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研究了由泵浦光和探测光同时驱动的石墨烯光力系统中的非线性光学现象, 如光学双稳态和四波混频现象. 通过控制泵浦光功率强度和失谐能有效操控光学双稳态. 对石墨烯光力系统中的四波混频研究发现四波混频谱中尖峰的位置正对应石墨烯振子频率的数值, 因此给出一种测量石墨烯振子频率的非线性光学方法. 此外, 基于对石墨烯光力系统中四波混频的研究进一步理论提出一种非线性光学质量传感方案. 通过探测四波混频谱中由于纳米颗粒质量引起的机械共振频移可直接测出沉积在石墨烯振子面上的纳米颗粒的质量. 该非线性光学质量传感方案将对探测噪声免疫, 并且将在高精度及高分辨率质量传感器件方面有着潜在应用.Graphene, atomically thin two-dimensional (2D) nanomaterial consisting of a single layer of carbon atoms, has received tremendous attention in the past few decades. Graphene may be considered as an excellent nanomaterial for fabricating nanomechanical resonator systems to investigate the quantum behavior of the motion of micromechanical resonators because of its unique properties of low mass density, high frequency, high quality-factor, and intrinsically small size. Additionally, graphene optomechanics based on a bilayer graphene resonator coupled to a microwave on-chip cavity, where light and micromechanical motion interact via the radiation pressure, has been demonstrtated experimentally recently. In this work, we demonstrate theoretically the nonlinear optical effect including optical bistability and four-wave mixing under the regimes woth different parameters and detunings in a graphene resonator-microwave cavity system. When the graphene optomechanics is driven by one strong pump laser beam, we find that the optical bistability can be controlled by tuning the power and the frequency of the pump beam. The four-wave mixing (FWM) phenomenon is also investigated and we find that sharp peaks in the FWM spectrum exactly are located at the resonant frequency of graphene resonator. Therefore, a straight nonlinear optical means for determining the resonant frequency of the graphene resonator is presented. Setting the cavity field resonating with pump field, and then scanning the probe frequency across the cavity frequency, one can easily and exactly obtain the resonant frequency of the resonator from the FWM spectrum. We further theoretically propose a mass sensor based on the graphene optomechanical system. The mass of external nanoparticles deposited onto the graphene resonator can be measured conveniently by tracking the shift of resonant frequency due to mass changing in the FWM spectrum. Compared with optomechanical mass sensors in linear regime, the nonlinear optical mass sensor may be immune to the detection noise. The system may have potential applications in communication networks for frequency conversion and provide a new platform for high sensitive sensing devices.
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Keywords:
- graphene optomechanics /
- optical bistability /
- four-wave mixing /
- mass sensor
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图 3 (a)在失谐
${\varDelta _{\rm{p}}} = {\omega _{\rm{m}}}$ 时, 腔内光子数${n_{\rm{c}}}$ 作为泵浦功率P的函数; (b) 在失谐${\varDelta _{\rm{p}}} = - {\omega _{\rm{m}}}$ 时, 腔内光子数${n_{\rm{c}}}$ 作为泵浦功率P的函数Fig. 3. (a) The mean intracavity photon number
${n_{\rm{c}}}$ as a function of P for${\varDelta _{\rm{p}}} = {\omega _{\rm{m}}}$ ; (b) mean intracavity photon number${n_{\rm{c}}}$ as a function of P for${\varDelta _{\rm{p}}} = - {\omega _{\rm{m}}}$ .图 4 (a) 在四个不同石墨烯振子频率时, 四波混频谱FWM作为探测-腔失谐
${\varDelta _{\rm{s}}}$ 的函数; (b) 和 (c)分别是左边和右边尖峰的放大Fig. 4. (a) The four-wave mixing (FWM) spectrum as a function of probe-cavity detuning
${\varDelta _{\rm{s}}}$ under four different graphene resonator frequencies; (b) and (c) are the amplifications of the left and right peaks.图 5 当把纳米颗粒沉积到石墨烯振子表面上时, 四波混频谱的频移. 插图是纳米颗粒的质量与频移之间的线性关系
Fig. 5. The four-wave mixing (FWM) spectrum after landing the nanoparticles on the surface of graphene resonator and the color curves shows the mechanical frequency-shifts. The inset shows the linear relationship between the frequency-shifts and the mass of the nanoparticles.
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[1] Chen C, Rosenblatt S, Bolotin K I, Kalb W, Kim P, Kymissis I, Stormer H L, Heinz T F, Hone J 2009 Nat. Nanotechnol. 4 861
Google Scholar
[2] Eichler A, Moser J, Chaste J, Zdrojek M, Wilson-Rae I, Bachtold A 2011 Nat. Nanotechnol. 6 339
Google Scholar
[3] Song X, Oksanen M, Sillanpää M A, Craighead H G, Parpia J M, Hakonen P J 2012 Nano. Lett. 12 198
Google Scholar
[4] Chen C, Lee S, Deshpande V V, Lee G H, Lekas M, Shepard K, Hone J 2013 Nat. Nanotechnol. 8 923
Google Scholar
[5] Bunch J S, van der Zande A M, Verbridge S S, Frank I W, Tanenbaum D M, Parpia J M, Craighead H G, McEuen P L 2007 Science 315 490
Google Scholar
[6] Moser J, Güttinger J, Eichler A, Esplandiu M J, Liu D E, Dykman M I, Bachtold A 2013 Nat. Nanotechnol. 8 493
Google Scholar
[7] Stapfner S, Ost L, Hunger D, Reichel J, Favero I, Weig E M 2013 Appl. Phys. Lett. 102 151910
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[8] Chiu H Y, Hung P, Postma H W C 2008 Nano. Lett. 8 4342
Google Scholar
[9] Chaste J, Eichler A, Moser J, Ceballos G, Rurali R, Bachtold A A 2012 Nat. Nanotechnol. 7 301
Google Scholar
[10] Singh V, Sengupta S, Solanki H S, Dhall R, Allain A, Dhara S, Pant P, Deshmukh M M 2010 Nanotechnology 211 65204
[11] Aspelmeyer M, Kippenberg T J, Marquardt F 2014 Rev. Mod. Phys. 86 1391
Google Scholar
[12] O’Connell A D, Hofheinz M, Ansmann M, Bialczak R C, Lenander M, Lucero E, Neeley M, Sank D, Wang H, Weides M, Wenner J, Martinis J M, Cleland A N 2010 Nature 464 697
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[13] Teufel J D, Donner T, Li D, Harlow J W, Allman M S, Cicak K, Sirois A J, Whittaker J D, Lehnert K W, Simmonds R W 2011 Nature 475 359
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[14] Chan J, Alegre T P M, Safavi-Naeini A H, Hill J T, Krause A, Gröblacher S, Aspelmeyer M, Painter O 2011 Nature 478 89
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[15] Barton R A, Storch I R, Adiga V P, Sakakibara R, Cipriany B R, Ilic B, Wang S P, Ong P, McEuen P L, Parpia J M, Craighead F G 2012 Nano. Lett. 12 4681
Google Scholar
[16] Peterson R W, Purdy T P, Kampel N S, Andrews R W, Yu P L, Lehnert K W, Regal C A 2016 Phys. Rev. Lett. 116 063601
Google Scholar
[17] Chen H J 2018 J. Appl. Phys. 124 153102
Google Scholar
[18] Rossi M, Mason D, Chen J, Tsaturyan Y, Schliesser A 2018 Nature 563 53
Google Scholar
[19] Grudinin I S, Lee H, Painter O, Vahala K J, 2010 Phys. Rev. Lett. 104 083901
Google Scholar
[20] Jing H, Özdemir S K, Lü X Y, Zhang J, Yang L, Nori F 2014 Phys. Rev. Lett. 113 053604
Google Scholar
[21] Brooks D W C, Botter T, Schreppler S, Purdy T P, Brahms N, Stamper-Kurn D M 2012 Nature 488 476
Google Scholar
[22] Safavi-Naeini A H, Gröblacher S, Hill J T, Chan J, Aspelmeyer M, Painter O 2013 Nature 500 185
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[23] Purdy T P, Yu P L, Peterson R W, Kampel N S, Regal C A 2013 Phys. Rev. X 3 031012
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Google Scholar
[25] Weis S, Riviere R, Deleglise S, Gavartin E, Arcizet O, Schliesser A, Kippenberg T J 2010 Science 330 1520
Google Scholar
[26] Teufel J D, Li D, Allman M S, Cicak K, Sirois A J, Whittaker J D, Simmonds R W 2011 Nature 471 204
Google Scholar
[27] Safavi-Naeini A H, Alegre T P M, Chan J, Eichenfield M, Winger M, Lin Q, Hill J T, Chang D E, Painter O 2011 Nature 472 69
Google Scholar
[28] Karuza M, Biancofiore C, Bawaj M, Molinelli C, Galassi M, Natali R, Tombesi P, Di Giuseppe G, Vitali D 2013 Phys. Rev. A 88 013804
Google Scholar
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Google Scholar
[30] Fan L, Fong KY, Poot M, Tang H X 2015 Nat. Commun. 6 5850
Google Scholar
[31] Massel F, Heikkilä T T, Pirkkalainen J M, Cho S U, Saloniemi H, Hakonen P J, Sillanpää M A 2011 Nature 480 351
Google Scholar
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[33] Jiang Y, Maayani S, Carmon T, Nori F, Jing H 2018 Phys. Rev. Appl. 10 064037
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
Chen X, Liu X W, Zhang K Y, Yuan C H, Zhang W P 2015 Acta Phys. Sin. 64 164211
Google Scholar
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Google Scholar
[56] Liu Y L, Wang C, Zhang J, Liu Y X 2018 Chin. Phys. B 27 024204
Google Scholar
[57] Dobrindt J M, Kippenberg T J 2010 Phys. Rev. Lett. 104 033901
Google Scholar
[58] Aspelmeyer M, Kippenberg T J, Marquardt F 2014 Rev. Mod. Phys. 86 1391
[59] Ekinci K L, Yang Y T, Roukes M L 2004 J. Appl. Phys. 95 2682
Google Scholar
[60] Yie Z, Zielke M A, Burgner C B, Turner K L 2011 J. Micromech. Microeng. 21 025027
Google Scholar
[61] Ramos D, Mertens J, Calleja M, Tamayo J 2008 Appl. Phys. Lett. 92 173108
Google Scholar
[62] Dai M D, Eom K, Kim C W 2009 Appl. Phys. Lett. 95 203104
Google Scholar
[63] Li J J, Zhu K.D 2013 Phys. Rep. 525 223
Google Scholar
[64] 陈华俊, 方贤文, 陈昌兆, 李洋 2016 物理学报 65 194205
Google Scholar
Chen H J, Fang X W, Chen C Z, Li Y 2016 Acta Phys. Sin. 65 194205
Google Scholar
[65] Chen H J, Chen C Z, Li Y, Fang X W, Tang X D 2017 Opt. Commun. 382 73
Google Scholar
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