Abstract

Optical signal processing is considered to be a promising technique to overcome the speed limitation of electronics and accelerate next-generation high-speed optical networks. Among various optical signal processing operations, optical arithmetic functions have attracted increasing interest. Here, by exploiting the degenerate four-wave mixing progress in graphene and adopting (differential) quadrature phase-shift keying signals, we experimentally demonstrate 10 Gbaud two-input (A, B) hybrid quaternary arithmetic functions of doubling and subtraction (2A-B, 2B-A) in the optical domain. The measured optical signal-to-noise ratio penalties at a bit-error rate of 2 × 10−3 are about 7.4 dB for 2A-B and 7 dB for 2B-A.

© 2015 Optical Society of America

1. Introduction

Optical signal processing is regarded as an important technique for next-generation high-speed optical networks [1–3 ]. As the response speed of the current electronic processing systems reaches limits, achieving high-speed arithmetic functions in the optical domain are attracting increasing attention. Optical nonlinearities are potentially well suited to perform optical signal processing, such as various logic gates (NOT, AND, OR, XOR, NAND, NOR, XNOR), switching, (de)multiplexing, and coding/decoding [4–8 ]. Previously, optical logic gates of binary numbers were reported in various platforms for on-off keying (OOK) and phase-shift keying (PSK) formats, including the use of cross-gain modulation (XGM) [9] or four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) [10], nonlinear polarization rotation, FWM or cross-phase modulation (XPM) in highly nonlinear fibers (HNLFs) [11–13 ], second-order nonlinearities and their cascading in periodically poled lithium niobate (PPLN) waveguides [14] and silicon waveguide [15].

Recently, optical nonlinearities has also been observed in graphene in various configurations, e.g. slow-light graphene-silicon photonic crystal waveguide [16], graphene optically deposited onto fiber ferrules [17], and graphene based on microfiber [18]. Very recently, an experimental observation of FWM based wavelength conversion of a 10 Gb/s non-return-to-zero (NRZ) signal was reported [19]. Graphene as a purely two-dimensional material with only one carbon atom thickness has received great interest since it features many interesting and useful electrical, optical, chemical and mechanical properties [20, 21 ]. Over the last decade, many remarkable optical properties of graphene have been discovered, such as self-luminosity, tunable optical absorption, strong nonlinearity, saturable absorption, etc [22–24 ]. The large absorption and Pauli blocking effect in graphene, together with the ultrafast carrier dynamics and strong optical nonlinearity with a fast response time, make graphene-based photonic devices suitable for performing efficient nonlinear functions.

With the increasing demand of higher transmission capacity and spectral efficiency, optical high-order modulation formats and coherent detection have seen wide applications in optical communication systems [25]. Beyond transmission, multi-level modulation formats with multiple constellation points in the complex plane can be used to represent high-base (quaternary, octal, hexadecimal) numbers [26–28 ]. For example, a (differential) quadrature phase-shift keying ((D)QPSK) signal with four constellation points (four phase levels) can denote a quaternary number. The related optical signal processing functions to multilevel modulation formats could be addition and subtraction of high base numbers [29]. In this scenario, a laudable goal would be to perform optical hybrid quaternary arithmetic functions by employing graphene for its strong optical nonlinearity.

In this paper, we propose an innovative scheme to achieve optical hybrid quaternary arithmetic functions in a graphene-assisted nonlinear optical device. Using degenerate FWM process and (D)QPSK signals, we experimentally demonstrate 10 Gbaud two-input (A, B) hybrid doubling and subtraction of quaternary base numbers (2A-B, 2B-A). The optical signal-to-noise ratio (OSNR) penalties at a bit-error rate (BER) of 2 × 10−3 are about 7.4 dB for 2A-B and 7 dB for 2B-A.

2. Fabrication of graphene-assisted nonlinear optical device

Figure 1 illustrates the fabrication process of the graphene-assisted nonlinear optical device. First, a monolayer graphene was grown on a Cu foil by the chemical vapor deposition (CVD) method [30]. Poly (methyl methacrylate) (PMMA) film was next spin coated on the surface of the graphene-deposited Cu foil and the Cu foil was etched away with 1 M FeCl3 solution. The resultant PMMA/graphene film (5 mm × 5 mm) was then washed in deionized water several times and transferred to deionized water solution or Si/SiO2 substrate. Then, the floating PMMA/graphene sheet was mechanically transferred onto the fiber pigtail cross-section and dried in a cabinet. After drying at room temperature for about 24 hours, the carbon atoms could be self-assembled onto the fiber end-facet. The PMMA layer was finally removed by boiling acetone. By connecting this graphene-on-fiber component with another clean and dry fiber connector, the nonlinear optical device was thereby constructed for nonlinear optical signal processing applications.

 figure: Fig. 1

Fig. 1 Fabrication process of the graphene-assisted nonlinear optical device.

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Figure 2(a) depicts the optical microscope (OM) image of the grown graphene film transferred on a 300 nm SiO2/Si substrate. Figure 2(b) shows a scanning electron microscopy (SEM) image of the graphene sheet transferred on silicon-on-insulator (SOI). One can clearly see the evidence of the uniformity of the graphene. The Raman spectrum of the graphene, as displayed in Fig. 2(c), shows a weak D peak and a strong 2D peak. The D to G peak intensity ratios is ~0.08, which indicates that the graphene formed on a SiO2/Si substrate was almost defect-free.

 figure: Fig. 2

Fig. 2 (a) Optical microscope (OM) image of graphene transferred on a SiO2/Si substrate. (b) Scanning electron microscope (SEM) image of graphene transferred on silicon-on-insulator (SOI). (c) Typical Raman spectrum of single-layer graphene on a SiO2/Si substrate (excitation wavelength: 532 nm).

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3. Concept and working principle

Figure 3 illustrates the concept and principle of two-input hybrid quaternary arithmetic functions. From the constellation in the complex plane (Fig. 3(a)), it is clear that one can use four-phase levels (π/4, 3π/4, 5π/4,7π/4) of (D)QPSK to represent quaternary base numbers (0, 1, 2, 3). To implement two-input hybrid quaternary arithmetic functions, the aforementioned graphene-assisted nonlinear optical device is employed. Two-input quaternary numbers (A, B) are coupled into the nonlinear device, then two converted idlers (idler 1, idler 2) are simultaneously generated by two degenerate FWM processes. Figure 3(b) illustrates the degenerate FWM process. We derive the electrical field (Ε) and optical phase (ϕ) relationships of two degenerate FWM processes under the pump non-depletion approximation expressed as

Ei1EAEAEB*,ϕi1=ϕA+ϕAϕB
Ei2EBEBEA*,ϕi2=ϕB+ϕBϕA
where the subscripts A, B, i1, i2 denote input signal A, signal B, converted idler 1, idler 2, respectively. Owing to the phase wrap characteristic with a periodicity of 2π, it is implied from the linear phase relationships in Eqs. (1) and (2) that idler 1 and idler 2 carry out modulo 4 operations of hybrid quaternary arithmetic functions of doubling and subtraction (2A-B, 2B-A).

 figure: Fig. 3

Fig. 3 (a) Concept and (b) principle of hybrid quaternary arithmetic functions (2A-B, 2B-A) using degenerate FWM and (D)QPSK signals.

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4. Experimental setup

Figure 4 shows the experimental setup. Two continuous-wave (CW) lasers are sent to a (D)QPSK transmitter to produce two 215 NRZ-(D)QPSK signals (A, B). Then the (D)QPSK signals are amplified by an erbium-doped optical fiber amplifier (EDFA). A fiber bragg grating (FBG) thin film filter with a center wavelength of 1550.112 nm is employed to separate two signals A (transmission port) and B (reflection port). After undergoing relative integral symbols delay by tunable optical delay lines (ODLs), two 10 Gbaud 215 NRZ-(D)QPSK signals (A, B) are combined together and amplified using a high-power EDFA (HP-EDFA), and then launched into the single-layer graphene assisted nonlinear optical device. The polarization states of the two (D)QPSK signal are adjusted to achieve optimized conversion efficiency of degenerate FWM in graphene. Consequently, two converted idlers (idler 1, idler 2) are simultaneously generated carrying two hybrid quaternary arithmetic functions of 2A-B and 2B-A. At the receiver, two tunable filters together with an EDFA are used as receiving filter to select the converted idler. The real-time sampling oscilloscope (Tektronix DPO72004B) operating at 50 GS/s stores the electrical waveforms for processing offline. Both ECLs at the transmitter and local oscillator (LO) laser at the receiver have a linewidth of ~100 kHz.

 figure: Fig. 4

Fig. 4 Experimental setup for degenerate FWM-based 10-Gbaud optical hybrid quaternary arithmetic functions in a graphene-assisted nonlinear optical device. Inset: “sandwiched structure” graphene sample used as a nonlinear optical device. ECL: external cavity laser; AWG: arbitrary waveform generator; FBG: fiber Bragg grating; EDFA: erbium-doped fiber amplifier; ODL: optical delay line; TF: tunable filter; OC: optical coupler; HP-EDFA: high-power erbium-doped fiber amplifier; PC: polarization controller.

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5. Experimental results

Figure 5 depicts measured typical spectrum obtained after the CVD single-layer graphene coated fiber device. Two 10-Gbaud NRZ-(D)QPSK signals at 1550.10 (A) and 1553.60 nm (B) are employed as two inputs. The power of two input signals (A, B) is about 32 dBm. The conversion efficiency is measured to be around −36 dB. One can clearly see that two converted idlers are obtained by two degenerate FWM processes with idler 1 at 1546.60 nm (2A-B) and idler 2 at 1557.20 nm (2B-A). The resolution of the measured spectrum is set to 0.02 nm. The steps in the measured spectrum are actually the modulation sidebands of two NRZ-(D)QPSK carrying signals. In order to verify the hybrid quaternary arithmetic functions, we measure the phase of symbol sequence for two input signals and two converted idlers, as shown in Fig. 6 . By carefully comparing the quaternary base numbers for two input signals and two converted idlers, one can confirm the successful implementation of two-input hybrid quaternary arithmetic functions of 2A–B and 2B-A.

 figure: Fig. 5

Fig. 5 Measured spectrum for 10 Gbaud two-input hybrid quaternary arithmetic functions.

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 figure: Fig. 6

Fig. 6 Measured phase of symbol sequence with coherent detection for 10-Gbaud two-input hybrid quaternary arithmetic functions.

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We further investigate the BER performance for the proposed optical two-input hybrid quaternary arithmetic functions. The observed OSNR penalties at a BER of 2 × 10−3 for hybrid quaternary arithmetic functions are measured to be about 7.4 dB for 2A-B and 7.0 dB for 2B-A. The insets in Fig. 7(a) show constellations of the last point of the BER curves of output Sig. B and 2A-B. The constellation of Sig. B is measured under an OSNR of 12.6 dB, while the constellation of 2A-B is observed under an OSNR of 19.6 dB. To clearly show the differences between these two constellations, we also assess the error vector magnitude (EVM) of these two constellations, i.e. EVM = 27.61% for output Sig. B and EVM = 30.09% for output 2A-B. The significant performance degradations for the two-input hybrid quaternary arithmetic functions (2A-B, 2B-A) might be ascribed to the relatively low conversion efficiency for two converted idlers at 1546.60 nm and 1557.20 nm and accumulated distortions transferred from two-input signals (A, B). The main factors influencing the conversion efficiency can be briefly explained as follows. 1) In the experiment, only single-layer graphene is coated on the optical fiber pigtail cross-section. So the weak light–graphene interaction could decrease the conversion efficiency [31]. With future improvement, one might improve the conversion efficiency by mechanically transferring graphene sample onto the D-shaped fiber or microfiber to enhance the graphene-light interaction [18]. 2) The quality of graphene may also influence the conversion efficiency. Ideal graphene has unique dispersionless, broad band structure and strong third order nonlinearity [32]. However, practically fabricated graphene is not perfect and any imperfections during the fabrication of graphene can break the band structure and degrades third order nonlinearity. Thus the limited fabrication quality of the single-layer graphene employed in the experiment might also influence the conversion efficiency. 3) Previous work has demonstrated that the nonlinear response is also sensitive to the number of graphene layers [32]. It is expected that for a few graphene layers the nonlinearity increases in proportion to the number of layers. So it is possible to further enhance the conversion efficiency by appropriately increasing the number of graphene layers employed in the experiment. Figure 7(b) depicts the BER performance as a function of the relative time offset between two signals (signal offset) under an OSNR of ~20 dB. It is found that the BER is kept below enhanced forward error correction (EFEC) threshold when the signal offset/symbol time is within 15 ps, which indicates a favorable tolerance to the signal offset.

 figure: Fig. 7

Fig. 7 (a) Measured BER curves for two-input hybrid quaternary arithmetic functions of 2A-B and 2B-A; (b) BER versus signal offset.

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5. Conclusions

In this paper, we present an innovative scheme to achieve two-input hybrid quaternary arithmetic functions of doubling and subtraction using optical nonlinearities in graphene and (D)QPSK signals. By exploiting degenerate FWM in graphene, we experimentally demonstrate 10 Gbaud quaternary arithmetic functions of 2A-B and 2B-A. The power penalties of converted idlers at a BER of 2 × 10−3 are measured to be about 7.4 dB for 2A-B and 7.0 dB for 2B-A. With future improvement, graphene-assisted nonlinear optical devices might be employed to facilitate more optical signal processing applications.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (NSFC) under grants 61222502, 11274131 and 11574001, the National Basic Research Program of China (973 Program) under grant 2014CB340004, the Program for New Century Excellent Talents in University (NCET-11-0182), the Wuhan Science and Technology Plan Project under grant 2014070404010201, and the seed project of Wuhan National Laboratory for Optoelectronics (WNLO). The authors thank the engineer in the Center of Micro-Fabrication and Characterization (CMFC) of WNLO for the support in the fabrication of graphene-assisted nonlinear optical device and the facility support of the Center for Nanoscale Characterization and Devices of WNLO.

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 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. A. E. Willner, O. F. Yilmaz, J. Wang, X. X. Wu, A. Bogoni, L. Zhang, and S. R. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. 17(2), 320–332 (2011). [CrossRef]  

4. G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, and L. Potí, “Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate,” IEEE Photonics Technol. Lett. 18(8), 917–919 (2006). [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 FWM in semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 12(4), 702–707 (2006). [CrossRef]  

6. T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012). [CrossRef]  

7. Y. Xie, Y. Gao, S. Gao, X. Mou, and S. 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]  

8. 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]  

9. S. H. Kim, J. H. Kim, J. W. Choi, C. W. Son, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, “All-optical half adder using cross gain modulation in semiconductor optical amplifiers,” Opt. Express 14(22), 10693–10698 (2006). [CrossRef]   [PubMed]  

10. M. Matsuura and N. Kishi, “High-speed wavelength conversion of RZ-DPSK signal using FWM in a quantum-dot SOA,” IEEE Photonics Technol. Lett. 23(10), 615–617 (2011). [CrossRef]  

11. 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 Photonics Technol. Lett. 22(16), 1199–1201 (2010). [CrossRef]  

12. J. Wang, Q. Sun, J. Sun, and X. Zhang, “Experimental demonstration on 40 Gbit/s all-optical multicasting logic XOR gate for NRZ-DPSK signals using four-wave mixing in highly nonlinear fiber,” Opt. Commun. 282(13), 2615–2619 (2009). [CrossRef]  

13. J. Wang, Q. Sun, and J. Sun, “All-optical 40 Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing,” Opt. Express 17(15), 12555–12563 (2009). [CrossRef]   [PubMed]  

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 26(5), 951–958 (2009). [CrossRef]  

15. 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]  

16. H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. Zande, J. C. Hone, M. Yu, G.-Q. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Four-wave mixing in slow-light graphene-silicon photonic crystal waveguides,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2014), paper FF1K.8. [CrossRef]  

17. B. Xu, A. Martinez, K. Fuse, and S. Yamashita, “Generation of four wave mixing in graphene and carbon nanotubes optically deposited onto fiber ferrules,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CMAA6. [CrossRef]  

18. Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photonics Technol. Lett. 26(3), 249–252 (2014). [CrossRef]  

19. B. Xu, A. Martinez, and S. Yamashita, “Mechanically exfoliated graphene for four-wave-mixing-based wavelength conversion,” IEEE Photonics Technol. Lett. 24(20), 1792–1794 (2012). [CrossRef]  

20. S. Iijima and T. Ichihashi, “Single-shell carbon nanotubes of 1-nm diameter,” Nature 363(6430), 603–605 (1993). [CrossRef]  

21. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef]   [PubMed]  

22. D. Basko, “Applied physics. A photothermoelectric effect in graphene,” Science 334(6056), 610–611 (2011). [CrossRef]   [PubMed]  

23. L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett. 37(13), 2730–2732 (2012). [CrossRef]   [PubMed]  

24. Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010). [CrossRef]   [PubMed]  

25. M. Seimetz, High-Order Modulation for Optical Fiber Transmission (Springer, 2009).

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 18(23), 23740–23745 (2010). [CrossRef]   [PubMed]  

27. 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 19(19), 18246–18252 (2011). [CrossRef]   [PubMed]  

28. 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 Photonics Technol. Lett. 24(24), 2258–2261 (2012). [CrossRef]  

29. C. Gui and J. Wang, “Silicon-organic hybrid slot waveguide based three-input multicasted optical hexadecimal addition/subtraction,” Sci. Rep. 4, 7491 (2014). [CrossRef]   [PubMed]  

30. K. Yan, L. Fu, H. Peng, and Z. Liu, “Designed CVD growth of graphene via process engineering,” Acc. Chem. Res. 46(10), 2263–2274 (2013). [CrossRef]   [PubMed]  

31. X. Hu, M. Zeng, A. Wang, L. Zhu, L. Fu, and J. Wang, “Graphene-assisted nonlinear optical device for four-wave mixing based tunable wavelength conversion of QPSK signal,” Opt. Express 23(20), 26158–26167 (2015). [CrossRef]   [PubMed]  

32. E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010). [CrossRef]   [PubMed]  

References

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  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. A. E. Willner, O. F. Yilmaz, J. Wang, X. X. Wu, A. Bogoni, L. Zhang, and S. R. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. 17(2), 320–332 (2011).
    [Crossref]
  4. G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, and L. Potí, “Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate,” IEEE Photonics Technol. Lett. 18(8), 917–919 (2006).
    [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 FWM in semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 12(4), 702–707 (2006).
    [Crossref]
  6. T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
    [Crossref]
  7. Y. Xie, Y. Gao, S. Gao, X. Mou, and S. 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]
  8. 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]
  9. S. H. Kim, J. H. Kim, J. W. Choi, C. W. Son, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, “All-optical half adder using cross gain modulation in semiconductor optical amplifiers,” Opt. Express 14(22), 10693–10698 (2006).
    [Crossref] [PubMed]
  10. M. Matsuura and N. Kishi, “High-speed wavelength conversion of RZ-DPSK signal using FWM in a quantum-dot SOA,” IEEE Photonics Technol. Lett. 23(10), 615–617 (2011).
    [Crossref]
  11. 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 Photonics Technol. Lett. 22(16), 1199–1201 (2010).
    [Crossref]
  12. J. Wang, Q. Sun, J. Sun, and X. Zhang, “Experimental demonstration on 40 Gbit/s all-optical multicasting logic XOR gate for NRZ-DPSK signals using four-wave mixing in highly nonlinear fiber,” Opt. Commun. 282(13), 2615–2619 (2009).
    [Crossref]
  13. J. Wang, Q. Sun, and J. Sun, “All-optical 40 Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing,” Opt. Express 17(15), 12555–12563 (2009).
    [Crossref] [PubMed]
  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 26(5), 951–958 (2009).
    [Crossref]
  15. 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]
  16. H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. Zande, J. C. Hone, M. Yu, G.-Q. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Four-wave mixing in slow-light graphene-silicon photonic crystal waveguides,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2014), paper FF1K.8.
    [Crossref]
  17. B. Xu, A. Martinez, K. Fuse, and S. Yamashita, “Generation of four wave mixing in graphene and carbon nanotubes optically deposited onto fiber ferrules,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CMAA6.
    [Crossref]
  18. Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photonics Technol. Lett. 26(3), 249–252 (2014).
    [Crossref]
  19. B. Xu, A. Martinez, and S. Yamashita, “Mechanically exfoliated graphene for four-wave-mixing-based wavelength conversion,” IEEE Photonics Technol. Lett. 24(20), 1792–1794 (2012).
    [Crossref]
  20. S. Iijima and T. Ichihashi, “Single-shell carbon nanotubes of 1-nm diameter,” Nature 363(6430), 603–605 (1993).
    [Crossref]
  21. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
    [Crossref] [PubMed]
  22. D. Basko, “Applied physics. A photothermoelectric effect in graphene,” Science 334(6056), 610–611 (2011).
    [Crossref] [PubMed]
  23. L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett. 37(13), 2730–2732 (2012).
    [Crossref] [PubMed]
  24. Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
    [Crossref] [PubMed]
  25. M. Seimetz, High-Order Modulation for Optical Fiber Transmission (Springer, 2009).
  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 18(23), 23740–23745 (2010).
    [Crossref] [PubMed]
  27. 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 19(19), 18246–18252 (2011).
    [Crossref] [PubMed]
  28. 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 Photonics Technol. Lett. 24(24), 2258–2261 (2012).
    [Crossref]
  29. C. Gui and J. Wang, “Silicon-organic hybrid slot waveguide based three-input multicasted optical hexadecimal addition/subtraction,” Sci. Rep. 4, 7491 (2014).
    [Crossref] [PubMed]
  30. K. Yan, L. Fu, H. Peng, and Z. Liu, “Designed CVD growth of graphene via process engineering,” Acc. Chem. Res. 46(10), 2263–2274 (2013).
    [Crossref] [PubMed]
  31. X. Hu, M. Zeng, A. Wang, L. Zhu, L. Fu, and J. Wang, “Graphene-assisted nonlinear optical device for four-wave mixing based tunable wavelength conversion of QPSK signal,” Opt. Express 23(20), 26158–26167 (2015).
    [Crossref] [PubMed]
  32. E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
    [Crossref] [PubMed]

2015 (1)

2014 (2)

C. Gui and J. Wang, “Silicon-organic hybrid slot waveguide based three-input multicasted optical hexadecimal addition/subtraction,” Sci. Rep. 4, 7491 (2014).
[Crossref] [PubMed]

Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photonics Technol. Lett. 26(3), 249–252 (2014).
[Crossref]

2013 (1)

K. Yan, L. Fu, H. Peng, and Z. Liu, “Designed CVD growth of graphene via process engineering,” Acc. Chem. Res. 46(10), 2263–2274 (2013).
[Crossref] [PubMed]

2012 (5)

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett. 37(13), 2730–2732 (2012).
[Crossref] [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 Photonics Technol. Lett. 24(24), 2258–2261 (2012).
[Crossref]

B. Xu, A. Martinez, and S. Yamashita, “Mechanically exfoliated graphene for four-wave-mixing-based wavelength conversion,” IEEE Photonics Technol. Lett. 24(20), 1792–1794 (2012).
[Crossref]

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[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]

2011 (6)

2010 (5)

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[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. Express 18(23), 23740–23745 (2010).
[Crossref] [PubMed]

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[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 Photonics Technol. Lett. 22(16), 1199–1201 (2010).
[Crossref]

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]

2009 (3)

2007 (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

2006 (3)

G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, and L. Potí, “Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate,” IEEE Photonics Technol. Lett. 18(8), 917–919 (2006).
[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 FWM in semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 12(4), 702–707 (2006).
[Crossref]

S. H. Kim, J. H. Kim, J. W. Choi, C. W. Son, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, “All-optical half adder using cross gain modulation in semiconductor optical amplifiers,” Opt. Express 14(22), 10693–10698 (2006).
[Crossref] [PubMed]

1999 (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]

1993 (1)

S. Iijima and T. Ichihashi, “Single-shell carbon nanotubes of 1-nm diameter,” Nature 363(6430), 603–605 (1993).
[Crossref]

Badolato, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[Crossref]

Basko, D.

D. Basko, “Applied physics. A photothermoelectric effect in graphene,” Science 334(6056), 610–611 (2011).
[Crossref] [PubMed]

Basko, D. M.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Berrettini, G.

G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, and L. Potí, “Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate,” IEEE Photonics Technol. Lett. 18(8), 917–919 (2006).
[Crossref]

Blow, K. J.

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]

Bogoni, A.

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 Photonics Technol. Lett. 24(24), 2258–2261 (2012).
[Crossref]

A. E. Willner, O. F. Yilmaz, J. Wang, X. X. Wu, A. Bogoni, L. Zhang, and S. R. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. 17(2), 320–332 (2011).
[Crossref]

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]

G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, and L. Potí, “Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate,” IEEE Photonics Technol. Lett. 18(8), 917–919 (2006).
[Crossref]

Bonaccorso, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Byun, Y. T.

Cai, W.

Chan, C. K.

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

Chan, K.

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

Chen, L. K.

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

Chen, L. R.

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 Photonics Technol. Lett. 22(16), 1199–1201 (2010).
[Crossref]

Cheng, Y.

Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photonics Technol. Lett. 26(3), 249–252 (2014).
[Crossref]

Chiang, K. S.

Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photonics Technol. Lett. 26(3), 249–252 (2014).
[Crossref]

Choi, J. W.

Cotter, D.

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]

Deng, N.

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

Densmore, A.

Eggleton, B. J.

Ellis, A. D.

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]

Ferrari, A. C.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Fu, L.

Gao, S.

Gao, Y.

Geim, A. K.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Gong, Y.

Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photonics Technol. Lett. 26(3), 249–252 (2014).
[Crossref]

Gui, C.

C. Gui and J. Wang, “Silicon-organic hybrid slot waveguide based three-input multicasted optical hexadecimal addition/subtraction,” Sci. Rep. 4, 7491 (2014).
[Crossref] [PubMed]

Hale, P. J.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref] [PubMed]

Hasan, T.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

He, S.

Hendry, E.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref] [PubMed]

Hennessy, K. J.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[Crossref]

Hu, E. L.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[Crossref]

Hu, X.

Huang, H.

Husko, C.

Ichihashi, T.

S. Iijima and T. Ichihashi, “Single-shell carbon nanotubes of 1-nm diameter,” Nature 363(6430), 603–605 (1993).
[Crossref]

Iijima, S.

S. Iijima and T. Ichihashi, “Single-shell carbon nanotubes of 1-nm diameter,” Nature 363(6430), 603–605 (1993).
[Crossref]

Imamoglu, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[Crossref]

Janz, S.

Jhon, Y. M.

Kelly, A. E.

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]

Kim, J. H.

Kim, S. H.

Kishi, N.

M. Matsuura and N. Kishi, “High-speed wavelength conversion of RZ-DPSK signal using FWM in a quantum-dot SOA,” IEEE Photonics Technol. Lett. 23(10), 615–617 (2011).
[Crossref]

Lazzeri, E.

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 Photonics Technol. Lett. 24(24), 2258–2261 (2012).
[Crossref]

Lee, S.

Li, F.

Liu, Z.

K. Yan, L. Fu, H. Peng, and Z. Liu, “Designed CVD growth of graphene via process engineering,” Acc. Chem. Res. 46(10), 2263–2274 (2013).
[Crossref] [PubMed]

Ma, R.

Malacarne, A.

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 Photonics Technol. Lett. 24(24), 2258–2261 (2012).
[Crossref]

G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, and L. Potí, “Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate,” IEEE Photonics Technol. Lett. 18(8), 917–919 (2006).
[Crossref]

Manning, R. J.

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]

Martinez, A.

B. Xu, A. Martinez, and S. Yamashita, “Mechanically exfoliated graphene for four-wave-mixing-based wavelength conversion,” IEEE Photonics Technol. Lett. 24(20), 1792–1794 (2012).
[Crossref]

Matsuura, M.

M. Matsuura and N. Kishi, “High-speed wavelength conversion of RZ-DPSK signal using FWM in a quantum-dot SOA,” IEEE Photonics Technol. Lett. 23(10), 615–617 (2011).
[Crossref]

Mikhailov, S. A.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref] [PubMed]

Moger, J.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref] [PubMed]

Moss, D. J.

Mou, X.

Nesset, D.

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]

Novoselov, K. S.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Nuccio, S. R.

A. E. Willner, O. F. Yilmaz, J. Wang, X. X. Wu, A. Bogoni, L. Zhang, and S. R. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. 17(2), 320–332 (2011).
[Crossref]

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 18(23), 23740–23745 (2010).
[Crossref] [PubMed]

Pelusi, M.

Peng, H.

K. Yan, L. Fu, H. Peng, and Z. Liu, “Designed CVD growth of graphene via process engineering,” Acc. Chem. Res. 46(10), 2263–2274 (2013).
[Crossref] [PubMed]

Phillips, I. D.

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]

Popa, D.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Porzi, C.

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]

Potí, L.

G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, and L. Potí, “Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate,” IEEE Photonics Technol. Lett. 18(8), 917–919 (2006).
[Crossref]

Potì, L.

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]

Poustie, A. J.

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]

Privitera, G.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Qiu, J. F.

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 Photonics Technol. Lett. 22(16), 1199–1201 (2010).
[Crossref]

Rao, Y.

Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photonics Technol. Lett. 26(3), 249–252 (2014).
[Crossref]

Reinhard, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[Crossref]

Rochette, M.

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 Photonics Technol. Lett. 22(16), 1199–1201 (2010).
[Crossref]

Rogers, D. C.

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]

Savchenko, A. K.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref] [PubMed]

Scaffardi, M.

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]

Serafino, G.

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 Photonics Technol. Lett. 24(24), 2258–2261 (2012).
[Crossref]

Simi, A.

G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, and L. Potí, “Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate,” IEEE Photonics Technol. Lett. 18(8), 917–919 (2006).
[Crossref]

Son, C. W.

Sun, J.

J. Wang, Q. Sun, J. Sun, and X. Zhang, “Experimental demonstration on 40 Gbit/s all-optical multicasting logic XOR gate for NRZ-DPSK signals using four-wave mixing in highly nonlinear fiber,” Opt. Commun. 282(13), 2615–2619 (2009).
[Crossref]

J. Wang, Q. Sun, and J. Sun, “All-optical 40 Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing,” Opt. Express 17(15), 12555–12563 (2009).
[Crossref] [PubMed]

Sun, J. Q.

Sun, K.

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 Photonics Technol. Lett. 22(16), 1199–1201 (2010).
[Crossref]

Sun, Q.

J. Wang, Q. Sun, J. Sun, and X. Zhang, “Experimental demonstration on 40 Gbit/s all-optical multicasting logic XOR gate for NRZ-DPSK signals using four-wave mixing in highly nonlinear fiber,” Opt. Commun. 282(13), 2615–2619 (2009).
[Crossref]

J. Wang, Q. Sun, and J. Sun, “All-optical 40 Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing,” Opt. Express 17(15), 12555–12563 (2009).
[Crossref] [PubMed]

Sun, Q. Z.

Sun, Z.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Torrisi, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Vo, T. D.

Volz, T.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[Crossref]

Wang, A.

Wang, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Wang, J.

X. Hu, M. Zeng, A. Wang, L. Zhu, L. Fu, and J. Wang, “Graphene-assisted nonlinear optical device for four-wave mixing based tunable wavelength conversion of QPSK signal,” Opt. Express 23(20), 26158–26167 (2015).
[Crossref] [PubMed]

C. Gui and J. Wang, “Silicon-organic hybrid slot waveguide based three-input multicasted optical hexadecimal addition/subtraction,” Sci. Rep. 4, 7491 (2014).
[Crossref] [PubMed]

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]

A. E. Willner, O. F. Yilmaz, J. Wang, X. X. Wu, A. Bogoni, L. Zhang, and S. R. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. 17(2), 320–332 (2011).
[Crossref]

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 19(19), 18246–18252 (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. Express 18(23), 23740–23745 (2010).
[Crossref] [PubMed]

J. Wang, Q. Sun, and J. Sun, “All-optical 40 Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing,” Opt. Express 17(15), 12555–12563 (2009).
[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. B 26(5), 951–958 (2009).
[Crossref]

J. Wang, Q. Sun, J. Sun, and X. Zhang, “Experimental demonstration on 40 Gbit/s all-optical multicasting logic XOR gate for NRZ-DPSK signals using four-wave mixing in highly nonlinear fiber,” Opt. Commun. 282(13), 2615–2619 (2009).
[Crossref]

Wang, L.

Wang, X.

Willner, A. E.

Winger, M.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[Crossref]

Woo, D. H.

Wu, B.

Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photonics Technol. Lett. 26(3), 249–252 (2014).
[Crossref]

Wu, X. X.

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]

A. E. Willner, O. F. Yilmaz, J. Wang, X. X. Wu, A. Bogoni, L. Zhang, and S. R. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. 17(2), 320–332 (2011).
[Crossref]

Wu, Y.

Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photonics Technol. Lett. 26(3), 249–252 (2014).
[Crossref]

Xie, Y.

Xu, B.

B. Xu, A. Martinez, and S. Yamashita, “Mechanically exfoliated graphene for four-wave-mixing-based wavelength conversion,” IEEE Photonics Technol. Lett. 24(20), 1792–1794 (2012).
[Crossref]

Xu, D.-X.

Xu, J.

Yamashita, S.

B. Xu, A. Martinez, and S. Yamashita, “Mechanically exfoliated graphene for four-wave-mixing-based wavelength conversion,” IEEE Photonics Technol. Lett. 24(20), 1792–1794 (2012).
[Crossref]

Yan, K.

K. Yan, L. Fu, H. Peng, and Z. Liu, “Designed CVD growth of graphene via process engineering,” Acc. Chem. Res. 46(10), 2263–2274 (2013).
[Crossref] [PubMed]

Yang, J.-Y.

Yao, B.

Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photonics Technol. Lett. 26(3), 249–252 (2014).
[Crossref]

Yilmaz, O. F.

A. E. Willner, O. F. Yilmaz, J. Wang, X. X. Wu, A. Bogoni, L. Zhang, and S. R. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. 17(2), 320–332 (2011).
[Crossref]

Zeng, M.

Zhang, L.

A. E. Willner, O. F. Yilmaz, J. Wang, X. X. Wu, A. Bogoni, L. Zhang, and S. R. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. 17(2), 320–332 (2011).
[Crossref]

Zhang, X.

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett. 37(13), 2730–2732 (2012).
[Crossref] [PubMed]

J. Wang, Q. Sun, J. Sun, and X. Zhang, “Experimental demonstration on 40 Gbit/s all-optical multicasting logic XOR gate for NRZ-DPSK signals using four-wave mixing in highly nonlinear fiber,” Opt. Commun. 282(13), 2615–2619 (2009).
[Crossref]

Zhou, X.

Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photonics Technol. Lett. 26(3), 249–252 (2014).
[Crossref]

Zhu, L.

Acc. Chem. Res. (1)

K. Yan, L. Fu, H. Peng, and Z. Liu, “Designed CVD growth of graphene via process engineering,” Acc. Chem. Res. 46(10), 2263–2274 (2013).
[Crossref] [PubMed]

ACS Nano (1)

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (3)

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]

A. E. Willner, O. F. Yilmaz, J. Wang, X. X. Wu, A. Bogoni, L. Zhang, and S. R. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. 17(2), 320–332 (2011).
[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 FWM in semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 12(4), 702–707 (2006).
[Crossref]

IEEE Photonics Technol. Lett. (6)

G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, and L. Potí, “Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate,” IEEE Photonics Technol. Lett. 18(8), 917–919 (2006).
[Crossref]

M. Matsuura and N. Kishi, “High-speed wavelength conversion of RZ-DPSK signal using FWM in a quantum-dot SOA,” IEEE Photonics Technol. Lett. 23(10), 615–617 (2011).
[Crossref]

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 Photonics Technol. Lett. 22(16), 1199–1201 (2010).
[Crossref]

Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photonics Technol. Lett. 26(3), 249–252 (2014).
[Crossref]

B. Xu, A. Martinez, and S. Yamashita, “Mechanically exfoliated graphene for four-wave-mixing-based wavelength conversion,” IEEE Photonics Technol. Lett. 24(20), 1792–1794 (2012).
[Crossref]

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 Photonics Technol. Lett. 24(24), 2258–2261 (2012).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Nat. Photonics (1)

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[Crossref]

Nature (1)

S. Iijima and T. Ichihashi, “Single-shell carbon nanotubes of 1-nm diameter,” Nature 363(6430), 603–605 (1993).
[Crossref]

Opt. Commun. (1)

J. Wang, Q. Sun, J. Sun, and X. Zhang, “Experimental demonstration on 40 Gbit/s all-optical multicasting logic XOR gate for NRZ-DPSK signals using four-wave mixing in highly nonlinear fiber,” Opt. Commun. 282(13), 2615–2619 (2009).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref] [PubMed]

Sci. Rep. (1)

C. Gui and J. Wang, “Silicon-organic hybrid slot waveguide based three-input multicasted optical hexadecimal addition/subtraction,” Sci. Rep. 4, 7491 (2014).
[Crossref] [PubMed]

Science (2)

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]

D. Basko, “Applied physics. A photothermoelectric effect in graphene,” Science 334(6056), 610–611 (2011).
[Crossref] [PubMed]

Other (3)

M. Seimetz, High-Order Modulation for Optical Fiber Transmission (Springer, 2009).

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. Zande, J. C. Hone, M. Yu, G.-Q. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Four-wave mixing in slow-light graphene-silicon photonic crystal waveguides,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2014), paper FF1K.8.
[Crossref]

B. Xu, A. Martinez, K. Fuse, and S. Yamashita, “Generation of four wave mixing in graphene and carbon nanotubes optically deposited onto fiber ferrules,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CMAA6.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Fabrication process of the graphene-assisted nonlinear optical device.
Fig. 2
Fig. 2 (a) Optical microscope (OM) image of graphene transferred on a SiO2/Si substrate. (b) Scanning electron microscope (SEM) image of graphene transferred on silicon-on-insulator (SOI). (c) Typical Raman spectrum of single-layer graphene on a SiO2/Si substrate (excitation wavelength: 532 nm).
Fig. 3
Fig. 3 (a) Concept and (b) principle of hybrid quaternary arithmetic functions (2A-B, 2B-A) using degenerate FWM and (D)QPSK signals.
Fig. 4
Fig. 4 Experimental setup for degenerate FWM-based 10-Gbaud optical hybrid quaternary arithmetic functions in a graphene-assisted nonlinear optical device. Inset: “sandwiched structure” graphene sample used as a nonlinear optical device. ECL: external cavity laser; AWG: arbitrary waveform generator; FBG: fiber Bragg grating; EDFA: erbium-doped fiber amplifier; ODL: optical delay line; TF: tunable filter; OC: optical coupler; HP-EDFA: high-power erbium-doped fiber amplifier; PC: polarization controller.
Fig. 5
Fig. 5 Measured spectrum for 10 Gbaud two-input hybrid quaternary arithmetic functions.
Fig. 6
Fig. 6 Measured phase of symbol sequence with coherent detection for 10-Gbaud two-input hybrid quaternary arithmetic functions.
Fig. 7
Fig. 7 (a) Measured BER curves for two-input hybrid quaternary arithmetic functions of 2A-B and 2B-A; (b) BER versus signal offset.

Equations (2)

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E i 1 E A E A E B * , ϕ i 1 = ϕ A + ϕ A ϕ B
E i 2 E B E B E A * , ϕ i 2 = ϕ B + ϕ B ϕ A

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