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Nonlinear optical effect and nonlinear optical mass sensor based on graphene optomechanical system

Chen Hua-Jun

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Nonlinear optical effect and nonlinear optical mass sensor based on graphene optomechanical system

Chen Hua-Jun
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  • 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.
      Corresponding author: Chen Hua-Jun, chenphysics@126.com
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    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 861Google Scholar

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    Eichler A, Moser J, Chaste J, Zdrojek M, Wilson-Rae I, Bachtold A 2011 Nat. Nanotechnol. 6 339Google Scholar

    [3]

    Song X, Oksanen M, Sillanpää M A, Craighead H G, Parpia J M, Hakonen P J 2012 Nano. Lett. 12 198Google Scholar

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    Chen C, Lee S, Deshpande V V, Lee G H, Lekas M, Shepard K, Hone J 2013 Nat. Nanotechnol. 8 923Google Scholar

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    Moser J, Güttinger J, Eichler A, Esplandiu M J, Liu D E, Dykman M I, Bachtold A 2013 Nat. Nanotechnol. 8 493Google Scholar

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    Stapfner S, Ost L, Hunger D, Reichel J, Favero I, Weig E M 2013 Appl. Phys. Lett. 102 151910Google Scholar

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    Chiu H Y, Hung P, Postma H W C 2008 Nano. Lett. 8 4342Google Scholar

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    Chan J, Alegre T P M, Safavi-Naeini A H, Hill J T, Krause A, Gröblacher S, Aspelmeyer M, Painter O 2011 Nature 478 89Google Scholar

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    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 4681Google Scholar

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    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 063601Google Scholar

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    Chen H J 2018 J. Appl. Phys. 124 153102Google Scholar

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    Rossi M, Mason D, Chen J, Tsaturyan Y, Schliesser A 2018 Nature 563 53Google Scholar

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    Grudinin I S, Lee H, Painter O, Vahala K J, 2010 Phys. Rev. Lett. 104 083901Google Scholar

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    Jing H, Özdemir S K, Lü X Y, Zhang J, Yang L, Nori F 2014 Phys. Rev. Lett. 113 053604Google Scholar

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    Brooks D W C, Botter T, Schreppler S, Purdy T P, Brahms N, Stamper-Kurn D M 2012 Nature 488 476Google Scholar

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    Safavi-Naeini A H, Gröblacher S, Hill J T, Chan J, Aspelmeyer M, Painter O 2013 Nature 500 185Google Scholar

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    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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    Agarwal G S, Huang S M 2010 Phys. Rev. A 81 041803Google Scholar

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    Teufel J D, Li D, Allman M S, Cicak K, Sirois A J, Whittaker J D, Simmonds R W 2011 Nature 471 204Google Scholar

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    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 69Google Scholar

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    Karuza M, Biancofiore C, Bawaj M, Molinelli C, Galassi M, Natali R, Tombesi P, Di Giuseppe G, Vitali D 2013 Phys. Rev. A 88 013804Google Scholar

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    Zhou X, Hocke F, Schliesser A, Marx A, Huebl H, Gross R, Kippenberg T J 2013 Nat. Phys. 9 179Google Scholar

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    Fan L, Fong KY, Poot M, Tang H X 2015 Nat. Commun. 6 5850Google Scholar

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    Massel F, Heikkilä T T, Pirkkalainen J M, Cho S U, Saloniemi H, Hakonen P J, Sillanpää M A 2011 Nature 480 351Google Scholar

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    Jing H, Özdemir S K, Lü X Y, Zhang J, Yang L, Nori F 2014 Phys. Rev. Lett. 113 053604

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    Jiang Y, Maayani S, Carmon T, Nori F, Jing H 2018 Phys. Rev. Appl. 10 064037Google Scholar

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    Jiao Y, Lü H, Qian J, Li Y, Jing H 2016 New J. Phys. 18 083034Google Scholar

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    Lu T X, Jiao Y F, Zhang H L, Saif F, Jing H 2019 Phys. Rev. A 100 013813Google Scholar

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    Lü H, Özdemir S K, Kuang L M, Nori F, Jing H 2017 Phys. Rev. Appl. 8 044020Google Scholar

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    Lü H, Wang C, Yang L, Jing H 2018 Phys. Rev. Appl. 10 014006Google Scholar

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    Li B, Huang R, Xu X, Miranowicz A, Jing H 2019 Photonics Res. 7 630Google Scholar

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    Weber P, Guttinger J, Tsioutsios I, Chang D E, Bachtold A 2014 Nano. Lett. 14 2854Google Scholar

    [42]

    Singh V, Bosman S J, Schneider B H, Blanter Y M, Castellanos-Gomez A, Steele G A 2014 Nat. Nanotechnol. 9 820Google Scholar

    [43]

    Song X, Oksanen M, Li J, Hakonen P J, Sillanpää M A 2014 Phys. Rev. Lett. 113 027404Google Scholar

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    Chen B, Jiang C, Zhu K D 2011 Phys. Rev. A 83 055803Google Scholar

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    Chen B, Jiang C, Li J J, Zhu K D 2011 Phys. Rev. A 84 055802Google Scholar

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    Sete E A, Eleuch H 2012 Phys. Rev. A 85 043824Google Scholar

    [47]

    Kanamoto R, Meystre P 2010 Phys. Rev. Lett. 104 063601Google Scholar

    [48]

    Purdy T P, Brooks. D W C, Botter T, Brahms N, Ma Z Y, Stamper-Kurn D M 2010 Phys. Rev. Lett. 105 133602Google Scholar

    [49]

    Yan D, Wang Z H, Ren C N, Gao H, Li Y, Wu J H 2015 Phys. Rev. A 91 023813Google Scholar

    [50]

    Xiong W, Jin D Y, Qiu Y, Lam C H, You J Q 2016 Phys. Rev. A 93 023844Google Scholar

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    Huang S, Agarwal G S 2010 Phys. Rev. A 81 033830Google Scholar

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    Jiang C, Cui Y, Liu H 2013 Europhys. Lett. 104 34004Google Scholar

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    严晓波, 杨柳, 田雪冬, 刘一谋, 张岩 2014 物理学报 63 204201Google Scholar

    Yan X B, Yang L, Tian X D, Liu Y M, Zhang Y 2014 Acta Phys. Sin. 63 204201Google Scholar

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    陈雪, 刘晓威, 张可烨, 袁春华, 张卫平 2015 物理学报 64 164211Google Scholar

    Chen X, Liu X W, Zhang K Y, Yuan C H, Zhang W P 2015 Acta Phys. Sin. 64 164211Google Scholar

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    Liu Y C, Hu Y W, Wong C W, Xiao Y F 2013 Chin. Phys. B 22 114213Google Scholar

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    Liu Y L, Wang C, Zhang J, Liu Y X 2018 Chin. Phys. B 27 024204Google Scholar

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    Dobrindt J M, Kippenberg T J 2010 Phys. Rev. Lett. 104 033901Google 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 2682Google Scholar

    [60]

    Yie Z, Zielke M A, Burgner C B, Turner K L 2011 J. Micromech. Microeng. 21 025027Google Scholar

    [61]

    Ramos D, Mertens J, Calleja M, Tamayo J 2008 Appl. Phys. Lett. 92 173108Google Scholar

    [62]

    Dai M D, Eom K, Kim C W 2009 Appl. Phys. Lett. 95 203104Google Scholar

    [63]

    Li J J, Zhu K.D 2013 Phys. Rep. 525 223Google Scholar

    [64]

    陈华俊, 方贤文, 陈昌兆, 李洋 2016 物理学报 65 194205Google Scholar

    Chen H J, Fang X W, Chen C Z, Li Y 2016 Acta Phys. Sin. 65 194205Google Scholar

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    Chen H J, Chen C Z, Li Y, Fang X W, Tang X D 2017 Opt. Commun. 382 73Google Scholar

  • 图 1  石墨烯光力系统与非线性质量传感示意图, 其中该系统由一束频率为${\omega _{\rm{p}}}$的泵浦光和一束频率${\omega _{\rm{s}}}$的信号光驱动

    Figure 1.  Schematic of graphene optomechanical system and nonlinear optical mass sensor driven by a strong pump field ${\omega _{\rm{p}}}$ and a weak signal field ${\omega _{\rm{s}}}$.

    图 2  在三个不同泵浦功率条件下石墨烯光力腔内光子数作为腔-泵浦失谐${\varDelta _{\rm{p}}}$的函数

    Figure 2.  Mean intracavity photon number of graphene optomechanical cavity as a function of the cavity-pump detuning ${\varDelta _{\rm{p}}}$ with four pump powers.

    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

    Figure 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

    Figure 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

    Figure 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.

  • [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 861Google Scholar

    [2]

    Eichler A, Moser J, Chaste J, Zdrojek M, Wilson-Rae I, Bachtold A 2011 Nat. Nanotechnol. 6 339Google Scholar

    [3]

    Song X, Oksanen M, Sillanpää M A, Craighead H G, Parpia J M, Hakonen P J 2012 Nano. Lett. 12 198Google Scholar

    [4]

    Chen C, Lee S, Deshpande V V, Lee G H, Lekas M, Shepard K, Hone J 2013 Nat. Nanotechnol. 8 923Google 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 490Google Scholar

    [6]

    Moser J, Güttinger J, Eichler A, Esplandiu M J, Liu D E, Dykman M I, Bachtold A 2013 Nat. Nanotechnol. 8 493Google Scholar

    [7]

    Stapfner S, Ost L, Hunger D, Reichel J, Favero I, Weig E M 2013 Appl. Phys. Lett. 102 151910Google Scholar

    [8]

    Chiu H Y, Hung P, Postma H W C 2008 Nano. Lett. 8 4342Google Scholar

    [9]

    Chaste J, Eichler A, Moser J, Ceballos G, Rurali R, Bachtold A A 2012 Nat. Nanotechnol. 7 301Google 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 1391Google 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 697Google Scholar

    [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 359Google Scholar

    [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 89Google Scholar

    [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 4681Google 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 063601Google Scholar

    [17]

    Chen H J 2018 J. Appl. Phys. 124 153102Google Scholar

    [18]

    Rossi M, Mason D, Chen J, Tsaturyan Y, Schliesser A 2018 Nature 563 53Google Scholar

    [19]

    Grudinin I S, Lee H, Painter O, Vahala K J, 2010 Phys. Rev. Lett. 104 083901Google Scholar

    [20]

    Jing H, Özdemir S K, Lü X Y, Zhang J, Yang L, Nori F 2014 Phys. Rev. Lett. 113 053604Google Scholar

    [21]

    Brooks D W C, Botter T, Schreppler S, Purdy T P, Brahms N, Stamper-Kurn D M 2012 Nature 488 476Google Scholar

    [22]

    Safavi-Naeini A H, Gröblacher S, Hill J T, Chan J, Aspelmeyer M, Painter O 2013 Nature 500 185Google Scholar

    [23]

    Purdy T P, Yu P L, Peterson R W, Kampel N S, Regal C A 2013 Phys. Rev. X 3 031012

    [24]

    Agarwal G S, Huang S M 2010 Phys. Rev. A 81 041803Google Scholar

    [25]

    Weis S, Riviere R, Deleglise S, Gavartin E, Arcizet O, Schliesser A, Kippenberg T J 2010 Science 330 1520Google Scholar

    [26]

    Teufel J D, Li D, Allman M S, Cicak K, Sirois A J, Whittaker J D, Simmonds R W 2011 Nature 471 204Google 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 69Google 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 013804Google Scholar

    [29]

    Zhou X, Hocke F, Schliesser A, Marx A, Huebl H, Gross R, Kippenberg T J 2013 Nat. Phys. 9 179Google Scholar

    [30]

    Fan L, Fong KY, Poot M, Tang H X 2015 Nat. Commun. 6 5850Google Scholar

    [31]

    Massel F, Heikkilä T T, Pirkkalainen J M, Cho S U, Saloniemi H, Hakonen P J, Sillanpää M A 2011 Nature 480 351Google Scholar

    [32]

    Jing H, Özdemir S K, Lü X Y, Zhang J, Yang L, Nori F 2014 Phys. Rev. Lett. 113 053604

    [33]

    Jiang Y, Maayani S, Carmon T, Nori F, Jing H 2018 Phys. Rev. Appl. 10 064037Google Scholar

    [34]

    Jiao Y, Lü H, Qian J, Li Y, Jing H 2016 New J. Phys. 18 083034Google Scholar

    [35]

    Lu T X, Jiao Y F, Zhang H L, Saif F, Jing H 2019 Phys. Rev. A 100 013813Google Scholar

    [36]

    Zhang H, Saif F, Jiao Y, Jing H 2018 Opt. Express 26 25199Google Scholar

    [37]

    Jiao Y F, Lu T X, Jing H 2018 Phys. Rev. A 97 013843Google Scholar

    [38]

    Lü H, Özdemir S K, Kuang L M, Nori F, Jing H 2017 Phys. Rev. Appl. 8 044020Google Scholar

    [39]

    Lü H, Wang C, Yang L, Jing H 2018 Phys. Rev. Appl. 10 014006Google Scholar

    [40]

    Li B, Huang R, Xu X, Miranowicz A, Jing H 2019 Photonics Res. 7 630Google Scholar

    [41]

    Weber P, Guttinger J, Tsioutsios I, Chang D E, Bachtold A 2014 Nano. Lett. 14 2854Google Scholar

    [42]

    Singh V, Bosman S J, Schneider B H, Blanter Y M, Castellanos-Gomez A, Steele G A 2014 Nat. Nanotechnol. 9 820Google Scholar

    [43]

    Song X, Oksanen M, Li J, Hakonen P J, Sillanpää M A 2014 Phys. Rev. Lett. 113 027404Google Scholar

    [44]

    Chen B, Jiang C, Zhu K D 2011 Phys. Rev. A 83 055803Google Scholar

    [45]

    Chen B, Jiang C, Li J J, Zhu K D 2011 Phys. Rev. A 84 055802Google Scholar

    [46]

    Sete E A, Eleuch H 2012 Phys. Rev. A 85 043824Google Scholar

    [47]

    Kanamoto R, Meystre P 2010 Phys. Rev. Lett. 104 063601Google Scholar

    [48]

    Purdy T P, Brooks. D W C, Botter T, Brahms N, Ma Z Y, Stamper-Kurn D M 2010 Phys. Rev. Lett. 105 133602Google Scholar

    [49]

    Yan D, Wang Z H, Ren C N, Gao H, Li Y, Wu J H 2015 Phys. Rev. A 91 023813Google Scholar

    [50]

    Xiong W, Jin D Y, Qiu Y, Lam C H, You J Q 2016 Phys. Rev. A 93 023844Google Scholar

    [51]

    Huang S, Agarwal G S 2010 Phys. Rev. A 81 033830Google Scholar

    [52]

    Jiang C, Cui Y, Liu H 2013 Europhys. Lett. 104 34004Google Scholar

    [53]

    严晓波, 杨柳, 田雪冬, 刘一谋, 张岩 2014 物理学报 63 204201Google Scholar

    Yan X B, Yang L, Tian X D, Liu Y M, Zhang Y 2014 Acta Phys. Sin. 63 204201Google Scholar

    [54]

    陈雪, 刘晓威, 张可烨, 袁春华, 张卫平 2015 物理学报 64 164211Google Scholar

    Chen X, Liu X W, Zhang K Y, Yuan C H, Zhang W P 2015 Acta Phys. Sin. 64 164211Google Scholar

    [55]

    Liu Y C, Hu Y W, Wong C W, Xiao Y F 2013 Chin. Phys. B 22 114213Google Scholar

    [56]

    Liu Y L, Wang C, Zhang J, Liu Y X 2018 Chin. Phys. B 27 024204Google Scholar

    [57]

    Dobrindt J M, Kippenberg T J 2010 Phys. Rev. Lett. 104 033901Google 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 2682Google Scholar

    [60]

    Yie Z, Zielke M A, Burgner C B, Turner K L 2011 J. Micromech. Microeng. 21 025027Google Scholar

    [61]

    Ramos D, Mertens J, Calleja M, Tamayo J 2008 Appl. Phys. Lett. 92 173108Google Scholar

    [62]

    Dai M D, Eom K, Kim C W 2009 Appl. Phys. Lett. 95 203104Google Scholar

    [63]

    Li J J, Zhu K.D 2013 Phys. Rep. 525 223Google Scholar

    [64]

    陈华俊, 方贤文, 陈昌兆, 李洋 2016 物理学报 65 194205Google Scholar

    Chen H J, Fang X W, Chen C Z, Li Y 2016 Acta Phys. Sin. 65 194205Google Scholar

    [65]

    Chen H J, Chen C Z, Li Y, Fang X W, Tang X D 2017 Opt. Commun. 382 73Google Scholar

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Metrics
  • Abstract views:  5197
  • PDF Downloads:  124
  • Cited By: 0
Publishing process
  • Received Date:  13 November 2019
  • Accepted Date:  15 April 2020
  • Available Online:  09 May 2020
  • Published Online:  05 July 2020

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