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

Chen Hua-Jun

doi:10.7498/aps.69.20191745

Abstract

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.

Keywords:

Authors and contacts

Chen Hua-Jun

School of Mechanics and Photoelectric Physics, Anhui University of Science and Technology, Huainan 232001, China

Corresponding author: Chen Hua-Jun, chenphysics@126.com

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References

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[7]	Stapfner S, Ost L, Hunger D, Reichel J, Favero I, Weig E M 2013 Appl. Phys. Lett. 102 151910 Google Scholar
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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 Google 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 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
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[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
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[32]	Jing H, Özdemir S K, Lü X Y, Zhang J, Yang L, Nori F 2014 Phys. Rev. Lett. 113 053604
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[42]	Singh V, Bosman S J, Schneider B H, Blanter Y M, Castellanos-Gomez A, Steele G A 2014 Nat. Nanotechnol. 9 820 Google Scholar
[43]	Song X, Oksanen M, Li J, Hakonen P J, Sillanpää M A 2014 Phys. Rev. Lett. 113 027404 Google Scholar
[44]	Chen B, Jiang C, Zhu K D 2011 Phys. Rev. A 83 055803 Google Scholar
[45]	Chen B, Jiang C, Li J J, Zhu K D 2011 Phys. Rev. A 84 055802 Google Scholar
[46]	Sete E A, Eleuch H 2012 Phys. Rev. A 85 043824 Google Scholar
[47]	Kanamoto R, Meystre P 2010 Phys. Rev. Lett. 104 063601 Google 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 133602 Google Scholar
[49]	Yan D, Wang Z H, Ren C N, Gao H, Li Y, Wu J H 2015 Phys. Rev. A 91 023813 Google Scholar
[50]	Xiong W, Jin D Y, Qiu Y, Lam C H, You J Q 2016 Phys. Rev. A 93 023844 Google Scholar
[51]	Huang S, Agarwal G S 2010 Phys. Rev. A 81 033830 Google Scholar
[52]	Jiang C, Cui Y, Liu H 2013 Europhys. Lett. 104 34004 Google Scholar
[53]	严晓波, 杨柳, 田雪冬, 刘一谋, 张岩 2014 63 204201 Google Scholar Yan X B, Yang L, Tian X D, Liu Y M, Zhang Y 2014 Acta Phys. Sin. 63 204201 Google Scholar
[54]	陈雪, 刘晓威, 张可烨, 袁春华, 张卫平 2015 64 164211 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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[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
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[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 65 194205 Google Scholar Chen H J, Fang X W, Chen C Z, Li Y 2016 Acta Phys. Sin. 65 194205 Google Scholar
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Cited By

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 ${\omega _{\rm{s}}}$.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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 ${\varDelta _{\rm{p}}} = - {\omega _{\rm{m}}}$.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

map

[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 Google Scholar
[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 Google 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 475 359 Google 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 89 Google 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 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 Google 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 041803 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
[29]	Zhou X, Hocke F, Schliesser A, Marx A, Huebl H, Gross R, Kippenberg T J 2013 Nat. Phys. 9 179 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
[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 064037 Google Scholar
[34]	Jiao Y, Lü H, Qian J, Li Y, Jing H 2016 New J. Phys. 18 083034 Google Scholar
[35]	Lu T X, Jiao Y F, Zhang H L, Saif F, Jing H 2019 Phys. Rev. A 100 013813 Google Scholar
[36]	Zhang H, Saif F, Jiao Y, Jing H 2018 Opt. Express 26 25199 Google Scholar
[37]	Jiao Y F, Lu T X, Jing H 2018 Phys. Rev. A 97 013843 Google Scholar
[38]	Lü H, Özdemir S K, Kuang L M, Nori F, Jing H 2017 Phys. Rev. Appl. 8 044020 Google Scholar
[39]	Lü H, Wang C, Yang L, Jing H 2018 Phys. Rev. Appl. 10 014006 Google Scholar
[40]	Li B, Huang R, Xu X, Miranowicz A, Jing H 2019 Photonics Res. 7 630 Google Scholar
[41]	Weber P, Guttinger J, Tsioutsios I, Chang D E, Bachtold A 2014 Nano. Lett. 14 2854 Google Scholar
[42]	Singh V, Bosman S J, Schneider B H, Blanter Y M, Castellanos-Gomez A, Steele G A 2014 Nat. Nanotechnol. 9 820 Google Scholar
[43]	Song X, Oksanen M, Li J, Hakonen P J, Sillanpää M A 2014 Phys. Rev. Lett. 113 027404 Google Scholar
[44]	Chen B, Jiang C, Zhu K D 2011 Phys. Rev. A 83 055803 Google Scholar
[45]	Chen B, Jiang C, Li J J, Zhu K D 2011 Phys. Rev. A 84 055802 Google Scholar
[46]	Sete E A, Eleuch H 2012 Phys. Rev. A 85 043824 Google Scholar
[47]	Kanamoto R, Meystre P 2010 Phys. Rev. Lett. 104 063601 Google 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 133602 Google Scholar
[49]	Yan D, Wang Z H, Ren C N, Gao H, Li Y, Wu J H 2015 Phys. Rev. A 91 023813 Google Scholar
[50]	Xiong W, Jin D Y, Qiu Y, Lam C H, You J Q 2016 Phys. Rev. A 93 023844 Google Scholar
[51]	Huang S, Agarwal G S 2010 Phys. Rev. A 81 033830 Google Scholar
[52]	Jiang C, Cui Y, Liu H 2013 Europhys. Lett. 104 34004 Google Scholar
[53]	严晓波, 杨柳, 田雪冬, 刘一谋, 张岩 2014 63 204201 Google Scholar Yan X B, Yang L, Tian X D, Liu Y M, Zhang Y 2014 Acta Phys. Sin. 63 204201 Google Scholar
[54]	陈雪, 刘晓威, 张可烨, 袁春华, 张卫平 2015 64 164211 Google Scholar Chen X, Liu X W, Zhang K Y, Yuan C H, Zhang W P 2015 Acta Phys. Sin. 64 164211 Google Scholar
[55]	Liu Y C, Hu Y W, Wong C W, Xiao Y F 2013 Chin. Phys. B 22 114213 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 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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Vol. 69, Issue 13 - 2020-07-05

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