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Multilevel quantization of optical phase in a novel coherent parametric mixer architecture


The exponentially increasing capacity demand in information systems will be met by carefully exploiting the complementary strengths of electronics and optics1,2. Optical signal processing provides simple but powerful pipeline functions that offer high speed, low power, low latency and a route to densely parallel execution3. A number of functions such as modulation and sampling4,5,6,7, complex filtering8 and Fourier transformation9 have already been demonstrated. However, the key functionality of all-optical quantization has still not been addressed effectively. Here, we report an all-optical signal processing architecture that enables, for the first time, multilevel all-optical quantization of phase-encoded optical signals. A four-wave-mixing process is used to generate a comb of phase harmonics of the input signal, and a two-pump parametric process to coherently combine a selected harmonic with the input signal, realizing phase quantization. We experimentally demonstrate operation up to six levels.

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Figure 1: Staircase quantization.
Figure 2: Illustration of how the M-level staircase transfer function necessary for phase quantization is achieved.
Figure 3: Experimental set-up.
Figure 4: Signal constellation diagrams.
Figure 5: Constellation data when the quantizer is operated as a multilevel phase regenerator with a noisy input signal.


  1. Caulfield, H. J. & Dolev, S. Why future supercomputing requires optics. Nature Photon. 4, 261–263 (2010).

    Article  Google Scholar 

  2. Miller, D. Device requirements for optical interconnects to silicon chips. Proc. IEEE 97, 1166–1185 (2009).

    Article  Google Scholar 

  3. Miller, D. A. B. Are optical transistors the logical next step? Nature Photon. 4, 3–5 (2010).

    Article  ADS  Google Scholar 

  4. Offside, M. J., Carroll, J. E., Bray, M. E. & Hadjifotiou, A. Optical wavelength converters. Electron. Commun. Eng. 7, 59–71 (1995).

    Article  Google Scholar 

  5. Koos, C. et al. All-optical high-speed signal processing with silicon–organic hybrid slot waveguides. Nature Photon. 3, 216–219 (2009).

    Article  ADS  Google Scholar 

  6. Hochberg, M. et al. Terahertz all-optical modulation in a silicon–polymer hybrid system. Nature Mater. 5, 703–709 (2006).

    Article  ADS  Google Scholar 

  7. Skold, M., Westlund, M., Sunnerud, H. & Andrekson, P. A. All-optical waveform sampling in high-speed optical communication systems using advanced modulation formats. J. Lightwave Technol. 27, 3662–3671 (2009).

    Article  ADS  Google Scholar 

  8. Azana, J. Ultrafast analog all-optical signal processors based on fiber-grating devices. IEEE Photon. J. 2, 359–386 (2010).

    Article  ADS  Google Scholar 

  9. Hillerkuss, D. et al. 26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing. Nature Photon. 5, 364–371 (2011).

    Article  ADS  Google Scholar 

  10. Liao, L. et al. High-speed graphene transistors with a self-aligned nanowire gate Nature 467, 305–308 (2010).

    Article  ADS  Google Scholar 

  11. Levenson, J. A., Abram, I., Rivera, T. & Grangier, P. Reduction of quantum noise in optical parametric amplification. J. Opt. Soc. Am. B 10, 2233–2238 (1993).

    Article  ADS  Google Scholar 

  12. Slavik, R. et al. All-optical phase and amplitude regenerator for next-generation telecommunications systems. Nature Photon. 4, 690–695 (2010).

    Article  ADS  Google Scholar 

  13. Valley, G. C. Photonic analog-to-digital converters. Opt. Express 15, 1955–1982 (2007).

    Article  ADS  Google Scholar 

  14. Capmany, J. & Novak, D. Microwave photonics combines two worlds. Nature Photon. 1, 319–330 (2007).

    Article  ADS  Google Scholar 

  15. Mamyshev, P. V. All-optical data regeneration based on self-phase modulation effect, in Proceedings of the 24th European Conference on Optical Communications (ECOC 1998) Vol. 471, 475–476 (1998).

  16. Armstrong, J. A., Bloembergen, N., Ducuing, J. & Pershan, P. S. Interactions between light waves in a nonlinear dielectric. Phys. Rev. 127, 1918–1939 (1962).

    Article  ADS  Google Scholar 

  17. Agrawal, G. Nonlinear Fiber Optics (Academic Press, 2001).

  18. Doran, N. J. & Wood, D. Nonlinear-optical loop mirror. Opt. Lett. 13, 56–58 (1988).

    Article  ADS  Google Scholar 

  19. Gordon, J. P. & Mollenauer, L. F. Phase noise in photonic communications systems using linear amplifiers. Opt. Lett. 15, 1351–1353 (1990).

    Article  ADS  Google Scholar 

  20. Croussore, K., Kim, I., Kim, C., Han, Y. & Li, G. F. Phase-and-amplitude regeneration of differential phase-shift keyed signals using a phase-sensitive amplifier. Opt. Express 14, 2085–2094 (2006).

    Article  ADS  Google Scholar 

  21. Croussore, K. & Li, G. F. Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification. IEEE Photon. Technol. Lett. 19, 864–866 (2007).

    Article  ADS  Google Scholar 

  22. Walden, R. H. Analog-to-digital converter survey and analysis. IEEE J. Sel. Areas Commun. 17, 539–550 (1999).

    Article  Google Scholar 

  23. Kakande, J. et al. First demonstration of all-optical QPSK signal regeneration in a novel multi-format phase sensitive amplifier, in Proceedings of the 36th European Conference on Optical Communications (ECOC 2010) PD 3.3 (2010).

  24. Fukushima, S., Silva, C. F. C., Muramoto, Y. & Seeds, A. J. Optoelectronic millimeter-wave synthesis using an optical frequency comb generator, optically injection locked lasers, and a unitraveling-carrier photodiode. J. Lightwave Technol. 21, 3043–3051 (2003).

    Article  ADS  Google Scholar 

  25. Gough, O. P., Silva, C. F. C., Bennett, S. & Seeds, A. J. Zero frequency error DWDM channel synthesis using optical injection-locked comb line selection. Electron. Lett. 35, 2050–2052 (1999).

    Article  Google Scholar 

  26. Grüner-Nielsen, L. et al. Silica-based highly nonlinear fibers with a high SBS threshold, in Proceedings of the IEEE Photonics Society 2011 Winter Topical meeting, Paper MD4.2 (IEEE, 2011).

  27. Salem, R. et al. Signal regeneration using low-power four-wave mixing on silicon chip. Nature Photon. 2, 35–38 (2008).

    Article  ADS  Google Scholar 

  28. Pelusi, M. D. et al. Applications of highly-nonlinear chalcogenide glass devices tailored for high-speed all-optical signal processing. IEEE J. Sel. Topics Quantum Electron. 14, 529–539 (2008).

    Article  ADS  Google Scholar 

  29. Levy, J. S. et al. CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects. Nature Photon. 4, 37–40 (2010).

    Article  ADS  Google Scholar 

  30. Kikuchi, K. Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation. IEEE J. Sel. Topics Quantum Electron. 12, 563–570 (2006).

    Article  ADS  Google Scholar 

  31. Fragkos, A. et al. Amplitude regeneration of phase encoded signals using injection locking in semiconductor lasers, in Proceedings of the Optical Fiber Communication Conference (OFC/NFOEC 2011), paper OWG1 (2011).

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This research received funding from the European Communities Seventh Framework Programme FP/2007-2013 (grant agreements 224547 (PHASORS) and 216863 (BONE)). The authors thank P. Horak and P. Smith for useful discussions. This work was supported in part by the EPSRC grant EP/I01196X.

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Authors and Affiliations



J.K. devised the concept and carried out the experiment and data analysis. R.S. provided support during all stages. L.G.N. supplied the HNFs. R.P. supplied the semiconductor slave laser. A.B. and D.S. contributed to theoretical and numerical analysis. F.P. and P.P. co-supervised the work. D.J.R. provided overall technical leadership and supervision.

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Correspondence to Joseph Kakande.

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Kakande, J., Slavík, R., Parmigiani, F. et al. Multilevel quantization of optical phase in a novel coherent parametric mixer architecture. Nature Photon 5, 748–752 (2011).

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