Abstract

Gold nanorods can be optically trapped in aqueous solution and forced to rotate at kilohertz rates by circularly polarized laser light. This enables detailed investigations of local environmental parameters and processes, such as medium viscosity and nanoparticle–molecule reactions. Future applications may include nanoactuation and single-cell analysis. However, the influence of photothermal heating on the nanoparticle dynamics needs to be better understood in order to realize widespread and quantitative use. Here we analyze the hot Brownian motion of a rotating gold nanorod trapped in two dimensions by an optical tweezers using experiments and stochastic simulations. We show that, for typical settings, the effective rotational and translational Brownian temperatures are drastically different, being closer to the nanorod surface temperature and ambient temperature, respectively. Further, we show that translational dynamics can have a non-negligible influence on the rotational fluctuations due to the small size of a nanorod in comparison to the focal spot. These results are crucial for the development of gold nanorods into generic and quantitative optomechanical sensor and actuator elements.

© 2017 Optical Society of America

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References

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    [Crossref]
  36. A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13, 3129–3134 (2013).
    [Crossref]
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    [Crossref]
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    [Crossref]

2016 (2)

H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.-F. Joanny, G. Gompper, and T. Betz, “Equilibrium physics breakdown reveals the active nature of red blood cell flickering,” Nat. Phys. 12, 513–519 (2016).
[Crossref]

K. Neupane, D. A. Foster, D. R. Dee, H. Yu, F. Wang, and M. T. Woodside, “Direct observation of transition paths during the folding of proteins and nucleic acids,” Science 352, 239–242 (2016).
[Crossref]

2015 (2)

L. Shao, Z.-J. Yang, D. Andrén, P. Johansson, and M. Käll, “Gold nanorod rotary motors driven by resonant light scattering,” ACS Nano 9, 12542–12551 (2015).
[Crossref]

A. Lehmuskero, P. Johansson, H. Rubinsztein-Dunlop, L. M. Tong, and M. Käll, “Laser trapping of colloidal metal nanoparticles,” ACS Nano 9, 3453–3469 (2015).
[Crossref]

2014 (5)

G. Falasco, M. V. Gnann, D. Rings, and K. Kroy, “Effective temperatures of hot Brownian motion,” Phys. Rev. E 90, 032131 (2014).
[Crossref]

F. Hajizadeh, S. M. Mousavi, Z. S. Khaksar, and S. N. S. Reihani, “Extended linear detection range for optical tweezers using image-plane detection scheme,” J. Opt. 16, 105706 (2014).
[Crossref]

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

S. Kheifets, A. Simha, K. Melin, T. C. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
[Crossref]

M. Grießhammer and A. Rohrbach, “5D-Tracking of a nanorod in a focused laser beam—a theoretical concept,” Opt. Express 22, 6114–6132 (2014).
[Crossref]

2013 (6)

M. Braun and F. Cichos, “Optically controlled thermophoretic trapping of single nano-objects,” ACS Nano 7, 11200–11208 (2013).
[Crossref]

G. Baffou and R. Quidant, “Thermo-plasmonics: using metallic nanostructures as nano-sources of heat,” Laser Photon. Rev. 7, 171–187 (2013).
[Crossref]

L. Osinkina, S. Carretero-Palacios, J. Stehr, A. A. Lutich, F. Jäckel, and J. Feldmann, “Tuning DNA binding kinetics in an optical trap by plasmonic nanoparticle heating,” Nano Lett. 13, 3140–3144 (2013).
[Crossref]

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13, 3129–3134 (2013).
[Crossref]

G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
[Crossref]

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref]

2012 (3)

A. Ohlinger, A. Deak, A. A. Lutich, and J. Feldmann, “Optically trapped gold nanoparticle enables listening at the microscale,” Phys. Rev. Lett. 108, 018101 (2012).
[Crossref]

J. Croissant and J. I. Zink, “Nanovalve-controlled cargo release activated by plasmonic heating,” J. Am. Chem. Soc. 134, 7628–7631 (2012).
[Crossref]

D. Rings, D. Chakraborty, and K. Kroy, “Rotational hot Brownian motion,” New J. Phys. 14, 053012 (2012).
[Crossref]

2011 (1)

P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, “Brownian fluctuations and heating of an optically aligned gold nanorod,” Phys. Rev. Lett. 107, 037401 (2011).
[Crossref]

2010 (4)

L. M. Tong, V. D. Miljković, and M. Käll, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano Lett. 10, 268–273 (2010).
[Crossref]

D. Rings, R. Schachoff, M. Selmke, F. Cichos, and K. Kroy, “Hot Brownian motion,” Phys. Rev. Lett. 105, 090604 (2010).
[Crossref]

S. E. Lee and L. P. Lee, “Biomolecular plasmonics for quantitative biology and nanomedicine,” Curr. Opin. Biotechnol. 21, 489–497 (2010).
[Crossref]

F. Hajizadeh and S. N. S. Reihani, “Optimized optical trapping of gold nanoparticles,” Opt. Express 18, 551–559 (2010).
[Crossref]

2008 (3)

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[Crossref]

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Ann. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

C.-K. Chou, W.-L. Chen, P. T. Fwu, S.-J. Lin, H.-S. Lee, and C.-Y. Dong, “Polarization ellipticity compensation in polarization second-harmonic generation microscopy without specimen rotation,” J. Biomed. Opt. 13, 014005 (2008).
[Crossref]

2006 (3)

G. Volpe and D. Petrov, “Torque detection using Brownian fluctuations,” Phys. Rev. Lett. 97, 210603 (2006).
[Crossref]

X. H. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, “Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods,” J. Am. Chem. Soc. 128, 2115–2120 (2006).
[Crossref]

M. Pelton, M. Z. Liu, H. Y. Kim, G. Smith, P. Guyot-Sionnest, and N. F. Scherer, “Optical trapping and alignment of single gold nanorods by using plasmon resonances,” Opt. Lett. 31, 2075–2077 (2006).
[Crossref]

2004 (3)

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).
[Crossref]

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594–612 (2004).
[Crossref]

I. M. Tolić-Nørrelykke, K. Berg-Sørensen, and H. Flyvbjerg, “MatLab program for precision calibration of optical tweezers,” Comput. Phys. Commun. 159, 225–240 (2004).
[Crossref]

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 21–22 (2003).
[Crossref]

2001 (1)

R. L. Fogel’son and E. R. Likhachev, “Temperature dependence of viscosity,” Tech. Phys. 46, 1056–1059 (2001).
[Crossref]

1998 (2)

F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23, 7–9 (1998).
[Crossref]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[Crossref]

1994 (1)

1967 (1)

P. D. Welch, “The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust. 15, 70–73 (1967).
[Crossref]

1943 (1)

S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15, 1–89 (1943).
[Crossref]

Anders, J.

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

Andrén, D.

L. Shao, Z.-J. Yang, D. Andrén, P. Johansson, and M. Käll, “Gold nanorod rotary motors driven by resonant light scattering,” ACS Nano 9, 12542–12551 (2015).
[Crossref]

Audoly, B.

H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.-F. Joanny, G. Gompper, and T. Betz, “Equilibrium physics breakdown reveals the active nature of red blood cell flickering,” Nat. Phys. 12, 513–519 (2016).
[Crossref]

Auth, T.

H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.-F. Joanny, G. Gompper, and T. Betz, “Equilibrium physics breakdown reveals the active nature of red blood cell flickering,” Nat. Phys. 12, 513–519 (2016).
[Crossref]

Baffou, G.

G. Baffou and R. Quidant, “Thermo-plasmonics: using metallic nanostructures as nano-sources of heat,” Laser Photon. Rev. 7, 171–187 (2013).
[Crossref]

Barker, P.

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594–612 (2004).
[Crossref]

I. M. Tolić-Nørrelykke, K. Berg-Sørensen, and H. Flyvbjerg, “MatLab program for precision calibration of optical tweezers,” Comput. Phys. Commun. 159, 225–240 (2004).
[Crossref]

Betz, T.

H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.-F. Joanny, G. Gompper, and T. Betz, “Equilibrium physics breakdown reveals the active nature of red blood cell flickering,” Nat. Phys. 12, 513–519 (2016).
[Crossref]

Bishop, A. I.

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).
[Crossref]

Block, S. M.

Braun, M.

M. Braun and F. Cichos, “Optically controlled thermophoretic trapping of single nano-objects,” ACS Nano 7, 11200–11208 (2013).
[Crossref]

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Ann. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

Carretero-Palacios, S.

L. Osinkina, S. Carretero-Palacios, J. Stehr, A. A. Lutich, F. Jäckel, and J. Feldmann, “Tuning DNA binding kinetics in an optical trap by plasmonic nanoparticle heating,” Nano Lett. 13, 3140–3144 (2013).
[Crossref]

Chakraborty, D.

D. Rings, D. Chakraborty, and K. Kroy, “Rotational hot Brownian motion,” New J. Phys. 14, 053012 (2012).
[Crossref]

Chandrasekhar, S.

S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15, 1–89 (1943).
[Crossref]

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Ann. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

Chen, W.-L.

C.-K. Chou, W.-L. Chen, P. T. Fwu, S.-J. Lin, H.-S. Lee, and C.-Y. Dong, “Polarization ellipticity compensation in polarization second-harmonic generation microscopy without specimen rotation,” J. Biomed. Opt. 13, 014005 (2008).
[Crossref]

Chou, C.-K.

C.-K. Chou, W.-L. Chen, P. T. Fwu, S.-J. Lin, H.-S. Lee, and C.-Y. Dong, “Polarization ellipticity compensation in polarization second-harmonic generation microscopy without specimen rotation,” J. Biomed. Opt. 13, 014005 (2008).
[Crossref]

Cichos, F.

M. Braun and F. Cichos, “Optically controlled thermophoretic trapping of single nano-objects,” ACS Nano 7, 11200–11208 (2013).
[Crossref]

D. Rings, R. Schachoff, M. Selmke, F. Cichos, and K. Kroy, “Hot Brownian motion,” Phys. Rev. Lett. 105, 090604 (2010).
[Crossref]

Croissant, J.

J. Croissant and J. I. Zink, “Nanovalve-controlled cargo release activated by plasmonic heating,” J. Am. Chem. Soc. 134, 7628–7631 (2012).
[Crossref]

Deak, A.

A. Ohlinger, A. Deak, A. A. Lutich, and J. Feldmann, “Optically trapped gold nanoparticle enables listening at the microscale,” Phys. Rev. Lett. 108, 018101 (2012).
[Crossref]

Dee, D. R.

K. Neupane, D. A. Foster, D. R. Dee, H. Yu, F. Wang, and M. T. Woodside, “Direct observation of transition paths during the folding of proteins and nucleic acids,” Science 352, 239–242 (2016).
[Crossref]

Deesuwan, T.

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

Dhont, J. K. G.

J. K. G. Dhont, An Introduction to Dynamics of Colloids (Elsevier, 1996).

Dong, C.-Y.

C.-K. Chou, W.-L. Chen, P. T. Fwu, S.-J. Lin, H.-S. Lee, and C.-Y. Dong, “Polarization ellipticity compensation in polarization second-harmonic generation microscopy without specimen rotation,” J. Biomed. Opt. 13, 014005 (2008).
[Crossref]

El-Sayed, I. H.

X. H. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, “Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods,” J. Am. Chem. Soc. 128, 2115–2120 (2006).
[Crossref]

El-Sayed, M. A.

X. H. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, “Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods,” J. Am. Chem. Soc. 128, 2115–2120 (2006).
[Crossref]

Falasco, G.

G. Falasco, M. V. Gnann, D. Rings, and K. Kroy, “Effective temperatures of hot Brownian motion,” Phys. Rev. E 90, 032131 (2014).
[Crossref]

Fedosov, D. A.

H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.-F. Joanny, G. Gompper, and T. Betz, “Equilibrium physics breakdown reveals the active nature of red blood cell flickering,” Nat. Phys. 12, 513–519 (2016).
[Crossref]

Feldmann, J.

L. Osinkina, S. Carretero-Palacios, J. Stehr, A. A. Lutich, F. Jäckel, and J. Feldmann, “Tuning DNA binding kinetics in an optical trap by plasmonic nanoparticle heating,” Nano Lett. 13, 3140–3144 (2013).
[Crossref]

A. Ohlinger, A. Deak, A. A. Lutich, and J. Feldmann, “Optically trapped gold nanoparticle enables listening at the microscale,” Phys. Rev. Lett. 108, 018101 (2012).
[Crossref]

Ferrari, A. C.

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref]

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594–612 (2004).
[Crossref]

I. M. Tolić-Nørrelykke, K. Berg-Sørensen, and H. Flyvbjerg, “MatLab program for precision calibration of optical tweezers,” Comput. Phys. Commun. 159, 225–240 (2004).
[Crossref]

Fogel’son, R. L.

R. L. Fogel’son and E. R. Likhachev, “Temperature dependence of viscosity,” Tech. Phys. 46, 1056–1059 (2001).
[Crossref]

Foster, D. A.

K. Neupane, D. A. Foster, D. R. Dee, H. Yu, F. Wang, and M. T. Woodside, “Direct observation of transition paths during the folding of proteins and nucleic acids,” Science 352, 239–242 (2016).
[Crossref]

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[Crossref]

Fwu, P. T.

C.-K. Chou, W.-L. Chen, P. T. Fwu, S.-J. Lin, H.-S. Lee, and C.-Y. Dong, “Polarization ellipticity compensation in polarization second-harmonic generation microscopy without specimen rotation,” J. Biomed. Opt. 13, 014005 (2008).
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G. Falasco, M. V. Gnann, D. Rings, and K. Kroy, “Effective temperatures of hot Brownian motion,” Phys. Rev. E 90, 032131 (2014).
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H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.-F. Joanny, G. Gompper, and T. Betz, “Equilibrium physics breakdown reveals the active nature of red blood cell flickering,” Nat. Phys. 12, 513–519 (2016).
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H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.-F. Joanny, G. Gompper, and T. Betz, “Equilibrium physics breakdown reveals the active nature of red blood cell flickering,” Nat. Phys. 12, 513–519 (2016).
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D. G. Grier, “A revolution in optical manipulation,” Nature 424, 21–22 (2003).
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Gschneidtner, T.

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13, 3129–3134 (2013).
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O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref]

Guyot-Sionnest, P.

Hajizadeh, F.

F. Hajizadeh, S. M. Mousavi, Z. S. Khaksar, and S. N. S. Reihani, “Extended linear detection range for optical tweezers using image-plane detection scheme,” J. Opt. 16, 105706 (2014).
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F. Hajizadeh and S. N. S. Reihani, “Optimized optical trapping of gold nanoparticles,” Opt. Express 18, 551–559 (2010).
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A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).
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M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
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Huang, X. H.

X. H. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, “Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods,” J. Am. Chem. Soc. 128, 2115–2120 (2006).
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L. Osinkina, S. Carretero-Palacios, J. Stehr, A. A. Lutich, F. Jäckel, and J. Feldmann, “Tuning DNA binding kinetics in an optical trap by plasmonic nanoparticle heating,” Nano Lett. 13, 3140–3144 (2013).
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H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.-F. Joanny, G. Gompper, and T. Betz, “Equilibrium physics breakdown reveals the active nature of red blood cell flickering,” Nat. Phys. 12, 513–519 (2016).
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A. Lehmuskero, P. Johansson, H. Rubinsztein-Dunlop, L. M. Tong, and M. Käll, “Laser trapping of colloidal metal nanoparticles,” ACS Nano 9, 3453–3469 (2015).
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L. Shao, Z.-J. Yang, D. Andrén, P. Johansson, and M. Käll, “Gold nanorod rotary motors driven by resonant light scattering,” ACS Nano 9, 12542–12551 (2015).
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A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13, 3129–3134 (2013).
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O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
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L. Shao, Z.-J. Yang, D. Andrén, P. Johansson, and M. Käll, “Gold nanorod rotary motors driven by resonant light scattering,” ACS Nano 9, 12542–12551 (2015).
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A. Lehmuskero, P. Johansson, H. Rubinsztein-Dunlop, L. M. Tong, and M. Käll, “Laser trapping of colloidal metal nanoparticles,” ACS Nano 9, 3453–3469 (2015).
[Crossref]

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13, 3129–3134 (2013).
[Crossref]

L. M. Tong, V. D. Miljković, and M. Käll, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano Lett. 10, 268–273 (2010).
[Crossref]

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F. Hajizadeh, S. M. Mousavi, Z. S. Khaksar, and S. N. S. Reihani, “Extended linear detection range for optical tweezers using image-plane detection scheme,” J. Opt. 16, 105706 (2014).
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S. Kheifets, A. Simha, K. Melin, T. C. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
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Kroy, K.

G. Falasco, M. V. Gnann, D. Rings, and K. Kroy, “Effective temperatures of hot Brownian motion,” Phys. Rev. E 90, 032131 (2014).
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D. Rings, D. Chakraborty, and K. Kroy, “Rotational hot Brownian motion,” New J. Phys. 14, 053012 (2012).
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D. Rings, R. Schachoff, M. Selmke, F. Cichos, and K. Kroy, “Hot Brownian motion,” Phys. Rev. Lett. 105, 090604 (2010).
[Crossref]

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C.-K. Chou, W.-L. Chen, P. T. Fwu, S.-J. Lin, H.-S. Lee, and C.-Y. Dong, “Polarization ellipticity compensation in polarization second-harmonic generation microscopy without specimen rotation,” J. Biomed. Opt. 13, 014005 (2008).
[Crossref]

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S. E. Lee and L. P. Lee, “Biomolecular plasmonics for quantitative biology and nanomedicine,” Curr. Opin. Biotechnol. 21, 489–497 (2010).
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S. E. Lee and L. P. Lee, “Biomolecular plasmonics for quantitative biology and nanomedicine,” Curr. Opin. Biotechnol. 21, 489–497 (2010).
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A. Lehmuskero, P. Johansson, H. Rubinsztein-Dunlop, L. M. Tong, and M. Käll, “Laser trapping of colloidal metal nanoparticles,” ACS Nano 9, 3453–3469 (2015).
[Crossref]

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13, 3129–3134 (2013).
[Crossref]

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S. Kheifets, A. Simha, K. Melin, T. C. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
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C.-K. Chou, W.-L. Chen, P. T. Fwu, S.-J. Lin, H.-S. Lee, and C.-Y. Dong, “Polarization ellipticity compensation in polarization second-harmonic generation microscopy without specimen rotation,” J. Biomed. Opt. 13, 014005 (2008).
[Crossref]

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Lutich, A. A.

L. Osinkina, S. Carretero-Palacios, J. Stehr, A. A. Lutich, F. Jäckel, and J. Feldmann, “Tuning DNA binding kinetics in an optical trap by plasmonic nanoparticle heating,” Nano Lett. 13, 3140–3144 (2013).
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O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref]

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S. Kheifets, A. Simha, K. Melin, T. C. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
[Crossref]

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L. M. Tong, V. D. Miljković, and M. Käll, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano Lett. 10, 268–273 (2010).
[Crossref]

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J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
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J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Ann. Rev. Biochem. 77, 205–228 (2008).
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F. Hajizadeh, S. M. Mousavi, Z. S. Khaksar, and S. N. S. Reihani, “Extended linear detection range for optical tweezers using image-plane detection scheme,” J. Opt. 16, 105706 (2014).
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K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
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K. Neupane, D. A. Foster, D. R. Dee, H. Yu, F. Wang, and M. T. Woodside, “Direct observation of transition paths during the folding of proteins and nucleic acids,” Science 352, 239–242 (2016).
[Crossref]

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A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).
[Crossref]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[Crossref]

Ogier, R.

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13, 3129–3134 (2013).
[Crossref]

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A. Ohlinger, A. Deak, A. A. Lutich, and J. Feldmann, “Optically trapped gold nanoparticle enables listening at the microscale,” Phys. Rev. Lett. 108, 018101 (2012).
[Crossref]

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P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, “Brownian fluctuations and heating of an optically aligned gold nanorod,” Phys. Rev. Lett. 107, 037401 (2011).
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L. Osinkina, S. Carretero-Palacios, J. Stehr, A. A. Lutich, F. Jäckel, and J. Feldmann, “Tuning DNA binding kinetics in an optical trap by plasmonic nanoparticle heating,” Nano Lett. 13, 3140–3144 (2013).
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Petrov, D.

G. Volpe and D. Petrov, “Torque detection using Brownian fluctuations,” Phys. Rev. Lett. 97, 210603 (2006).
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X. H. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, “Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods,” J. Am. Chem. Soc. 128, 2115–2120 (2006).
[Crossref]

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G. Baffou and R. Quidant, “Thermo-plasmonics: using metallic nanostructures as nano-sources of heat,” Laser Photon. Rev. 7, 171–187 (2013).
[Crossref]

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S. Kheifets, A. Simha, K. Melin, T. C. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
[Crossref]

Reihani, S. N. S.

F. Hajizadeh, S. M. Mousavi, Z. S. Khaksar, and S. N. S. Reihani, “Extended linear detection range for optical tweezers using image-plane detection scheme,” J. Opt. 16, 105706 (2014).
[Crossref]

F. Hajizadeh and S. N. S. Reihani, “Optimized optical trapping of gold nanoparticles,” Opt. Express 18, 551–559 (2010).
[Crossref]

Rings, D.

G. Falasco, M. V. Gnann, D. Rings, and K. Kroy, “Effective temperatures of hot Brownian motion,” Phys. Rev. E 90, 032131 (2014).
[Crossref]

D. Rings, D. Chakraborty, and K. Kroy, “Rotational hot Brownian motion,” New J. Phys. 14, 053012 (2012).
[Crossref]

D. Rings, R. Schachoff, M. Selmke, F. Cichos, and K. Kroy, “Hot Brownian motion,” Phys. Rev. Lett. 105, 090604 (2010).
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H. Risken, Fokker-Planck Equation (Springer, 1996).

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A. Lehmuskero, P. Johansson, H. Rubinsztein-Dunlop, L. M. Tong, and M. Käll, “Laser trapping of colloidal metal nanoparticles,” ACS Nano 9, 3453–3469 (2015).
[Crossref]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).
[Crossref]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[Crossref]

Ruijgrok, P. V.

P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, “Brownian fluctuations and heating of an optically aligned gold nanorod,” Phys. Rev. Lett. 107, 037401 (2011).
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D. Rings, R. Schachoff, M. Selmke, F. Cichos, and K. Kroy, “Hot Brownian motion,” Phys. Rev. Lett. 105, 090604 (2010).
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Schmidt, C. F.

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D. Rings, R. Schachoff, M. Selmke, F. Cichos, and K. Kroy, “Hot Brownian motion,” Phys. Rev. Lett. 105, 090604 (2010).
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L. Shao, Z.-J. Yang, D. Andrén, P. Johansson, and M. Käll, “Gold nanorod rotary motors driven by resonant light scattering,” ACS Nano 9, 12542–12551 (2015).
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L. Shao and J. F. Wang, “Functional metal nanocrystals for biomedical applications,” in Handbook of Photonics for Biomedical Engineering, A. H.-P. Ho, D. Kim, and M. G. Somekh, eds. (Springer, 2015), pp. 1–32.

Simha, A.

S. Kheifets, A. Simha, K. Melin, T. C. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
[Crossref]

Smith, G.

Smith, S. B.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Ann. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

Stehr, J.

L. Osinkina, S. Carretero-Palacios, J. Stehr, A. A. Lutich, F. Jäckel, and J. Feldmann, “Tuning DNA binding kinetics in an optical trap by plasmonic nanoparticle heating,” Nano Lett. 13, 3140–3144 (2013).
[Crossref]

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Sykes, C.

H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.-F. Joanny, G. Gompper, and T. Betz, “Equilibrium physics breakdown reveals the active nature of red blood cell flickering,” Nat. Phys. 12, 513–519 (2016).
[Crossref]

Tchebotareva, A. L.

P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, “Brownian fluctuations and heating of an optically aligned gold nanorod,” Phys. Rev. Lett. 107, 037401 (2011).
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I. M. Tolić-Nørrelykke, K. Berg-Sørensen, and H. Flyvbjerg, “MatLab program for precision calibration of optical tweezers,” Comput. Phys. Commun. 159, 225–240 (2004).
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Tong, L. M.

A. Lehmuskero, P. Johansson, H. Rubinsztein-Dunlop, L. M. Tong, and M. Käll, “Laser trapping of colloidal metal nanoparticles,” ACS Nano 9, 3453–3469 (2015).
[Crossref]

L. M. Tong, V. D. Miljković, and M. Käll, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano Lett. 10, 268–273 (2010).
[Crossref]

Turlier, H.

H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.-F. Joanny, G. Gompper, and T. Betz, “Equilibrium physics breakdown reveals the active nature of red blood cell flickering,” Nat. Phys. 12, 513–519 (2016).
[Crossref]

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P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, “Brownian fluctuations and heating of an optically aligned gold nanorod,” Phys. Rev. Lett. 107, 037401 (2011).
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G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
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G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
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O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref]

G. Volpe and D. Petrov, “Torque detection using Brownian fluctuations,” Phys. Rev. Lett. 97, 210603 (2006).
[Crossref]

Wang, F.

K. Neupane, D. A. Foster, D. R. Dee, H. Yu, F. Wang, and M. T. Woodside, “Direct observation of transition paths during the folding of proteins and nucleic acids,” Science 352, 239–242 (2016).
[Crossref]

Wang, J. F.

L. Shao and J. F. Wang, “Functional metal nanocrystals for biomedical applications,” in Handbook of Photonics for Biomedical Engineering, A. H.-P. Ho, D. Kim, and M. G. Somekh, eds. (Springer, 2015), pp. 1–32.

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P. D. Welch, “The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust. 15, 70–73 (1967).
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Woodside, M. T.

K. Neupane, D. A. Foster, D. R. Dee, H. Yu, F. Wang, and M. T. Woodside, “Direct observation of transition paths during the folding of proteins and nucleic acids,” Science 352, 239–242 (2016).
[Crossref]

Yang, Z.-J.

L. Shao, Z.-J. Yang, D. Andrén, P. Johansson, and M. Käll, “Gold nanorod rotary motors driven by resonant light scattering,” ACS Nano 9, 12542–12551 (2015).
[Crossref]

Yu, H.

K. Neupane, D. A. Foster, D. R. Dee, H. Yu, F. Wang, and M. T. Woodside, “Direct observation of transition paths during the folding of proteins and nucleic acids,” Science 352, 239–242 (2016).
[Crossref]

Zijlstra, P.

P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, “Brownian fluctuations and heating of an optically aligned gold nanorod,” Phys. Rev. Lett. 107, 037401 (2011).
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J. Croissant and J. I. Zink, “Nanovalve-controlled cargo release activated by plasmonic heating,” J. Am. Chem. Soc. 134, 7628–7631 (2012).
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ACS Nano (3)

L. Shao, Z.-J. Yang, D. Andrén, P. Johansson, and M. Käll, “Gold nanorod rotary motors driven by resonant light scattering,” ACS Nano 9, 12542–12551 (2015).
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M. Braun and F. Cichos, “Optically controlled thermophoretic trapping of single nano-objects,” ACS Nano 7, 11200–11208 (2013).
[Crossref]

A. Lehmuskero, P. Johansson, H. Rubinsztein-Dunlop, L. M. Tong, and M. Käll, “Laser trapping of colloidal metal nanoparticles,” ACS Nano 9, 3453–3469 (2015).
[Crossref]

Am. J. Phys. (1)

G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
[Crossref]

Ann. Rev. Biochem. (1)

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Ann. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

Comput. Phys. Commun. (1)

I. M. Tolić-Nørrelykke, K. Berg-Sørensen, and H. Flyvbjerg, “MatLab program for precision calibration of optical tweezers,” Comput. Phys. Commun. 159, 225–240 (2004).
[Crossref]

Curr. Opin. Biotechnol. (1)

S. E. Lee and L. P. Lee, “Biomolecular plasmonics for quantitative biology and nanomedicine,” Curr. Opin. Biotechnol. 21, 489–497 (2010).
[Crossref]

IEEE Trans. Audio Electroacoust. (1)

P. D. Welch, “The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust. 15, 70–73 (1967).
[Crossref]

J. Am. Chem. Soc. (2)

J. Croissant and J. I. Zink, “Nanovalve-controlled cargo release activated by plasmonic heating,” J. Am. Chem. Soc. 134, 7628–7631 (2012).
[Crossref]

X. H. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, “Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods,” J. Am. Chem. Soc. 128, 2115–2120 (2006).
[Crossref]

J. Biomed. Opt. (1)

C.-K. Chou, W.-L. Chen, P. T. Fwu, S.-J. Lin, H.-S. Lee, and C.-Y. Dong, “Polarization ellipticity compensation in polarization second-harmonic generation microscopy without specimen rotation,” J. Biomed. Opt. 13, 014005 (2008).
[Crossref]

J. Opt. (1)

F. Hajizadeh, S. M. Mousavi, Z. S. Khaksar, and S. N. S. Reihani, “Extended linear detection range for optical tweezers using image-plane detection scheme,” J. Opt. 16, 105706 (2014).
[Crossref]

Laser Photon. Rev. (1)

G. Baffou and R. Quidant, “Thermo-plasmonics: using metallic nanostructures as nano-sources of heat,” Laser Photon. Rev. 7, 171–187 (2013).
[Crossref]

Nano Lett. (3)

L. Osinkina, S. Carretero-Palacios, J. Stehr, A. A. Lutich, F. Jäckel, and J. Feldmann, “Tuning DNA binding kinetics in an optical trap by plasmonic nanoparticle heating,” Nano Lett. 13, 3140–3144 (2013).
[Crossref]

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13, 3129–3134 (2013).
[Crossref]

L. M. Tong, V. D. Miljković, and M. Käll, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano Lett. 10, 268–273 (2010).
[Crossref]

Nat. Methods (1)

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[Crossref]

Nat. Nanotechnol. (2)

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref]

Nat. Phys. (1)

H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.-F. Joanny, G. Gompper, and T. Betz, “Equilibrium physics breakdown reveals the active nature of red blood cell flickering,” Nat. Phys. 12, 513–519 (2016).
[Crossref]

Nature (2)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 21–22 (2003).
[Crossref]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1.

Measurement of the rotation dynamics of a 2D trapped gold nanorod. (a) Schematic of the optical tweezers setup. (Inset) Scanning electron microscopy image of the used gold nanorods. (b) Measured QPD voltage dependence on immobilized nanorod displacement from the laser focus at different laser powers. The dashed line shows a fit to the central linear range of the data measured at 11.7 mW. (c) and (d) QPD-measured trajectory of a rotating nanorod in the optical trap (c) and distribution of the rod position (d). The laser power was set at 6.4 mW. (e) PSD of the measured nanorod x displacement. The red smooth curve is the fitting at ffavg to obtain the corner frequency.

Fig. 2.
Fig. 2.

Experimentally measured rotation dynamics and estimated Brownian temperatures of a rotating gold nanorod under varying laser powers. (a) PSD of the backscattered laser light intensity collected by the QPD. (b) Autocorrelation plots of scattering intensity after an analyzer collected by the APD. (c) Laser power-dependent rotation frequencies of nanorods measured by APD and QPD. Error bars reveal the standard deviations of the autocorrelation fitting (red) and of a Lorentzian distribution fit to PSD peak (green), respectively. (d) Power spectrum peak widths of signals shown in (a) and ACF decay rates of signals shown in (b). (e) Estimated Tt and Tr from the experimental corner frequency fc and ACF decay time τ0, respectively. Error bars represent 95% confidence intervals. The red solid line indicates the calculated surface temperature of the nanorod while the green solid line indicates the calculated temperature in solution 110 nm away from the nanorod surface. (f) Calculated temperature profile around the gold nanorod when heated by the circularly polarized trapping laser. The yellow and white dashed circles indicate the sizes of the laser beam waist and the movement range of the nanorod center of mass, respectively, with the latter representing two standard deviations of the nanorod displacement.

Fig. 3.
Fig. 3.

Simulation of the translational movement of a rotating Brownian gold nanorod in a 2D optical trap. The incident laser power is set to 5 mW. (a) Translational trajectory of the nanorod. (b) Probability distribution of the nanorod position along x. The orange line is a fit to the data using a Gaussian distribution function. (c) Power spectral density (PSD) of the simulated x displacement. The orange line is an averaged PSD obtained using Welch’s method to reduce the noise [41]. (d) and (e) x-displacement standard deviation σx (d) and PSD corner frequency fc (e) of the trapped nanorod as the translational effective Brownian temperature Tt varies. The triangles in the plots are calculated from theoretical formulas while the red circles represent the results obtained by fitting the calculated probability distribution and the PSD curve. Error bars in (d) and (e) correspond to 95% confidence intervals obtained from the fits.

Fig. 4.
Fig. 4.

Simulation results of the rotational movement of a rotating Brownian gold nanorod in 2D optical trap. (a) Probability distribution of the nanorod rotational frequency. (b) Calculated intensity of the scattered light by the nanorod recorded after a polarizer IscaP. The intensity variation indicates the rotational movement of the nanorod. (c) and (d) ACFs (c) and PSDs (d) of the calculated IscaP. The autocorrelation decay and PSD peak broadening result from the rotational fluctuation caused by nanorod Brownian motion. The orange lines in the ACF plots represent fits to the data using the theoretically derived correlation function. The rotation frequency and autocorrelation decay time are obtained from the fitting. The orange lines in the PSD plots are averaged PSDs using Welch’s method to reduce the noise [41].

Equations (3)

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{σ=(kBTt/k)1/2fc=k/(2πγt(Tt))favg=Mopt/(2πγr(Tr))τ0=γr(Tr)/(4kBTr),
mx¨(t)=γtx˙(t)+kxx(t)+(2kBTtγt)1/2Wx(t),my¨(t)=γty˙(t)+kyy(t)+(2kBTtγt)1/2Wy(t),Jφ¨(t)=γrφ˙(t)+Mopt+(2kBTrγr)1/2Wφ(t).
xi=xi1(kxi1/γt)Δt+(2DtΔt)1/2wi,x,yi=yi1(kyi1/γt)Δt+(2DtΔt)1/2wi,y,φi=φi1Mopt(xi1,yi1)γr·Δt+(2DrΔt)12wi,φ.

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