Experimental investigation of the timing jitter in self ... - OSA Publishing

Experimental investigation of the timing jitter in self-pulsating quantum-dash lasers operating at 1.55 µm J.P. Tourrenc1, A. Akrout1,2*, K. Merghem1, A. Martinez1, F. Lelarge2, A. Shen2, G.H. Duan2, and A. Ramdane1 1

CNRS, Laboratory for Photonics and Nanostructures, Route de Nozay, 91460 Marcoussis, France 2 Alcatel-Thales III-V Lab, Marcoussis & Palaiseau, France * Corresponding author: [email protected]

Abstract: We report for the first time on the systematic measurement of timing jitter of 40-GHz self-pulsating Fabry-Perot laser based on InAs/InP quantum dashes emitting at 1.55 µm. Two different methods, one based on optical cross-correlation and one on electrical spectrum sideband integration are used and show a good agreement, yielding a jitter of 0.86 ps in the 1 MHz – 20 MHz frequency range with a potential of 280 fs for optimized driving conditions. Amplitude noise and high-frequency timing jitter contributions are also discussed. ©2008 Optical Society of America OCIS codes: (250.0250) Optoelectronics; (140.0140) Lasers and laser optics; (140.5960) Semiconductor lasers; (140.4050) Mode Locked lasers.

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Received 21 Jul 2008; revised 29 Aug 2008; accepted 1 Sep 2008; published 17 Oct 2008

27 October 2008 / Vol. 16, No. 22 / OPTICS EXPRESS 17706

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C. Gosset, K. Merghem, G. Moreau, A. Martinez, G. Aubin, J. L. Oudar, A. Ramdane, and F. Lelarge, "Phase-amplitude characterization of a high-repetition-rate quantum dash passively mode-locked laser," Opt. Lett. 31, 1848-1850 (2006). D. Eliyahu, R. A. Slavatore, and A. Yariv, “Noise characterization of a pulse train generated by actively mode-locked lasers,” J. Opt. Soc. Am. B 13, 1619-1626 (1996). K. Yvind, D. Larsson, L. J. Christiansen, J. Mork, J. M. Hvam, and J. Hanberg "High performance 10 GHz all-active monolithic modelocked semiconductor lasers" IEE Electron. Lett. 40, 735-737 (2004). A. R. Rae, M. G. Thompson, R. V. Penty, I. H. White, A. R. Kovsh, S. S. Mikhrin, D. A. Livshits, I. L. Krestnikov, "Absorber length optimization for sub-picosecond generation in passively mode-locked 1.3µ m quantum-dot laser diodes," Proc. SPIE 6184, 61841F1-8 (2006). K. L. Sala, G. A. Kenney-Wallace, and G. E. Hall, “CW autocorrelation measurements of picosecond laser pulses,” IEEE J.of Quantum Electron. 16, 990-996 (1980). L. A. Jiang, S. T.Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. of Quantum Electron. 38, 1047-1052 (2002). F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. VanDijk, D. Make, O. LeGouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 µ m” IEEE J. Sel. Top. Quantum. Electron. 13, 111-124 (2007).

1. Introduction Mode-locked (ML) laser diodes (LD) are ideal candidates for the generation of coherent, stable and highly periodical pulse trains. Therefore, they have been the subject of intense investigation as they can be used in several applications, ranging from high-speed optical communications to all-optical signal-processing, optical sampling and clock distribution [1]. Among these applications, some require not only high peak power short pulse operation, but also the smallest possible timing jitter, as the fluctuation of the time interval between pulses degrades the quality of the expected system performance. More precisely, if the long term wander of the repetition period of the laser pulses can be easily corrected, the high frequency timing jitter is a major issue in optical sampling, where a 20-fs pulse-to-pulse deviation is the upper limit for an 8-bit 40-Gb/s optical sampler [2]. In optical communications, ITU-T specifies the performance of digital networks based on synchronous digital hierarchy (SDH) at 40 Gb/s in term of integrated timing jitter in the 20 kHz – 320 MHz and 16 MHz – 320 MHz bands to be respectively less than 2.79 ps and 0.34 ps [3]. For this purpose, low dimension quantum-dot/quantum dash (QD) based active materials are of primary interest as compared to their quantum-well (QW) based counterparts. Indeed, the inhomogeneous broadening of the gain spectrum due to the dot-size distribution and the expected low linewidth enhancement factor [4] have allowed sub-picosecond pulse generation with QD-MLLD in the 1.3 µm range in the InAs/GaAs system with 2-section passively modelocked monolithic lasers [5]. Sub-picosecond pulses have also been obtained in the 1.5 µm range in the InAs/InP system with self-pulsating Fabry-Perot (SP-FP) laser based on fourwave mixing (FWM) [6]. In addition, 1.3 µm 2-section QD-MLLD demonstrated a reduced timing jitter of 500 fs (1 MHz – 100 MHz) in passive mode-locking operation at 8 GHz repetition rate [7] owing to reduced spontaneous emission allowed by the 3D confinement of carriers, low coupling of amplitude-phase fluctuations and high damping of relaxation frequency. For low repetition rate MLLD, the measurement of the timing jitter can be performed by integration of the electrical noise sidebands of high order harmonics of the photodetected signal [8]. Further improvements of the method also allowed precise evaluation of timing noise, amplitude noise and their correlations [9]. However, this method is hardly compatible with high repetition-frequency devices, where it is impossible to detect a sufficient number of signal harmonics to obtain a precise estimation of the timing jitter. Moreover, the upper limit for frequency analysis is set by the electrical bandwidth of currently available photodetectors and amplifiers. Alternatively, one should use optical cross-correlation (OXC) to obtain a precise estimation of the timing fluctuations of the pulse train [10], method which was recently successfully used to evaluate the timing jitter of QD-MLLD at 1.3 µm [11].

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Recent work on Quantum Dash SP-FP lasers has shown that the linewidth of the radiofrequency (RF) spectrum was especially narrow [6, 12] which implies low “high frequency” timing jitter. However, no measurement of device timing jitter has been carried out on this kind of structure up to date to the best of our knowledge. In this paper, we apply the OXC technique to investigate the timing jitter properties of a Quantum Dash based SP laser at 40 GHz around 1.55 µm. By comparison with electrical spectrum measurements, we can infer a low amplitude noise in this structure, as well as a limited contribution of the high-frequency timing jitter above 20 MHz. 2. Device fabrication and static measurements The structure was grown by gas source molecular beam epitaxy (GS-MBE) on n-doped InP substrate. The active layer consists of 9 layers of InAs QDs embedded in 40-nm thick undoped InGaAsP barriers, and is surrounded by two separate confinement layers. The wafers are processed using standard buried ridge structure (BRS) technology validated for both bulk and quantum well structures, and cleaved to form 1064-µm long devices. Figure 1(a) represents the L(I) curve of the device under test, with threshold current of 25mA, and a 20-mW output power at an injection current of 300 mA. Optical spectrum at 260 mA current is shown in Fig. 1(b), showing an almost flat optical spectrum with a full-width at half-maximum (FWHM) of 13-nm.

Fig. 1. (a) L(I) curve of the SP laser. (b) Optical spectrum at 260 mA

The different modes of the FP laser are locked together owing to four-wave mixing process occurring in the laser cavity. However, the static phase is not the same for all these longitudinal modes and spectral filtering has to be performed in order to obtain pulses with high enough extinction ratio [13]. The optimization of both the center wavelength and the width of this optical filter is carried out in order to maximize the extinction ratio of the pulses detected using a background-free intensity autocorrelator. As can be seen from Fig. 2, the maximized extinction ratio of the pulses is around 20 dB, and full width at half maximum of the autocorrelation trace is 5.25 ps, corresponding to a deconvolved pulsewidth of 3.71 ps assuming a Gaussian shape. Given the 2-nm optical filter width, the time-bandwidth product is thus equal to 0.93, indicating a residual amount of chirp in the optical modes selected inside the filter bandwidth.

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Fig. 2. Autocorrelation trace of filtered optical spectrum. Left: general view. Right: Isolated pulse and Gaussian fit.

3. Timing jitter characterization In order to gain further insight into timing fluctuations occurring inside the structure, timing jitter was evaluated based on two approaches: OXC and RF electrical spectrum analysis, at an injection current of 260 mA. This value was chosen in order to guarantee the stability of the RF spectrum, and thus avoid any long term drift of the pulse repetition frequency detrimental to our OXC set-up as we will see later. 3.1 RF Electrical Spectrum Characterization The measurement was made using a 50 GHz bandwidth photodiode followed by 45 GHz bandwidth amplifiers connected to a 50 GHz electrical spectrum analyzer with 10 kHz resolution bandwidth. As illustrated in Fig. 3(a), the SP frequency is 39.658 GHz, the 3-dB RF linewidth being as narrow as 240 kHz, according to the Lorentzian fit shown in the inset, indicating a small amount of noise. As the noise centered around the RF carrier is induced by incomplete locking of the modes involved in the mode-locking process only, the tight optical filtering used in the pulse characterization is not required any more: we experimentally obtained the same RF spectrum with and without the 2-nm filter. Corresponding measured single-sideband phase noise (SSB-PN) spectrum L(f) given by the electrical spectrum analyzer and its Lorentzian fit are represented in Fig. 3(b). Integrated timing jitter tJ between fmin and fmax is given by the well-known Eq. (1).

tj =

f max 1 2.∫ L ( f ) df f min 2π . f R

(1)

Care has to be taken before performing sideband integration to calculate the timing jitter inside a frequency band. As the laser is passively mode-locked through self-pulsation, there is no restoring force induced by active modulation to limit the long term drift of the timing fluctuations which are left unbounded, in contrast with the actively mode-locked case where the laser is driven by an electrical RF carrier. We also expect additional low frequency drift due to thermal and mechanical fluctuations. As a consequence, the measured phase noise spectrum has a -20 dB/decade slope being noticeable only far above the cutoff frequency [14]. Phase noise integration is therefore only significant in the frequency range in which the 20 dB/decade slope is observed. We hence fix the phase noise integration lower limit at 1 MHz. Moreover, above 20 MHz away from the carrier, amplification is not sufficient and the electrical spectrum analyzer floor begins to have an impact on the measured signal which sets phase noise sideband integration upper limit to 20 MHz. Taking into account these two points,

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we can evaluate the timing jitter in the 1 MHz – 20 MHz range to be 0.79 ps according to the data, and 0.86 ps using the fit.

Fig. 3. (a) RF spectrum of SP laser. Inset: close up view with Lorentzian fit. Resolution bandwidth is 10 kHz in both cases (b) SSB-PN spectral density around the first harmonic of the detected RF signal.

Further spectral measurements on this QD-SP laser lead to reduced RF linewidth as narrow as 30 kHz at an injection current of 242 mA, but far less stable in time. Even though this long term stability is not an issue in real systems, it proved to be problematic for the following OXC experiment. Indeed, data acquisition with our OXC set-up is longer than a phase noise diagram acquisition through the electrical spectrum analyzer. However, this 8fold RF-linewidth reduction should thus allow a reduction by a factor of 8 of the timing jitter compared to the above mentioned value, down to 280 fs for the 1 MHz – 20 MHz range. This value measured is twice smaller than the jitter obtained with optimized monolithic QWs laser [15], and almost comparable to the jitter of optimized 2-section 1.3-µm QD lasers [16]. It is hence difficult to have an estimate of the timing jitter of the self-pulsating laser under test on a wide bandwidth range using electrical spectrum measurement solely. As we will see in the next sub-section, OXC measurements can provide an alternative measurement technique. In addition, this electrical spectrum analyzer technique does not distinguish between amplitude noise and timing noise, unless a large number of harmonics is taken into account for the measurement [8]. As the bandwidth of the detection system is limited to 45 GHz, we can only integrate noise sidebands around the 1st harmonic, thus making the probability to overestimate the timing noise the largest. 3.2 Optical Cross-Correlation The set-up for such a measurement is shown in Fig. 4(a) [10]. The laser light is launched into an optical fiber by means of an antireflective-coated micro-lens, passes through a 40-dB optical isolator (OI), the 2-nm tunable optical filter (TOF), and is split into two beams. One arm of the coupler is sent to variable delay by means of 1x8 optical switches (OS) and variable lengths of dispersion-shifted fiber (DSF), to minimize pulse broadening or compression induced by fiber dispersion. The other arm passes through a step-motorcontrolled fine-delay stage with 5-fs resolution and polarization controller (PC) and both beams are then recombined. Scanning the fine delay stage over a time greater than the pulse period allows for the measurement of the correlation between a fixed laser pulse and a delayed one. The signal is then amplified using an erbium-doped fiber amplifier (EDFA) and sent to a non linear crystal for second harmonic generation (SHG), followed by detection using a photomultiplier (PM) tube.

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Fig. 4. (a) Optical cross-correlation measurement set-up. (b) Cross-correlation trace with 37.5 m delay. (c) Evolution of the timing jitter with increasing delay in the cross-correlation measurement. Solid line: theoretical square-root fit

The pulse intensity in the short delay arm can be expressed as I 1 ( t + J t ) with Jt being the timing noise at time t, whereas it is I 2 ( t − (τ + J t + N T ) ) in the long delay arm, with NTR R

( (

I 2 t − τ + Jt + NTR

))

being the average delay introduced by the DSF fiber, and τ being the time variable introduced by the fine delay stage. The normalized intensity detected at the PM tube can thus be expressed as a modified version of the intercorrelation of optical pulses with background [17], the timing jitter appearing as an extra correlation term, as expressed in Eq. (2):

( G (τ ) = 1 + K 2 B

+∞

∫−∞

) {

(

I1 ( t ) I 2 ( t − τ ) dt * F −1 exp ⎡⎣ − j.2π .υ J t + NTR − J t +∞

∫−∞

( I ( t ) + I ( t )) dt 2 1

)⎤⎦ }

(2)

2 2

with K being a prefactor taking into account the eventual excess losses of one of the correlator arm compared to the other, F-1{.} being the inverse Fourier transform relative to the frequency υ, and . representing a time average. As the timing noise is a stationary process, we obtain in the case of Gaussian pulses: ⎡

G B2 (τ ) = 1 + K ' . exp ⎢

⎢2 ⎣

(σ

2 P1

⎤ −τ 2 ⎥ 2 + σ + σ PP ( NTR ) ) ⎦⎥ 2 P2

(3)

with σ P1 and σ P 2 being the standard deviations of pulse 1 and pulse 2 respectively. These values are different as the pulses do not experience the same dispersion in each arm of the correlator, and are estimated by preliminary auto-correlation measurement for each DSF delay. K' is a proportionality factor dependent on K, σ P1 and σ P 2 . The cross-correlation pulse is broadened by the timing jitter noise term detailed in Eq. (4): 2 σ PP ( NTR ) =

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(J

t

− J t + NTR

)

2

=∫

+∞

0

4 ⎣⎡1 − cos ( 2π . f .NTR ) ⎦⎤ S J ( f ) df

(4)



with SJ (f) the power spectral density of timing jitter fluctuations. Equations (3) and (4) thus show that a cross-correlation with a delay corresponding to NTR pulses will integrate timing jitter noise from f min = 1 / 4 NTR [Hz] to ∞ [Hz]. Despite a loss of sensitivity for discrete frequencies at multiples of 1/NTR, OXC allows an estimate of the timing jitter on a much broader frequency band than the electrical spectrum analyzer technique. Figure 4(b) illustrates the theoretical calculations, by representing the experimental crosscorrelation trace of the laser pulses for a DSF delay of 37.5 m, and for a fine delay scan of 50 ps. This time span permits the scan of 2 pulses, which can be very realistically fitted using Gaussian pulses of standard deviation σXC=3.81±0.11 ps. The pulse correlation broadening from a standard deviation of σAC1=2.23 ps to σXC=3.81 ps is mainly due to timing jitter, as the dispersion effect in the DSF delay arm induces a very limited broadening in pulsewidth, the standard deviation after the 37.5 m delay being σAC2=2.45 ps. Taking into account dispersion effects, we can obtain the timing jitter corresponding to the integration of the jitter noise on the frequency interval [1.33MHz, +∞] [18]:

tj =

2 σ XC −

2 2 σ AC 1 + σ AC 2

2 2

= 1.05 ± 0.06 ps

(5)

Repeating the experiment for all possible optical delays, one obtains the evolution of the timing jitter as a function of the delay, as displayed in Fig. 4(c), as well as a square-root fit t J = 0.201 L with tJ in units of picoseconds and L in units of meter, corresponding to the theoretical 1/f² slope of the phase noise in passively mode-locked lasers. This corresponds to an rms pulse-to-pulse timing kick of 17.4 fs/round-trip, of high interest for high frequency optical sampling. It is noticeable that the error in the timing jitter measurement tends to increase with increasing delay. Indeed, as we increase the delay, the cross-correlation trace becomes broader due to timing noise, but, as the pulse energy remains constant, the detected peak power becomes weaker. Thus the trace is noisier, and the Gaussian fitting procedure loses precision. 3.3 Discussion On one hand, we can compare the obtained results from both measurement methods for the same frequency range. From the OXC method, the timing jitter in the 1 MHz – 20 MHz frequency band is the difference between the timing jitter accumulated after a 50-m delay and the one after a 2.5-m delay. According to the fit of Fig. 4(c), we deduce a value of 1.08 ps, which is slightly larger than the value of 0.86 ps found by integrating the first harmonic sideband. The electrical spectrum analyzer method integrates both amplitude and timing jitter, especially when performed for 1st signal harmonic, where both noises contribute equally. On the contrary, the OXC method, which remains in the time domain, only takes into account the timing jitter contribution, as amplitude noise effects average out. Thus, noise values with OXC should be smaller than the one performed with electrical spectrum analyzer. However, as already discussed, the cross-correlation measurements lose progressively precision when increasing the optical delay, thus making the fitting procedure less accurate too. This explains the slight discrepancy we observe. Further improvements in the OXC set-up such as the use of an optical chopper and a lock-in amplifier, should allow a much higher precision. Nevertheless, we can deduce from the close values obtained by both methods that the highfrequency amplitude noise is negligible in the SP mode-locked laser. Integration of noise sidebands of low order harmonics is therefore a simple and valid method to obtain a meaningful value of timing jitter in these structures, without any important overestimation. #99108 - $15.00 USD

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On the other hand, we can have an insight in the high-frequency timing jitter. Indeed, according to the OXC method, the timing jitter from 1 MHz up to ∞ Hz is 1.4 ps, whereas the electrical spectrum method gives a value of 0.86 ps in the 1 MHz – 20 MHz range. Bearing in mind the uncertainty related to the OXC technique, this means that the timing jitter above 20 MHz only contribute to about 500 fs out of 1.4 ps, even though timing noise power spectral density extend to several giga-hertz. In addition, the broad peak around the relaxation oscillation frequency induced by carrier-photon population interaction can significantly contributes to the high frequency noise. However, the QD active medium is likely to be responsible for such a low contribution in our case. Indeed, recent measurements on the relative intensity noise (RIN) of QD based lasers at 1.55 µm showed a very low highfrequency noise level in these 3D confined structures [19]. The same feature is certainly occurring in our structure, thus limiting the contribution of the high frequency components (> 20 MHz) to the timing jitter. 4. Conclusion

In this paper, we have investigated the timing jitter properties of InAs/InP quantum-dash based self-pulsating lasers operating at 1.55 µm. Spectral filtering allowed the generation of 3.7 ps pulses at nearly 40 GHz repetition frequency with extinction ratio close to 20 dB and time bandwidth product of 0.93. Jitter was measured thanks to optical cross-correlation and radio-frequency electrical spectrum noise sidebands. Both methods yielded close results, with device jitter estimated to be around 0.86 ps in the 1 MHz – 20 MHz range, corresponding to 17.4 fs/round-trip, of particular interest for optical sampling. By comparison of both methods, a reduced amplitude noise was estimated, as well as a limited impact of the high-frequency components above 20 MHz to the total timing jitter. Despite some low frequency instabilities, the device should allow an estimated 280-fs high-frequency timing jitter, which should be further reduced using active retiming of the pulse train using low-noise electrical modulation for applications in optical communications. Acknowledgment

This work has been supported in part by the European Network of Excellence SANDiE.

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