to display the optical output from the laser diode after the detection from a fast pin photodiode with a full width half maximum response of about 45 ps. The pattern displayed by the oscilloscope, which is formed by the superposition of samples belonging to different switch-on trajectories, is processed by a two parameter statistical analyzer. The ver- tical output from the oscilloscope is sent to they-axis of the analyzer, while the horizontal scanning of the oscilloscope is sent to the x-axis. In this way a three-dimensional plot is obtained in which the z-axis represents the number of counts pertaining to a given time-intensity pair.

Our numerical simulations of the switching process are based on a set of single mode stochastic rate equations for the number of photons I and the carrier number N inside the cavity

dI z= (G-Y)~+WN+~(O @i=,

dN dt=C(t)-yfl-GI,

(1)

where G=g(N-Nc)/(l+sl), g=1.6X lo4 s ’ is the gain rate per carrier, y= 1.33 X 10” .s -’ is the inverse photon lifetime, ~/e= 1.33X 10’ s-’ is the inverse carrier lifetime, N0=6.8X 10’ is the carrier number at transparency, s =1.25X lop7 is the inverse saturation intensity, and fl

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LASER PHOTODIODE

FIG. 1. Experimental setup.

=1.5x104s i is the spontaneous emission rate. The ran- dom spontaneous emission process is modeled by a Gaussian white noise term g(t) of zero mean and correla- tion (&t)g(t’>>=26(t-t’). The injection current C(t) is modeled as a train of two triangular pulses of amplitude Ct and C, superimposed on a bias C, and separated by a time t OF

The values of the time jitter o are reported in Fig. 2(a) for both the experimental and numerical results. The ex- perimental values have been deconvolved with the noise of the oscilloscope vertical amplifier and the electrical jitter of the detection system. A very good agreement has been ob- tained when C, = 1.25 Cth and C,= Cth is used in the sim- ulations. It is seen in Fig. 2(a) that when the bias current is above threshold, the jitter a, affecting the second pulse is

_- I * 8 ’ I ’ 1 1.1 1.2 1.3

‘;; ,a .d 0 x 0 2

3 1

Eb 1 Og :: flj

OOlg-.3

C$*

FIG. 2. Time jitter vs normalized bias current of the first and of the second pulse. (a) 0 and + refer to the first pulse for the experimental and numerical results, respectively, q and X refer to the second pulse for the experimental and numerical results, respectively. The numerical re- sults have been obtained for C,= 1.25 C,,, C2=Cth, and r,,=75 ps. (b) Numerical results of the time jitter for C, =2.5 C,,, Cs=ZC,,. Circles refer to the first pulse, squares and crosses refer to the second pulse for top= 75 ps and for= 150 ps, respectively.

200 280 El -.

150- m .P,. n . ---+ 72

‘s; 23

0 mm -230 ,a l q a .

loo- l 0

c- l . G -

50- Jo -180 /;

-2 v-

00 0 . pa I I r 130

0.9 1.0 1.1 1.2 1.3 1.4 I.5

% ‘% FIG. 3. Tie delay between the second and first pulse (squares) and relative delay of the first pulse (dots) vs normalized bias current. The open and closed symbols refer to the numerical and experimental results, respectively. The triangle indicates the delay between the two electrical pulses.

larger than that affecting the first pulse (a,), their values becoming similar only for bias values well above threshold. In addition, the value -of 0, is rather insensitive to C,. These results are consistent with those of Ref. 6 if the second pulse is identified with a typical pulse under high- speed modulation. Further confirmation that the second pulse starts from an effective condition in which the carrier density is lower than its threshold value is supplied by the measurement of the average delay (t2) - (ft) between the first and the second optical pulse. These results are re- ported in Fig. 3 as a function of the bias current normal- ized to its threshold value. In this figure the delay is defined as the difference between the times at which the two pulses reach the half of their peak value. In the same figure the relative delay of the first pulse, with respect to the position it assumes when the bias is 1.2 Cth, is also shown. It is quite evident in Fig. 3 that the delay of the first optical pulse is almost constant above threshold (apart from experimental errors), while that of the second pulse continues to de- crease tending to the delay between the electrical pulses.

Given the good agreement in Fig. 2(a) the expected behavior of the optical pulses can be predicted by numer- ical simulations for other practical regimes of operation not covered by our setup. The experimental results and the simulations evidentiate that (T, can be much larger than a2

. . . .’ .-

4 .-a -3

*fi

* . .-q . a. ‘c.. .- . . 3’ . . . . .

‘2 . . : -2: I . s . . . . *. ..-. . .

‘1.. --- “‘f. ,- _ ,

0 time (ps)

FIG. 4. Measured distribution of times at ,which the optical intensity reaches a value equal to l/2 of the maximum intensity (dots). The data refer to the leading edge of the second pulse at C/C,,,= 1.04. The crosses refer to the statistical distribution of delay due to the experimental appa- ratus, evaluated through the electrical pulses. The continuous curve is the Gaussian best fit.

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for C, < C,,. This indicates a large jitter for optical pulses connected with the injection of a low number of carriers. However, we show in Fig. 2(b) that a larger value of C, results in a reduction of (it which becomes independent of C, for C, < Cth, as expected from Ref. 4, and a larger value of q for larger values of totr because of an effective initial condition further beloti threshold.”

As a last remark one should note that the low values of time jitter reported in Fig. 2 might be deceiving. These values, which indeed seem too low to affect the perfor- mances of real communication systems, represent only the standard deviations of the statistical delays. The statistics of delays, however, is not Gaussian, as shown in Fig. 4, where the distribution of the times at which the optical intensity reaches a fixed value is reported together with that due only to the detection system. The former distri- bution clearly shows an asymmetry with higher tails on the long delay side, which are able to appreciably affect the bit error rate even for values of the jitter much lower than the bit period, as found in Ref. 2.

C.R.M., P.C., and M.S.M. acknowledge financial sup-

port from the Commission Interministerial Ciencia y Tec- nologia (Spain), Project TIC90/080.

‘See, for exampIe, P. Spano, A. Mecozzi, A. Sapia, and A. D’Ottavi, Springer Proceedings in Physics, edited by R. Villaseca and R. Corbalan (Springer, Berlin, Heidelberg, 1991), Vol. 55, p. 259, and references therein.

‘P. 0. Andersson and K. Akermark, Proceedings of 17th European Conference on Optical Communication ECOC ‘91 and 8th Interna- tional Conference on Integrated Optics and Optical Fiber Communica- tion IOOC’91, Paris, Sept. 9-12, 1991, Vol. 1, part 2,721 paper WePS2- 13.

‘G. Aureli, S. Betti, G. De Marchis, E. Iannone, and A. Mecozzi, Opt. Quantum Electron. 23, 1077 (1991).

4A. Mecozzi, P. Spano, and A. D’Ottavi, Appl. Phys. Lett. 55, 769 (1989).

‘M. M. Choy, P. L. Liu, P. W. Shumate, T. P. Lee, and S. Tsuji,~ Appl. Phys. Lett. 47, 448 (1985); E. H. Bottcher, K. K. Ketterer, and D. Bimberg, J. Appl. Phys. 63, 2460 (1988); P. Spano, A. D’Ottavi, A. Mecozzi, B. Daino, and S. Piazzolla, IEEE J. Quantum Electron. QE- 25, 1440 (1989).

‘C. R. Mirasso; P. Colet, and M. San Miguel, Opt. Lett. 26, 1753 (1991); C. R; Mirasso, P. Colet, and M. San Miguel, IEEE J. Quantum Electron. (to be published).

1750 Appl. Phys. Lett., Vol. 61, No. 15, 12 October 1992 Sapia et al. 1750 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

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