Tunable terahertz wave difference frequency generation in a graphene/AlGaAs surface plasmon waveguide
Graphene-based surface plasmon waveguides (SPWs) show high confinement well beyond the diffraction limit at terahertz frequencies. By combining a graphene SPW and nonlinear material, we propose a novel graphene/AlGaAs SPW structure for terahertz wave difference frequency generation (DFG) under near-infrared pumps. The composite waveguide, which supports single-mode operation at terahertz frequencies and guides two pumps by a high-index-contrast AlGaAs/AlOx structure, can confine terahertz waves tightly and realize good mode field overlap of three waves. The phase-matching condition is satisfied via artificial birefringence in an AlGaAs/AlOx waveguide together with the tunability of graphene, and the phase-matching terahertz wave frequency varies from 4 to 7 THz when the Fermi energy level of graphene changes from 0.848 to 2.456 eV. Based on the coupled-mode theory, we investigate the power-normalized conversion efficiency for the tunable terahertz wave DFG process by using the finite difference method under continuous wave pumps, where the tunable bandwidth can reach 2 THz with considerable conversion efficiency. To exploit the high peak powers of pulses, we also discuss optical pulse evolutions for pulse-pumped terahertz wave DFG processes.
基金项目：National Natural Science Foundation of China (NSFC)10.13039/501100001809 (11547187, 11405073, 61405073); Shandong Provincial Key R&D Program (2017CXGC0416).
Liangling Wang：School of Physics and Technology, University of Jinan, Jinan 250022, China
Lijuan Chen：School of Physics and Technology, University of Jinan, Jinan 250022, China
Jing Wang：School of Physics and Technology, University of Jinan, Jinan 250022, China
Haikun Zhang：School of Physics and Technology, University of Jinan, Jinan 250022, China
Wei Xia：School of Physics and Technology, University of Jinan, Jinan 250022, Chinae-mail: firstname.lastname@example.org
【1】K. S. Novoselov, V. I. Fal’Ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490 , 192–200 (2012).
【2】Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4 , 803–810 (2010).
【3】S. Liu, Z. Li, Y. Ge, H. Wang, R. Yue, X. Jiang, J. Li, Q. Wen, and H. Zhang, “Graphene/phosphorene nano-heterojunction: facile synthesis, nonlinear optics, and ultrafast photonics applications with enhanced performance,” Photon. Res. 5 , 662–668 (2017).
【4】Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5 , 411–415 (2011).
【5】Y. Wu, B. C. Yao, A. Q. Zhang, X. L. Cao, Z. G. Wang, Y. J. Rao, Y. Gong, W. Zhang, Y. F. Chen, and K. S. Chiang, “Graphene-based D-shaped fiber multicore mode interferometer for chemical gas sensing,” Opt. Lett. 39 , 6030–6033 (2014).
【6】M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12 , 1482–1485 (2012).
【7】L. Luo, K. Wang, C. Ge, K. Guo, F. Shen, Z. Yin, and Z. Guo, “Actively controllable terahertz switches with graphene-based nongroove gratings,” Photon. Res. 5 , 604–611 (2017).
【8】T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4 , 297–301 (2010).
【9】H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105 , 091111 (2014).
【10】L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12 , 3711–3715 (2012).
【11】A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6 , 749–758 (2012).
【12】H. Lu, X. Gan, D. Mao, and J. Zhao, “Graphene-supported manipulation of surface plasmon polaritons in metallic nanowaveguides,” Photon. Res. 5 , 162–167 (2017).
【13】M. Jablan, M. Solja?i?, and H. Buljan, “Plasmons in graphene: fundamental properties and potential applications,” Proc. IEEE 101 , 1689–1704 (2013).
【14】A. Vakil, and N. Engheta, “Transformation optics using graphene,” Science 332 , 1291–1294 (2011).
【15】C. Zhao, D. Mao, J. Zhao, L. Han, L. Fang, X. Gan, and Y. Wang, “Graphene-assisted all-fiber phase shifter and switching,” Optica 2 , 468–471 (2015).
【16】F. Xie, H. J. Li, J. P. Liu, L. L. Wang, S. X. Xia, X. Zhai, X. Luo, and X. J. Shang, “Graphene-based long-range SPP hybrid waveguide with ultra-long propagation length in mid-infrared range,” Opt. Express 24 , 5376–5386 (2016).
【17】L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, and Y. R. Shen, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6 , 630–634 (2011).
【18】C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101 , 111609 (2012).
【19】T. J. Constant, S. M. Hornett, D. E. Chang, and E. Hendry, “All-optical generation of surface plasmons in graphene,” Nat. Phys. 12 , 124–127 (2016).
【20】X. He, and S. Kim, “Graphene-supported tunable waveguide structure in the terahertz regime,” J. Opt. Soc. Am. B 30 , 2461–2468 (2013).
【21】X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32 , 4199–4203 (2014).
【22】W. Xu, Z. H. Zhu, K. Liu, J. F. Zhang, X. D. Yuan, Q. S. Lu, and S. Q. Qin, “Dielectric loaded graphene plasmon waveguide,” Opt. Express 23 , 5147–5153 (2015).
【23】M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1 , 97–105 (2007).
【24】A. Barh, B. M. A. Rahman, B. P. Pal, G. P. Agrawal, and R. K. Varshney, “Plastic fiber design for THz generation through wavelength translation,” Opt. Lett. 40 , 2107–2110 (2015).
【25】Y. Sun, G. Qiao, and G. Sun, “Direct generation of graphene plasmonic polaritons at THz frequencies via four wave mixing in the hybrid graphene sheets waveguides,” Opt. Express 22 , 27880–27891 (2014).
【26】Y. Takushima, S. Shin, and Y. C. Chung, “Design of a LiNbO3 ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration,” Opt. Express 15 , 14783–14792 (2007).
【27】Y. Huang, T. Wang, Y. Lin, C. Lee, M. Chuang, Y. Lin, and F. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express 19 , 24577–24582 (2011).
【28】Y. H. Avetisyan, “Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique,” Opt. Lett. 35 , 2508–2510 (2010).
【29】C. M. Staus, T. F. Kuech, and L. McCaughan, “AlxGa1?xAs nested waveguide heterostructures for continuously phase-matched terahertz difference frequency generation,” Opt. Express 18 , 2332–2338 (2010).
【30】T. Chen, J. Sun, L. Li, and J. Tang, “Proposal for efficient terahertz-wave difference frequency generation in an AlGaAs photonic crystal waveguide,” J. Lightwave Technol. 30 , 2156–2162 (2012).
【31】Z. Ruan, G. Veronis, K. L. Vodopyanov, M. M. Fejer, and S. Fan, “Enhancement of optics-to-THz conversion efficiency by metallic slot waveguides,” Opt. Express 17 , 13502–13515 (2009).
【32】Y. Ge, J. Cao, Z. Shen, Y. Zheng, X. Chen, and W. Wan, “Terahertz wave generation by plasmonic-enhanced difference-frequency generation,” J. Opt. Soc. Am. B 31 , 1533–1538 (2014).
【33】S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, “Influence of scattering and two-photon absorption on the optical loss in GaAs–A2O3 nonlinear waveguides measured using femtosecond pulses,” IEEE J. Quantum. Electron. 39 , 478–486 (2003).
【34】J. Ota, W. Narita, I. Ohta, T. Matsushita, and T. Kondo, “Fabrication of periodically-inverted AlGaAs waveguides for quasi-phase-matched wavelength conversion at 1.55?μm,” Jpn. J. Appl. Phys. 48 , 04C110 (2009).
【35】E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
【36】M. Pu, L. Ottaviano, E. Semenova, and K. Yvind, “Efficient frequency comb generation in AlGaAs-on-insulator,” Optica 3 , 823–826 (2016).
【37】T. W. Kim, T. Matsushita, and T. Kondo, “Phase-matched second-harmonic generation in thin rectangular high-index-contrast AlGaAs waveguides,” Appl. Phys. Express 4 , 082201 (2011).
【38】Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15 , 8271–8276 (2015).
【39】C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30?GHz bandwidth,” Nat. Photonics 9 , 511–514 (2015).
【40】J. Wang, J. Sun, and Q. Sun, “Proposal for all-optical format conversion based on a periodically poled lithium niobate loop mirror,” Opt. Lett. 32 , 1477–1479 (2007).
【41】P. Y. Chen, and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5 , 5855–5863 (2011).
【42】M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474 , 64–67 (2011).
【43】F. H. L. Koppens, D. E. Chang, and F. J. G. D. Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11 , 3370–3377 (2011).
【44】G. Agrawal, Nonlinear Fiber Optics , 4th ed. (Academic, 2007).
【45】L. Ottaviano, M. Pu, E. Semenova, and K. Yvind, “Low-loss high-confinement waveguides and microring resonators in AlGaAs-on-insulator,” Opt. Lett. 41 , 3996–3999 (2016).
【46】Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487 , 82–85 (2012).
【47】K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146 , 351–355 (2008).
Tao Chen, Liangling Wang, Lijuan Chen, Jing Wang, Haikun Zhang, and Wei Xia, "Tunable terahertz wave difference frequency generation in a graphene/AlGaAs surface plasmon waveguide," Photonics Research 6(3), 186-192 (2018)