Abstract

We demonstrate four-wave mixing (FWM) in a 10-μm-radius silicon microring resonator with the assistance of giant nonlinearity of the monolayer graphene. A maximum enhancement of 6.8 dB of conversion efficiency in the silicon-graphene microring (SGM) resonator is observed. A nonlinear propagation model is established and the optical Kerr coefficient of the silicon-graphene hybrid waveguide is three times larger than that of the silicon waveguide.

© 2015 Optical Society of America

1. Introduction

Four-wave mixing (FWM) is an important parametric process that has numerous applications, such as parametric amplification [1–3 ], phase conjugation [4, 5 ], wavelength conversion [6, 7 ], optical sampling [8], signal regeneration [9] and even photon pairs generation [10, 11 ]. Due to the feature of low loss propagation, optical fiber had been investigated to realize FWM several decades ago [12–14 ]. However, kilometers-scale silica fiber with high pump power is required for achieving FWM, due to the low nonlinear coefficient of silica and poor optical confinement of fiber, which is not applicable for scalable photonic integration.

In the telecommunication band, due to the large refractive index of silicon, the silicon waveguides on the silicon-on-insulator platform provide strong light field confinement in the nanoscale. Furthermore, the nonlinear Kerr coefficient of silicon is larger than that of silica by two orders of magnitude [15, 16 ]. The unique optical characteristics of the silicon waveguides enable them to realize FWM in chip-scale with rather low power consumption. However, the conversion efficiency of FWM in the silicon waveguides is fundamentally hampered by the large nonlinear losses of silicon, which is caused by two-photon absorption (TPA) and free carrier absorption (FCA) in silicon [17]. Therefore, the saturation of the conversion efficiency is consequence of the nonlinear absorption increment when the intensity of the input light reaches a certain level at the near-infrared region. The incorporation of reverse biased p-i-n junctions in the silicon waveguides can remove the free carrier and fasten the lifetime of the free carrier. In such a way the conversion efficiency of FWM is increased [18]. However, the external electric modulation gives rise to the power consumption which is not available for large-scale photonic integration.

Graphene, a single sheet of carbon atoms in a hexagonal lattice, has a third-order nonlinear susceptibility which is several orders of magnitude larger than that of silicon [19, 20 ]. The nonlinearity of monolayer graphene was firstly characterized by normally incident light using a high sensitivity photomultiplier [21], where the input lights interact with graphene within sub-nanometer scale. In order to exploit the features of the giant nonlinearity of graphene and the strong electromagnetic field confinement of silicon waveguides, the monolayer graphene is transferred on the silicon waveguides and the nonlinear optical performances of the device are improved owing to the evanescently coupling between the silicon waveguide and graphene over a distance of hundreds of micrometers [22, 23 ].

In this letter, we demonstrate the FWM enhancement in a compact silicon-graphene microring (SGM) resonator with a radius of 10 μm. The maximum conversion efficiency of the FWM, defined as the ratio of the output idler to the input signal, is 6.8 dB. A nonlinear propagation model in the microring resonator is established to analyze the conversion efficiency. Comparing the theoretical model with the experimental results, a threefold increment of the nonlinear Kerr coefficient of the silicon-graphene hybrid waveguide is obtained.

2. Experimental setup and results

The device we use consists of a silicon microring resonator coupled to a straight waveguide with a gap of 150 nm. The waveguide is bidirectionally tapered up to a width of 20 μm over a length of 600 μm to connect dual TE-polarized grating couplers. A scanning electron micrograph (SEM) of the SGM resonator with partial part of the straight waveguide is shown in Fig. 1 . It is fabricated by standard CMOS processes on a silicon-on-insulator substrate with a 3 μm-thick buried oxide layer. The ridge waveguide in the structure has a width of 450 nm, a total height of 340 nm and a ridge height of 200 nm. The total insertion loss is about 15 dB at input wavelength of 1550 nm. Here the input power is defined as the power in the straight waveguide coupled into the microring resonator. We use standard polymer-based transfer method to cover a graphene sample on the top of the silicon waveguides and the detailed picture of the straight waveguide coupled with an arc region of the microring resonator is shown in the inset of Fig. 1. Because the polymer is deposited on the device, the gap is covered and the silicon waveguides before transfer are marked with red dashed lines.

 figure: Fig. 1

Fig. 1 SEM image of the SGM resonator. The inset shows the detail view of the coupling region. Red dashed lines show the outline of the silicon waveguides.

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The large linear absorption effect of the monolayer graphene seriously reduces the Q factor of the resonator, which can be removed through graphene doping [24] or gate tuning [25] of graphene. In the experiment, the doped graphene is realized in the transfer process by the inclusion of fluoropolymer (CYTOP) due to the electrical conductivity improvement in the monolayer graphene. Figure 2 illustrates the Raman spectrum of the transferred graphene on the silicon microring resonator. Compared to pristine graphene, the blue shifts of the positions of the G and 2D peaks are consistent to the nature of the p-doped graphene [26]. Besides, the intensity ratio of the 2D to the G peak is about 1.8, significantly smaller than that of the pristine graphene (4~5), which is another evidence of the p-doped graphene [26]. The transmission spectra of the resonant wavelength around 1557 nm before and after graphene transfer are given in the inset of Fig. 2. The linear absorption of monolayer graphene is tremendously mitigated and the Q factor of the SGM resonator is about 9000, which is almost same as that of the silicon microring resonator (~9100). The monolayer graphene with p-type doping shows the FWHM of the G and 2D peaks are ~18 cm−1 and ~40 cm−1, respectively [27]. Since the silicon microring resonator has a radius of 10 μm, the corresponding free spectrum range is around 10 nm. The grating coupler exhibits a 50-nm coupling range with 3-dB coupling loss and the central wavelength of the grating is 1550 nm. Because of those, two neighboring resonant wavelengths, 1557 nm and 1567 nm are chosen for the pump and the signal light and the wavelength for the idler is around 1547 nm.

 figure: Fig. 2

Fig. 2 Raman spectrum of the graphene sample. The inset shows the transmission spectra of the microring resonator before and after graphene transfer.

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Figure 3 presents the experimental setup which is used to measure the FWM process in the resonator. One tunable laser (APEX, AP100-8) is amplified by the erbium-doped fiber amplifier (Amonics, AEDFA-300-B-FA) and serve as the pump light. A tunable filter (Alnair, BVF-200) is used to suppress the sideband noise of the EDFA. Another tunable laser (Santec, TSL-510) serves as the signal light. The pump and signal lights are combined by a 50:50 coupler and then coupled to the silicon waveguides. The output light is collected and measured by an optical spectrum analyzer (YOKOGAWA, AQ6370). The wavelength of pump and signal light is carefully tuned to satisfy the phase-matching condition.

 figure: Fig. 3

Fig. 3 Experimental setup for FWM. EDFA: erbium-doped fiber amplifier; BPF: band pass filter; PC: polarization controller; OSA: optical spectrum analyzer.

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A pump power of 8 mW and a signal power of 1 mW are sent into the SGM resonator and the spectrum of the FWM in the SGM resonator is shown by the red line in Fig. 4 . The obtained conversion efficiency of the FWM is −37 dB. The same measurement of the FWM is repeated in the silicon microring resonator by setting the power of the pump and signal light to be equivalent to those in SGM resonator and the result of the nonlinear optical measurement is shown in black line in Fig. 4. The conversion efficiency enhancement of the FWM in the SGM resonator is 6.8 dB at the idler wavelength of 1547 nm.

 figure: Fig. 4

Fig. 4 FWM spectra with input pump power of 8 mW and signal power of 1mW before and after graphene transfer.

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3. Discussion

We adopt a theoretical model as ref [28, 29 ]. to simulate the conversion efficiency of the FWM in the microring resonator which is described in Eqs. (1)-(4) ,

η=|γPpumpLeff|2FEp4FEs2FEi2,
γ=(n2ω0)/(Aeffc),
Leff=Lexp(12αL)|1exp(αL+jΔβL)αLjΔβL|,
FEp,s,i=|σ1τexp(12αL+jkp,s,iL)|,
where η is the conversion efficiency, γis the effective nonlinearity, n2is the nonlinear Kerr coefficient, ω0is the center frequency, cis the speed of light in vacuum, Aeffis the effective mode area, Ppumpis the input pump power, Leffis the effective length, FEp, FEs, and FEiare the resonant intensity enhancement factors for the pump, signal and idler, respectively, α is the total loss inside the microring resonator including the linear loss and the nonlinear loss, Δβ is the total phase mismatch caused by nonlinear phase shift and dispersion of the waveguide, Lis the circumference of the microring resonator, σand τare the coupling and transmission coefficients, respectively, and kp,s,iare respectively the wavenumbers of the pump, signal, and idler. Equation (1) shows the physics of the FWM in a resonator. The first factor is the FWM conversion efficiency in a straight waveguide with a length equal to the effective length of the ring resonator. The last three factors show the enhancement of the fields inside the resonator for the pump, signal, and idler beams, respectively. Equation (3) expresses that the effective length of the microring is closely related to the loss and phase mismatch mechanism. Equation (4) describes the physics of field enhancement inside the resonator. When the wavelengths of the pump, signal and idler are tuned to the resonants of the microring, both the field enhancement and the conversion efficiency will be maximized. The theoretical model is applied to explain the nonlinear optical performance of the microring resonator. We use the experimental results obtained for the propagation loss of 7 dB/cm, the Q factor of 9100, the extinction ratio of 6 dB, the nonlinear Kerr coefficient of 0.44 × 10-13 cm2/W for silicon, TPA value of 1.5 cm/GW [30], and group velocity dispersion (GVD) of -400 ps/(nm·km). The black line in Fig. 5 shows excellent agreement between the simulated prediction and the experimental results. The conversion efficiency of the FWM in the silicon microring resonator exhibits a dependence on the power of the pump light, with an inverse parabolic relationship. The saturation of the conversion efficiency at the high pump power level originates from the high volume production of free carriers when the processes of TPA and FCA happen in silicon at near-infrared wavelength.

 figure: Fig. 5

Fig. 5 Experimental and simulated conversion efficiency as a function of input pump power. The red dots represent the measured FWM conversion efficiencies in the SGM; the black dots represent the measured FWM conversion efficiencies in the silicon microring; the red solid line shows the fitted curve according to the experimental results in the SGM; the black solid line shows the simulated result according to the nonlinear propagation model.

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Then the nonlinear performance of the SGM resonator as a function of increased pump power is plotted by the red dots in Fig. 5 and the averaged enhancement of conversion efficiency is 5.3 dB in the SGM resonator. Due to the high mobility of the graphene and strong TPA effect in the silicon-graphene hybrid waveguide, we assume the carrier lifetime and TPA coefficient of the hybrid waveguide to be 200 ps and 25 cm/GW [22], respectively. The fitted line in red agrees well with the experimental results when the nonlinear Kerr coefficient of the silicon-graphene waveguide is about 1.5 × 10−13 cm2/W, which is three times larger than that of the silicon waveguide. The nonlinear Kerr coefficient increment is responsible for the enhanced FWM in the SGM resonator.

We use a full-vector finite-element-method to calculate the effective nonlinearity γ of the waveguide. Then, according to Eq. (2), we can estimate the nonlinear Kerr coefficient for the silicon-graphene hybrid waveguide. Figure 6 shows the field distribution of the fundamental quasi-TE mode. Upon determination of the modal profile, the effective nonlinearity is evaluated by the following equation [31, 32 ]:

γ=2πλSz2n2(x,y)dxdy(Szdxdy)2,
where Sz is the longitudinal component of the time-averaged Poynting vector, and the integrals are evaluated over the transverse profile. In the calculation, we assume that n2 for our graphene sample is 1.5 × 10−9 cm2/W [21]. Since the pump, signal and idler lights in our FWM experiment are in the telecommunication band, the typical fundamental quasi-TE mode profile of the silicon-graphene hybrid waveguide is given using an input wavelength of 1550 nm, of which the polarization is along the dimension of the waveguide width. According to Eq. (5) and Eq. (2), we obtain a nonlinear Kerr coefficient of 2.5 × 10−13 cm2/W, which agrees with the experimental result of 1.5 × 10−13 cm2/W.

 figure: Fig. 6

Fig. 6 Fundamental quasi-TE mode field distribution of silicon ridge waveguide with graphene monolayer at the wavelength of 1550 nm.

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4. Conclusion

In conclusion, we have achieved FWM enhancement in a 10-μm-radius SGM resonator. The largest conversion efficiency enhancement in the SGM resonator is 6.8 dB comparison to that of the silicon microring resonator. These experiment results are in excellent agreement with the theoretical model. Our work shows that silicon-graphene hybrid waveguides have great potential for large-scale photonic integration for signal processing and on-chip heralded photon source.

Acknowledgments

This work is partially supported by National Basic Research Program under No. 2012CB922103, 2013CB933303 and 2013CB632104, National Scientific Founding of China under No. 60806016 and 61177049.

References and links

1. M. Ohashi, K. Kitayama, Y. Ishida, and N. Uchida, “Phase-matched light amplification by three-wave mixing process in a birefringent fiber due to externally applied stress,” Appl. Phys. Lett. 41(12), 1111–1113 (1982). [CrossRef]  

2. M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21(8), 573–575 (1996). [CrossRef]   [PubMed]  

3. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006). [CrossRef]   [PubMed]  

4. A. Yariv and D. M. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1(1), 16–18 (1977). [CrossRef]   [PubMed]  

5. S. Ayotte, H. Rong, S. Xu, O. Cohen, and M. J. Paniccia, “Multichannel dispersion compensation using a silicon waveguide-based optical phase conjugator,” Opt. Lett. 32(16), 2393–2395 (2007). [CrossRef]   [PubMed]  

6. E. A. Swanson and J. D. Moores, “A fiber frequency shifter with broad bandwidth, high conversion efficiency, pump and pump ASE cancellation, and rapid tunability for WDM optical networks,” IEEE Photon. Technol. Lett. 6(11), 1341–1343 (1994). [CrossRef]  

7. R. Espinola, J. Dadap, R. Osgood Jr, S. McNab, and Y. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express 13(11), 4341–4349 (2005). [CrossRef]   [PubMed]  

8. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002). [CrossRef]  

9. 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(1), 35–38 (2008). [CrossRef]  

10. J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006). [CrossRef]   [PubMed]  

11. S. Clemmen, K. Phan Huy, W. Bogaerts, R. G. Baets, P. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17(19), 16558–16570 (2009). [PubMed]  

12. R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974). [CrossRef]  

13. C. Lin, W. A. Reed, A. D. Pearson, and H. T. Shang, “Phase matching in the minimum-chromatic-dispersion region of single-mode fibers for stimulated four-photon mixing,” Opt. Lett. 6(10), 493–495 (1981). [CrossRef]   [PubMed]  

14. M. Ohashi, K. Kitayama, N. Shibata, and S. Seikai, “Frequency tuning of a Stokes wave for stimulated four-photon mixing by temperature-induced birefringence change,” Opt. Lett. 10(2), 77–79 (1985). [CrossRef]   [PubMed]  

15. T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. H. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21(26), 32192–32198 (2013). [CrossRef]   [PubMed]  

16. M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett. 23(18), 961–963 (1987). [CrossRef]  

17. T. Uesugi, B. S. Song, T. Asano, and S. Noda, “Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab,” Opt. Express 14(1), 377–386 (2006). [CrossRef]   [PubMed]  

18. A. Gajda, L. Zimmermann, M. Jazayerifar, G. Winzer, H. Tian, R. Elschner, T. Richter, C. Schubert, B. Tillack, and K. Petermann, “Highly efficient CW parametric conversion at 1550 nm in SOI waveguides by reverse biased p-i-n junction,” Opt. Express 20(12), 13100–13107 (2012). [CrossRef]   [PubMed]  

19. J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16(5), 053014 (2014). [CrossRef]  

20. M. M. Glazov and S. D. Ganichev, “High frequency electric field induced nonlinear effects in graphene,” Phys. Rep. 535(3), 101–138 (2014). [CrossRef]  

21. 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]  

22. T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012). [CrossRef]  

23. H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014). [CrossRef]  

24. I. Gierz, C. Riedl, U. Starke, C. R. Ast, and K. Kern, “Atomic hole doping of graphene,” Nano Lett. 8(12), 4603–4607 (2008). [CrossRef]   [PubMed]  

25. F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008). [CrossRef]   [PubMed]  

26. M. Kalbac, A. Reina-Cecco, H. Farhat, J. Kong, L. Kavan, and M. S. Dresselhaus, “The influence of strong electron and hole doping on the Raman intensity of chemical vapor-deposition graphene,” ACS Nano 4(10), 6055–6063 (2010). [CrossRef]   [PubMed]  

27. W. Zhao, P. H. Tan, J. Liu, and A. C. Ferrari, “Intercalation of few-layer graphite flakes with FeCl3: Raman determination of Fermi level, layer by layer decoupling, and stability,” J. Am. Chem. Soc. 133(15), 5941–5946 (2011). [CrossRef]   [PubMed]  

28. P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P. T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25(8), 554–556 (2000). [CrossRef]   [PubMed]  

29. A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008). [CrossRef]   [PubMed]  

30. A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007). [CrossRef]  

31. M. Foster, K. Moll, and A. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12(13), 2880–2887 (2004). [CrossRef]   [PubMed]  

32. C. Donnelly and D. T. H. Tan, “Ultra-large nonlinear parameter in graphene-silicon waveguide structures,” Opt. Express 22(19), 22820–22830 (2014). [PubMed]  

References

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  1. M. Ohashi, K. Kitayama, Y. Ishida, and N. Uchida, “Phase-matched light amplification by three-wave mixing process in a birefringent fiber due to externally applied stress,” Appl. Phys. Lett. 41(12), 1111–1113 (1982).
    [Crossref]
  2. M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21(8), 573–575 (1996).
    [Crossref] [PubMed]
  3. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
    [Crossref] [PubMed]
  4. A. Yariv and D. M. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1(1), 16–18 (1977).
    [Crossref] [PubMed]
  5. S. Ayotte, H. Rong, S. Xu, O. Cohen, and M. J. Paniccia, “Multichannel dispersion compensation using a silicon waveguide-based optical phase conjugator,” Opt. Lett. 32(16), 2393–2395 (2007).
    [Crossref] [PubMed]
  6. E. A. Swanson and J. D. Moores, “A fiber frequency shifter with broad bandwidth, high conversion efficiency, pump and pump ASE cancellation, and rapid tunability for WDM optical networks,” IEEE Photon. Technol. Lett. 6(11), 1341–1343 (1994).
    [Crossref]
  7. R. Espinola, J. Dadap, R. Osgood, S. McNab, and Y. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express 13(11), 4341–4349 (2005).
    [Crossref] [PubMed]
  8. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
    [Crossref]
  9. 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(1), 35–38 (2008).
    [Crossref]
  10. J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
    [Crossref] [PubMed]
  11. S. Clemmen, K. Phan Huy, W. Bogaerts, R. G. Baets, P. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17(19), 16558–16570 (2009).
    [PubMed]
  12. R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
    [Crossref]
  13. C. Lin, W. A. Reed, A. D. Pearson, and H. T. Shang, “Phase matching in the minimum-chromatic-dispersion region of single-mode fibers for stimulated four-photon mixing,” Opt. Lett. 6(10), 493–495 (1981).
    [Crossref] [PubMed]
  14. M. Ohashi, K. Kitayama, N. Shibata, and S. Seikai, “Frequency tuning of a Stokes wave for stimulated four-photon mixing by temperature-induced birefringence change,” Opt. Lett. 10(2), 77–79 (1985).
    [Crossref] [PubMed]
  15. T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. H. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21(26), 32192–32198 (2013).
    [Crossref] [PubMed]
  16. M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett. 23(18), 961–963 (1987).
    [Crossref]
  17. T. Uesugi, B. S. Song, T. Asano, and S. Noda, “Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab,” Opt. Express 14(1), 377–386 (2006).
    [Crossref] [PubMed]
  18. A. Gajda, L. Zimmermann, M. Jazayerifar, G. Winzer, H. Tian, R. Elschner, T. Richter, C. Schubert, B. Tillack, and K. Petermann, “Highly efficient CW parametric conversion at 1550 nm in SOI waveguides by reverse biased p-i-n junction,” Opt. Express 20(12), 13100–13107 (2012).
    [Crossref] [PubMed]
  19. J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16(5), 053014 (2014).
    [Crossref]
  20. M. M. Glazov and S. D. Ganichev, “High frequency electric field induced nonlinear effects in graphene,” Phys. Rep. 535(3), 101–138 (2014).
    [Crossref]
  21. 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]
  22. T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
    [Crossref]
  23. H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
    [Crossref]
  24. I. Gierz, C. Riedl, U. Starke, C. R. Ast, and K. Kern, “Atomic hole doping of graphene,” Nano Lett. 8(12), 4603–4607 (2008).
    [Crossref] [PubMed]
  25. F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
    [Crossref] [PubMed]
  26. M. Kalbac, A. Reina-Cecco, H. Farhat, J. Kong, L. Kavan, and M. S. Dresselhaus, “The influence of strong electron and hole doping on the Raman intensity of chemical vapor-deposition graphene,” ACS Nano 4(10), 6055–6063 (2010).
    [Crossref] [PubMed]
  27. W. Zhao, P. H. Tan, J. Liu, and A. C. Ferrari, “Intercalation of few-layer graphite flakes with FeCl3: Raman determination of Fermi level, layer by layer decoupling, and stability,” J. Am. Chem. Soc. 133(15), 5941–5946 (2011).
    [Crossref] [PubMed]
  28. P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P. T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25(8), 554–556 (2000).
    [Crossref] [PubMed]
  29. A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
    [Crossref] [PubMed]
  30. A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
    [Crossref]
  31. M. Foster, K. Moll, and A. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12(13), 2880–2887 (2004).
    [Crossref] [PubMed]
  32. C. Donnelly and D. T. H. Tan, “Ultra-large nonlinear parameter in graphene-silicon waveguide structures,” Opt. Express 22(19), 22820–22830 (2014).
    [PubMed]

2014 (4)

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16(5), 053014 (2014).
[Crossref]

M. M. Glazov and S. D. Ganichev, “High frequency electric field induced nonlinear effects in graphene,” Phys. Rep. 535(3), 101–138 (2014).
[Crossref]

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

C. Donnelly and D. T. H. Tan, “Ultra-large nonlinear parameter in graphene-silicon waveguide structures,” Opt. Express 22(19), 22820–22830 (2014).
[PubMed]

2013 (1)

2012 (2)

T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

A. Gajda, L. Zimmermann, M. Jazayerifar, G. Winzer, H. Tian, R. Elschner, T. Richter, C. Schubert, B. Tillack, and K. Petermann, “Highly efficient CW parametric conversion at 1550 nm in SOI waveguides by reverse biased p-i-n junction,” Opt. Express 20(12), 13100–13107 (2012).
[Crossref] [PubMed]

2011 (1)

W. Zhao, P. H. Tan, J. Liu, and A. C. Ferrari, “Intercalation of few-layer graphite flakes with FeCl3: Raman determination of Fermi level, layer by layer decoupling, and stability,” J. Am. Chem. Soc. 133(15), 5941–5946 (2011).
[Crossref] [PubMed]

2010 (2)

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]

M. Kalbac, A. Reina-Cecco, H. Farhat, J. Kong, L. Kavan, and M. S. Dresselhaus, “The influence of strong electron and hole doping on the Raman intensity of chemical vapor-deposition graphene,” ACS Nano 4(10), 6055–6063 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (4)

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(1), 35–38 (2008).
[Crossref]

I. Gierz, C. Riedl, U. Starke, C. R. Ast, and K. Kern, “Atomic hole doping of graphene,” Nano Lett. 8(12), 4603–4607 (2008).
[Crossref] [PubMed]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[Crossref] [PubMed]

2007 (2)

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

S. Ayotte, H. Rong, S. Xu, O. Cohen, and M. J. Paniccia, “Multichannel dispersion compensation using a silicon waveguide-based optical phase conjugator,” Opt. Lett. 32(16), 2393–2395 (2007).
[Crossref] [PubMed]

2006 (3)

2005 (1)

2004 (1)

2002 (1)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

2000 (1)

1996 (1)

1994 (1)

E. A. Swanson and J. D. Moores, “A fiber frequency shifter with broad bandwidth, high conversion efficiency, pump and pump ASE cancellation, and rapid tunability for WDM optical networks,” IEEE Photon. Technol. Lett. 6(11), 1341–1343 (1994).
[Crossref]

1987 (1)

M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett. 23(18), 961–963 (1987).
[Crossref]

1985 (1)

1982 (1)

M. Ohashi, K. Kitayama, Y. Ishida, and N. Uchida, “Phase-matched light amplification by three-wave mixing process in a birefringent fiber due to externally applied stress,” Appl. Phys. Lett. 41(12), 1111–1113 (1982).
[Crossref]

1981 (1)

1977 (1)

1974 (1)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Absil, P. P.

Andrekson, P. A.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Asano, T.

Ashkin, A.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Ast, C. R.

I. Gierz, C. Riedl, U. Starke, C. R. Ast, and K. Kern, “Atomic hole doping of graphene,” Nano Lett. 8(12), 4603–4607 (2008).
[Crossref] [PubMed]

Ayotte, S.

Baets, R. G.

Bjorkholm, J. E.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Bogaerts, W.

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

Cheng, J. L.

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16(5), 053014 (2014).
[Crossref]

Chiang, T. K.

Cho, P. S.

Clemmen, S.

Cohen, O.

Crommie, M.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Cui, Y.

Dadap, J.

Donnelly, C.

Dresselhaus, M. S.

M. Kalbac, A. Reina-Cecco, H. Farhat, J. Kong, L. Kavan, and M. S. Dresselhaus, “The influence of strong electron and hole doping on the Raman intensity of chemical vapor-deposition graphene,” ACS Nano 4(10), 6055–6063 (2010).
[Crossref] [PubMed]

Durteste, Y.

M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett. 23(18), 961–963 (1987).
[Crossref]

Elschner, R.

Emplit, P.

Espinola, R.

Farhat, H.

M. Kalbac, A. Reina-Cecco, H. Farhat, J. Kong, L. Kavan, and M. S. Dresselhaus, “The influence of strong electron and hole doping on the Raman intensity of chemical vapor-deposition graphene,” ACS Nano 4(10), 6055–6063 (2010).
[Crossref] [PubMed]

Feng, G.

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

Ferrari, A. C.

W. Zhao, P. H. Tan, J. Liu, and A. C. Ferrari, “Intercalation of few-layer graphite flakes with FeCl3: Raman determination of Fermi level, layer by layer decoupling, and stability,” J. Am. Chem. Soc. 133(15), 5941–5946 (2011).
[Crossref] [PubMed]

Foster, M.

Foster, M. A.

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[Crossref] [PubMed]

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(1), 35–38 (2008).
[Crossref]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
[Crossref] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

Gaeta, A.

Gaeta, A. L.

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[Crossref] [PubMed]

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(1), 35–38 (2008).
[Crossref]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
[Crossref] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

Gajda, A.

Ganichev, S. D.

M. M. Glazov and S. D. Ganichev, “High frequency electric field induced nonlinear effects in graphene,” Phys. Rep. 535(3), 101–138 (2014).
[Crossref]

Geraghty, D. F.

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(1), 35–38 (2008).
[Crossref]

Gierz, I.

I. Gierz, C. Riedl, U. Starke, C. R. Ast, and K. Kern, “Atomic hole doping of graphene,” Nano Lett. 8(12), 4603–4607 (2008).
[Crossref] [PubMed]

Girit, C.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Glazov, M. M.

M. M. Glazov and S. D. Ganichev, “High frequency electric field induced nonlinear effects in graphene,” Phys. Rep. 535(3), 101–138 (2014).
[Crossref]

Gosciniak, J.

Gu, T.

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

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]

Hansryd, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Hedekvist, P.-O.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

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]

Ho, P. T.

Hone, J.

T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

Hone, J. C.

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

Hryniewicz, J. V.

Ishida, Y.

M. Ohashi, K. Kitayama, Y. Ishida, and N. Uchida, “Phase-matched light amplification by three-wave mixing process in a birefringent fiber due to externally applied stress,” Appl. Phys. Lett. 41(12), 1111–1113 (1982).
[Crossref]

Jazayerifar, M.

Ji, W.

Joneckis, L. G.

Kagi, N.

Kalbac, M.

M. Kalbac, A. Reina-Cecco, H. Farhat, J. Kong, L. Kavan, and M. S. Dresselhaus, “The influence of strong electron and hole doping on the Raman intensity of chemical vapor-deposition graphene,” ACS Nano 4(10), 6055–6063 (2010).
[Crossref] [PubMed]

Kavan, L.

M. Kalbac, A. Reina-Cecco, H. Farhat, J. Kong, L. Kavan, and M. S. Dresselhaus, “The influence of strong electron and hole doping on the Raman intensity of chemical vapor-deposition graphene,” ACS Nano 4(10), 6055–6063 (2010).
[Crossref] [PubMed]

Kazovsky, L. G.

Kern, K.

I. Gierz, C. Riedl, U. Starke, C. R. Ast, and K. Kern, “Atomic hole doping of graphene,” Nano Lett. 8(12), 4603–4607 (2008).
[Crossref] [PubMed]

Kitayama, K.

M. Ohashi, K. Kitayama, N. Shibata, and S. Seikai, “Frequency tuning of a Stokes wave for stimulated four-photon mixing by temperature-induced birefringence change,” Opt. Lett. 10(2), 77–79 (1985).
[Crossref] [PubMed]

M. Ohashi, K. Kitayama, Y. Ishida, and N. Uchida, “Phase-matched light amplification by three-wave mixing process in a birefringent fiber due to externally applied stress,” Appl. Phys. Lett. 41(12), 1111–1113 (1982).
[Crossref]

Kong, J.

M. Kalbac, A. Reina-Cecco, H. Farhat, J. Kong, L. Kavan, and M. S. Dresselhaus, “The influence of strong electron and hole doping on the Raman intensity of chemical vapor-deposition graphene,” ACS Nano 4(10), 6055–6063 (2010).
[Crossref] [PubMed]

Kumar, P.

Kwong, D. L.

T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

Kwong, D.-L.

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

Lee, K. F.

Li, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Lin, C.

Lipson, M.

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(1), 35–38 (2008).
[Crossref]

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[Crossref] [PubMed]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
[Crossref] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

Little, B. E.

Liu, J.

W. Zhao, P. H. Tan, J. Liu, and A. C. Ferrari, “Intercalation of few-layer graphite flakes with FeCl3: Raman determination of Fermi level, layer by layer decoupling, and stability,” J. Am. Chem. Soc. 133(15), 5941–5946 (2011).
[Crossref] [PubMed]

Lo, G.

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

Lo, G. Q.

T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

Marhic, M. E.

Massar, S.

McMillan, J.

T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

McMillan, J. F.

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

McNab, S.

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]

Moll, K.

Monerie, M.

M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett. 23(18), 961–963 (1987).
[Crossref]

Moores, J. D.

E. A. Swanson and J. D. Moores, “A fiber frequency shifter with broad bandwidth, high conversion efficiency, pump and pump ASE cancellation, and rapid tunability for WDM optical networks,” IEEE Photon. Technol. Lett. 6(11), 1341–1343 (1994).
[Crossref]

Noda, S.

Ohashi, M.

M. Ohashi, K. Kitayama, N. Shibata, and S. Seikai, “Frequency tuning of a Stokes wave for stimulated four-photon mixing by temperature-induced birefringence change,” Opt. Lett. 10(2), 77–79 (1985).
[Crossref] [PubMed]

M. Ohashi, K. Kitayama, Y. Ishida, and N. Uchida, “Phase-matched light amplification by three-wave mixing process in a birefringent fiber due to externally applied stress,” Appl. Phys. Lett. 41(12), 1111–1113 (1982).
[Crossref]

Osgood, R.

Paniccia, M. J.

Pearson, A. D.

Pepper, D. M.

Petermann, K.

Petrone, N.

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

Phan Huy, K.

Qian, G.

Reed, W. A.

Reina-Cecco, A.

M. Kalbac, A. Reina-Cecco, H. Farhat, J. Kong, L. Kavan, and M. S. Dresselhaus, “The influence of strong electron and hole doping on the Raman intensity of chemical vapor-deposition graphene,” ACS Nano 4(10), 6055–6063 (2010).
[Crossref] [PubMed]

Richter, T.

Riedl, C.

I. Gierz, C. Riedl, U. Starke, C. R. Ast, and K. Kern, “Atomic hole doping of graphene,” Nano Lett. 8(12), 4603–4607 (2008).
[Crossref] [PubMed]

Rong, H.

Rotenberg, N.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

Salem, R.

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(1), 35–38 (2008).
[Crossref]

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]

Schmidt, B. S.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
[Crossref] [PubMed]

Schubert, C.

Seikai, S.

Shang, H. T.

Sharping, J. E.

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
[Crossref] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

Shen, Y. R.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Shibata, N.

Sipe, J. E.

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16(5), 053014 (2014).
[Crossref]

Song, B. S.

Starke, U.

I. Gierz, C. Riedl, U. Starke, C. R. Ast, and K. Kern, “Atomic hole doping of graphene,” Nano Lett. 8(12), 4603–4607 (2008).
[Crossref] [PubMed]

Stolen, R. H.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Swanson, E. A.

E. A. Swanson and J. D. Moores, “A fiber frequency shifter with broad bandwidth, high conversion efficiency, pump and pump ASE cancellation, and rapid tunability for WDM optical networks,” IEEE Photon. Technol. Lett. 6(11), 1341–1343 (1994).
[Crossref]

Tan, D. T. H.

Tan, P. H.

W. Zhao, P. H. Tan, J. Liu, and A. C. Ferrari, “Intercalation of few-layer graphite flakes with FeCl3: Raman determination of Fermi level, layer by layer decoupling, and stability,” J. Am. Chem. Soc. 133(15), 5941–5946 (2011).
[Crossref] [PubMed]

Tian, C.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Tian, H.

Tillack, B.

Turner, A. C.

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(1), 35–38 (2008).
[Crossref]

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[Crossref] [PubMed]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
[Crossref] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

Uchida, N.

M. Ohashi, K. Kitayama, Y. Ishida, and N. Uchida, “Phase-matched light amplification by three-wave mixing process in a birefringent fiber due to externally applied stress,” Appl. Phys. Lett. 41(12), 1111–1113 (1982).
[Crossref]

Uesugi, T.

van der Zande, A.

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

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A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

Venkatram, N.

Vermeulen, N.

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16(5), 053014 (2014).
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Wang, F.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
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Wang, T.

Westlund, M.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Wilson, R. A.

Winzer, G.

Wong, C. W.

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

Xu, S.

Yariv, A.

Yu, M.

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

Zettl, A.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Zhang, Y.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Zhao, W.

W. Zhao, P. H. Tan, J. Liu, and A. C. Ferrari, “Intercalation of few-layer graphite flakes with FeCl3: Raman determination of Fermi level, layer by layer decoupling, and stability,” J. Am. Chem. Soc. 133(15), 5941–5946 (2011).
[Crossref] [PubMed]

Zhou, H.

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

Zhou, S.

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

Zimmermann, L.

ACS Nano (1)

M. Kalbac, A. Reina-Cecco, H. Farhat, J. Kong, L. Kavan, and M. S. Dresselhaus, “The influence of strong electron and hole doping on the Raman intensity of chemical vapor-deposition graphene,” ACS Nano 4(10), 6055–6063 (2010).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

H. Zhou, T. Gu, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105(9), 091111 (2014).
[Crossref]

M. Ohashi, K. Kitayama, Y. Ishida, and N. Uchida, “Phase-matched light amplification by three-wave mixing process in a birefringent fiber due to externally applied stress,” Appl. Phys. Lett. 41(12), 1111–1113 (1982).
[Crossref]

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Electron. Lett. (1)

M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett. 23(18), 961–963 (1987).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

IEEE Photon. Technol. Lett. (1)

E. A. Swanson and J. D. Moores, “A fiber frequency shifter with broad bandwidth, high conversion efficiency, pump and pump ASE cancellation, and rapid tunability for WDM optical networks,” IEEE Photon. Technol. Lett. 6(11), 1341–1343 (1994).
[Crossref]

J. Am. Chem. Soc. (1)

W. Zhao, P. H. Tan, J. Liu, and A. C. Ferrari, “Intercalation of few-layer graphite flakes with FeCl3: Raman determination of Fermi level, layer by layer decoupling, and stability,” J. Am. Chem. Soc. 133(15), 5941–5946 (2011).
[Crossref] [PubMed]

Nano Lett. (1)

I. Gierz, C. Riedl, U. Starke, C. R. Ast, and K. Kern, “Atomic hole doping of graphene,” Nano Lett. 8(12), 4603–4607 (2008).
[Crossref] [PubMed]

Nat. Photonics (2)

T. Gu, N. Petrone, J. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

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(1), 35–38 (2008).
[Crossref]

Nature (1)

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

New J. Phys. (1)

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16(5), 053014 (2014).
[Crossref]

Opt. Express (9)

T. Uesugi, B. S. Song, T. Asano, and S. Noda, “Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab,” Opt. Express 14(1), 377–386 (2006).
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A. Gajda, L. Zimmermann, M. Jazayerifar, G. Winzer, H. Tian, R. Elschner, T. Richter, C. Schubert, B. Tillack, and K. Petermann, “Highly efficient CW parametric conversion at 1550 nm in SOI waveguides by reverse biased p-i-n junction,” Opt. Express 20(12), 13100–13107 (2012).
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R. Espinola, J. Dadap, R. Osgood, S. McNab, and Y. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express 13(11), 4341–4349 (2005).
[Crossref] [PubMed]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
[Crossref] [PubMed]

S. Clemmen, K. Phan Huy, W. Bogaerts, R. G. Baets, P. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17(19), 16558–16570 (2009).
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T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. H. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21(26), 32192–32198 (2013).
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M. Foster, K. Moll, and A. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12(13), 2880–2887 (2004).
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C. Donnelly and D. T. H. Tan, “Ultra-large nonlinear parameter in graphene-silicon waveguide structures,” Opt. Express 22(19), 22820–22830 (2014).
[PubMed]

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[Crossref] [PubMed]

Opt. Lett. (6)

Phys. Rep. (1)

M. M. Glazov and S. D. Ganichev, “High frequency electric field induced nonlinear effects in graphene,” Phys. Rep. 535(3), 101–138 (2014).
[Crossref]

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]

Science (1)

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 SEM image of the SGM resonator. The inset shows the detail view of the coupling region. Red dashed lines show the outline of the silicon waveguides.
Fig. 2
Fig. 2 Raman spectrum of the graphene sample. The inset shows the transmission spectra of the microring resonator before and after graphene transfer.
Fig. 3
Fig. 3 Experimental setup for FWM. EDFA: erbium-doped fiber amplifier; BPF: band pass filter; PC: polarization controller; OSA: optical spectrum analyzer.
Fig. 4
Fig. 4 FWM spectra with input pump power of 8 mW and signal power of 1mW before and after graphene transfer.
Fig. 5
Fig. 5 Experimental and simulated conversion efficiency as a function of input pump power. The red dots represent the measured FWM conversion efficiencies in the SGM; the black dots represent the measured FWM conversion efficiencies in the silicon microring; the red solid line shows the fitted curve according to the experimental results in the SGM; the black solid line shows the simulated result according to the nonlinear propagation model.
Fig. 6
Fig. 6 Fundamental quasi-TE mode field distribution of silicon ridge waveguide with graphene monolayer at the wavelength of 1550 nm.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

η = | γ P p u m p L e f f | 2 F E p 4 F E s 2 F E i 2 ,
γ = ( n 2 ω 0 ) / ( A e f f c ) ,
L e f f = L exp ( 1 2 α L ) | 1 exp ( α L + j Δ β L ) α L j Δ β L | ,
F E p , s , i = | σ 1 τ exp ( 1 2 α L + j k p , s , i L ) | ,
γ = 2 π λ S z 2 n 2 ( x , y ) d x d y ( S z d x d y ) 2 ,

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