OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 21 — Oct. 10, 2011
  • pp: 20681–20690
« Show journal navigation

Ultracompact all-optical XOR logic gate in a slow-light silicon photonic crystal waveguide

C. Husko, T. D. Vo, B. Corcoran, J. Li, T. F. Krauss, and B. J. Eggleton  »View Author Affiliations


Optics Express, Vol. 19, Issue 21, pp. 20681-20690 (2011)
http://dx.doi.org/10.1364/OE.19.020681


View Full Text Article

Acrobat PDF (1968 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We demonstrate an ultracompact, chip-based, all-optical exclusive-OR (XOR) logic gate via slow-light enhanced four-wave mixing (FWM) in a silicon photonic crystal waveguide (PhCWG). We achieve error-free operation (<10−9) for 40 Gbit/s differential phase-shift keying (DPSK) signals with a 2.8 dB power penalty. Slowing the light to vg = c/32 enables a FWM conversion efficiency, η, of −30 dB for a 396 μm device. The nonlinear FWM process is enhanced by 20 dB compared to a relatively fast mode of vg = c/5. The XOR operation requires ≈ 41 mW, corresponding to a switching energy of 1 pJ/bit. We compare the slow-light PhCWG device performance with experimentally demonstrated XOR DPSK logic gates in other platforms and discuss scaling the device operation to higher bit-rates. The ultracompact structure suggests the potential for device integration.

© 2011 OSA

1. Introduction

All-optical nonlinear signal processing is advancing rapidly, with recent demonstrations of functionalities such as all-optical signal regeneration [1

1. R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010). [CrossRef]

], THz bandwidth multi-impairment monitoring [2

2. T. D. Vo, M. D. Pelusi, J. Schröder, F. Luan, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, B. Luther-Davies, and B. J. Eggleton, “Simultaneous multi-impairment monitoring of 640 gb/s signals using photonic chip based rf spectrum analyzer,” Opt. Express 18, 3938–3945 (2010). [CrossRef] [PubMed]

], and 1.28 Terabit/s demultiplexing [3

3. H. Ji, M. Pu, H. Hu, M. Galili, L. Oxenløwe, K. Yvind, J. Hvam, and P. Jeppesen, “Optical waveform sampling and error-free demultiplexing of 1.28 Tb/s serial data in a nanoengineered silicon waveguide,” J. Lightwave Technol. 29, 426–431 (2011). [CrossRef]

]. All-optical logic functions are one of the components expected to compose such a system [4

4. A. Willner, O. Yilmaz, J. Wang, X. Wu, A. Bogoni, L. Zhang, and S. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. 17320–332 (2010).

]. To this end, a variety of all-optical logic gates have been demonstrated at speeds up to 640 Gb/s [5

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

]. Research efforts into advanced modulation formats involving phase-encoded signals, such as differential phase-shift keying (DPSK), have received significant attention due to their tolerance to system impairments and nonlinearities [1

1. R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010). [CrossRef]

, 6

6. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23, 115–130 (2005). [CrossRef]

]. On the device side, all-optical logic functions employing DPSK have been demonstrated in a variety of platforms: highly nonlinear silica fiber (HNLF) [7

7. 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, 12555–12563 (2009). [CrossRef] [PubMed]

], semiconductor optical amplifiers (SOAs) [8

8. 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, 496–498 (2004). [CrossRef]

, 9

9. 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, 702–707 (2006). [CrossRef]

], and periodically poled lithium niobate (PPLN) [10

10. J. Wang, J. Sun, X. Zhang, D. 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, 1419–1421 (2008). [CrossRef] [PubMed]

]. These platforms, however, experience different limitations, including stimulated Brillouin scattering in HNLF, free-carrier patterning effects and a bias current that adds to the energy requirements of SOA, and, in the case of PPLN, temperature control, though a route forward has been suggested [11

11. M. V. Drummond, J. D. Reis, R. N. Nogueira, P. P. Monteiro, A. L. Teixeira, S. Shinada, N. Wada, and H. Ito, “Error-free wavelength conversion at 160 Gbit/s in PPLN waveguide at room temperature,” Electron. Lett. 45, 1135–1137 (2009). [CrossRef]

].

This past year, an all-optical DPSK XOR logic gate up to 160 Gb/s was demonstrated in a 5 cm integrated chalcogenide glass waveguide [12

12. 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, 710–712 (2011). [CrossRef] [PubMed]

]. The increased nonlinear parameter, γ of integrated waveguides, ∼10 (W-m)−1 for chalcogenide and 300 (W-m)−1 in silicon nanowires [13

13. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2007). [CrossRef]

], allows for reduced power thresholds to observe a given nonlinear process. Silicon all-optical on-off keying (OOK) logic devices based on micro-ring resonators [14

14. L. Zhang, R. Ji, L. Jia, L. Yang, P. Zhou, Y. Tian, P. Chen, Y. Lu, Z. Jiang, and Y. Liu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622 (2010). [CrossRef] [PubMed]

], two-photon absorption [15

15. D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-on-insulator waveguides,” Electron. Lett. 41, 320–321 (2005). [CrossRef]

, 16

16. T. K. Liang, L. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun. 265, 171–174 (2006). [CrossRef]

], or Raman gain [17

17. V. M. N. Passaro and F. de Passaro, “All-optical and gate based on raman effect in silicon-on-insulator waveguide,” Opt. Quantum Electron. 38, 877–888 (2006). [CrossRef]

] phenomena are also capable of low power thresholds, though these devices are limited to bit rates less than 1 Gb/s due to the inherent bandwidth of the resonant structures. This is not an intrinsic limit of silicon, as all-optical functions at much faster rates (> 1 Tb/s) have been demonstrated [3

3. H. Ji, M. Pu, H. Hu, M. Galili, L. Oxenløwe, K. Yvind, J. Hvam, and P. Jeppesen, “Optical waveform sampling and error-free demultiplexing of 1.28 Tb/s serial data in a nanoengineered silicon waveguide,” J. Lightwave Technol. 29, 426–431 (2011). [CrossRef]

, 13

13. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2007). [CrossRef]

, 18

18. A. Biberman, B. G. Lee, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Wavelength multicasting in silicon photonic nanowires,” Opt. Express 18, 18047–18055 (2010). [CrossRef] [PubMed]

, 19

19. B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640 Gb/s using slow-light,” Opt. Express 18, 7770–7781 (2010). [CrossRef] [PubMed]

].

The periodic lattice of the photonic crystal waveguide (PhCWG) gives rise to so-called slow-light effects in which the light travels at a decreased group velocity, vg, allowing for high intensity light inside the photonic crystal even though small energies are injected. Enhancement of third-order χ(3) optical processes have been shown to scale as S2, where S = ng/n0 is the ‘slow-down’ factor of the light in the slow medium with group index ng, and the phase index n0 [20

20. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008). [CrossRef]

, 21

21. M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211–219 (2004). [CrossRef]

]. This scaling results from: (i) the increased effective path length of light in the medium, and (ii) the spatial compression of the pulse intensity in the slow medium, each contributing a factor of S [21

21. M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211–219 (2004). [CrossRef]

24

24. C. Monat, M. de Sterke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt. 12, 104003 (2010). [CrossRef]

]. This slow light effect can give rise to nonlinear parameters near γ ∼ 104 [25

25. C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. Eggleton, T. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17, 2944–2953 (2009). [CrossRef] [PubMed]

], more than an order of magnitude larger than nanowires made of the same material γ ∼ 102. Slow-light enhanced nonlinear processes such as soliton generation [26

26. P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Observation of soliton pulse compression in photonic crystal waveguides,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper QPDA10. http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2010-QPDA10.

], self-phase modulation [25

25. C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. Eggleton, T. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17, 2944–2953 (2009). [CrossRef] [PubMed]

,27

27. C. Husko, S. Combrié, Q. Tran, F. Raineri, C. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorption in III–V photonic crystal waveguides,” Opt. Express 17, 22442–22451 (2009). [CrossRef]

,28

28. K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line defect,” Opt. Express 17, 7206–7216 (2009). [CrossRef] [PubMed]

], and third-harmonic generation [29

29. B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009). [CrossRef]

] have been demonstrated in photonic crystal waveguides.

Most recently, four-wave mixing (FWM) in photonic crystals was realized by several groups [30

30. J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express 19, 4458–4463 (2011). [CrossRef] [PubMed]

34

34. K. Suzuki, Y. Hamachi, and T. Baba, “Fabrication and characterization of chalcogenide glass photonic crystal waveguides,” Opt. Express 17, 22393–22400 (2009). [CrossRef]

], including all-optical demultiplexing of a 160 Gbaud signal in a Si PhCWG [35

35. B. Corcoran, M. D. Pelusi, C. Monat, J. Li, L. O’Faolain, T. F. Krauss, and B. J. Eggleton, “Ultracompact 160 gbaud all-optical demultiplexing exploiting slow light in an engineered silicon photonic crystal waveguide,” Opt. Lett. 36, 1728–1730 (2011). [CrossRef] [PubMed]

]. In contrast to the single beam interactions above, slow-light enhances the FWM process as S4, though the change in mode area with slow-light must also be taken into account [30

30. J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express 19, 4458–4463 (2011). [CrossRef] [PubMed]

, 36

36. M. Santagiustina, C. Someda, G. Vadala, S. Combrie, and A. De Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express 18, 21024–21029 (2010). [CrossRef] [PubMed]

]. The development of dispersion engineering in photonic crystals over the past few years has opened the possibility to generate a flat dispersion band of greater than >THz bandwidth, while simultaneously maintaining slow group velocities [37

37. A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004). [CrossRef]

, 38

38. J. Li, T. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16, 6227–6232 (2008). [CrossRef] [PubMed]

]. In brief, the slow-light enhancement of optical signals in PhCWGs, combined with broader bandwidth operation provides the means to generate FWM, and therefore all-optical signal processing, over compact ≈ 100 μm length scales.

In this paper we demonstrate for the first time, to our knowledge, an all-optical exclusive-OR (XOR) logic gate in photonic crystal waveguides. Our approach employs four-wave mixing (FWM) to perform the logic operation at 40 Gbit/s with return-to-zero (RZ) differential phase-shift keying (DPSK) signals. Slow-light enhancement (vg=c/30) of the optical signal in the photonic crystal waveguide (PhCWG) [9

9. 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, 702–707 (2006). [CrossRef]

, 12

12. 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, 710–712 (2011). [CrossRef] [PubMed]

] allows for an ultracompact device (396 μm) and suggests potential for integration in future all-optical communication systems.

2. All-optical XOR gate operating principal, sample description, and slow-light four-wave mixing

A schematic of the all-optical XOR logic gate is shown in Fig. 1(a). The all-optical XOR operation arises from non-degenerate four-wave mixing of two phase encoded data signals at λ1 and λ2 with a CW probe at λp. This generates an XOR output at the idler wavelength λi inside the PhCWG. There are in fact three idlers that carry the XOR product [7

7. 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, 12555–12563 (2009). [CrossRef] [PubMed]

]. Here we focus on the idler generated by the product of ωi = ω2 + ωpω1. The associated phases of the data channels therefore mix according to: ϕi = ϕ2 + ϕpϕ1, with the CW signal ϕp contributing a constant phase offset between the two data signals. In contrast to the intensity modulation OOK format, the optical signals of DPSK data are encoded with a differential phase of ‘0’ or ‘π’. Thus the phase of the generated idler contains the differential ‘0’ or ‘π’ states at the output of the XOR gate, with a difference of ‘0’ and ‘2π’ being equivalent. Fig. 1(b) indicates the full truth table of the device, including the output after demodulation in a one-bit-delay interferometer.

Fig. 1 (a) Schematic of the all-optical XOR logic gate employing non-degenerate four-wave mixing in a dispersion-engineered photonic crystal waveguide (b) Truth table for the XOR logic gate based on DPSK

The device is a 396 μm long dispersion engineered silicon PhCWG air-suspended structure with a slab thickness of 220 nm, lattice period of 404 nm, hole radii of 115 nm, and first hole lattice shift s1 = −50 nm, similar to that in Ref. [35

35. B. Corcoran, M. D. Pelusi, C. Monat, J. Li, L. O’Faolain, T. F. Krauss, and B. J. Eggleton, “Ultracompact 160 gbaud all-optical demultiplexing exploiting slow light in an engineered silicon photonic crystal waveguide,” Opt. Lett. 36, 1728–1730 (2011). [CrossRef] [PubMed]

]. The device includes mode converters to enhance power injection into the device. The adapters include short (100 μm) Si channel waveguide sections, which contribute negligibly to the nonlinear process [30

30. J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express 19, 4458–4463 (2011). [CrossRef] [PubMed]

,31

31. C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010). [CrossRef] [PubMed]

]. The photonic crystal region exhibits slow-light enhancement, inducing large intensity in the waveguide allowing for efficient four-wave mixing on a short lengthscale. Fig. 2 shows the measured group index ng ∼30 covers a 12 nm range centered around 1540 nm, sufficient bandwidth to accommodate the two 40 Gb/s data channels, CW pump signal, and the generated idler. The linear propagation loss in the slow light region was estimated from cutback measurements to be 65 dB/cm [30

30. J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express 19, 4458–4463 (2011). [CrossRef] [PubMed]

] with a total insertion loss of −11.8 dB. From the mode area (Aeff ∼0.5μm2) and the Kerr coefficient n2 = 5×1018 m2/W of silicon, we estimate the effective nonlinear parameter γeffγS2 ∼ [2πn2/λAeff]S2 ∼3000 (W/m)−1 for the slow light PhC waveguide [31

31. C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010). [CrossRef] [PubMed]

]. The small change in group-velocity dispersion (GVD), β2= −0.6 ×10−21 s2/m, over the device bandwidth ensures efficient phase matching of the four-wave mixing process over the device length [30

30. J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express 19, 4458–4463 (2011). [CrossRef] [PubMed]

]. The slow-light region is sufficiently flat such that walk-off of the two-pulsed data signals is negligible for this device length. The FWM conversion efficiency, η, in the presence of slow-light and in the undepleted pump approximation, is defined as [31

31. C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010). [CrossRef] [PubMed]

]:
η=Pidler(L)Psignal(0)=S4(γPpumpLeff)2ϕeαL,
(1)
where ϕ=[sinh(gL)gL]2, Leff = (1 − exp(−αL))/α, α is the linear loss, and g the parametric gain coefficient as in Ref. [31

31. C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010). [CrossRef] [PubMed]

]. A recent theoretical work derived the effective nonlinear parameters for FWM in photonic crystal waveguides, concluding that the process scales as S4ngData1 × ngData2 × ngCW × ngidler [36

36. M. Santagiustina, C. Someda, G. Vadala, S. Combrie, and A. De Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express 18, 21024–21029 (2010). [CrossRef] [PubMed]

], extending prior work on single beam interactions [22

22. N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E 64, 056604 (2001). [CrossRef]

]. Though alluded to for some time in the literature, only this past year was the S4 scaling experimentally confirmed taking into account the change in mode shape Aeff with group index ng in a single study [30

30. J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express 19, 4458–4463 (2011). [CrossRef] [PubMed]

]. In the present device, we thus expect an increase of ng from 5 to 30 to decrease the device length substantially. A quantitative analysis of the FWM enhancement due to slow light, critical to the short device length in this demonstration, is carried out below in the discussion section.

Fig. 2 Measured linear transmission and group index ng of the sample [30]

3. Description of experimental setup

Fig. 3 shows the experimental setup. Two 40 Gbit/s RZ-DPSK signals were generated from two CW sources at λ1=1538.1 nm and λ2=1539.5 nm (Pave ∼39 mW, or ∼13mW coupled in the waveguide for each data signal) and a pair of Mach-Zender modulators (MZ). The first MZ carves out the 40 GHz RZ pulses with 33% duty cycle, while the second encodes a 40 Gbit/s pseudorandom bit sequence (PRBS) of 27−1 pattern length. The two DPSK signals were amplified, then demultiplexed spectrally in a pulse shaper [39

39. M. A. F. Roelens, S. Frisken, J. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion trimming in a reconfigurable wavelength selective switch,” J. Lightwave Technol. 26, 73–78 (2008). [CrossRef]

], with one of the branches passing through an optical delay line (ΔT) to separate the signals temporally. These signals are then mixed with the CW pump (λp = 1541.7 nm, Pave ∼15 mW coupled) via a coupler before being sent to the chip. The three signals combined for a total of 41 mW coupled to the waveguide. We measured negligible two-photon absorption in the Si PhCWG at this power level, consistent with our prior measurements [30

30. J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express 19, 4458–4463 (2011). [CrossRef] [PubMed]

, 31

31. C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010). [CrossRef] [PubMed]

]. Each channel had a polarization controller to ensure proper alignment to the device transverse-electric mode (TE), e.g. transmission in the plane of the slab. The collected signal is amplified, with the XOR idler then extracted by a 1 nm filter before being demodulated, filtered again to improve the optical signal-to-noise ratio (OSNR), and detected by a 40 Gbit/s receiver.

Fig. 3 Experimental setup for the 40 Gbit/s DPSK all-optical XOR logic gate in the compact silicon photonic crystal waveguide

4. Experimental results

4.1. Role of slow-light enhanced four-wave mixing

Fig. 4 shows the measured output spectrum at the output of the Si PhCWG. The two input 40 Gbit/s DPSK data channels, CW probe signal and the XOR idler generated at λi = 1543.0 nm (shaded region), are indicated. We tuned the CW pump signal over a spectral range of approximately 4.5 nm with flattop FWM conversion efficiency, Fig. 4 (inset). Including the separation bandwidth of the two data signals here (1.6 nm), this range is in relative agreement with our prior degenerate FWM measurements [30

30. J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express 19, 4458–4463 (2011). [CrossRef] [PubMed]

]. The conversion bandwidth offers the potential for wavelength multicasting of the XOR gate [18

18. A. Biberman, B. G. Lee, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Wavelength multicasting in silicon photonic nanowires,” Opt. Express 18, 18047–18055 (2010). [CrossRef] [PubMed]

]. From our experimental parameters, ϕ ≈ 1 and γeffPpumpLeff ≈ 0.05. According to Eqn. 1, the estimated FWM efficiency is ηtheory = −30 dB. As the CW is the largest signal, it acts as the pump in this scheme, and we take the data signals as the probe. This yields a measured FWM efficiency of ηexp = −30 to −32 dB, depending on whether Data 1 or Data 2 is the reference signal. The converted idler exhibits some of the structure of the PhCWG transmission, deviating from a smooth curve, due to structural disorder induced during fabrication. Additional discussion of this topic is detailed below.

Fig. 4 Four-wave mixing spectra at the output of the chip. The two input data channels, CW probe and generated XOR idler are indicated. Inset: Measured four-wave mixing (FWM) conversion efficiency.

Table 1. Quantitative enhancement of four-wave mixing due to slow-light. Po = 40 mW.

table-icon
View This Table
| View All Tables

4.2. DPSK XOR logic gate results

Figure 5(a) shows the demodulated temporal waveforms captured on a sampling oscilloscope of the two input data and output XOR channels. One can see the FWM idler is the XOR output from the two input DPSK channels, confirming the all-optical logic gate functionality. The eye diagrams of the 40 Gbit/s signals after the chip and demodulation are seen in Fig. 5(b). While the eyes of the data signals are relatively crisp, the XOR product is noisier due to the small energy of the idler coming from the photonic chip. The 396 μm device achieves the XOR operation at estimated energy of ∼1 pJ/bit, including all signal beams.

Fig. 5 (a) Temporal waveforms of the two input data channels and output XOR idler. (b) Eye diagrams of the respective channels. (c) Bit-error rate measurements of the various data 40 Gb/s DPSK signals. The device is error free (BER< 10−9) with ∼2.8 dB power penalty, primarily attributed to the small signal amplified off-chip.

5. Discussion

All-optical XOR gates have been demonstrated in a variety of platforms. We focus here on DPSK results for the reasons we mentioned in the introduction, namely robustness against system impairments. The key parameters of the devices are listed in Table 2. These include: length, experimental bit rate, energy per bit (Pavg / bit-rate), bit-error rate results (if provided), and the nonlinear conversion efficiency. For this section we use the instantaneous FWM efficiency, ηo=Pidler(L)Psignal(L), since the input power values of several systems are not readily available. The output optical spectrum is presented, however, and allows direct comparison. We ignore external amplifiers in all cases and focus solely on the FWM process in the energy calculation. Note that the electrical power required for SOAs is not taken into consideration in this estimate [42

42. R. Tucker, “Green Optical Communications—Part II: Energy Limitations in Networks,” IEEE J. Selected Topics in Quantum Electronics, pp. 1–14 (2011).

]. All of the demonstrations thus far have been based on four-wave mixing, with the exception of PPLN [10

10. J. Wang, J. Sun, X. Zhang, D. 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, 1419–1421 (2008). [CrossRef] [PubMed]

] which is based on sum-frequency generation, where we define the conversion efficiency as η1.

Table 2. Comparison of experimentally demonstrated exclusive-OR (XOR) logic gates

table-icon
View This Table
| View All Tables

The Si PhCWG XOR operation presented here compares favorably well across a broad range of categories, the most salient advantage being nearly an order of magnitude shorter device length (∼ 400 μm) and the most notable drawback being bandwidth (∼ 1 THz). This tradeoff is well-documented in the PhC literature [20

20. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008). [CrossRef]

, 21

21. M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211–219 (2004). [CrossRef]

, 38

38. J. Li, T. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16, 6227–6232 (2008). [CrossRef] [PubMed]

]. This bandwidth however, is capable of performing the 40 Gb/s XOR logic operation here, and other all-optical signal operations, such as optical signal to noise ratio (OSNR) monitoring, up to 640 Gb/s [19

19. B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640 Gb/s using slow-light,” Opt. Express 18, 7770–7781 (2010). [CrossRef] [PubMed]

]. The energy consumption of the device is close to its integrated counterparts (Si and ChG), with expected parity due to improved fabrication [41

41. L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010). [CrossRef]

]. Though XOR logic gates have been demonstrated qualitatively in a number of platforms, relatively few have measured the bit-error rate (BER) of the operation. The best reported BER results are in ChG waveguides and SOAs, though the latter was at 10 Gb/s. The measured power penalty of the PhCWG in this work could be improved as noted in the BER measurements above. The ChG experiment also included a demonstration at 160 Gb/s, though no BER was measured in that case. We note that 640 Gb/s XOR logic has been demonstrated with OOK [5

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

].

We conclude with a few statements on scaling the device to higher baud-rates (>100 Gb/s). Photonic crystal waveguides exhibit a well known tradeoff between the group index and bandwidth, commonly called the group index-bandwidth product (GBP) [38

38. J. Li, T. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16, 6227–6232 (2008). [CrossRef] [PubMed]

]. The broader bandwidth of a 160 Gb/s XOR logic gate would thus require a device with a smaller group index, e.g. ng = 24. Taking into account the smaller mode size and decreased linear scattering loss at this faster group velocity, we estimate a device length of 600 μm would be required to achieve the same FWM efficiency, η= −30 dB. All-optical XOR operation at even higher bit-rates is possible with dispersion management of shorter temporal signals and careful design of the group index-bandwidth properties.

6. Conclusion

We have demonstrated an ultra-compact all-optical XOR gate using non-degenerate four-wave mixing in a dispersion-engineered photonic crystal waveguide for 40 Gbit/s DPSK signals. Error-free XOR operation was achieved with a 2.8 dB power penalty. Slowing the optical signals to velocities of ∼ c/30 enhance the nonlinear process by 20 dB, allowing for the operation in a 396 μm long device, approximately an order of magnitude shorter than prior demonstrations. Compact device operation suggests the potential for integration on an integrated photonic chip. The device operation is scalable to increased baud rates in slow light structures with increased bandwidth.

Acknowledgments

This research was supported by the Australian Research Council (ARC) Centres of Excellence (COE) and Federation Fellowship programs. J. Li was supported by FP7 Marie Curie IIF “Osiris” and UK Silicon Photonics.

References and links

1.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010). [CrossRef]

2.

T. D. Vo, M. D. Pelusi, J. Schröder, F. Luan, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, B. Luther-Davies, and B. J. Eggleton, “Simultaneous multi-impairment monitoring of 640 gb/s signals using photonic chip based rf spectrum analyzer,” Opt. Express 18, 3938–3945 (2010). [CrossRef] [PubMed]

3.

H. Ji, M. Pu, H. Hu, M. Galili, L. Oxenløwe, K. Yvind, J. Hvam, and P. Jeppesen, “Optical waveform sampling and error-free demultiplexing of 1.28 Tb/s serial data in a nanoengineered silicon waveguide,” J. Lightwave Technol. 29, 426–431 (2011). [CrossRef]

4.

A. Willner, O. Yilmaz, J. Wang, X. Wu, A. Bogoni, L. Zhang, and S. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. 17320–332 (2010).

5.

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

6.

A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23, 115–130 (2005). [CrossRef]

7.

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, 12555–12563 (2009). [CrossRef] [PubMed]

8.

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, 496–498 (2004). [CrossRef]

9.

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, 702–707 (2006). [CrossRef]

10.

J. Wang, J. Sun, X. Zhang, D. 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, 1419–1421 (2008). [CrossRef] [PubMed]

11.

M. V. Drummond, J. D. Reis, R. N. Nogueira, P. P. Monteiro, A. L. Teixeira, S. Shinada, N. Wada, and H. Ito, “Error-free wavelength conversion at 160 Gbit/s in PPLN waveguide at room temperature,” Electron. Lett. 45, 1135–1137 (2009). [CrossRef]

12.

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, 710–712 (2011). [CrossRef] [PubMed]

13.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2007). [CrossRef]

14.

L. Zhang, R. Ji, L. Jia, L. Yang, P. Zhou, Y. Tian, P. Chen, Y. Lu, Z. Jiang, and Y. Liu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622 (2010). [CrossRef] [PubMed]

15.

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-on-insulator waveguides,” Electron. Lett. 41, 320–321 (2005). [CrossRef]

16.

T. K. Liang, L. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun. 265, 171–174 (2006). [CrossRef]

17.

V. M. N. Passaro and F. de Passaro, “All-optical and gate based on raman effect in silicon-on-insulator waveguide,” Opt. Quantum Electron. 38, 877–888 (2006). [CrossRef]

18.

A. Biberman, B. G. Lee, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Wavelength multicasting in silicon photonic nanowires,” Opt. Express 18, 18047–18055 (2010). [CrossRef] [PubMed]

19.

B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640 Gb/s using slow-light,” Opt. Express 18, 7770–7781 (2010). [CrossRef] [PubMed]

20.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008). [CrossRef]

21.

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211–219 (2004). [CrossRef]

22.

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E 64, 056604 (2001). [CrossRef]

23.

T. F. Krauss, “−2670,” J. Phys. D: Appl. Phys. 40, 2666 (2007). [CrossRef]

24.

C. Monat, M. de Sterke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt. 12, 104003 (2010). [CrossRef]

25.

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. Eggleton, T. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17, 2944–2953 (2009). [CrossRef] [PubMed]

26.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Observation of soliton pulse compression in photonic crystal waveguides,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper QPDA10. http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2010-QPDA10.

27.

C. Husko, S. Combrié, Q. Tran, F. Raineri, C. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorption in III–V photonic crystal waveguides,” Opt. Express 17, 22442–22451 (2009). [CrossRef]

28.

K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line defect,” Opt. Express 17, 7206–7216 (2009). [CrossRef] [PubMed]

29.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009). [CrossRef]

30.

J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express 19, 4458–4463 (2011). [CrossRef] [PubMed]

31.

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010). [CrossRef] [PubMed]

32.

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observation of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18, 15484–15497 (2010). [CrossRef] [PubMed]

33.

V. Eckhouse, I. Cestier, G. Eisenstein, S. Combrié, P. Colman, A. De Rossi, M. Santagiustina, C. Someda, and G. Vadalà, “Highly efficient four wave mixing in GaInP photonic crystal waveguides,” Opt. Lett. 35, 1440–1442 (2010). [CrossRef] [PubMed]

34.

K. Suzuki, Y. Hamachi, and T. Baba, “Fabrication and characterization of chalcogenide glass photonic crystal waveguides,” Opt. Express 17, 22393–22400 (2009). [CrossRef]

35.

B. Corcoran, M. D. Pelusi, C. Monat, J. Li, L. O’Faolain, T. F. Krauss, and B. J. Eggleton, “Ultracompact 160 gbaud all-optical demultiplexing exploiting slow light in an engineered silicon photonic crystal waveguide,” Opt. Lett. 36, 1728–1730 (2011). [CrossRef] [PubMed]

36.

M. Santagiustina, C. Someda, G. Vadala, S. Combrie, and A. De Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express 18, 21024–21029 (2010). [CrossRef] [PubMed]

37.

A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004). [CrossRef]

38.

J. Li, T. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16, 6227–6232 (2008). [CrossRef] [PubMed]

39.

M. A. F. Roelens, S. Frisken, J. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion trimming in a reconfigurable wavelength selective switch,” J. Lightwave Technol. 26, 73–78 (2008). [CrossRef]

40.

L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties,” Opt. Express 14, 9444–9450 (2006). [CrossRef] [PubMed]

41.

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010). [CrossRef]

42.

R. Tucker, “Green Optical Communications—Part II: Energy Limitations in Networks,” IEEE J. Selected Topics in Quantum Electronics, pp. 1–14 (2011).

43.

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,” IEEE Photonics ConferenceArlington, VA, USA (2011).

OCIS Codes
(060.5060) Fiber optics and optical communications : Phase modulation
(130.3750) Integrated optics : Optical logic devices
(130.5296) Integrated optics : Photonic crystal waveguides

ToC Category:
Integrated Optics

History
Original Manuscript: August 16, 2011
Revised Manuscript: September 23, 2011
Manuscript Accepted: September 26, 2011
Published: October 4, 2011

Citation
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, 20681-20690 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-20681


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics4, 690–695 (2010). [CrossRef]
  2. T. D. Vo, M. D. Pelusi, J. Schröder, F. Luan, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, B. Luther-Davies, and B. J. Eggleton, “Simultaneous multi-impairment monitoring of 640 gb/s signals using photonic chip based rf spectrum analyzer,” Opt. Express18, 3938–3945 (2010). [CrossRef] [PubMed]
  3. H. Ji, M. Pu, H. Hu, M. Galili, L. Oxenløwe, K. Yvind, J. Hvam, and P. Jeppesen, “Optical waveform sampling and error-free demultiplexing of 1.28 Tb/s serial data in a nanoengineered silicon waveguide,” J. Lightwave Technol.29, 426–431 (2011). [CrossRef]
  4. A. Willner, O. Yilmaz, J. Wang, X. Wu, A. Bogoni, L. Zhang, and S. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron.17320–332 (2010).
  5. A. Bogoni, X. Wu, Z. Bakhtiari, S. Nuccio, and A. E. Willner, “640 Gbits/s photonic logic gates,” Opt. Lett.35, 3955–3957 (2010). [CrossRef] [PubMed]
  6. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol.23, 115–130 (2005). [CrossRef]
  7. 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. Express17, 12555–12563 (2009). [CrossRef] [PubMed]
  8. 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, 496–498 (2004). [CrossRef]
  9. 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, 702–707 (2006). [CrossRef]
  10. J. Wang, J. Sun, X. Zhang, D. 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, 1419–1421 (2008). [CrossRef] [PubMed]
  11. M. V. Drummond, J. D. Reis, R. N. Nogueira, P. P. Monteiro, A. L. Teixeira, S. Shinada, N. Wada, and H. Ito, “Error-free wavelength conversion at 160 Gbit/s in PPLN waveguide at room temperature,” Electron. Lett.45, 1135–1137 (2009). [CrossRef]
  12. 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, 710–712 (2011). [CrossRef] [PubMed]
  13. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics2, 35–38 (2007). [CrossRef]
  14. L. Zhang, R. Ji, L. Jia, L. Yang, P. Zhou, Y. Tian, P. Chen, Y. Lu, Z. Jiang, Y. Liu, and , “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett.35, 1620–1622 (2010). [CrossRef] [PubMed]
  15. D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-on-insulator waveguides,” Electron. Lett.41, 320–321 (2005). [CrossRef]
  16. T. K. Liang, L. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun.265, 171–174 (2006). [CrossRef]
  17. V. M. N. Passaro and F. de Passaro, “All-optical and gate based on raman effect in silicon-on-insulator waveguide,” Opt. Quantum Electron.38, 877–888 (2006). [CrossRef]
  18. A. Biberman, B. G. Lee, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Wavelength multicasting in silicon photonic nanowires,” Opt. Express18, 18047–18055 (2010). [CrossRef] [PubMed]
  19. B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640 Gb/s using slow-light,” Opt. Express18, 7770–7781 (2010). [CrossRef] [PubMed]
  20. T. Baba, “Slow light in photonic crystals,” Nat. Photonics2, 465–473 (2008). [CrossRef]
  21. M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater.3, 211–219 (2004). [CrossRef]
  22. N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E64, 056604 (2001). [CrossRef]
  23. T. F. Krauss, “−2670,” J. Phys. D: Appl. Phys.40, 2666 (2007). [CrossRef]
  24. C. Monat, M. de Sterke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt.12, 104003 (2010). [CrossRef]
  25. C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. Eggleton, T. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express17, 2944–2953 (2009). [CrossRef] [PubMed]
  26. P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Observation of soliton pulse compression in photonic crystal waveguides,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper QPDA10. http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2010-QPDA10 .
  27. C. Husko, S. Combrié, Q. Tran, F. Raineri, C. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorption in III–V photonic crystal waveguides,” Opt. Express17, 22442–22451 (2009). [CrossRef]
  28. K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line defect,” Opt. Express17, 7206–7216 (2009). [CrossRef] [PubMed]
  29. B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics3, 206–210 (2009). [CrossRef]
  30. J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express19, 4458–4463 (2011). [CrossRef] [PubMed]
  31. C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express18, 22915–22927 (2010). [CrossRef] [PubMed]
  32. J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observation of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express18, 15484–15497 (2010). [CrossRef] [PubMed]
  33. V. Eckhouse, I. Cestier, G. Eisenstein, S. Combrié, P. Colman, A. De Rossi, M. Santagiustina, C. Someda, and G. Vadalà, “Highly efficient four wave mixing in GaInP photonic crystal waveguides,” Opt. Lett.35, 1440–1442 (2010). [CrossRef] [PubMed]
  34. K. Suzuki, Y. Hamachi, and T. Baba, “Fabrication and characterization of chalcogenide glass photonic crystal waveguides,” Opt. Express17, 22393–22400 (2009). [CrossRef]
  35. B. Corcoran, M. D. Pelusi, C. Monat, J. Li, L. O’Faolain, T. F. Krauss, and B. J. Eggleton, “Ultracompact 160 gbaud all-optical demultiplexing exploiting slow light in an engineered silicon photonic crystal waveguide,” Opt. Lett.36, 1728–1730 (2011). [CrossRef] [PubMed]
  36. M. Santagiustina, C. Someda, G. Vadala, S. Combrie, and A. De Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express18, 21024–21029 (2010). [CrossRef] [PubMed]
  37. A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett.85, 4866–4868 (2004). [CrossRef]
  38. J. Li, T. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express16, 6227–6232 (2008). [CrossRef] [PubMed]
  39. M. A. F. Roelens, S. Frisken, J. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion trimming in a reconfigurable wavelength selective switch,” J. Lightwave Technol.26, 73–78 (2008). [CrossRef]
  40. L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties,” Opt. Express14, 9444–9450 (2006). [CrossRef] [PubMed]
  41. L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express18, 27627–27638 (2010). [CrossRef]
  42. R. Tucker, “Green Optical Communications—Part II: Energy Limitations in Networks,” IEEE J. Selected Topics in Quantum Electronics, pp. 1–14 (2011).
  43. 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,” IEEE Photonics ConferenceArlington, VA, USA (2011).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited