Efficient terahertz-wave generation via fourwave mixing in silicon membrane waveguides Zhaolu Wang, Hongjun Liu*, Nan Huang, Qibing Sun, and Jin Wen State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Science (CAS), Xi'an, 710119, China *
[email protected]
Abstract: Terahertz (THz) wave generation via four-wave mixing (FWM) in silicon membrane waveguides is theoretically investigated with midinfrared laser pulses. Compared with the conventional parametric amplification or wavelength conversion based on FWM in silicon waveguides, which needs a pump wavelength located in the anomalous group-velocity dispersion (GVD) regime to realize broad phase matching, the pump wavelength located in the normal GVD regime is required to realize collinear phase matching for the THz-wave generation via FWM. The pump wavelength and rib height of the silicon membrane waveguide can be tuned to obtain a broadband phase matching. Moreover, the conversion efficiency of the THz-wave generation is studied with different pump wavelengths and rib heights of the silicon membrane waveguides, and broadband THz-wave can be obtained with high efficiency exceeding 1%. ©2012 Optical Society of America OCIS codes: (190.4380) Nonlinear optics, four-wave mixing; (230.7370) Waveguides; (310.2790) Guided waves.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Y. Takushima, S. Y. Shin, and Y. C. Chung, “Design of a LiNbO(3) ribbon waveguide for efficient differencefrequency generation of terahertz wave in the collinear configuration,” Opt. Express 15(22), 14783–14792 (2007). K. Kawase, H. Minamide, K. Imai, J. Shikata, and H. Ito, “Injection-seeded terahertz-wave parametric generator with wide tenability,” Appl. Phys. Lett. 80(2), 195–198 (2002). A. C. Chiang, T. D. Wang, Y. Y. Lin, S. T. Lin, H. H. Lee, Y. C. Huang, and Y. H. Chen, “Enhanced terahertzwave parametric generation and oscillation in lithium niobate waveguides at terahertz frequencies,” Opt. Lett. 30(24), 3392–3394 (2005). X. Xie, J. Xu, and X.-C. Zhang, “Terahertz wave generation and detection from a cdte crystal characterized by different excitation wavelengths,” Opt. Lett. 31(7), 978–980 (2006). T. D. Wang, S. T. Lin, Y. Y. Lin, A. C. Chiang, and Y. C. Huang, “Forward and backward terahertz-wave difference-frequency generations from periodically poled lithium niobate,” Opt. Express 16(9), 6471–6478 (2008). K. L. Vodopyanov and Y. H. Avetisyan, “Optical terahertz wave generation in a planar GaAs waveguide,” Opt. Lett. 33(20), 2314–2316 (2008). Y. J. Ding, “Efficient generation of high-frequency terahertz waves from highly lossy second-order nonlinear medium at polariton resonance under transverse-pumping geometry,” Opt. Lett. 35(2), 262–264 (2010). Y. Sasaki, Y. Avetisyan, H. Yokoyama, and H. Ito, “Surface-emitted terahertz-wave difference-frequency generation in two-dimensional periodically poled lithium niobate,” Opt. Lett. 30(21), 2927–2929 (2005). K. Suizu, Y. Suzuki, Y. Sasaki, H. Ito, and Y. Avetisyan, “Surface-emitted terahertz-wave generation by ridged periodically poled lithium niobate and enhancement by mixing of two terahertz waves,” Opt. Lett. 31(7), 957– 959 (2006). T. Ikari, X. Zhang, H. Minamide, and H. Ito, “THz-wave parametric oscillator with a surface-emitted configuration,” Opt. Express 14(4), 1604–1610 (2006). Y. H. Avetisyan, “Terahertz-wave surface-emitted difference-frequency generation without quasi-phasematching technique,” Opt. Lett. 35(15), 2508–2510 (2010). K. Suizu and K. Kawase, “Terahertz-wave generation in a conventional optical fiber,” Opt. Lett. 32(20), 2990– 2992 (2007). H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005). R. L. Espinola, J. I. Dadap, R. M. Osgood, Jr., S. J. McNab, and Y. A. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express 13(11), 4341–4349 (2005).
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15. R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840 (2006). 16. L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32(4), 391–393 (2007). 17. R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006). 18. B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express 19(18), 17212–17219 (2011). 19. M. Wächter, C. Matheisen, M. Waldow, T. Wahlbrink, J. Bolten, M. Nagel, and H. Kurz, “Optical generation of terahertz and second-harmonic light in plasma-activated silicon nanophotonic structures,” Appl. Phys. Lett. 97(16), 161107 (2010). 20. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007). 21. 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). 22. Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express 14(11), 4786–4799 (2006). 23. G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. 23(6), 064002 (2008). 24. T. E. Murphy, software available at http://www.photonics.umd.edu. 25. Q. Lin, T. J. Johnson, R. Perahia, C. P. Michael, and O. J. Painter, “A proposal for highly tunable optical parametric oscillation in silicon micro-resonators,” Opt. Express 16(14), 10596–10610 (2008). 26. X. Liu, R. M. Osgood, Jr., Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophtonic waveguides,” Nat. Photonics 4(8), 557–560 (2010). 27. R. M. Osgood, Jr., N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. Hsieh, E. Dulkeith, W. M. J. Green, and Y. A. Vlasov, “Engineering nonlinearities in nanoscale optical systems: physics and applications in dispersionengineered silicon nanophotonic wires,” Adv. Opt. Photon. 1(1), 162–235 (2009). 28. Z. Wang, H. Liu, N. Huang, Q. Sun, and J. Wen, “Impact of dispersion profiles of silicon waveguides on optical parametric amplification in the femtosecond regime,” Opt. Express 19(24), 24730–24737 (2011). 29. E. K. Tien, Y. Huang, S. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express 18(21), 21981–21989 (2010). 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). 31. N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011). 32. G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express 19(8), 7112–7119 (2011). 33. http://www.nature.com/nphoton/journal/v4/n8/full/nphoton.2010.173.html.
1. Introduction The development of efficient and compact sources of THz-wave is of great interest for applications in various fields such as applied physics, communications, sensing, and life sciences [1]. The difference-frequency generation (DFG) in nonlinear optical crystals is an important technique for coherent THz-wave generation [2–7]. However, it is difficult to increase the conversion efficiency for DFG based THz-wave generation, because most of nonlinear optical crystals have a large absorption in the THz–wave region. Surface-emitting THz-wave generation can be used to overcome the high absorption loss [8–11]. Unfortunately, this method requires a specially designed crystal, and the interaction length is limited by the size of the base material [12]. To cope with these difficulties, Suizu et al. proposed a way to generate THz-waves in an optical fiber via FWM process, which is a promising method for realizing a reasonable THzwave source [12]. FWM in silicon waveguide had been studied not only theoretically but also experimentally [13, 14]. Compared with conventional fiber, the silicon rib membrane waveguide will be a more viable structure for THz-wave generation via FWM. There are five major inherent advantages. First, the silicon membrane has an absorption loss below 0.23 cm−1 over 1.2-6.9 µm and 25-200 µm [15], while the absorption coefficient of the optical fiber in the THz-wave region is about 5 cm−1. Second, the nonlinear refractive index n2 of silicon is about 200 times larger than that of silica [16]. Third, the refractive index of silicon (around 3.5) is much larger than that of air, which implies a much stronger light confinement. Fourth, the crystalline nature of silicon that makes stimulated Raman scattering (SRS) depend #163221 - $15.00 USD (C) 2012 OSA
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strongly on the waveguide geometry and mode polarization, and SRS cannot occur when an input pulse excites the TM mode [16]. Fifth, the silicon membrane waveguide is also CMOS compatible and enable low-cost large-scale integration [15]. Moreover, the silicon waveguide also have been modified to show second-order nonlinearity at technically relevant levels [17, 18]. Even the THz-wave generation based on DFG has already been experimentally demonstrated in a silicon waveguide by Waechter et al [19]. Despite this progress, there is still a strong motivation to investigate the THz-wave generation based on FWM due to the high third-order nonlinearity of silicon waveguide. In this paper, we investigate efficient THz-wave generation via FWM in silicon membrane waveguides using Mid-infrared pump and signal waves. The organization of the paper is as follows. In Section 2, we analyze the collinear phase matching condition and phase matching bandwidth with the dispersion relation of silicon membrane waveguides. In section 3, we numerically investigate the conversion efficiency of the THz-wave generation for different pump wavelengths and rib heights of the waveguides. Finally, we summarize this paper in Section 4. 2. Phase matching condition and phase matching bandwidth for THz-wave generation We use degenerate FWM to generate THz-wave, which typically involves two pump photons at angular frequency ωp passing their energy to a signal wave at angular frequency ωs and a THz-wave at angular frequency ωTHz. Figure 1 shows the energy conservation diagrams and phase-matching condition for collinear configuration, which ensures that the THz-wave is generated through FWM and grows while copropagating with the pump and signal beam. These relationships can be written as the following equations [20]:
2ωp − ωs − ωTHz = 0,
(1)
ks + kTHz − 2kp + k NL = 0,
(2)
where kp, ks and kTHz represent the propagation wave number of pump, signal and THz-wave, respectively. kNL is the nonlinear phase mismatch, which induced by self phase modulation (SPM) and cross phase modulation (XPM) [21]. We can also define kL = ks + kTHz-2kp as the linear phase mismatch due to dispersion [22]. Since the signal and THz-wave are located symmetrically around the pump frequency, the linear phase mismatch only depends on evenorder dispersion parameters as [20] ∞
k L = β 2p Ωsp2 + 2∑
β 2mp
m=2 (2m)!
Ωsp2 m ,
(3)
where β2p is the group-velocity dispersion, and β2mp is the even-order dispersion at the pump frequency. Ωsp = ωs-ωp = ωp-ωTHz is the signal-pump (or pump-THz) frequency detuning, which is a large value due to ωTHz
