All-Optical Clock Recovery Using the Temporal Talbot Effect D. Pudo, M. Depa, L. R. Chen Photonic Systems Group, Department of Electrical and Computer Engineering, McGill University, Montreal, Quebec, Canada, H3A 2A7, E-mail:
[email protected]
Abstract We demonstrate novel all-optical clock recovery for short pulse communication systems based on the temporal Talbot effect. By simply propagating a data stream through 80 km of single-mode fiber, we generate a periodic pulse train. ©2006 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (320.5550) Pulses
1. Introduction All-optical clock recovery is a crucial requirement for future, high speed optical network systems. Several methods have already been considered, based amongst others on self-pulsating laser diodes, [1] optically modulated semiconductor amplifier-based fiber lasers, [2] fiber parametric oscillators, [3], or two-photon absorption in avalanche photodiodes [4]. Another simple all-optical approach consists of using a Fabry-Perot cavity whose roundtrip time corresponds to the incident bit period [5]. The temporal Talbot effect [6-8] has been extensively studied as a lossless mean to multiply the repetition rate of optical pulse trains. In short, the multiplication occurs in a 1st order dispersive medium provided that the dispersion Ф (ps2), and the pulse period T (ps) satisfy the following condition: T2=m/s⋅ 2π⋅ |Ф| where m and s are integers such that s/m is an irreducible rational number. For the m=1 case, the output and input repetition rates and amplitude envelopes are identical. However, as the Talbot effect is based on the interference of dispersed pulses, there is no direct one-to-one correspondence in between the input and output pulses. As a result, it has the inherent ability to generate a periodic output even for an intermittent input pulse train. In this paper, we demonstrate a simple, passive, polarization insensitive, all optical clock recovery based on the temporal Talbot effect on a 9.25 Gbps, 2.2 ps short pulse pseudo-random bit sequence [9]. The system consists only of an 80 km long span of single-mode fiber providing the necessary dispersion. First, we review and quantify the buffering ability of the Talbot effect, following which demonstrate the clock recovery operation. 2. Optical Pulse Buffering and Clock Extraction Simulations In the temporal Talbot effect, the dispersion broadens individual pulses to the point where they overlap and their mutual interference results in the self-imaging process. Consequently, each individual output pulse results from the cumulative contribution of a sequence of input pulses. Azana et.al. [10] defined the minimum number of pulses required to establish a stable output through the Talbot effect by K s T1 (1) ⋅ ⋅ N Pulses 2π m Δt0 where K is the time-bandwidth (ΔtΔω) product of the input pulse burst envelope, T1 the input pulse period, and ∆t0 the full duration of the input pulse. Assuming a square burst whose time-bandwidth product can be roughly estimated to be 2π·0.8859 the minimum length of a square pulse burst will therefore approximately be:
N min
s T1 ⋅ m Δt0
(2)
As the Talbot transfer function is an even, quadratic phase term, the aforementioned analysis also establishes de facto the number of trailing output pulses resulting from a sufficiently long input pulse sequence. In the m=1 case, where the input and output repetition rates are equal, let us define nd is as number of pulses (or equivalently, bits) during which the output pulse train amplitude drops from 90% to 10% of its steady state value. The analysis assumes a sufficiently long, Gaussian pulse train propagating through an ideal dispersive filter with sufficient bandwidth. Through simulations, we determined nd to be approximately given by: (3) nd 0.57 ⋅ s ⋅ tFWHM −1 ⋅ Fin −1 Here, tFWHM is the input full-width half maximum Gaussian pulse width, and Fin is the input repetition rate frequency, or bit rate. As illustrated in Fig. 1 below, a 2 ps, 10 Gbps, m=1, s=1 Talbot temporal imaging system will result in a ~ 28 bit long trailing edge once the input ceases.
Intensity
nd
1
90 %
0.5 10 %
0 0
1
2
3 Time (ps)
4
5
6
Fig. 1. Illustration of a decay time for a m=1 Talbot self-imaging of a square pulse burst
Intensity
a)
b)
1
0
0.5
-20
-20
-40
-40
-60
-60
0 0
1
2 3 Time (ps)
4
Power (dB)
Intensity
This property of the Talbot effect allows us to infer a clock extraction ability for short pulse communication systems. Figure 2 shows the simulated output (lower trace) of an ideal Talbot clock extractor (TCE) system for a 2 ps, 10 Gbps pseudo-random bit signal (upper trace) showing the presence of a regular output train. Moreover, Fig. 3 depicts the predicted input (a) and output (b) radio-frequency spectra with a clear peak at 10 GHz.
5
0.5
0 0
-80 1
2 3 Time (ps)
4
5
Fig. 2. Input (a) and output (b) of a m=1 Talbot imaging system
0
a)
8 10 12 Frequency (GHz)
-80
b)
8 10 12 Frequency (GHz)
Fig. 3. RF spectra a) before and b) after the TCE
3. Experimental Results Figure 4 depicts the experimental setup. The pulse source was a Pritel fiber laser mode-locked at 9.25 GHz, generating 2.2-ps pulses, connected to a Mach-Zender electro-optic modulator (EOM) driven by a pulse pattern generator. A polarization controller (PC) was used to optimize the polarization before the modulator, following which the signal went through a 10/90 splitter so as to monitor the modulated signal. The signal was then propagated through 80 km of SMF-28, acting as a Talbot self-imaging system. An erbium-doped fiber amplifier (EDFA) compensated for the overall losses, estimated to be 20 dB. Autocorellation
Loop mirror
2.2ps
Mode-locked laser
PC
EOM
40 km of SMF
Time
EDFA 1555.5
1558
1560.5
RF source
Pulse pattern generator
Wavelength (nm)
Fig. 4. Experimental setup (insets depict the input autocorrelation trace, and optical spectrum)
Figure 5 below on the left depicts the output (lower trace) of the Talbot clock extraction system when fed with a periodic sequence of 12 ones followed by 24 zeros (upper trace). Nevertheless, the output exhibits a continuous train of pulses without any blanks.
input
1 ns
20 ps
output
Figure 5. A burst of ones and the corresponding output
Figure 6. Output eye diagram and peak intensity histogram
Figure 6 above shows an eye diagram of the output pulse along with an intensity distribution histogram, measured within a 4 ps window centered at the pulse’s peak. Clearly, the pulse peak is confined within an interval well above the ground level. Finally, figure 7 below depicts the input RF spectrum (left), eye diagram (middle), and the output RF spectrum (right) for a 231-1 PRBS signal with a 50/50 ratio of ones to zeros. input 40 dB output
100 ps 2 GHz
Figure 7. Input RF spectrum, eye diagram, and output RF spectrum for a 2 ps, 9.25 GHz PRBS signal
The output eye diagram shows a periodic output pulse train with a distinct pulse minimum, indicating the constant presence of a clock signal. Those results are indeed confirmed by the RF spectrum measurements: the 9.25 GHz peak is clearly visible, and the temporal Talbot effect reduces the noise floor by an additional 10-12 dB within 500 MHz from the center frequency, an improvement which occurred for input ones-to-zeros ratios of 25/75, 50/50 and 75/25. 4. Discussion and conclusion We have demonstrated a novel, simple way to generate a clock signal from a pseudo-random sequence of short pulses. The process is based on the temporal Talbot effect, and can be implemented using any appropriate dispersive device. In our case, we used a length of single-mode fiber, offering the advantage of a large bandwidth and negligible 3rd order dispersion for picoseconds pulse widths, at the expense of loss and bulkiness. However, these issues can be addressed by using, for example, an appropriately designed fiber Bragg grating. The main advantages of our approach reside in a theoretically lossless operation, as well as in the generation of an output pulse train with the exact same frequency as the input data rate. Here, we can contrast the Talbotbased approach with a Fabry-Perot resonant structure, whose temporal response is determined by its free spectral range [5]. In addition, the Talbot effect has been shown to significantly reduce timing jitter, an additional asset in any clock-recovery system [11, 12]. The results show that the output signal exhibits a slowly varying envelope, which can be dealt with using any all-optical device with a non-linear transfer function such as a nonlinear fiber pulse regenerator [13], or a saturated semiconductor optical amplifier based device [5]. 5. References 1. P. E. Barnsley, H. J. Wickes, G. E. Wickens, D. M. Spirit, "All-optical clock recovery from 5 Gb/s RZ data using a self-pulsating 1.56 um laser diode," IEEE Photonics Technology Letters 3, 942 (1991). 2. K. Vlachos, G. Theophilopoulos, A. Hatziefremidis, H. Avramopoulos, "30 Gb/s all-optical clock recovery circuit," IEEE Photonics Technology Letters 12, 705 (2000). 3. S. Yikai, W. Lijun, P. Kumar, "Wavelength tunable all-optical clock recovery using a fiber parametric oscillator," 1999. 4. R. Salem, T. E. Murphy, "Broad-band optical clock recovery system using two-photon absorption," IEEE Photonics Technology Letters 16, 2141 (2004). 5. C. Bintjas, K. Yiannopoulos, N. Pleros, G. Theophilopoulos, M. Kalyvas, H. Avramopoulos, G. Guekos, "Clock recovery circuit for optical packets," IEEE Photonics Technology Letters 14, 1363 (2002). 6. T. Jannson, J. Jannson, "Temporal self-imaging effect in single-mode fibers," Journal of the Optical Society of America B 71, 1373-1376 (1981). 7. J. Azana, M. A. Muriel, "Temporal self-imaging effects: theory and application for multiplying pulse repetition rates," IEEE Journal of Selected Topics in Quantum Electronics 7, 728 (2001). 8. D. Pudo, L. R. Chen, "Tunable passive all-optical pulse repetition rate multiplier using fiber Bragg gratings," Journal of Lightwave Technology, 23, 1729 (2005). 9. D. Pudo, "Talbot Clock Extractor for Optical Clock Recovery," U.S. Provisional Patent 60/804,735 (2006). 10. J. Azana, "Temporal self-imaging effects for periodic optical pulse sequences of finite duration," JOSA B 20, 83-90 (2003). 11. C. R. Fernández-Pousa, F. Mateos, L. Chantada, M. T. Flores-Arias, C. Bao, M. V. Pérez, C. Gómez-Reino, "Timing jitter smoothing by Talbot effect. I. Variance," JOSA B 21, 1170-1177 (2004). 12. C. R. Fernández-Pousa, F. Mateos, L. Chantada, M. T. Flores-Aria, C. Bao, M. V. Pérez, C. Gómez-Reino, "Timing jitter smoothing by Talbot effect. II. Intensity spectrum," JOSA B 22, 753-763 (2005). 13. V. Ta'eed, M. Shokooh-Saremi, L. Fu, D. Moss, M. Rochette, I. Littler, B. Eggleton, Y. Ruan, B. Luther-Davies, "Integrated all-optical pulse regenerator in chalcogenide waveguides," Optics Letters 30, 2900-2902 (2005).
