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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 25 — Dec. 7, 2009
  • pp: 22553–22565
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Radio-frequency waveform generator with time-multiplexing capabilities based on multi-wavelength pulse compression

Víctor Torres-Company and Lawrence R. Chen  »View Author Affiliations


Optics Express, Vol. 17, Issue 25, pp. 22553-22565 (2009)
http://dx.doi.org/10.1364/OE.17.022553


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Abstract

We demonstrate a new photonically assisted reconfigurable radio-frequency waveform generator. The setup is based on phase modulating a multi-wavelength pulse source and subsequent compression in a dispersive medium. Under the appropriate conditions, we show that the photodetected electrical signal is broadband and coherent. Specifically, we show that this system allows for the synthesis of a reconfigurable finite-impulse-response filter where the number of filter taps is given by the number of wavelengths available from the multi-wavelength source and the reconfiguration is determined simply by their power and wavelength separation. We also show that this technique allows for time-multiplexing the synthesized waveforms, thus leading to an effective switching speed fixed by the clock rate. In particular, we show transitions between synthesized waveforms with a frequency content > 60 GHz in periods shorter than 100 ps.

© 2009 OSA

1. Introduction

Many interesting optical solutions exist that provide the desired wideband capabilities. Among these, AWGs based on pulse shapers implemented either in bulk [1

1. Y. Liu, S.-G. Park, and A. M. Weiner, “Terahertz waveform synthesis via optical pulse shaping,” IEEE J. Sel. Top. Quantum Electron. 2(3), 709–719 ( 1996). [CrossRef]

4

4. J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 15(4), 581–583 ( 2003). [CrossRef]

,11

11. V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “Reconfigurable RF-waveform generator based on incoherent filter design,” J. Lightwave Technol. 26(15), 2476–2483 ( 2008). [CrossRef]

13

13. S. Anzai, Y. Komai, M. Mieno, N. Wada, T. Yoda, T. Miyazaki, and K. Kodate, “Terahertz optical clock generation with tunable repetition rate and central wavelength using variable-bandwidth spectrum shaper,” Opt. Express 17(7), 4932–4937 ( 2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-4932. [CrossRef] [PubMed]

] or arrayed waveguide grating technology [7

7. D. Miyamoto, K. Mandai, T. Jurokawa, S. Takeda, T. Shioda, and H. Tsuda, “Waveform-controllable optical pulse generation using an optical pulse synthesizer,” IEEE Photon. Technol. Lett. 18(5), 721–723 ( 2006). [CrossRef]

] lead a better performance in terms of reconfigurability and complexity of the achievable waveform. In this case, the waveform is tailored through Fourier synthesis of a coherent [1

1. Y. Liu, S.-G. Park, and A. M. Weiner, “Terahertz waveform synthesis via optical pulse shaping,” IEEE J. Sel. Top. Quantum Electron. 2(3), 709–719 ( 1996). [CrossRef]

4

4. J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 15(4), 581–583 ( 2003). [CrossRef]

, 13

13. S. Anzai, Y. Komai, M. Mieno, N. Wada, T. Yoda, T. Miyazaki, and K. Kodate, “Terahertz optical clock generation with tunable repetition rate and central wavelength using variable-bandwidth spectrum shaper,” Opt. Express 17(7), 4932–4937 ( 2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-4932. [CrossRef] [PubMed]

] or even incoherent optical source [11

11. V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “Reconfigurable RF-waveform generator based on incoherent filter design,” J. Lightwave Technol. 26(15), 2476–2483 ( 2008). [CrossRef]

, 12

12. V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “20 GHz arbitrary radio-frequency waveform generator based on incoherent pulse shaping,” Opt. Express 16(26), 21564–21569 ( 2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-26-21564. [CrossRef] [PubMed]

]. Usually, since the generated pulses have temporal features on the order of ps, the maximum achievable bandwidth is ultimately limited by the photodetector response time. A significant drawback of these devices is that they do not offer a reconfiguration speed in the GHz regime, mainly due to the limited response time of the spectral shaper element (usually based on liquid crystal or thermo-optic modulation).

In this work, we propose and demonstrate an alternative, reconfigurable and rapidly switchable RF-AWG. It is based on the generation and compression of a multi-wavelength pulse train [23

23. J. van Howe, J. Hansryd, and C. Xu, “Multiwavelength pulse generator using time-lens compression,” Opt. Lett. 29(13), 1470–1472 ( 2004). [CrossRef] [PubMed]

]. The generation of ultrashort light pulses with an electro-optic phase modulator (EOPM) and subsequent intensity conversion in a dispersive medium is a well established technique [24

24. T. Kobayashi, H. Yao, K. Amano, Y. Fukushima, A. Morimoto, and T. Sueta, “Optical pulse compression using high-frequency electrooptic phase modulation,” IEEE J. Quantum Electron. 24(2), 382–387 ( 1988). [CrossRef]

27

27. S. Yang and X. Bao, “Generating a high-extinction-ratio pulse from a phase-modulated optical signal with a dispersion-imbalanced nonlinear loop mirror,” Opt. Lett. 31(8), 1032–1034 ( 2006). [CrossRef] [PubMed]

]. In a recent work, this concept was extended to multiple wavelengths [23

23. J. van Howe, J. Hansryd, and C. Xu, “Multiwavelength pulse generator using time-lens compression,” Opt. Lett. 29(13), 1470–1472 ( 2004). [CrossRef] [PubMed]

], proving to be a very useful and reliable approach for generating a time-interleaved pulse train with alternate carriers. The key is to note that the time separation between pulses at two wavelengths can be precisely controlled by the combined effect of dispersion and wavelength separation. Here, we study the suitability of this technique for RF-AWG. Specifically, we show that when the photodiode bandwidth is smaller than any possible beating from the spectra of adjacent phase-modulated lasers, the generated electrical signal is given by a sum of weighted and delayed replicas of the compressed intensity pulses. The tap weights and delays are controllable by the power and wavelength spacing of the lasers. In mathematical terms, this means that we can implement a finite impulse response (FIR) filter over the shape of the compressed pulse intensity. Essentially, this is an incoherent scheme in the sense that intensities are summed at the photodetector, but which provides a coherent electrical signal. Since the shaping relies on the tunability of the laser sources, no active shaping element is required, leading to a simple yet powerful technique to perform an RF-AWG. We note that the complexity of the filter synthesis is limited by the number of taps and the fact that they can be only positive. Nevertheless, we show that several interesting waveforms can be created with only four taps. Finally, we show that this scheme also offers the possibility for time-multiplexing of waveforms that are synthesized using different arrays of lasers.

The remainder of this paper is structured as follows. In Section 2 we provide the basic theory and the experimental results for our static RF-AWG. We investigate the effects of the finite linewidth and analyze the limits of the technique. In Section 3, we describe the experimental verification for the time-multiplexing operation. Finally, we summarize the work and present the main conclusions in Section 4.

2. Multi-wavelength pulse compression and static waveform generation

2.1 Heuristic description of the physical principle

Consider a multi-wavelength pulse source like the one shown in the cartoon of Fig. 1(a)
Fig. 1 (a) Cartoon of the physical process behind the proposed setup: generation of a multiwavelength pulse train where the power and delay can be controlled in the optical domain. (b) Particular proposal in this work.
. Let us assume that each of the color pulses travels, possibly although not necessarily, with distortion through a device that delays each pair of two neighboring pulses in a quantity proportional to their carrier separation. Later on, the intensities are summed at the photodetector. It is clear that by controlling the wavelength separation (and therefore the delay) and the power of each light pulse, one can synthesize the received electrical signal. The effect of the photodiode’s finite bandwidth is to broaden the received intensity pulse.

This is exactly the scheme that we proposed in [6

6. V. Torres-Company, J. Lancis, and P. Andrés, “Arbitrary waveform generator based on all-incoherent pulse shaping,” IEEE Photon. Technol. Lett. 18(24), 2626–2628 ( 2006). [CrossRef]

] and verified in [11

11. V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “Reconfigurable RF-waveform generator based on incoherent filter design,” J. Lightwave Technol. 26(15), 2476–2483 ( 2008). [CrossRef]

, 12

12. V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “20 GHz arbitrary radio-frequency waveform generator based on incoherent pulse shaping,” Opt. Express 16(26), 21564–21569 ( 2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-26-21564. [CrossRef] [PubMed]

]. There, the array of wavelengths was a continuous distribution (a broadband amplified spontaneous emission source), which was modulated by an external modulator and the delay element was simply a first-order dispersive medium. The continuous nature of the source allowed us to identify the reshaping process as a “frequency-to-time mapping”. The intensity summation was due to the uncorrelation of the different spectral components. However, this comes at the expense that the detected signal has a low signal-to-noise ratio (SNR), therefore limiting the range of applications of this RF-AWG. Intuitively, the origin of this noise comes from the random beating of the different spectral components at the photodetector. In consequence, by reducing the photodetection bandwidth, the SNR increases. Further details and calculations can be found in [28

28. C. Dorrer, “Statistical analysis of incoherent pulse shaping,” Opt. Express 17(5), 3341–3352 ( 2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3341. [CrossRef] [PubMed]

].

2.2 Theory

Here we provide a mathematical model that describes the above heuristic picture. We follow the approach developed in [23

23. J. van Howe, J. Hansryd, and C. Xu, “Multiwavelength pulse generator using time-lens compression,” Opt. Lett. 29(13), 1470–1472 ( 2004). [CrossRef] [PubMed]

], but we include now the effect of the lasers’ linewidth. We consider an array of N tunable lasers phase-modulated by a time lens and carved by an intensity modulator. The complex electric field before the dispersion stage is given by
Uin(t)=m(t)n=0N1Pnexp[j{ωnt+ϕn(t)}].
(1)
Here, m(t) represents the complex field gate provided by the carved pulse and phase modulation, i.e., m(t)=ψ(t)exp[jKt2/2], where ψ(t) is the complex field of the carved pulse and K is the chirping rate of the time lens. For a time lens implemented in an electro-optic phase modulator K=4Δθπ2fr2, with Δθ denoting the modulation index and fr the repetition rate. For simplicity, we will assume an aberration-free time lens. ωn is the carrier frequency of the nth laser, Pn its power, and ϕn(t) is a real random phase function accounting for the possible phase noise. The linewidth shape for the nth laser is given by the inverse Fourier transform (with respect to the variable τ) of the autocorrelation function exp[j{ϕn(t)ϕn(τt)}, with denoting time average. Assuming that the propagation through the linear dispersive medium is given by the transfer function H(ω)=exp[j{Φ1(ωω0)+Φ2(ωω0)2/2}], with Φ1 and Φ2 being respectively the group-delay and group-delay-dispersion coefficients, the output field becomes
Uout(t')=n=0N1αnan(t'tn)exp[jωnt'],
(2)
where an irrelevant constant phase factor has been dropped for convenience. Here, the time reference t’ is expressed as t'=tΦ1; αn=Pnexp[j(Φ2ωn2/2ωnω0Φ2)], and an(t)=Mn(ω)exp[jΦ2ω2/2]exp[jωt]dω, with Mn(ω) being the Fourier transform of m(t)exp[jϕn(t)]. The delay is given by
tn=Φ2(ωnω0).
(3)
Therefore, the laser arbitrarily marked as “0” sets the time origin. The delays for the rest of the lasers are measured with respect to this time reference. Giving one step further we can calculate the instantaneous optical intensity
Iout(t')=n=0|αn|2|an(t'tn)|2+nlnαn*αlan*(t'tn)al(t'tl)exp[j(ωnωl)t'].
(4)
Equation (4) states that the intensity is composed by two different contributions: an incoherent term, given by the sum of the delayed and weighted replicas of the distorted pulse, and a second interference term, containing the correlation of the distorted complex fields. We note that the first incoherent term is centered at dc, whereas the interference term is composed by several contributions centered at the beating frequencies |ωnωl|/2π, with nl. Our aim now is to filter only the dc component with a finite-bandwidth photodiode. This can be done by selecting the wavelength spacing between any two consecutive lasers to satisfy the following inequality
|ωn+1ωn|/2π>B+σα,f,
(5)
where B is the photodiode bandwidth and σα,f is the spectral width of an+1*(ttn+1)an(ttn). Therefore, σα,f is roughly given by the optical spectrum width of m(t). Under these conditions, we get that the photodetected intensity becomes iout(t')(n=0Pn|an(t'tn)|2)hPD(t'), with hPD(t) being the impulse response of the photodiode. But let us provide a further inspection into the structure of an(t), and in particular an assessment of the effects of the laser linewidth. We have
an(t')=exp[jt'2/2Φ2]ψ(t)exp[jϕn(t)]exp[j(K1/Φ2)t2/2]exp[jtt'/Φ2]dt.
(6)
If the dispersive medium is designed to compensate for the chirping rate of the time lens, KΦ2=1, then we get the well-known result for optical Fourier transformation [31

31. T. Jannson, “Real-time Fourier transformation in dispersive optical fibers,” Opt. Lett. 8(4), 232–234 ( 1983). [CrossRef] [PubMed]

,32

32. M. Nakazawa, T. Hirooka, F. Futami, and S. Watanabe, “Ideal distortion-free transmission using optical Fourier transformation and Fourier transform-limited pulses,” IEEE Photon. Technol. Lett. 16(4), 1059–1061 ( 2004). [CrossRef]

]
an(t')=exp[jt'2/2Φ2]ψ(t)exp[jϕn(t)]exp[jtt'/Φ2]dt.
(7)
Now, if the laser phase noise can be considered to be smooth in the region of the pulse carver duration, we can approximate an(t')exp[jt'2/2Φ2]ψ(t)exp[jtt'/Φ2]dt. This is valid whenever the laser linewidth becomes smaller than the optical spectrum of the pulse carver. This is the case in the experiments that we have carried out in this work, since the optical sources we used were either distributed feedback (DFB) or tunable lasers, whose linewidths are < 1 MHz. However, the above approximation might fail if one considers a spectrally sliced optical source, where the width of the slices can be >1 GHz. In the narrow-linewidth regime, we get
iout(t'){n=0PnI0(t'tn)}hPD(t'),
(8)
where we are denoting by I0(t') the optical intensity profile of the compressed pulse,
I0(t')=|ψ(t)exp(jtt'/Φ2)dt|2.
(9)
By Fourier transformation Eq. (8) we find
i˜out(f)HPD(f){n=0N1Pnexp(j2πftn)}I˜0(f).
(10)
Here, HPD(f) and I˜0(f) denote the Fourier transform of hPD(t) and I0(t), respectively.

It is important to realize that despite the semblance with a microwave photonic filter (MWPF) with N taps [33

33. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic fitlers,” J. Lightwave Technol. 24(1), 201–229 ( 2006). [CrossRef]

,34

34. J. Capmany, D. Pastor, and B. Ortega, “New and flexible fiber-optic delay line filters using chirped fibre Bragg gratings and laser arrays,” IEEE Trans. Microw. Theory Tech. 47(7), 1321–1326 ( 1999). [CrossRef]

], the device we are proposing is not an incoherent MWPF. The subtle yet important difference in our configuration is the introduction of the time lens. In the deep modulation regime, this device makes it impossible to establish a linear relation between the output and input electrical signals (a sinusoid in this case). In our configuration however, the linear relation is established between the output electrical signal and the compressed optical intensity at a single wavelength. However, we recognize that since our system defines an FIR with positive taps, the same techniques developed in the microwave photonics literature [33

33. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic fitlers,” J. Lightwave Technol. 24(1), 201–229 ( 2006). [CrossRef]

] for achieving a particular filter response can be easily adapted for our configuration [35

35. S. Sales, J. Capmany, J. Martí, and D. Pastor, “Solutions to the synthesis problem of optical delay line filters,” Opt. Lett. 20(23), 2438–2440 ( 1995). [CrossRef] [PubMed]

,36

36. T. A. Cusick, S. Iezekiel, and R. E. Miles; “All-optical microwave filter design employing a genetic algorithm,” IEEE Photon. Technol. Lett. 10(8), 1156–1158 ( 1998). [CrossRef]

]. Furthermore, although here an FIR operation with positive taps only has been performed, it is not difficult to envision an upgrade of our system to include negative taps by, for example, using balanced photodetection or cross-gain modulation. Similar solutions have been previously reported to implement incoherent MWPFs with negative taps [16

16. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 ( 2007). [CrossRef]

, 17

17. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 ( 2009). [CrossRef]

, 33

33. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic fitlers,” J. Lightwave Technol. 24(1), 201–229 ( 2006). [CrossRef]

].

2.3 Complexity and resolution limits of the technique

The minimum temporal feature that can be achieved in our RF waveform generator depends on the temporal duration of the compressed pulse. For deep modulation indices (>> π rad) and high clock frequencies (~ 10 GHz), it is possible to obtain few ps and even sub-ps short pulses [23

23. J. van Howe, J. Hansryd, and C. Xu, “Multiwavelength pulse generator using time-lens compression,” Opt. Lett. 29(13), 1470–1472 ( 2004). [CrossRef] [PubMed]

27

27. S. Yang and X. Bao, “Generating a high-extinction-ratio pulse from a phase-modulated optical signal with a dispersion-imbalanced nonlinear loop mirror,” Opt. Lett. 31(8), 1032–1034 ( 2006). [CrossRef] [PubMed]

], providing few tens to hundreds of GHz RF bandwidth to be shaped.

2.4 Experimental results

Figure 2
Fig. 2 Scheme of the experimental setup. PC: polarization controller; EDFA; Erbium-doped fiber amplifier; OSA: optical spectrum analyzer; PPG: pulse pattern generator.
shows the scheme implemented for the generation of static (although reconfigurable) RF signals. 2 tunable lasers in the C-band and 2 DFB lasers with a limited tunable range are used as light sources. The pulse carving operation is implemented by an electro-optic modulator (EOM) driven by a periodic signal at 12 GHz. It is biased to produce a nearly 45% duty-cycle pulse train. The pulse train is optically phase modulated by an EOPM driven by an amplified sinusoidal electrical signal. From an analysis of the dependence of the relative optical power in the spectrum sidebands with the voltage value applied on the EOPM, we measured the Vπ parameter at 12 GHz. From this parameter, we inferred a maximum achievable value of Δθ0.7π rad. We used a second EOM driven by a 12.5 Gb/s pulse pattern generator (PPG) to reduce the repetition rate of the pulse train without altering the clock frequency (therefore keeping the chirping rate intact). We used here the code “1010” (leading to a 6 GHz repetition rate). The expected and measured characteristics of the compressed pulse at a single wavelength after propagation in a dispersive single-mode fiber (SMF) of 3.2 km length are illustrated in Fig. 3
Fig. 3 Single pulse characteristics. Simulation results show (a) the compressed intensity pulse with 11.9 ps duration assuming a 55 GHz bandwidth (at 3dB) photodiode; (b) corresponding RF spectrum in blue solid line and filter response in green dash-dotted line; and (c) expected optical spectrum for 0.7 π rad of modulation index. Measurement results show (d) a compressed pulse with 10.9 ps width; (e) pulse train at 6 GHz and (f) optical spectrum.
. We observed a compressed pulse with 10.9 ps pulse width [Fig. 3(d)], in close agreement with the expected value of 11.9 ps [Fig. 3(a)]. All the time measurements are taken with a 55 GHz sampling scope with no averaging and 400 ms persistence time. The slight discrepancy could be due to an underestimation of the modulation index, which can be confirmed from the fact that the measured optical spectrum [Fig. 3(f)] is slightly broader than the expected [Fig. 3(c)]. According to Eq. (8), the pulse profile illustrated in Fig. 3 (d) represents our unit cell I0(t)hPD(t). Note that since our technique is based on the intensity profile of the achieved pulse, it is irrelevant whether the optical pulse is chirp free or not. The optical spectrum is measured after the modulation stage using an optical spectrum analyzer (OSA) with 0.8 pm resolution (Apex AP2443B), which allows for observing the comb structure with a line spacing of 6 GHz. We did not appreciate significant differences neither in the intensity pulse shapes nor optical spectra for different carriers in the 1525-1560 nm range. The small pedestal on the compressed pulse is due to the time lens aberrations [23

23. J. van Howe, J. Hansryd, and C. Xu, “Multiwavelength pulse generator using time-lens compression,” Opt. Lett. 29(13), 1470–1472 ( 2004). [CrossRef] [PubMed]

, 25

25. T. Otsuji, M. Yaita, T. Nagatsuma, and E. Sano, “10-80 Gb/s highly exctinctive electrooptic pulse pattern generation,” IEEE J. Sel. Top. Quantum Electron. 2(3), 643–649 ( 1996). [CrossRef]

], but it does not represent a significant issue for the particular electrical waveforms synthesized in this work. If needed, it could be removed by introducing an extra EOPM to compensate for the non-quadratic phase profile in the chirping [23

23. J. van Howe, J. Hansryd, and C. Xu, “Multiwavelength pulse generator using time-lens compression,” Opt. Lett. 29(13), 1470–1472 ( 2004). [CrossRef] [PubMed]

].The simulated RF spectrum of the signal is displayed in Fig. 3(b). A bell-shape signal appears with a frequency content higher than 60 GHz at the −20 dB level.

We emphasize that unlike with frequency-comb based shaping, where the amplitude and/or phase of the individual lines is manipulated, our proposal is an incoherent scheme and only relies on the spectral position and the global power of the comb. By switching on the remaining lasers, the same pulse profile appears shifted in time by a quantity proportional to the wavelength separation and dispersion.

We now proceed to show some examples illustrating the capabilities of the technique. Basing on Eq. (3), and taking into account the 3.2 km fiber dispersion (Φ2=69ps2), we are able to achieve a relative delay per wavelength separation of 0.43 ps/GHz. Owing to the incoherent regime dictated by Eq. (5), the minimum achievable delay without producing a beating should be ~57 ps. Although this is a large delay compared to the period, we remind that thanks to the periodicity of the compressed train, by separating further apart each comb, several unit cell pulses may overlap inside a period and electrical waveforms can be composed with an accuracy as good as 0.43 ps/GHz. Additionally, we measured the optical bandwidth of the SMF with a time-of-flight technique (the available bandwidth is defined as the spectral region where the third-order-dispersion effects can be disregarded), leading to ~2.5 THz. Basing on Eq. (12) and taking into account the previously mentioned parameters, with our setup we can introduce a maximum number of 18 taps. The small number of taps here used is limited by the tunable lasers available in our facilities.

We start with the formation of a square pulse. Figure 4 (a)-(d)
Fig. 4 Illustration of the AWG technique in the static regime. (a)-(d) screen images of the scope for each of the individual taps. (e)-(h) are the corresponding optical spectra in false color. (i) screen image of the optical spectrum when the four lasers are on. (j) and (l) show the achieved electrical waveform in different scale. (k) shows the superposition of the raw data from (a)-(d) and (j).
show the intensity profiles achieved when only the corresponding optical tap is switched on. Their respective optical spectra are shown in (e)-(h) in false color. The incoherent regime is guaranteed because we avoided spectral overlapping between the frequency combs, as illustrated by the optical spectrum measured in Fig. 4 (i). Note that these spectra show that the overlapping inside the waveform period comes from individual unit cell pulses whose P value from Eq. (11) is not the same (the position of each comb is not increasing linearly with the wavelength). This is not a problem because the meaningful quantity is the relative delay inside the period, δT, and not the absolute value tn. We selected the wavelength spacing and power values so that when the four lasers are on, these individual intensity pulses generate a square-wave pulse. We have measured a pulse width of 40.4 ps duration, and a rise and fall time of 7.3 and 6.1 ps, respectively. We note that the summation is not exactly linear. This is due to gain redistribution in the optical amplifiers when all the lasers are on. It is thus a deterministic effect that can be taken into account for the waveform synthesis problem. For completeness, Figs. 4(k) and (k,l) show the raw data superimposed in time and a snapshot of the electrical pulse sequence. Typical peak-to-peak amplitudes without electrical amplification are ~100 mV when ~5 dBm optical power is launched to the photodiode.

Figure 5
Fig. 5 Triplet and intensity decreasing burst examples. (a) and (e) show the raw data with the superimposed intensities for each tap. (b) and (f) show the screen images of the optical spectra when all the lasers are on and (c-d) and (g-h) show the screen images of the scope traces in different scales.
shows two more examples involving the generation of a triplet and a burst pulse with increasing intensity. Again, we see that due to the gain redistribution, the intensity summation for all the taps is not exact.

3. Time-multiplexing of radio-frequency waveforms

From a practical perspective, one could use the same array of lasers to drive both modulators and then use individual amplitude controllers. However, we have noted that due to the finite extinction ratio of the EOMs driven by the PPG, a remaining optical signal appears even when the EOM is in the off state. This effect leads to beating noise when the laser wavelengths are close each other. Therefore, each waveform was synthesized using different laser arrays.

Figure 7
Fig. 7 Time-multiplexing of two different waveforms at a 12 GHz rate. (a) and (b) are the data and data bar gates measured in the optical domain. (c) and (d) the synthesized compressed waveforms coming from EOM1 and EOM2, respectively. (e) and (f) are a zoomed version of (c) and (d). (g) and (h) show the multiplexing possibilities when all the lasers are on.
shows an example of the time multiplexing capabilities of our scheme. We have implemented two different filters with three taps each. Figures 7 (a) and (b) show the intensity pulse gates from each modulator when a code “1010” is applied on the PPG. Figures 7 (c) and (d) represent the achieved waveforms from the taps coming from modulators 1 and 2, respectively. We see that we are able to synthesize the multi-wavelength pulse train in order to keep the taps inside a period. Figures 7 (e) and (f) show a zoomed version of the waveforms shown in (c) and (d), respectively. The waveforms are multiplexed when both arrays of lasers are on, as illustrated in Figs. 7 (g) and (h). This is a pulse burst with increasing and decreasing intensity.

Finally, Fig. 8
Fig. 8 Time-multiplexing of two different waveforms at a 12 GHz rate with the switching code 1000. (a) and (b) are the data and data bar gates measured in the optical domain. (c) and (d) the synthesized waveforms from EOM1 and EOM2, respectively. (e) and (f) are a zoomed version of (c) and (d). (g) and (h) show the multiplexing possibilities when all the lasers are on.
shows another example using a different code length (“1000”). A single tap coming from EOM1 produces a compressed pulse, while three taps switched in EOM2 lead to a continuous high-repetition pulse train. We believe this type of rapidly changing pulses could be useful to evaluate the response of electronic equipment to rapid transients of broadband RF signals.

4. Summary and conclusions

We have studied the capabilities of multi-wavelength time-lens compression for the development of an incoherent RF-AWG. The incoherent operation is achieved by avoiding spectral overlapping from different frequency combs. In this way, the interference is lost and the electrical signal generated in the photodetector is the sum of the optical powers from the individual wavelengths, leading to a highly coherent waveform if the linewidth of the individual optical sources is narrow. In this incoherent regime, the RF signal can be precisely and straightforwardly tailored through an FIR filter easily reconfigurable through the lasers’ wavelength separation and power, therefore avoiding the use of any active spectral shaper element. The main limitation of our scheme is the requirement of N tunable lasers for implementing an N-tap FIR filter. However, we believe that our setup constitutes an interesting alternative to RF-AWG implemented by coherent frequency comb technology when the desired electrical target waveforms are not extremely complex (such as squares, triangles or high-speed bursts, for example).

Additionally, we have shown that this technique enables the time-multiplexing of different waveforms. This allows for fast transitions (at GHz rates) between alternating waveforms, a feature that is gaining increasing attention. We have reported switching at 12 GHz rate between waveforms containing a bandwidth higher than 60 GHz. We believe this technique could be used, for example, for testing the behavior of broad-bandwidth optoelectronic components to fast transitions.

Finally, we would like to mention that this technique might benefit from the recent advances in WDM photonic integrated circuits [39

39. M. K. Smit, “Past and future of InP-based photonic integration,” IEEE LEOS annual meeting, 51–52 (2008).

], in particular by the possibility of integrating in a single photonic chip the transmitter part from the scheme of Fig. 6 extended to several arrays of N lasers.

Acknowledgments

This work was supported in part by the National Science and Engineering Research Council (NSERC) of Canada. Victor Torres-Company acknowledges funding from the Spanish Ministry of Science and Innovation, and the Spanish Foundation for Science and Technology (FECYT) through a postdoctoral fellowship.

References and links

1.

Y. Liu, S.-G. Park, and A. M. Weiner, “Terahertz waveform synthesis via optical pulse shaping,” IEEE J. Sel. Top. Quantum Electron. 2(3), 709–719 ( 1996). [CrossRef]

2.

J. D. McKinney, D. E. Leaird, and A. M. Weiner, “Millimeter-wave arbitrary waveform generation with a direct space-to-time pulse shaper,” Opt. Lett. 27(15), 1345–1347 ( 2002). [CrossRef] [PubMed]

3.

T. Yilmaz, C. M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett Jr., “Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett. 14(11), 1608–1610 ( 2002). [CrossRef]

4.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 15(4), 581–583 ( 2003). [CrossRef]

5.

J. Azaña, N. K. Berger, B. Levit, and B. Fischer, “Reconfigurable generation of high-repetition rate pulse sequences based on time-domain phase-only filtering,” Opt. Lett. 30(23), 3228–3230 ( 2005). [CrossRef] [PubMed]

6.

V. Torres-Company, J. Lancis, and P. Andrés, “Arbitrary waveform generator based on all-incoherent pulse shaping,” IEEE Photon. Technol. Lett. 18(24), 2626–2628 ( 2006). [CrossRef]

7.

D. Miyamoto, K. Mandai, T. Jurokawa, S. Takeda, T. Shioda, and H. Tsuda, “Waveform-controllable optical pulse generation using an optical pulse synthesizer,” IEEE Photon. Technol. Lett. 18(5), 721–723 ( 2006). [CrossRef]

8.

J. Yao, F. Zeng, and Q. Wang, “Photonic generation of ultrawideband signals,” J. Lightwave Technol. 25(11), 3219–3235 ( 2007). [CrossRef]

9.

Y. Dai and J. Yao, “Arbitrary phase-modulated RF signal generation based on optical pulse position modulation,” J. Lightwave Technol. 26(19), 3329–3336 ( 2008). [CrossRef]

10.

R. E. Saperstein and Y. Fainman, “Information processing with longitudinal spectral decomposition of ultrafast pulses,” Appl. Opt. 47(4), A21–A31 ( 2008). [CrossRef] [PubMed]

11.

V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “Reconfigurable RF-waveform generator based on incoherent filter design,” J. Lightwave Technol. 26(15), 2476–2483 ( 2008). [CrossRef]

12.

V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “20 GHz arbitrary radio-frequency waveform generator based on incoherent pulse shaping,” Opt. Express 16(26), 21564–21569 ( 2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-26-21564. [CrossRef] [PubMed]

13.

S. Anzai, Y. Komai, M. Mieno, N. Wada, T. Yoda, T. Miyazaki, and K. Kodate, “Terahertz optical clock generation with tunable repetition rate and central wavelength using variable-bandwidth spectrum shaper,” Opt. Express 17(7), 4932–4937 ( 2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-4932. [CrossRef] [PubMed]

14.

A. J. Seeds, “Photonic techniques for microwave frequency synthesis,” IEEE LEOS Annual meeting 1, 72–73 (2000).

15.

R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 ( 2006). [CrossRef]

16.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 ( 2007). [CrossRef]

17.

J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 ( 2009). [CrossRef]

18.

D. E. Leaird, Z. Jiang, and A. M. Weiner, “Experimental investigation of security issues in OCDMA: a code-switching scheme,” Electron. Lett. 41(14), 817–819 ( 2005). [CrossRef]

19.

S. Ozharar, F. Quinlan, S. Gee, and P. J. Delfyett, “Demonstration of endless phase modulation for arbitrary waveform generation,” IEEE Photon. Technol. Lett. 17(12), 2739–2741 ( 2005). [CrossRef]

20.

C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 ( 2007). [CrossRef] [PubMed]

21.

R. P. Scott, N. K. Fontaine, C. Yang, D. J. Geisler, K. Okamoto, J. P. Heritage, and S. J. B. Yoo, “Rapid updating of optical arbitrary waveforms via time-domain multiplexing,” Opt. Lett. 33(10), 1068–1070 ( 2008). [CrossRef] [PubMed]

22.

J. Caraquitena and J. Martí, “Dynamic spectral line-by-line pulse shaping by frequency comb shifting,” Opt. Lett. 34(13), 2084–2086 ( 2009). [CrossRef] [PubMed]

23.

J. van Howe, J. Hansryd, and C. Xu, “Multiwavelength pulse generator using time-lens compression,” Opt. Lett. 29(13), 1470–1472 ( 2004). [CrossRef] [PubMed]

24.

T. Kobayashi, H. Yao, K. Amano, Y. Fukushima, A. Morimoto, and T. Sueta, “Optical pulse compression using high-frequency electrooptic phase modulation,” IEEE J. Quantum Electron. 24(2), 382–387 ( 1988). [CrossRef]

25.

T. Otsuji, M. Yaita, T. Nagatsuma, and E. Sano, “10-80 Gb/s highly exctinctive electrooptic pulse pattern generation,” IEEE J. Sel. Top. Quantum Electron. 2(3), 643–649 ( 1996). [CrossRef]

26.

T. Komukai, T. Yamamoto, and S. Kawanishi, “Optical pulse generator using phase modulator and linearly chirped fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17(8), 1746–1748 ( 2005). [CrossRef]

27.

S. Yang and X. Bao, “Generating a high-extinction-ratio pulse from a phase-modulated optical signal with a dispersion-imbalanced nonlinear loop mirror,” Opt. Lett. 31(8), 1032–1034 ( 2006). [CrossRef] [PubMed]

28.

C. Dorrer, “Statistical analysis of incoherent pulse shaping,” Opt. Express 17(5), 3341–3352 ( 2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3341. [CrossRef] [PubMed]

29.

V. Torres-Company, C. R. Fernández-Pousa, and L. R. Chen, “Temporal Lau effect: a multiwavelength self-imaging phenomenon,” Opt. Lett. 34(12), 1885–1887 ( 2009). [CrossRef] [PubMed]

30.

X. Yi and R. A. Minasian, “Noise mitigation in spectrum sliced microwave photonic signal processors,” J. Lightwave Technol. 24(12), 4959–4965 ( 2006). [CrossRef]

31.

T. Jannson, “Real-time Fourier transformation in dispersive optical fibers,” Opt. Lett. 8(4), 232–234 ( 1983). [CrossRef] [PubMed]

32.

M. Nakazawa, T. Hirooka, F. Futami, and S. Watanabe, “Ideal distortion-free transmission using optical Fourier transformation and Fourier transform-limited pulses,” IEEE Photon. Technol. Lett. 16(4), 1059–1061 ( 2004). [CrossRef]

33.

J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic fitlers,” J. Lightwave Technol. 24(1), 201–229 ( 2006). [CrossRef]

34.

J. Capmany, D. Pastor, and B. Ortega, “New and flexible fiber-optic delay line filters using chirped fibre Bragg gratings and laser arrays,” IEEE Trans. Microw. Theory Tech. 47(7), 1321–1326 ( 1999). [CrossRef]

35.

S. Sales, J. Capmany, J. Martí, and D. Pastor, “Solutions to the synthesis problem of optical delay line filters,” Opt. Lett. 20(23), 2438–2440 ( 1995). [CrossRef] [PubMed]

36.

T. A. Cusick, S. Iezekiel, and R. E. Miles; “All-optical microwave filter design employing a genetic algorithm,” IEEE Photon. Technol. Lett. 10(8), 1156–1158 ( 1998). [CrossRef]

37.

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 ( 2007). [CrossRef] [PubMed]

38.

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 ( 2007). [CrossRef]

39.

M. K. Smit, “Past and future of InP-based photonic integration,” IEEE LEOS annual meeting, 51–52 (2008).

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(320.7080) Ultrafast optics : Ultrafast devices
(060.5625) Fiber optics and optical communications : Radio frequency photonics

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 21, 2009
Revised Manuscript: November 5, 2009
Manuscript Accepted: November 5, 2009
Published: November 24, 2009

Citation
Víctor Torres-Company and Lawrence R. Chen, "Radio-frequency waveform generator with time-multiplexing capabilities based on multi-wavelength pulse compression," Opt. Express 17, 22553-22565 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-22553


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References

  1. Y. Liu, S.-G. Park, and A. M. Weiner, “Terahertz waveform synthesis via optical pulse shaping,” IEEE J. Sel. Top. Quantum Electron. 2(3), 709–719 (1996). [CrossRef]
  2. J. D. McKinney, D. E. Leaird, and A. M. Weiner, “Millimeter-wave arbitrary waveform generation with a direct space-to-time pulse shaper,” Opt. Lett. 27(15), 1345–1347 (2002). [CrossRef] [PubMed]
  3. T. Yilmaz, C. M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett., “Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett. 14(11), 1608–1610 (2002). [CrossRef]
  4. J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 15(4), 581–583 (2003). [CrossRef]
  5. J. Azaña, N. K. Berger, B. Levit, and B. Fischer, “Reconfigurable generation of high-repetition rate pulse sequences based on time-domain phase-only filtering,” Opt. Lett. 30(23), 3228–3230 (2005). [CrossRef] [PubMed]
  6. V. Torres-Company, J. Lancis, and P. Andrés, “Arbitrary waveform generator based on all-incoherent pulse shaping,” IEEE Photon. Technol. Lett. 18(24), 2626–2628 (2006). [CrossRef]
  7. D. Miyamoto, K. Mandai, T. Jurokawa, S. Takeda, T. Shioda, and H. Tsuda, “Waveform-controllable optical pulse generation using an optical pulse synthesizer,” IEEE Photon. Technol. Lett. 18(5), 721–723 (2006). [CrossRef]
  8. J. Yao, F. Zeng, and Q. Wang, “Photonic generation of ultrawideband signals,” J. Lightwave Technol. 25(11), 3219–3235 (2007). [CrossRef]
  9. Y. Dai and J. Yao, “Arbitrary phase-modulated RF signal generation based on optical pulse position modulation,” J. Lightwave Technol. 26(19), 3329–3336 (2008). [CrossRef]
  10. R. E. Saperstein and Y. Fainman, “Information processing with longitudinal spectral decomposition of ultrafast pulses,” Appl. Opt. 47(4), A21–A31 (2008). [CrossRef] [PubMed]
  11. V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “Reconfigurable RF-waveform generator based on incoherent filter design,” J. Lightwave Technol. 26(15), 2476–2483 (2008). [CrossRef]
  12. V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “20 GHz arbitrary radio-frequency waveform generator based on incoherent pulse shaping,” Opt. Express 16(26), 21564–21569 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-26-21564 . [CrossRef] [PubMed]
  13. S. Anzai, Y. Komai, M. Mieno, N. Wada, T. Yoda, T. Miyazaki, and K. Kodate, “Terahertz optical clock generation with tunable repetition rate and central wavelength using variable-bandwidth spectrum shaper,” Opt. Express 17(7), 4932–4937 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-4932 . [CrossRef] [PubMed]
  14. A. J. Seeds, “Photonic techniques for microwave frequency synthesis,” IEEE LEOS Annual meeting 1, 72–73 (2000).
  15. R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006). [CrossRef]
  16. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]
  17. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]
  18. D. E. Leaird, Z. Jiang, and A. M. Weiner, “Experimental investigation of security issues in OCDMA: a code-switching scheme,” Electron. Lett. 41(14), 817–819 (2005). [CrossRef]
  19. S. Ozharar, F. Quinlan, S. Gee, and P. J. Delfyett, “Demonstration of endless phase modulation for arbitrary waveform generation,” IEEE Photon. Technol. Lett. 17(12), 2739–2741 (2005). [CrossRef]
  20. C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 (2007). [CrossRef] [PubMed]
  21. R. P. Scott, N. K. Fontaine, C. Yang, D. J. Geisler, K. Okamoto, J. P. Heritage, and S. J. B. Yoo, “Rapid updating of optical arbitrary waveforms via time-domain multiplexing,” Opt. Lett. 33(10), 1068–1070 (2008). [CrossRef] [PubMed]
  22. J. Caraquitena and J. Martí, “Dynamic spectral line-by-line pulse shaping by frequency comb shifting,” Opt. Lett. 34(13), 2084–2086 (2009). [CrossRef] [PubMed]
  23. J. van Howe, J. Hansryd, and C. Xu, “Multiwavelength pulse generator using time-lens compression,” Opt. Lett. 29(13), 1470–1472 (2004). [CrossRef] [PubMed]
  24. T. Kobayashi, H. Yao, K. Amano, Y. Fukushima, A. Morimoto, and T. Sueta, “Optical pulse compression using high-frequency electrooptic phase modulation,” IEEE J. Quantum Electron. 24(2), 382–387 (1988). [CrossRef]
  25. T. Otsuji, M. Yaita, T. Nagatsuma, and E. Sano, “10-80 Gb/s highly exctinctive electrooptic pulse pattern generation,” IEEE J. Sel. Top. Quantum Electron. 2(3), 643–649 (1996). [CrossRef]
  26. T. Komukai, T. Yamamoto, and S. Kawanishi, “Optical pulse generator using phase modulator and linearly chirped fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17(8), 1746–1748 (2005). [CrossRef]
  27. S. Yang and X. Bao, “Generating a high-extinction-ratio pulse from a phase-modulated optical signal with a dispersion-imbalanced nonlinear loop mirror,” Opt. Lett. 31(8), 1032–1034 (2006). [CrossRef] [PubMed]
  28. C. Dorrer, “Statistical analysis of incoherent pulse shaping,” Opt. Express 17(5), 3341–3352 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3341 . [CrossRef] [PubMed]
  29. V. Torres-Company, C. R. Fernández-Pousa, and L. R. Chen, “Temporal Lau effect: a multiwavelength self-imaging phenomenon,” Opt. Lett. 34(12), 1885–1887 (2009). [CrossRef] [PubMed]
  30. X. Yi and R. A. Minasian, “Noise mitigation in spectrum sliced microwave photonic signal processors,” J. Lightwave Technol. 24(12), 4959–4965 (2006). [CrossRef]
  31. T. Jannson, “Real-time Fourier transformation in dispersive optical fibers,” Opt. Lett. 8(4), 232–234 (1983). [CrossRef] [PubMed]
  32. M. Nakazawa, T. Hirooka, F. Futami, and S. Watanabe, “Ideal distortion-free transmission using optical Fourier transformation and Fourier transform-limited pulses,” IEEE Photon. Technol. Lett. 16(4), 1059–1061 (2004). [CrossRef]
  33. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic fitlers,” J. Lightwave Technol. 24(1), 201–229 (2006). [CrossRef]
  34. J. Capmany, D. Pastor, and B. Ortega, “New and flexible fiber-optic delay line filters using chirped fibre Bragg gratings and laser arrays,” IEEE Trans. Microw. Theory Tech. 47(7), 1321–1326 (1999). [CrossRef]
  35. S. Sales, J. Capmany, J. Martí, and D. Pastor, “Solutions to the synthesis problem of optical delay line filters,” Opt. Lett. 20(23), 2438–2440 (1995). [CrossRef] [PubMed]
  36. T. A. Cusick, S. Iezekiel, and R. E. Miles; “All-optical microwave filter design employing a genetic algorithm,” IEEE Photon. Technol. Lett. 10(8), 1156–1158 (1998). [CrossRef]
  37. N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007). [CrossRef] [PubMed]
  38. Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007). [CrossRef]
  39. M. K. Smit, “Past and future of InP-based photonic integration,” IEEE LEOS annual meeting, 51–52 (2008).

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