## Three-input optical addition and subtraction of quaternary base numbers |

Optics Express, Vol. 21, Issue 1, pp. 488-499 (2013)

http://dx.doi.org/10.1364/OE.21.000488

Acrobat PDF (2828 KB)

### Abstract

We present an approach to implementing three-input addition and subtraction of quaternary base numbers in the optical domain using multiple non-degenerate four-wave mixing (FWM) processes in a single highly nonlinear fiber (HNLF) and differential quadrature phase-shift keying (DQPSK) signals. By employing 100-Gbit/s three-input return-to-zero DQPSK (RZ-DQPSK) signals (A, B, C), we demonstrate 50-Gbaud/s three-input quaternary hybrid addition and subtraction (A + B-C, A + C-B, B + C-A). Moreover, by adding a conversion stage from C to –C via conjugated degenerate FWM, we also demonstrate 50-Gbaud/s three-input quaternary addition (A + B + C). The power penalties of three-input quaternary addition and subtraction (A + B-C, A + C-B, B + C-A, A + B + C) are measured to be less than 6 dB at a bit-error rate (BER) of 10^{−9}. In addition, no significant degradations are observed for RZ-DQPSK signals (A, B, C or –C) after the operations of quaternary addition and subtraction.

© 2013 OSA

## 1. Introduction

1. D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science **286**(5444), 1523–1528 (1999). [CrossRef] [PubMed]

2. C. Porzi, M. Scaffardi, L. Potì, and A. Bogoni, “Optical digital signal processing in a single SOA without assist probe light,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1469–1475 (2010). [CrossRef]

3. J. H. Kim, Y. M. Jhon, Y. T. Byun, S. Lee, D. H. Woo, and S. H. Kim, “All-optical XOR gate using semiconductor optical amplifiers without additional input beam,” IEEE Photon. Technol. Lett. **14**(10), 1436–1438 (2002). [CrossRef]

22. J. Wang, J.-Y. Yang, X. X. Wu, and A. E. Willner, “Optical hexadecimal coding/decoding using 16-QAM signal and FWM in HNLFs,” J. Lightwave Technol. **30**(17), 2890–2900 (2012). [CrossRef]

3. J. H. Kim, Y. M. Jhon, Y. T. Byun, S. Lee, D. H. Woo, and S. H. Kim, “All-optical XOR gate using semiconductor optical amplifiers without additional input beam,” IEEE Photon. Technol. Lett. **14**(10), 1436–1438 (2002). [CrossRef]

19. C. Husko, T. D. Vo, B. Corcoran, J. Li, T. F. Krauss, and B. J. Eggleton, “Ultracompact all-optical XOR logic gate in a slow-light silicon photonic crystal waveguide,” Opt. Express **19**(21), 20681–20690 (2011). [CrossRef] [PubMed]

3. J. H. Kim, Y. M. Jhon, Y. T. Byun, S. Lee, D. H. Woo, and S. H. Kim, “All-optical XOR gate using semiconductor optical amplifiers without additional input beam,” IEEE Photon. Technol. Lett. **14**(10), 1436–1438 (2002). [CrossRef]

5. N. Deng, K. Chan, C. K. Chan, and L. K. Chen, “An all-optical XOR logic gate for high-speed RZ-DPSK signals by FWMin semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. **12**(4), 702–707 (2006). [CrossRef]

6. C. Yu, L. Christen, T. Luo, Y. Wang, Z. Pan, L. S. Yan, and A. E. Willner, “All-optical XOR gate using polarization rotation in single highly nonlinear fiber,” IEEE Photon. Technol. Lett. **17**(6), 1232–1234 (2005). [CrossRef]

9. J. F. Qiu, K. Sun, M. Rochette, and L. R. Chen, “Reconfigurable all-optical multilogic gate (XOR, AND, and OR) based on cross-phase modulation in a highly nonlinear fiber,” IEEE Photon. Technol. Lett. **22**(16), 1199–1201 (2010). [CrossRef]

10. S. Kumar, A. E. Willner, D. Gurkan, K. R. Parameswaran, and M. M. Fejer, “All-optical half adder using an SOA and a PPLN waveguide for signal processing in optical networks,” Opt. Express **14**(22), 10255–10260 (2006). [CrossRef] [PubMed]

15. A. Bogoni, X. Wu, Z. Bakhtiari, S. Nuccio, and A. E. Willner, “640 Gbits/s photonic logic gates,” Opt. Lett. **35**(23), 3955–3957 (2010). [CrossRef] [PubMed]

_{2}S

_{3}) waveguides [16

16. T. D. Vo, R. Pant, M. D. Pelusi, J. Schröder, D.-Y. Choi, S. K. Debbarma, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic chip-based all-optical XOR gate for 40 and 160 Gbit/s DPSK signals,” Opt. Lett. **36**(5), 710–712 (2011). [CrossRef] [PubMed]

17. F. Li, T. D. Vo, C. Husko, M. Pelusi, D.-X. Xu, A. Densmore, R. Ma, S. Janz, B. J. Eggleton, and D. J. Moss, “All-optical XOR logic gate for 40Gb/s DPSK signals via FWM in a silicon nanowire,” Opt. Express **19**(21), 20364–20371 (2011). [CrossRef] [PubMed]

18. Y. Q. Xie, Y. Gao, S. M. Gao, X. D. Mou, and S. L. He, “All-optical multiple-channel logic XOR gate for NRZ-DPSK signals based on nondegenerate four-wave mixing in a silicon waveguide,” Opt. Lett. **36**(21), 4260–4262 (2011). [CrossRef] [PubMed]

19. C. Husko, T. D. Vo, B. Corcoran, J. Li, T. F. Krauss, and B. J. Eggleton, “Ultracompact all-optical XOR logic gate in a slow-light silicon photonic crystal waveguide,” Opt. Express **19**(21), 20681–20690 (2011). [CrossRef] [PubMed]

33. J. Wang, J. Yang, H. Huang, and A. Willner, “All-optical 50-Gbaud/s three-input hybrid addition/subtraction of quaternary base numbers using multiple non-degenerate FWM processes and 100-Gbit/s DQPSK signals,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (online) (Optical Society of America, 2012), paper Tu.1.A.4.

^{−9}. Moreover, by exploiting an additional degenerate FWM process to obtain –C from C, we also demonstrate 50-Gbaud/s three-input quaternary addition of A + B + C using A, B and –C as three inputs. The power penalty is measured to be less than 6 dB at a BER of 10

^{−9}. Additionally, negligible power penalties are observed for three DQPSK signals after addition and subtraction operations.

## 2. Concept and working principle

## 3. Experimental setup

^{7}-1 RZ-DQPSK signals (A, B, C). The duty cycle of RZ-DQPSK is 50%. After undergoing relative delay, three 100-Gbit/s 2

^{7}-1 RZ-DQPSK signals (A, B, C) are fed into a 460-m piece of HNLF which has a nonlinear coefficient (γ) of 20 W

^{−1}·km

^{−1}, a zero-dispersion wavelength (ZDW) of ~1556 nm, and a dispersion slope (S) of ~0.026 ps/nm

^{2}/km. Note that the low and flat dispersion of HNLF enables multiple non-degenerate FWM processes. Consequently, three converted idlers (idler 1, idler 2, idler 3) are simultaneously generated carrying three quaternary hybrid addition and subtraction results of A + B-C, A + C-B and B + C-A, respectively.

## 4. Experimental results and discussions

^{−9}. Figure 7 plots BER curves for 50-Gbaud/s conversion from C to –C and three-input quaternary addition of A + B + C. Negligible power penalty is observed for the conversion from C to –C. The power penalty of quaternary addition of A + B + C is measured to be less than 6 dB at a BER of 10

^{−9}. Remarkably, according to the electrical field and optical phase relationships in Eqs. (1)-(3), we believe that the degradations of quaternary addition and subtraction (A + B-C, A + C-B, B + C-A, A + B + C) are mainly induced by accumulated distortions from three-input signals (A, B, C or –C). In addition, the presence of unwanted FWM components shown in the spectrum and the relative polarization rotation among different signals might also influence the overall operation performance. Figure 6(c)(d) and Fig. 7(a)(b) also show measured BER curves for three signals (A, B, C or –C) after quaternary addition and subtraction (i.e., after HNLF) operations. It can be clearly seen that no significant degradations are observed for the three signals during the operations of quaternary addition and subtraction.

_{2}S

_{3}waveguides, and silicon waveguides.

## 5. Conclusion

^{−9}. Negligible power penalties are observed for RZ-DQPSK signals after the operations of quaternary addition and subtraction. The proposed approach might be further extended in three-input addition and subtraction of even higher base numbers, more complicated arithmetic functions, and other platforms.

## Acknowledgments

## References and links

1. | D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science |

2. | C. Porzi, M. Scaffardi, L. Potì, and A. Bogoni, “Optical digital signal processing in a single SOA without assist probe light,” IEEE J. Sel. Top. Quantum Electron. |

3. | J. H. Kim, Y. M. Jhon, Y. T. Byun, S. Lee, D. H. Woo, and S. H. Kim, “All-optical XOR gate using semiconductor optical amplifiers without additional input beam,” IEEE Photon. Technol. Lett. |

4. | I. Kang, C. Dorrer, and J. Leuthold, “All-optical XOR operation of 40 Gbit/s phase-shift-keyed data using four-wave mixing in semiconductor optical amplifier,” Electron. Lett. |

5. | N. Deng, K. Chan, C. K. Chan, and L. K. Chen, “An all-optical XOR logic gate for high-speed RZ-DPSK signals by FWMin semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. |

6. | C. Yu, L. Christen, T. Luo, Y. Wang, Z. Pan, L. S. Yan, and A. E. Willner, “All-optical XOR gate using polarization rotation in single highly nonlinear fiber,” IEEE Photon. Technol. Lett. |

7. | J. Wang, Q. Sun, J. Sun, and X. Zhang, “Experimental demonstration on 40 Gbit/s all-optical multicasting logic XOR gate for NRZDPSK signals using four-wave mixing in highly nonlinear fiber,” Opt. Commun. |

8. | J. Wang, Q. Z. Sun, and J. Q. Sun, “All-optical 40 Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing,” Opt. Express |

9. | J. F. Qiu, K. Sun, M. Rochette, and L. R. Chen, “Reconfigurable all-optical multilogic gate (XOR, AND, and OR) based on cross-phase modulation in a highly nonlinear fiber,” IEEE Photon. Technol. Lett. |

10. | S. Kumar, A. E. Willner, D. Gurkan, K. R. Parameswaran, and M. M. Fejer, “All-optical half adder using an SOA and a PPLN waveguide for signal processing in optical networks,” Opt. Express |

11. | J. Wang, J. Q. Sun, and Q. Z. Sun, “Single-PPLN-based simultaneous half-adder, half-subtracter, and OR logic gate: proposal and simulation,” Opt. Express |

12. | J. Wang, J. Sun, Q. Sun, D. Wang, M. Zhou, X. Zhang, D. Huang, and M. M. Fejer, “Dual-channel-output all-optical logic AND gate at 20 Gbit/s based on cascaded second-order nonlinearity in PPLN waveguide,” Electron. Lett. |

13. | J. Wang, J. Q. Sun, X. L. Zhang, D. X. Huang, and M. M. Fejer, “Ultrafast all-optical three-input boolean XOR operation for differential phase-shift keying signals using periodically poled lithium niobate,” Opt. Lett. |

14. | J. Wang, Q. Z. Sun, and J. Q. Sun, “Ultrafast all-optical logic AND gate for CSRZ signals using periodically poled lithium niobate,” J. Opt. Soc. Am. B |

15. | A. Bogoni, X. Wu, Z. Bakhtiari, S. Nuccio, and A. E. Willner, “640 Gbits/s photonic logic gates,” Opt. Lett. |

16. | T. D. Vo, R. Pant, M. D. Pelusi, J. Schröder, D.-Y. Choi, S. K. Debbarma, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic chip-based all-optical XOR gate for 40 and 160 Gbit/s DPSK signals,” Opt. Lett. |

17. | F. Li, T. D. Vo, C. Husko, M. Pelusi, D.-X. Xu, A. Densmore, R. Ma, S. Janz, B. J. Eggleton, and D. J. Moss, “All-optical XOR logic gate for 40Gb/s DPSK signals via FWM in a silicon nanowire,” Opt. Express |

18. | Y. Q. Xie, Y. Gao, S. M. Gao, X. D. Mou, and S. L. He, “All-optical multiple-channel logic XOR gate for NRZ-DPSK signals based on nondegenerate four-wave mixing in a silicon waveguide,” Opt. Lett. |

19. | C. Husko, T. D. Vo, B. Corcoran, J. Li, T. F. Krauss, and B. J. Eggleton, “Ultracompact all-optical XOR logic gate in a slow-light silicon photonic crystal waveguide,” Opt. Express |

20. | C. Porzi, A. Bogoni, and G. Contestabile, “Regeneration of DPSK signals in a saturated SOA,” IEEE Photon. Technol. Lett. |

21. | Y. J. Jung, C. W. Son, S. Lee, S. Gil, H. S. Kim, and N. Park, “Demonstration of 10 Gbps, all-optical encryption and decryption system utilizing SOA XOR logic gates,” Opt. Quantum Electron. |

22. | J. Wang, J.-Y. Yang, X. X. Wu, and A. E. Willner, “Optical hexadecimal coding/decoding using 16-QAM signal and FWM in HNLFs,” J. Lightwave Technol. |

23. | X. Zhou and J. Yu, “Multi-level, multi-dimensional coding for high-speed and high spectral-efficiency optical transmission,” J. Lightwave Technol. |

24. | P. J. Winzer, G. Raybon, H. Song, A. Adamiecki, S. Corteselli, A. H. Gnauck, D. A. Fishman, C. R. Doerr, S. Chandrasekhar, L. L. Buhl, T. J. Xia, G. Wellbrock, W. Lee, B. Basch, T. Kawanishi, K. Higuma, and Y. Painchaud, “100-Gb/s DQPSK transmission: from laboratory experiments to field trials,” J. Lightwave Technol. |

25. | P. Guan, T. Hirano, K. Harako, Y. Tomiyama, T. Hirooka, and M. Nakazawa, “2.56 Tbit/s/ch polarization-multiplexed DQPSK transmission over 300 km using time-domain optical Fourier transformation,” Opt. Express |

26. | J. Wang, S. R. Nuccio, H. Huang, X. Wang, J.-Y. Yang, and A. E. Willner, “Optical data exchange of 100-Gbit/s DQPSK signals,” Opt. Express |

27. | J. Wang, H. Huang, X. Wang, J.-Y. Yang, and A. E. Willner, “Multi-channel 100-Gbit/s DQPSK data exchange using bidirectional degenerate four-wave mixing,” Opt. Express |

28. | J. Wang, H. Huang, X. Wang, J.-Y. Yang, and A. E. Willner, “Reconfigurable 2.3-Tbit/s DQPSK simultaneous add/drop, data exchange and equalization using double-pass LCoS and bidirectional HNLF,” Opt. Express |

29. | A. Malacarne, E. Lazzeri, V. Vercesi, M. Scaffardi, and A. Bogoni, “Colorless all-optical sum and subtraction of phases for phase-shift keying signals based on a periodically poled lithium niobate waveguide,” Opt. Lett. |

30. | E. Lazzeri, A. Malacarne, G. Serafino, and A. Bogoni, “Optical XOR for error detection and coding of QPSK I and Q components in PPLN waveguide,” IEEE Photon. Technol. Lett. |

31. | J. Wang, S. R. Nuccio, J.-Y. Yang, X. X. Wu, A. Bogoni, and A. E. Willner, “High-speed addition/subtraction/complement/doubling of quaternary numbers using optical nonlinearities and DQPSK signals,” Opt. Lett. |

32. | J. Wang, J. Yang, X. Wu, O. F. Yilmaz, S. R. Nuccio, and A. E. Willner, “40-Gbaud/s (120-Gbit/s) octal and 10-Gbaud/s (40-Gbit/s) hexadecimal simultaneous addition and subtraction using 8PSK/16PSK and highly nonlinear fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThC3. |

33. | J. Wang, J. Yang, H. Huang, and A. Willner, “All-optical 50-Gbaud/s three-input hybrid addition/subtraction of quaternary base numbers using multiple non-degenerate FWM processes and 100-Gbit/s DQPSK signals,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (online) (Optical Society of America, 2012), paper Tu.1.A.4. |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(070.4560) Fourier optics and signal processing : Data processing by optical means

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(200.3760) Optics in computing : Logic-based optical processing

**ToC Category:**

Subsystems for Optical Networks

**History**

Original Manuscript: October 22, 2012

Revised Manuscript: November 19, 2012

Manuscript Accepted: November 19, 2012

Published: January 7, 2013

**Virtual Issues**

European Conference on Optical Communication 2012 (2012) *Optics Express*

**Citation**

Jian Wang, Jeng-Yuan Yang, Hao Huang, and Alan E. Willner, "Three-input optical addition and subtraction of quaternary base numbers," Opt. Express **21**, 488-499 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-488

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### References

- D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science286(5444), 1523–1528 (1999). [CrossRef] [PubMed]
- C. Porzi, M. Scaffardi, L. Potì, and A. Bogoni, “Optical digital signal processing in a single SOA without assist probe light,” IEEE J. Sel. Top. Quantum Electron.16(5), 1469–1475 (2010). [CrossRef]
- J. H. Kim, Y. M. Jhon, Y. T. Byun, S. Lee, D. H. Woo, and S. H. Kim, “All-optical XOR gate using semiconductor optical amplifiers without additional input beam,” IEEE Photon. Technol. Lett.14(10), 1436–1438 (2002). [CrossRef]
- I. Kang, C. Dorrer, and J. Leuthold, “All-optical XOR operation of 40 Gbit/s phase-shift-keyed data using four-wave mixing in semiconductor optical amplifier,” Electron. Lett.40(8), 496–498 (2004). [CrossRef]
- N. Deng, K. Chan, C. K. Chan, and L. K. Chen, “An all-optical XOR logic gate for high-speed RZ-DPSK signals by FWMin semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron.12(4), 702–707 (2006). [CrossRef]
- C. Yu, L. Christen, T. Luo, Y. Wang, Z. Pan, L. S. Yan, and A. E. Willner, “All-optical XOR gate using polarization rotation in single highly nonlinear fiber,” IEEE Photon. Technol. Lett.17(6), 1232–1234 (2005). [CrossRef]
- J. Wang, Q. Sun, J. Sun, and X. Zhang, “Experimental demonstration on 40 Gbit/s all-optical multicasting logic XOR gate for NRZDPSK signals using four-wave mixing in highly nonlinear fiber,” Opt. Commun.282(13), 2615–2619 (2009). [CrossRef]
- J. Wang, Q. Z. Sun, and J. Q. Sun, “All-optical 40 Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing,” Opt. Express17(15), 12555–12563 (2009). [CrossRef] [PubMed]
- J. F. Qiu, K. Sun, M. Rochette, and L. R. Chen, “Reconfigurable all-optical multilogic gate (XOR, AND, and OR) based on cross-phase modulation in a highly nonlinear fiber,” IEEE Photon. Technol. Lett.22(16), 1199–1201 (2010). [CrossRef]
- S. Kumar, A. E. Willner, D. Gurkan, K. R. Parameswaran, and M. M. Fejer, “All-optical half adder using an SOA and a PPLN waveguide for signal processing in optical networks,” Opt. Express14(22), 10255–10260 (2006). [CrossRef] [PubMed]
- J. Wang, J. Q. Sun, and Q. Z. Sun, “Single-PPLN-based simultaneous half-adder, half-subtracter, and OR logic gate: proposal and simulation,” Opt. Express15(4), 1690–1699 (2007). [CrossRef] [PubMed]
- J. Wang, J. Sun, Q. Sun, D. Wang, M. Zhou, X. Zhang, D. Huang, and M. M. Fejer, “Dual-channel-output all-optical logic AND gate at 20 Gbit/s based on cascaded second-order nonlinearity in PPLN waveguide,” Electron. Lett.43(17), 940–941 (2007). [CrossRef]
- J. Wang, J. Q. Sun, X. L. Zhang, D. X. Huang, and M. M. Fejer, “Ultrafast all-optical three-input boolean XOR operation for differential phase-shift keying signals using periodically poled lithium niobate,” Opt. Lett.33(13), 1419–1421 (2008). [CrossRef] [PubMed]
- J. Wang, Q. Z. Sun, and J. Q. Sun, “Ultrafast all-optical logic AND gate for CSRZ signals using periodically poled lithium niobate,” J. Opt. Soc. Am. B26(5), 951–958 (2009). [CrossRef]
- A. Bogoni, X. Wu, Z. Bakhtiari, S. Nuccio, and A. E. Willner, “640 Gbits/s photonic logic gates,” Opt. Lett.35(23), 3955–3957 (2010). [CrossRef] [PubMed]
- T. D. Vo, R. Pant, M. D. Pelusi, J. Schröder, D.-Y. Choi, S. K. Debbarma, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic chip-based all-optical XOR gate for 40 and 160 Gbit/s DPSK signals,” Opt. Lett.36(5), 710–712 (2011). [CrossRef] [PubMed]
- F. Li, T. D. Vo, C. Husko, M. Pelusi, D.-X. Xu, A. Densmore, R. Ma, S. Janz, B. J. Eggleton, and D. J. Moss, “All-optical XOR logic gate for 40Gb/s DPSK signals via FWM in a silicon nanowire,” Opt. Express19(21), 20364–20371 (2011). [CrossRef] [PubMed]
- Y. Q. Xie, Y. Gao, S. M. Gao, X. D. Mou, and S. L. He, “All-optical multiple-channel logic XOR gate for NRZ-DPSK signals based on nondegenerate four-wave mixing in a silicon waveguide,” Opt. Lett.36(21), 4260–4262 (2011). [CrossRef] [PubMed]
- C. Husko, T. D. Vo, B. Corcoran, J. Li, T. F. Krauss, and B. J. Eggleton, “Ultracompact all-optical XOR logic gate in a slow-light silicon photonic crystal waveguide,” Opt. Express19(21), 20681–20690 (2011). [CrossRef] [PubMed]
- C. Porzi, A. Bogoni, and G. Contestabile, “Regeneration of DPSK signals in a saturated SOA,” IEEE Photon. Technol. Lett.24(18), 1597–1599 (2012). [CrossRef]
- Y. J. Jung, C. W. Son, S. Lee, S. Gil, H. S. Kim, and N. Park, “Demonstration of 10 Gbps, all-optical encryption and decryption system utilizing SOA XOR logic gates,” Opt. Quantum Electron.40(5-6), 425–430 (2008). [CrossRef]
- J. Wang, J.-Y. Yang, X. X. Wu, and A. E. Willner, “Optical hexadecimal coding/decoding using 16-QAM signal and FWM in HNLFs,” J. Lightwave Technol.30(17), 2890–2900 (2012). [CrossRef]
- X. Zhou and J. Yu, “Multi-level, multi-dimensional coding for high-speed and high spectral-efficiency optical transmission,” J. Lightwave Technol.27(16), 3641–3653 (2009). [CrossRef]
- P. J. Winzer, G. Raybon, H. Song, A. Adamiecki, S. Corteselli, A. H. Gnauck, D. A. Fishman, C. R. Doerr, S. Chandrasekhar, L. L. Buhl, T. J. Xia, G. Wellbrock, W. Lee, B. Basch, T. Kawanishi, K. Higuma, and Y. Painchaud, “100-Gb/s DQPSK transmission: from laboratory experiments to field trials,” J. Lightwave Technol.26(20), 3388–3402 (2008). [CrossRef]
- P. Guan, T. Hirano, K. Harako, Y. Tomiyama, T. Hirooka, and M. Nakazawa, “2.56 Tbit/s/ch polarization-multiplexed DQPSK transmission over 300 km using time-domain optical Fourier transformation,” Opt. Express19(26), B567–B573 (2011). [CrossRef] [PubMed]
- J. Wang, S. R. Nuccio, H. Huang, X. Wang, J.-Y. Yang, and A. E. Willner, “Optical data exchange of 100-Gbit/s DQPSK signals,” Opt. Express18(23), 23740–23745 (2010). [CrossRef] [PubMed]
- J. Wang, H. Huang, X. Wang, J.-Y. Yang, and A. E. Willner, “Multi-channel 100-Gbit/s DQPSK data exchange using bidirectional degenerate four-wave mixing,” Opt. Express19(4), 3332–3338 (2011). [CrossRef] [PubMed]
- J. Wang, H. Huang, X. Wang, J.-Y. Yang, and A. E. Willner, “Reconfigurable 2.3-Tbit/s DQPSK simultaneous add/drop, data exchange and equalization using double-pass LCoS and bidirectional HNLF,” Opt. Express19(19), 18246–18252 (2011). [CrossRef] [PubMed]
- A. Malacarne, E. Lazzeri, V. Vercesi, M. Scaffardi, and A. Bogoni, “Colorless all-optical sum and subtraction of phases for phase-shift keying signals based on a periodically poled lithium niobate waveguide,” Opt. Lett.37(18), 3831–3833 (2012). [PubMed]
- E. Lazzeri, A. Malacarne, G. Serafino, and A. Bogoni, “Optical XOR for error detection and coding of QPSK I and Q components in PPLN waveguide,” IEEE Photon. Technol. Lett.24(24), 2258–2261 (2012), doi:. [CrossRef]
- J. Wang, S. R. Nuccio, J.-Y. Yang, X. X. Wu, A. Bogoni, and A. E. Willner, “High-speed addition/subtraction/complement/doubling of quaternary numbers using optical nonlinearities and DQPSK signals,” Opt. Lett.37(7), 1139–1141 (2012). [CrossRef] [PubMed]
- J. Wang, J. Yang, X. Wu, O. F. Yilmaz, S. R. Nuccio, and A. E. Willner, “40-Gbaud/s (120-Gbit/s) octal and 10-Gbaud/s (40-Gbit/s) hexadecimal simultaneous addition and subtraction using 8PSK/16PSK and highly nonlinear fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThC3.
- J. Wang, J. Yang, H. Huang, and A. Willner, “All-optical 50-Gbaud/s three-input hybrid addition/subtraction of quaternary base numbers using multiple non-degenerate FWM processes and 100-Gbit/s DQPSK signals,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (online) (Optical Society of America, 2012), paper Tu.1.A.4.

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