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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 9 — Apr. 27, 2009
  • pp: 7004–7010
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1 μs tunable delay using parametric mixing and optical phase conjugation in Si waveguides

Yitang Dai, Xianpei Chen, Yoshitomo Okawachi, Amy C. Turner-Foster, Mark. A. Foster, Michal Lipson, Alexander L. Gaeta, and Chris Xu  »View Author Affiliations


Optics Express, Vol. 17, Issue 9, pp. 7004-7010 (2009)
http://dx.doi.org/10.1364/OE.17.007004


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Abstract

We demonstrate continuously tunable optical delays as large as 1.1 μs range for 10 Gb/s NRZ optical signals based on four-wave mixing (FWM) process in silicon waveguide. The large delay range is made possible by a novel wavelength-optimized optical phase conjugation scheme, which allows for tunable dispersion compensation to minimize the residual group-velocity dispersion (GVD) for the entire tuning range.

© 2009 Optical Society of America

1. Introduction

The capability of buffering or delaying information is highly desired in communication networks. Specific applications include network buffering, data synchronization, and time-division multiplexing. While information is transmitted using optical fibers in current communication networks, components for data processing requires optical/electronic conversion of information, creating a bottleneck for further increasing the data transmission rate [1

1. M. K. Dhodhi, S. Tariq, and K. A. Saleh, “Bottlenecks in next generation DWDM-based optical networks,” Comput. Commun. 24, 1726–1733 (2001). [CrossRef]

]. The ability to create precise all-optical delays, i.e., being able to control the arrival times of data streams on the physical level, is then a critical requirement. Rather than discrete optical delays that can be generated by combining a series of fixed delay lines with different amounts of delay in parallel [2

2. S. J. B. Yoo, “Optical packet and burst switching technologies for the future photonic internet,” J. Lightwave Technol. 24, 4468–4492 (2006). [CrossRef]

], fine and continuous tuning of the delay is required as the data rate increases. The development of tunable optical delay lines is also important for other applications such as optical coherence tomography [3

3. E. Choi, J. H. Na, Y. Ryu, G. Mudhana, and B. H. Lee, “All-fiber variable optical delay line for applications in optical coherence tomography: feasibility study for a novel delay line,” Opt. Express 13, 1334–1345 (2005). [CrossRef] [PubMed]

], optical control of phased array antennas for radio frequency communication [4

4. J. L. Corral, J. Marti, J. M. Fuster, and R. I. Laming, “True time-delay scheme for feeding optically controlled phased-array antennas using chirped-fiber gratings,” Photon. Technol. Lett. 9,1529–1531 (1997). [CrossRef]

], light detection and sensing (LIDAR) [5

5. G. N. Pearson, K. D. Ridley, and D. V. Willetts, “Chirp-pulse-compression three dimensional lidar imager with fiber optics,” Appl. Opt. 44, 257–265 (2005). [CrossRef] [PubMed]

], optical sampling [6

6. Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: Fundamental concepts and practical considerations,” J. Lightwave Technol. 21, 3085–3103 (2003). [CrossRef]

], and pattern correlation [7

7. R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, 2002).

].

Recent research efforts include the ability to reduce the speed of an optical signal by several orders of magnitude, which takes advantage of the rapidly-varying refractive index that accompanies an optical resonance [8

8. R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘fast’ light,” Progress in Optics 43, edited by E. Wolf (Elsevier, Amsterdam, 2002), Chap. 6, p. 497–530.

]. However, the maximum delay that can be generated in practical slow-light delay lines has been limited to a few pulse widths [9

9. R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News 17, 18–22 (2006). [CrossRef]

]. An alternative technique for generating tunable delays utilizes wavelength conversion and dispersion [10–16

10. M. Burzio, P. Cinato, R. Finotti, P. Gambini, M. Puleo, E. Vezzoni, and L. Zucchelli, “Optical cell synchronization in an ATM optical switch,” in Proc. ECOC ’94, Florence, Italy, 2, 581–584 (1994).

]. This scheme takes advantage of the group-velocity dispersion (GVD) in an optical fiber for generating a wavelength-dependent optical delay. The wavelength of the input signal is shifted and injected into a medium with a large GVD, which generates a delay with respect to the initial unshifted pulse. The total delay is approximately a product of the GVD parameter D, the length of the dispersive fiber Ld, and the wavelength shift Δλ. To achieve large delays, however, the necessarily large GVD inevitably results in severe distortions to the delayed signal. The use of the inherent temporal phase conjugation associated with four-wave mixing (FWM) can overcome the GVD-induced pulse broadening and allows us to further extend the maximum achievable delay [17

17. Y. Okawachi, M. A. Foster, X. Chen, A. C. Turner-Foster, R. Salem, M. Lipson, C. Xu, and A. L. Gaeta, “Large tunable delays using parametric mixing and phase conjugation in Si nanowaveguides,” Opt. Express 16, 10349–10357 (2008). [CrossRef] [PubMed]

]. Such scheme consists of three stages: a dispersive fiber, a FWM wavelength conversion, and a second dispersive fiber which is typically the same fiber as the first stage. 243-ns delay for a 10-Gb/s NRZ signal has been demonstrated based on this design. However, since dispersive fibers also possess non-vanishing higher order dispersion, the large residual dispersion between the original and the converted wave limits the maximum delay range. A new scheme including a partial dispersion slope cancellation is proposed, and the maximum tunable delay range has been extended to 400 ns at 10 Gb/s [18

18. E. Myslivets, N. Alic, J. R. Windmiller, R. M. Jopson, and S. Radic, “400 ns continuously tunable delay of 10 Gbps intensity modulated optical signal,” Photon. Technol. Lett. , 21, 4,251–253 (2009). [CrossRef]

]. Unfortunately, residual dispersion at the output signal of more than 200 ps/nm still exists. Such a scheme has limited potential for further improvement in delay range and data rate.

In this paper we propose a novel tunable parametric optical delay system based on wavelength-optimized optical phase conjugation, which allows one half of the delay system to serve simultaneously as a tunable dispersion compensator with only fixed dispersion elements. Zero residual GVD at the output signal can be obtained throughout the delay range. Optical phase conjugation is realized in silicon waveguides. For fiber-based optical parametric schemes, pump modulation is necessary in order to suppress stimulated Brillouin scattering (SBS), which distorts the output if a single pump is used. Since the silicon waveguides do not exhibit SBS, a single CW pump can be used without any phase modulation [19

19. M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15, 12,949–12,958 (2007). [CrossRef]

]. This paper reports, for the first time to the best of our knowledge, continuously tunable optical delays at 10 Gb/s with greater than a 1-μs delay range.

2. Theory

Fig. 1. (a) Delay generator using two wavelength conversions via FWM and two dispersion links. (b) The principle of zero residual dispersion based on the wavelength-optimized optical phase conjugation.

The concept of the proposed system is illustrated in Fig. 1. The input signal is first wavelength-converted from λ 0 to λ 1 (can be with or without phase conjugation) and then transmitted along fiber I with a dispersion function χ 1(λ). After the second wavelength conversion to χ 2 (with phase conjugation), the signal is transmitted along the second dispersive link, fiber II with dispersion function χ 2(λ). The principle of zero residual dispersion at the output signal is shown in Fig. 1(b). As a result of the phase conjugation process in FWM II, the signal broadening effect induced by fiber I can be compensated by the dispersion in fiber II. In order to realize zero residual dispersion, the total dispersion that the signal experiences in the two fibers are required to be the same, that is,

χ1(λ1)=χ2(λ2).
(1)

τ(λ1)=λ10λ1χ1(λ)+λ20λ2χ2(λ),
(2)

where λ 10 is the reference point, and λ 20 and λ 2 are determined by λ 10 and λ 1, respectively, as shown in Eq. (1).

φ(Δω)=Δω22[β2,2(ω2)L2β2,1(ω1)L1]+Δω36[β3,2(ω2)L2+β2,1(ω1)L1],
+Δω424[β4,2(ω2)L2β4,1(ω1)L1]+
(3)

where L 1 and L 2 are the fiber lengths, and ω 1 and ω 2 are the optical frequencies of the signal in the two fibers.

φmax(Δω)=Δω24β3L̅ΔωC,
(4)

where β3L̅ is the mean third order dispersion (TOD) of the two fibers, which can be large when the fiber length is long. As a result, the large GVD variation in the wavelength conversion range [β3L̅ΔωC in Eq. (4)] ultimately limits the achievable maximum delay range and the highest data rate the system can support.

In our proposed system, however, the first term in the phase distortion is zero throughout the wavelength conversion range when Eq. (1) is satisfied, and the dominant phase distortion is now the second term. Similarly, a pre- or post-compensation with the optimized value of the mean residual TOD can be used to minimize the phase distortion, and then the maximum residual phase distortion is

φ'max(Δω)=Δω36β4L̅ΔωC,
(5)

where β4L̅ is the mean fourth order dispersion of the two fibers. Equation (5) shows that the system performance is now limited by the fourth-order dispersion instead of the TOD, which significantly increases the maximum delay range and the highest data rate that parametric delay system can support.

3. Experiment

Fig. 2. Experimental setup for the delay scheme based on wavelength-optimized optical phase conjugation. C: coupler; TBF: tunable bandpass filter; SSMF: standard single mode fiber, PC: polarization controller. NF: notch filter. Each of the four Raman amplifiers consists of four semiconductor LDs. Polarization multiplexing is used to combine the pump diodes, and the pump power for each amplifier is 23 dBm. The spectrum after each waveguide is inset. The resolution in the measurement is 0.1 nm.

Fig. 3. Measured delay as a function of λ1. Inset: the measured delay for λ1 = 1535.5 nm (top) and 1572 nm (bottom).

Figure 4 shows the bit-error-rate tests and the eye diagrams measured at the two edges and center point in the delay generator. A (223-1) pseudo-random bit sequence (PRBS) is used. The measured power penalty is around 3.3 to 4.5 dB for a BER of 10-9. The power penalty can be attributed in part to the degradation of the optical signal-to-noise ratio (OSNR) in the wavelength conversion process. Both linear propagation loss and nonlinear loss due to two-photon absorption and free-carrier absorption reduce the efficiency of the FWM process in the silicon waveguides.

Fig. 4. Measured eye diagrams and BER curves of back-to-back (B2B) signals and delayed signals when λ 1 is at different wavelengths.

The PMD of the system is estimated to be 6 ps, which shows no impact on a 10 Gb/s signal, but it will distort the signal at much higher data rate. A possible solution for this issue is to shorten the fiber length while enlarging the wavelength tuning range to keep the same tunable delay range. Furthermore, the polarization-dependent response of the Si-waveguide can be mitigated by two orthogonal pumps. For example, by injecting a single pump into both polarization states of the waveguide, we achieved wavelength conversion efficiency with less than 0.5 dB polarization sensitivity.

4. Conclusion

We proposed a novel parametric tunable delay system with a wavelength-optimized optical phase conjugation that allows for tunable dispersion compensation. Theoretical analysis showed that zero GVD can be obtained throughout the tuning range and predicts the potential of an even larger range of delays and operation at higher data rates. More than 1 μs continuously tunable delay was experimentally demonstrated at 10 Gb/s.

Acknowledgments

The authors gratefully acknowledge support from the DARPA MTO POPS Program. We also acknowledge valuable discussions with Prof. Keren Bergman and her research group at Columbia. OFS Denmark is acknowledged for loaning parts of the HFDK.

References and links

1.

M. K. Dhodhi, S. Tariq, and K. A. Saleh, “Bottlenecks in next generation DWDM-based optical networks,” Comput. Commun. 24, 1726–1733 (2001). [CrossRef]

2.

S. J. B. Yoo, “Optical packet and burst switching technologies for the future photonic internet,” J. Lightwave Technol. 24, 4468–4492 (2006). [CrossRef]

3.

E. Choi, J. H. Na, Y. Ryu, G. Mudhana, and B. H. Lee, “All-fiber variable optical delay line for applications in optical coherence tomography: feasibility study for a novel delay line,” Opt. Express 13, 1334–1345 (2005). [CrossRef] [PubMed]

4.

J. L. Corral, J. Marti, J. M. Fuster, and R. I. Laming, “True time-delay scheme for feeding optically controlled phased-array antennas using chirped-fiber gratings,” Photon. Technol. Lett. 9,1529–1531 (1997). [CrossRef]

5.

G. N. Pearson, K. D. Ridley, and D. V. Willetts, “Chirp-pulse-compression three dimensional lidar imager with fiber optics,” Appl. Opt. 44, 257–265 (2005). [CrossRef] [PubMed]

6.

Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: Fundamental concepts and practical considerations,” J. Lightwave Technol. 21, 3085–3103 (2003). [CrossRef]

7.

R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, 2002).

8.

R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘fast’ light,” Progress in Optics 43, edited by E. Wolf (Elsevier, Amsterdam, 2002), Chap. 6, p. 497–530.

9.

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News 17, 18–22 (2006). [CrossRef]

10.

M. Burzio, P. Cinato, R. Finotti, P. Gambini, M. Puleo, E. Vezzoni, and L. Zucchelli, “Optical cell synchronization in an ATM optical switch,” in Proc. ECOC ’94, Florence, Italy, 2, 581–584 (1994).

11.

L. Zucchelli, M. Burzio, and P. Gambini, “New solutions for optical packet delineation and synchronization in optical packet switched networks,” in Proc. ECOC ’96, Oslo, Norway, 3, 301–304 (1996).

12.

K. Shimizu, G. Kalogerakis, K. Wong, M. Marhic, and L. Kazovsky, “Timing jitter and amplitude noise reduction by a chirped pulsed-pump fiber OPA,” in Proc. OFC ’03, Anaheim, USA, 1, 197–198 (2003).

13.

J. van Howe and C. Xu, “Ultrafast optical delay line using soliton propagation between a time-prism pair,” Opt. Express 13,1138–1143 (2005). [CrossRef] [PubMed]

14.

Y. Wang, C. Yu, L. Yan, A. E. Willner, R. Roussev, C. Langrock, M. M. Fejer, J. E. Sharping, and A. E. Gaeta, “44-ns continuously tunable dispersionless optical delay element using a PPLN waveguide with two-pump configuration, DCF, and a dispersion compensator,” Photon. Technol. Lett. 19, 861–863 (2007). [CrossRef]

15.

L. C. Christen, O. F. Yilmaz, S. R. Nuccio, X. Wu, I. Fazal, A. E. Willner, C. Langrock, and M. M. Fejer, “Tunable 105 ns optical delay for 80 Gb/s RZ-DQPSK, 40 Gb/s RZ-DPSK, and 40 Gb/s RZ-OOK signals using wavelength conversion and chromatic dispersion,” Opt. Lett. 34, 542–544 (2009). [CrossRef] [PubMed]

16.

J. E. Sharping, Y. Okawachi, J. van Howe, C. Xu, Y. Wang, A. E. Willner, and A. L. Gaeta, “All-optical, wavelength and bandwidth preserving, pulse delay based on parametric wavelength conversion and dispersion,” Opt. Express 13, 7872–7877 (2005). [CrossRef] [PubMed]

17.

Y. Okawachi, M. A. Foster, X. Chen, A. C. Turner-Foster, R. Salem, M. Lipson, C. Xu, and A. L. Gaeta, “Large tunable delays using parametric mixing and phase conjugation in Si nanowaveguides,” Opt. Express 16, 10349–10357 (2008). [CrossRef] [PubMed]

18.

E. Myslivets, N. Alic, J. R. Windmiller, R. M. Jopson, and S. Radic, “400 ns continuously tunable delay of 10 Gbps intensity modulated optical signal,” Photon. Technol. Lett. , 21, 4,251–253 (2009). [CrossRef]

19.

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15, 12,949–12,958 (2007). [CrossRef]

20.

S. Namiki, “Wide-band and -range tunable dispersion compensation through parametric wavelength conversion and dispersion optical fibers,” J. Lightwave Technol. 26, 28–35 (2008). [CrossRef]

21.

A. Yariv, D. Fekete, and D. M. Pepper, “Compensation for channel dispersion by nonlinear optical phase conjugation,” Opt. Lett. 4, 52–54 (1979). [CrossRef] [PubMed]

22.

S. Ayotte, S. Xu, H. Rong, O. Cohen, and M. J. Paniccia, “Dispersion compensation by optical phase conjugation in silicon waveguide,” Electron. Lett. 43, 1037–1039 (2007). [CrossRef]

23.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, Boston, 1989).

24.

B. G. Lee, A. Biberman, M. A. Foster, A. C. Turner, M. Lipson, A. L. Gaeta, and K. Bergman, “Bit-error-rate characterization of Silicon four-wave-mixing wavelength converters at 10 and 40 Gb/s,” CLEO 2008, paper CPDB4.

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: January 29, 2009
Revised Manuscript: April 1, 2009
Manuscript Accepted: April 8, 2009
Published: April 13, 2009

Citation
Yitang Dai, Xianpei Chen, Yoshitomo Okawachi, Amy C. Turner-Foster, Mark A. Foster, Michal Lipson, Alexander L. Gaeta, and Chris Xu, "1 μs tunable delay using parametric mixing and optical phase conjugation in Si waveguides," Opt. Express 17, 7004-7010 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-7004


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References

  1. M. K. Dhodhi, S. Tariq, and K. A. Saleh, "Bottlenecks in next generation DWDM-based optical networks," Comput. Commun. 24, 1726-1733 (2001). [CrossRef]
  2. S. J. B. Yoo, "Optical packet and burst switching technologies for the future photonic internet," J. Lightwave Technol. 24, 4468-4492 (2006). [CrossRef]
  3. E. Choi, J. H. Na, Y. Ryu, G. Mudhana, and B. H. Lee, "All-fiber variable optical delay line for applications in optical coherence tomography: feasibility study for a novel delay line," Opt. Express 13, 1334-1345 (2005). [CrossRef] [PubMed]
  4. J. L. Corral, J. Marti, J. M. Fuster, and R. I. Laming, "True time-delay scheme for feeding optically controlled phased-array antennas using chirped-fiber gratings," Photon. Technol. Lett. 9, 1529-1531 (1997). [CrossRef]
  5. G. N. Pearson, K. D. Ridley, and D. V. Willetts, "Chirp-pulse-compression three dimensional lidar imager with fiber optics," Appl. Opt. 44, 257-265 (2005). [CrossRef] [PubMed]
  6. Y. Han and B. Jalali, "Photonic time-stretched analog-to-digital converter: Fundamental concepts and practical considerations," J. Lightwave Technol. 21, 3085-3103 (2003). [CrossRef]
  7. R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, 2002).
  8. R. W. Boyd and D. J. Gauthier, "‘Slow’ and ‘fast’ light," Progress in Optics 43, edited by E. Wolf (Elsevier, Amsterdam, 2002), Chap. 6, p. 497-530.
  9. R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, "Applications of slow light in telecommunications," Opt. Photon. News 17, 18-22 (2006). [CrossRef]
  10. M. Burzio, P. Cinato, R. Finotti, P. Gambini, M. Puleo, E. Vezzoni, and L. Zucchelli, "Optical cell synchronization in an ATM optical switch," in Proc. ECOC ’94, Florence, Italy, 2, 581-584 (1994).
  11. L. Zucchelli, M. Burzio, and P. Gambini, "New solutions for optical packet delineation and synchronization in optical packet switched networks," in Proc. ECOC ’96, Oslo, Norway, 3, 301-304 (1996).
  12. K. Shimizu, G. Kalogerakis, K. Wong, M. Marhic, and L. Kazovsky, "Timing jitter and amplitude noise reduction by a chirped pulsed-pump fiber OPA," in Proc. OFC ’03, Anaheim, USA, 1, 197-198 (2003).
  13. J. van Howe and C. Xu, "Ultrafast optical delay line using soliton propagation between a time-prism pair," Opt. Express 13, 1138-1143 (2005). [CrossRef] [PubMed]
  14. Y. Wang, C. Yu, L. Yan, A. E. Willner, R. Roussev, C. Langrock, M. M. Fejer, J. E. Sharping, and A. E. Gaeta, "44-ns continuously tunable dispersionless optical delay element using a PPLN waveguide with two-pump configuration, DCF, and a dispersion compensator," Photon. Technol. Lett. 19, 861-863 (2007). [CrossRef]
  15. L. C. Christen, O. F. Yilmaz, S. R. Nuccio, X. Wu, I. Fazal, A. E. Willner, C. Langrock, and M. M. Fejer, "Tunable 105 ns optical delay for 80 Gb/s RZ-DQPSK, 40 Gb/s RZ-DPSK, and 40 Gb/s RZ-OOK signals using wavelength conversion and chromatic dispersion," Opt. Lett. 34, 542-544 (2009). [CrossRef] [PubMed]
  16. J. E. Sharping, Y. Okawachi, J. van Howe, C. Xu, Y. Wang, A. E. Willner, and A. L. Gaeta, "All-optical, wavelength and bandwidth preserving, pulse delay based on parametric wavelength conversion and dispersion," Opt. Express 13, 7872-7877 (2005). [CrossRef] [PubMed]
  17. Y. Okawachi, M. A. Foster, X. Chen, A. C. Turner-Foster, R. Salem, M. Lipson, C. Xu, and A. L. Gaeta, "Large tunable delays using parametric mixing and phase conjugation in Si nanowaveguides," Opt. Express 16, 10349-10357 (2008). [CrossRef] [PubMed]
  18. E. Myslivets, N. Alic, J. R. Windmiller, R. M. Jopson, and S. Radic, "400 ns continuously tunable delay of 10 Gbps intensity modulated optical signal," Photon. Technol. Lett. 21, 251-253 (2009). [CrossRef]
  19. M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, "Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides," Opt. Express 15, 12,949-12,958 (2007). [CrossRef]
  20. S. Namiki, "Wide-band and -range tunable dispersion compensation through parametric wavelength conversion and dispersion optical fibers," J. Lightwave Technol. 26, 28-35 (2008). [CrossRef]
  21. A. Yariv, D. Fekete, and D. M. Pepper, "Compensation for channel dispersion by nonlinear optical phase conjugation," Opt. Lett. 4, 52-54 (1979). [CrossRef] [PubMed]
  22. S. Ayotte, S. Xu, H. Rong, O. Cohen, and M. J. Paniccia, "Dispersion compensation by optical phase conjugation in silicon waveguide," Electron. Lett. 43, 1037-1039 (2007). [CrossRef]
  23. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, Boston, 1989).
  24. B. G. Lee, A. Biberman, M. A. Foster, A. C. Turner, M. Lipson, A. L. Gaeta, and K. Bergman, "Bit-error-rate characterization of Silicon four-wave-mixing wavelength converters at 10 and 40 Gb/s," CLEO 2008, paper CPDB4.

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