Timing jitter values for power-equalized pulses at the input and at the output of the SOA
Abstract
During the last few years, large-scale efforts towards realizing high-photonic integration densities have put SOAs in the spotlight once again. Hence, the need to develop a complete framework for SOA-induced signal distortion to accurately evaluate a system’s performance has now become evident. To cope with this demand, we present a detailed theoretical and experimental investigation of the deterministic timing jitter and the pulse peak power equalization of SOA-amplified intensity-modulated optical pulses. The deterministic timing jitter model relies on the pulse mean arrival time estimation and its analytic formula reveals an approximate linear relationship between the deterministic timing jitter and the logarithmic values of intensity modulation when the SOA gain recovery time is faster than the pulse period. The theoretical analysis also arrives at an analytic expression for the intensity modulation reduction (IMR), which clearly elucidates the pulse peak power equalization mechanism of SOA. The IMR analysis shows that the output intensity modulation depth is linearly related to the respective input modulation depth of the optical pulses when the gain recovery time is faster than the pulse period. This novel theoretical platform provides a qualitative and quantitative insight into the SOA performance in case of intensity-modulated optical pulses.
Keywords
- Deterministic timing jitter
- Pulse peak power equalization
- Intensity modulation reduction
- Semiconductor optical amplifier
- Modulation depth index
1. Introduction
Semiconductor optical amplifiers (SOAs) have long been the subject of considerable research interest, mainly exploiting their nonlinear properties to provide fast all-optical signal processing [1], such as high-speed wavelength conversion (WC) [2, 3], bitwise logic operations [4-6], and signal regeneration [7]. The broad-scale efforts towards realizing high photonic integration densities have, however, put the use of SOAs as amplification elements in the spotlight once again, since any alternative integrated amplifier competitor [8] lags far behind in terms of integration maturity. SOAs currently emerge as the preeminent on-chip amplifier solution and their reintroduction in the toolbox of the optical network designer is now evident in many key network subsystems. As a result, multiple demonstrations of SOAs performing as pure amplifier stages [9, 10] or as ON-OFF gating elements [11], where amplification occurs in the ON state, have been presented. Their ubiquitous use spans diverse network segments, enabling leading edge applications that extend from metro [11] to access network environments [10] and to on-chip or on-board datacom systems [9].
A concerted research effort on SOA-based devices, spanning the last 20 years, has unraveled most of their underlying amplification secrets, addressing a variety of linear and nonlinear phenomena and their impact on a system’s performance [12]. Pulse-shaped asymmetry owing to SOA saturation effects, for example, has been one of the key findings and has been extensively studied for the past years [13]. However, it was only recently that a novel theoretical analysis correlated this behavior to SOA-induced deterministic timing jitter that optical pulses experience during the amplification process, also suggesting an analytic mathematical formula for its accurate estimation [14, 15]. On the other hand, amplitude modulation phenomena for SOA in-line amplification have been theoretically studied [16, 17] but the pulse peak power equalization properties of SOAs, although experimentally utilized in many cases [18–20], have never been expressed in an analytical form that would allow a straightforward estimation for any case of input signal. So far, the pulse peak power equalization properties of SOAs have been theoretically and experimentally investigated only for the SOA-based interferometric switches [20]. As a result, the proposed theoretical model cannot be applied for single SOA in-line amplification cases, since it relies on cross-phase modulation (XPM) phenomena that take place in SOA-based interferometric devices. Although research efforts have shed plenty of light on the SOA-based amplification process during the last few years, a complete framework for SOA-induced signal distortion in case of intensity-modulated optical pulses, including both deterministic timing jitter and the intensity modulation reduction analysis, is still missing.
In order to fill the current gap in the system’s performance assessment, we present here a holistic theoretical analysis for the SOA-based amplification process along with its experimental verification when intensity-modulated optical pulses are inserted into the amplifier. The aim of this chapter is to provide a systematic methodology on the origin, nature and quantification of SOA-induced deterministic timing jitter and pulse peak power equalization that intensity-modulated optical pulses experience during the amplification process. At first, an analytic formula for the pulse mean arrival time at the SOA exit is derived, providing a comprehensive picture of jitter origin and allowing for reliable estimation of the deterministic jitter induced during the SOA amplification. The theoretical analysis continues with an analytical mathematical expression of intensity modulation reduction induced by SOA amplification. More specifically, the output-versus-input modulation depth of the amplifier is examined for several saturation levels to thoroughly investigate the pulse peak power equalization capabilities of the SOA. The theoretical models are also experimentally verified with the obtained results proving good agreement between theory and experimental observations, in both cases. Moreover, the deterministic timing jitter analysis reveals an approximate linear relationship between jitter values and the logarithm of pulse peak power modulation. Both experimental and theoretical results show that deterministic timing jitter minimization can be achieved by operating the SOA in the strongly saturated region. On the other hand, pulse peak power equalization analysis indicates a linear dependence between the output and input modulation depth indices. In that case, results show that the amplifier yields higher intensity modulation reduction values when it is operated in the saturation regime and for increased SOA gain levels.
In this perspective, the following sections of the chapter have been organized so as to introduce the concept and provide the analytical theoretical framework of the SOA-induced deterministic timing jitter and the pulse peak power equalization properties for intensity-modulated optical pulses, as well as to describe the experimental setup along with the respective results obtained in each case and finally discuss potential extensions of the proposed theoretical models.
2. Concept and theoretical analysis
It is a well-known fact that intensity-modulated optical pulses will experience a pulse-shaped distortion and intensity modulation suppression when propagating through the SOA. The shift of the amplified pulse peak towards its rising edge owes to the higher gain that the leading edge of every incoming pulse experiences compared to the gain received by the trailing edge of the pulse [13]. This “center of gravity” deviation of the exiting optical pulse indicates a subsequent deviation of the mean pulse arrival time
Apart from the peak position deviation of the optical pulses, SOAs can also induce pulse peak power equalization of incoming intensity-modulated optical pulses. This can, in turn, yield in a reduction in intensity modulation of the optical pulses at the SOA output. Assuming, again, that the SOA gain recovery time is faster than the pulse period, the pulse peak power equalization originates from the amplification dissimilarities arising between the low and high pulse peak powers. A high gain is received by the lower peak-powered pulses whereas a lower gain is experienced by the higher peak-powered pulses, resulting in nearly power-equivalent amplified pulses obtained at the SOA exit. As a result, the modulation depth index of the input pulses will always be higher than the respective outputs of the amplifier pointing out an intensity modulation reduction of the exiting optical pulse stream.
The following analysis aims to provide a theoretical insight into the origin of the deterministic timing jitter and elucidate the pulse peak power equalization mechanism during the SOA amplification of intensity-modulated optical pulses. Considering the amplifier as a spatially concentrated device, the instantaneous amplifier gain
where
and the
by defining
2.1. Deterministic timing jitter analysis
Considering Gaussian pulses as input to the SOA, the input pulse power is defined as
where
By expanding
Eq. (7) determines the mean arrival time
In addition, according to Figure 1, the steepness of the slope of the
The monotonic slope of mean arrival time
where
An interesting conclusion for deterministic timing jitter can be drawn by expressing the peak power
Thus, Eq. (7) can be expanded into a second-order Taylor series around a reference peak power
where
where
This formula reveals a linear relationship between deterministic timing jitter and intensity modulation with the linearity factor b provided by Eq. (12).
By plotting Eq. (12) for different pulsewidths and SOA gain levels as shown in Figure 2(b) and in Figure 2(c), respectively, the absolute value of
2.2. Pulse peak power equalization analysis
By defining
where
Eq. (14) depicts that
where the
and the
Dividing all terms of Eq. (15) by the
Finally, the modulation depth index of the output pulse peak power
Eq. (19) provides a complete description of the SOA amplifier response to an injected intensity-modulated clock pulse sequence. It shows that the intensity modulation at the output is linearly related to the intensity modulation at the input and that the constant of proportionality depends on the SOA steady-state gain
Given that the intensity modulation depth indices
Figure 3 depicts the graphical representation of Eq. (20) for different SOA gains versus
3. Experiment and results
The scope of this section is to provide experimental verification of the theoretical analysis for the deterministic timing jitter and the intensity modulation reduction induced by the SOA amplification process. Figure 4 demonstrates the experimental setup that was used for measurements with different pulsewidths and SOA gain levels. It consists of a 1549.2 nm mode-locked laser (TMLL) and a Ti:LiNbO-3 electro-optic modulator (MOD) driven by a 10 Gb/s pattern of alternating “1”s and “0”s, to create clock pulses at 5 GHz, so as to ensure a pulse period greater than the SOA gain recovery time (160 ps 1/e).
In order to create an intensity-modulated pulse sequence, the clock signal is then injected into a second modulator driven by a 625 MHz sinusoidal signal that creates pulses with 8 different pulse peak power levels. The intensity-modulated clock signal is amplified via an erbium doped fiber amplifier (EDFA) in order to compensate the losses and properly adjust the required power levels of optical pulses before their introduction into the SOA. Two fiber spools of 800 m and 1225 m were employed to enable pulsewidth adjustment at 20 ps and 30 ps by exploiting the fiber dispersion. An additional CW beam at 1558.2 nm was utilized to adjust SOA gain level and as such to determine its operational regime. After setting the SOA gain to the desired value, the output pulse train was captured on a real-time oscilloscope with 16 GHz bandwidth and a jitter measurement floor of 300 fs, where the jittery pulses were collected for offline postprocessing. The experimental setup of Figure 4 was also used in order to experimentally verify the IMR graphs shown in Figure 3. By varying the CW signal inserted into the SOA in order to cover a broad operational SOA gain regime, the intensity modulation of the input signal, defined as the highest to the lowest pulse peak power ratio, was measured at the output of the SOA. The operation of the amplifier both in the nonsaturated regime and in the saturated regime was also ensured by properly adjusting the input signal power. By calculating the difference between the initial and the output modulation depth values, the experimental data of IMR for every different SOA gain level was obtained. The control and input signals were adjusted in terms of power and polarization by means of variable optical attenuators (VOA) and polarization controllers (PC). The SOA module was a 1.5-mm-long multiquantum well structure with a small signal gain of 31 dB. The device was driven at 450 mA and the
The total timing jitter at the output of the SOA in the absence of pulse peak power variations is uncorrelated to the timing jitter induced from an intensity-modulated pulse sequence [15]. As such, it represents the accumulated random timing jitter of our experimental system:
Based on this assumption, the deterministic timing jitter induced by the SOA amplification process can be calculated by subtracting the random jitter measurement floor from
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Nonsaturation | Saturation | ||||
20 30 |
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0.585 | 20 | 4.356 | 4.391 |
0.634 | 5.065 | 5.180 | |||
20 30 |
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4.048 | 31 | 6.082 | 4.223 |
4.460 | 6.596 | 5.779 |
3.1. Deterministic timing jitter: Theoretical and experimental results
Figure 5(a) and 5(b) show the eyediagrams of a 10 dB intensity-modulated input signal with 20 ps and 30 ps pulsewidths, respectively. Figure 5(c) and 5(d) depict the output eyediagrams for the two pulsewidths when the amplifier operates in the nonsaturated regime. Figure 5(e) and 5(f) illustrate similar results for the two pulsewidths in case the SOA is operated in the strongly saturated gain region. The experimental average peak power values for the eyediagrams obtained in Figure 5 are shown in Table 2. In the eyediagrams of Figure 5(c–f), the deterministic jitter is masked under the contribution of total jitter including the accumulated random jitter of the system as well. The irregular shapes of the output eye diagrams reveal, however, the pulse shape distortion that triggers the deterministic timing jitter.
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20 ps | 30 μW | 1.85 mW |
30 ps | 34 μW | 1.23 mW |
Figure 5(g–j) depicts the experimental and theoretical results of the deterministic timing jitter versus input signal intensity modulation expressed in dB, for different gain levels, saturation regimes of the SOA and pulsewidths.
According to Eq. (11), the theoretical deterministic timing jitter depends linearly on intensity modulation levels. On that account, a linear fit was applied to the experimental data revealing good agreement between theoretical and experimental results obtained in all cases [15]. Figure 5(g) and (h) show theoretical deterministic timing jitter results obtained by applying Eq. (7) into Eq. (8), as well as the experimental data with their linear fit for 30 ps pulsewidth and 31 dB SOA gain level. The average pulse peak power values used in this case were 11 μW and 235 μW for unsaturated and saturated SOA operations, respectively. The graphs reveal a reduction of deterministic timing jitter in excess of 25% for the case of the SOA saturated operational regime. Figure 5(i) illustrates deterministic timing jitter evolution versus intensity modulation levels for 20 dB SOA gain using an average pulse peak power value of 34 μW. When compared with Figure 5(g), a decrease of the deterministic timing jitter values with the SOA gain level is evident. Finally, Figure 5(i) and 5(j) depict the deterministic timing jitter results for 30 ps and 20 ps pulsewidths, respectively, when all other operating parameters are the same, confirming that shorter pulses generate lower deterministic timing jitter levels [30 W average pulse peak power values for Fig. 5(j)]. In all cases, good qualitative and quantitative agreement between experiment and theory was achieved retaining the same deterministic timing jitter trend.
3.2. Intensity modulation reduction: Theoretical and experimental results
Figure 6 depicts the theoretical and experimental results for the output
Comparison between dashed and solid lines in Figure 6(a–d) shows good agreement between theory and experiment and indicates the SOA potential to provide increased pulse peak power equalization at its output, when operating the amplifier in the saturation regime.
4. Discussion
The theoretical framework and its experimental verification for both deterministic timing jitter and intensity modulation reduction analysis have relied on the assumption that every pulse experiences the same initial steady-state gain. This assumption allowed for the treatment of the pulse sequence on a per pulse basis and for the use of clock pulses for its experimental validation. However, the theoretical analysis presented here can also be extended towards calculating both these phenomena, in the case of random data patterns with intensity-modulated pulses used as the input signal in SOAs.
In the case of deterministic timing jitter, when the SOA gain recovery time is faster than the bit period, all the incoming data pulses will again experience the same steady-state gain
According to Figure 1, the same pulse peak power level results in a lower absolute value for the pulse mean arrival time when a lower gain value is perceived by the pulse. In Figure 1, for example, the absolute value of
Following the same rationale, Eq. (19) of the modulation depth index of the output pulse peak power
5. Conclusion
Research interest in semiconductor optical amplifiers (SOAs) has been lately renewed since SOAs appear as the most preferable on-chip amplifier option in many key network subsystems. Although a concerted research effort on SOA-based devices spanning the last 20 years, has revealed most of their underlying amplification secrets, SOA effects on intensity-modulated optical pulses in terms of timing jitter and pulse peak power equalization have not yet been consolidated in a detailed analytical framework. On that account, we have presented in this chapter, a holistic theoretical framework verified by experimental results that establishes for the first time a systematic methodology for the deterministic timing jitter and peak power equalization estimation in case of intensity-modulated optical pulses entering the SOA. Experimental and theoretical results reveal a linear relationship between deterministic timing jitter and intensity modulation levels when the SOA gain recovery time is shorter than the bit period. The pulse mean arrival time is calculated as a function of the pulse peak power, the pulsewidth and the SOA steady-state gain. In addition, pulse peak power equalization analysis shows that intensity modulation at output is linearly related to the intensity modulation at the input and the constant of proportionality depends on the SOA steady-state gain
Acknowledgments
This work has been supported in part by the European Commission through FP7-ICT-IP project PhoxTrot (contract no. 318240) and FP7 MC-IAPP project COMANDER (contract no. 612257).
References
- 1.
W. Freude et al. Linear and nonlinear semiconductor optical amplifiers. In: Proceedings of 12th International Conference on Transparent Optical Networks (ICTON 2010); 27 June–1 July; Munich, Germany. IEEE; 2010. p. 1–4. DOI: 10.1109/ICTON.2010.5549097 - 2.
Dong, X. Zhang, S. Fu, J. Xu, P. Shum and D. Huang. Ultrafast all-optical signal processing based on single semiconductor optical amplifier. Journal of Selected Topics in Quantum Electronics. 2008; 14(3):770–778. DOI: 10.1109/JSTQE.2008.916248 - 3.
J. Leuthold. All-optical wavelength conversion up to 100 Gbit/s with SOA delayed-interference configuration. OSA Trends in Optics and Photonics. 2000; 44(Optical Amplifiers and Their Applications):OWB3. - 4.
Z. Li et al. All-optical logic gates using semiconductor optical amplifier assisted by optical filter. Electronic Letters. 2005; 41(25):1397–1399. DOI: 10.1049/el:20053385 - 5.
G. Berrettinni, A. Simi, A. Malacarne, A. Bogoni, and L. Potí. Ultrafast integrable and reconfigurable XNOR, AND, NOR and NOT photonic logic gate. IEEE Photonics Technology Letters. 2006; 18(8):917–919. DOI: 10.1109/LPT.2006.873570 - 6.
A. Hamie, A. Sharaiha, M. Guégan, and B. Puce. All-optical logic NOR gate using two-cascaded semiconductor optical amplifiers. IEEE Photonics Technology Letters. 2002;14(10):1439–1441. DOI: 10.1109/LPT.2002.802426 - 7.
G. T. Kanellos et al. All-optical 3R burst mode reception at 40 Gb/s using 4 integrated MZI switches. IEEE/OSA Journal of Lightwave Technology. 2007; 25(1):184–192. DOI: 10.1109/JLT.2006.888169 - 8.
L. Aggazi et al. Monolithic integration of the erbium-doped amplifier with silicon-on-insulator waveguides. OSA Optics Express. 2010;18(26):27703–27711. DOI: 10.1364/OE.18.027703 - 9.
C.S. Nicholes et al. An 8x8 InP monolithic tunable optical router (MOTOR) packet forwarding chip. IEEE/OSA Journal of Lightwave Technology. 2010;28(4):641–650. DOI: 10.1109/JLT.2009.2030145 - 10.
V.S. Pato et al. All-optical burst mode power equalizer based on cascaded SOAs for 10-Gb/s EPONs. IEEE Photonics Technology Letters. 2008;20(24):2078–2080. DOI: 10.1109/LPT.2008.2006629 - 11.
D. Chiaroni et al. Optical packet ring network offering bit rate and modulation formats transparency. In: Proceedings of Optical Fiber Communication (OFC) Conference; 21–25 March; San Diego, CA, USA. IEEE; 2010. p. 1–3. DOI: 10.1364/OFC.2010.OWI3 - 12.
M. Settembre et al. Cascaded optical communication systems with in-line semiconductor optical amplifiers. IEEE/OSA Journal of Lightwave Technology. 1997; 15(6):962–967. DOI: 10.1109/50.588666 - 13.
G.P. Agrawal and N.A. Olsson. Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers. IEEE Journal of Quantum Electronics. 1989; 25(11):2297–2306. DOI: 10.1109/3.42059 - 14.
T. Alexoudi, S. Dris, D. Kalavrouziotis, P. Bakopoulos, A. Miliou and N. Pleros. Timing jitter of SOA-amplified intensity modulated optical pulses. In: Optical Fiber Communication Conference (OFC); 4-8 March; Los Angeles, CA, USA. IEEE; 2012. p. 1–3. DOI: 10.1364/NFOEC.2012.JTh2A.13 - 15.
T. Alexoudi, G.T. Kanellos, S. Dris, D. Kalavrouziotis, P. Bakopoulos, A. Miliou and N. Pleros. Deterministic timing jitter analysis of SOA-amplified intensity modulated optical pulses. IEEE Photonics Journal. 2012; 4(5):1947–1955. DOI: 10.1109/JPHOT.2012.2220341 - 16.
R. G.-Castrejón and A. Filios. Pattern-effect reduction using a cross-gain modulated holding beam in semiconductor optical in-line amplifier. IEEE/OSA Journal of Lightwave Technology. 2006; 24(12):4912–4917. DOI: 10.1109/JLT.2006.884972 - 17.
S. Bischoff, M.L. Nielsen and J J. Mork. Improving the all-optical response of SOAs using a modulated holding signal. IEEE/OSA Journal of Lightwave Technology. 2004; 22(5):1303–1308. DOI: 10.1109/JLT.2004.825354 - 18.
G. T. Kanellos, N. Pleros, C. Bintjas, H. Avramopoulos. SOA-based interferometric optical hard-limiter. In: Proceedings of Optical Amplifiers and their Applications (OAA) Conference; 30 June; San Francisco, CA, USA. OSA; 2004. DOI: 10.1364/IPR.2004.JWB8 - 19.
K. Vlachos, G. Theophilopoulos, A. Hatziefremidis and H. Avramopoulos. 30 Gbps all-optical, clock recovery circuit. IEEE Photonics Technology Letters. 2000;12(6):705–707. DOI: 10.1109/LPT.2002.801095. - 20.
N. Pleros et al. Recipe for intensity modulation reduction in SOA-based interferometric switches. IEEE/OSA Journal of Lightwave Technology. 2004;22(12):2834–2841. DOI: 10.1109/JLT.2004.834834 - 21.
S.V. Kartalopoulos et al. Optical bit error rate: an estimation methodology. 1st ed. Willey-IEEE Press; 2004. 291 p. ISBN: 978-0-471-61545-3 - 22.
J. Peatross, S.A. Glasgow and M. Ware. Average energy flow of optical pulses in dispersive media. APS Physics Review Letters. 2000;84(11):2370–2373. DOI: http://dx.doi.org/10.1103/PhysRevLett.84.2370 - 23.
R. Stephens. Analyzing jitter at high data rates. IEEE Communications Magazine. 2004; 42(2):S6–10. DOI: 10.1109/MCOM.2003.1267095 - 24.
Agilent Technologies. Measuring jitter in digital systems, application note 1448-1 [Internet]. 1 June 2003. Available from http://www.colbyinstruments.com/pdfs/5988-9109EN.pdf [Accessed: 31-5-2015] - 25.
Maxim Integrated. Converting between RMS to peak-to-peak Jitter at a specified BER, application note 462 HFAN-04.0.2 [Internet]. 2008 [Updated: 04/2008]. Available from: http://pdfserv.maximintegrated.com/en/an/AN462.pdf [Accessed: 31-5-2015]