Hexagonal arrays of gold triangles as plasmonic tweezers

Mohsen Samadi; Shoaib Vasini; Sara Darbari; Ali Akbar Khorshad; Seyed Nader Seyed Reihani; Mohammad Kazem Moravvej-Farshi

doi:10.1364/OE.27.014754

Hexagonal arrays of gold triangles as plasmonic tweezers

Mohsen Samadi, Shoaib Vasini, Sara Darbari, Ali Akbar Khorshad, Seyed Nader Seyed Reihani, and Mohammad Kazem Moravvej-Farshi

Optics Express
Vol. 27,
Issue 10,
pp. 14754-14766
(2019)
•https://doi.org/10.1364/OE.27.014754

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Mohsen Samadi, Shoaib Vasini, Sara Darbari, Ali Akbar Khorshad, Seyed Nader Seyed Reihani, and Mohammad Kazem Moravvej-Farshi, "Hexagonal arrays of gold triangles as plasmonic tweezers," Opt. Express 27, 14754-14766 (2019)

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Table of Contents Category
- Plasmonics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: January 9, 2019
- Revised Manuscript: March 30, 2019
- Manuscript Accepted: April 24, 2019
- Published: May 7, 2019

Accessible

Open Access

Abstract

We present theoretical and experimental studies of the plasmonic properties of hexagonal arrays of gold triangles, fabricated by angle-resolved nanosphere lithography method. Our numerical and experimental results both show that a change in the angle of gold deposition affects the size and the distance between the triangles, leading to a controlled shift in their absorption and scattering spectra. We calculate the force exerted on the polystyrene particles of 650 nm radii numerically while passing above the hexagonal arrays. Simulation results show that the presented hexagonal arrays of gold triangles can operate as efficient plasmonic tweezers with a controllable operating wavelength and high trap strength, owing to the additive interaction of the neighboring triangles. Moreover, we apply the realized plasmonic nanostructures in a conventional optical tweezers configuration and show that the optical tweezers stiffness can be effectively modulated by the plasmonic forces, at the IR wavelength of 1064 nm.

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References

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Publication

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986).
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[Crossref]
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[Crossref] [PubMed]
A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 4853–4860 (1997).
[Crossref] [PubMed]
K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]
M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
[Crossref]
M. Righini, C. Girard, and R. Quidant, “Light-induced manipulation with surface plasmons,” J. Opt. A, Pure Appl. Opt. 10(9), 093001 (2008).
[Crossref]
M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett. 100(18), 186804 (2008).
[Crossref] [PubMed]
M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys. 3(7), 477–480 (2007).
[Crossref]
A. Grigorenko, N. Roberts, M. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
[Crossref]
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[Crossref] [PubMed]
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[Crossref] [PubMed]
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[Crossref]
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[Crossref] [PubMed]
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[Crossref] [PubMed]
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[Crossref]
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[Crossref] [PubMed]
M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
[Crossref]
M. Ghorbanzadeh, S. Jones, M. K. Moravvej-Farshi, and R. Gordon, “Improvement of Sensing and Trapping Efficiency of Double Nanohole Apertures via Enhancing the Wedge Plasmon Polariton Modes with Tapered Cusps,” ACS Photonics 4(5), 1108–1113 (2017).
[Crossref]
M. Ghorbanzadeh, S. Darbari, and M. Moravvej-Farshi, “Graphene-based plasmonic force switch,” Appl. Phys. Lett. 108(11), 111105 (2016).
[Crossref]
J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Towards nano-optical tweezers with graphene plasmons: Numerical investigation of trapping 10-nm particles with mid-infrared light,” Sci. Rep. 6(1), 38086 (2016).
[Crossref] [PubMed]
M. Samadi, S. Darbari, and M. K. Moravvej-Farshi, “Numerical Investigation of Tunable Plasmonic Tweezers based on Graphene Stripes,” Sci. Rep. 7(1), 14533 (2017).
[Crossref] [PubMed]
B. J. Roxworthy, K. D. Ko, A. Kumar, K. H. Fung, E. K. Chow, G. L. Liu, N. X. Fang, and K. C. Toussaint, “Application of plasmonic bowtie nanoantenna arrays for optical trapping, stacking, and sorting,” Nano Lett. 12(2), 796–801 (2012).
[Crossref] [PubMed]
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[Crossref]
Y. Tsuboi, T. Shoji, N. Kitamura, M. Takase, K. Murakoshi, Y. Mizumoto, and H. Ishihara, “Optical trapping of quantum dots based on gap-mode-excitation of localized surface plasmon,” J. Phys. Chem. Lett. 1(15), 2327–2333 (2010).
[Crossref]
J. Hong, C. K. Hong, and S. E. Shim, “Synthesis of polystyrene microspheres by dispersion polymerization using poly (vinyl alcohol) as a steric stabilizer in aqueous alcohol media,” Colloids Surf. A Physicochem. Eng. Asp. 302(1-3), 225–233 (2007).
[Crossref]
P. A. Kralchevsky and N. D. Denkov, “Capillary forces and structuring in layers of colloid particles,” Curr. Opin. Colloid Interface Sci. 6(4), 383–401 (2001).
[Crossref]
Y. Zheng, S. Chua, C. Huan, and Z. Miao, “Selective growth of GaAs quantum dots on the triangle nanocavities bounded by SiO2 mask on Si substrate by MBE,” J. Cryst. Growth 268(3-4), 369–374 (2004).
[Crossref]
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[Crossref]
O. A. Yeshchenko, I. M. Dmitruk, A. A. Alexeenko, A. V. Kotko, J. Verdal, and A. O. Pinchuk, “Size and temperature effects on the surface plasmon resonance in silver nanoparticles,” Plasmonics 7(4), 685–694 (2012).
[Crossref]
K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[Crossref]
S. M. Mousavi, S. N. S. Reihani, G. Anvari, M. Anvari, H. G. Alinezhad, and M. R. R. Tabar, “Stochastic analysis of time series for the spatial positions of particles trapped in optical tweezers,” Sci. Rep. 7(1), 4832 (2017).
[Crossref] [PubMed]
P. Mestres, J. Berthelot, S. S. Aćimović, and R. Quidant, “Unraveling the optomechanical nature of plasmonic trapping,” Light Sci. Appl. 5(7), e16092 (2016).
[Crossref] [PubMed]

2017 (3)

M. Ghorbanzadeh, S. Jones, M. K. Moravvej-Farshi, and R. Gordon, “Improvement of Sensing and Trapping Efficiency of Double Nanohole Apertures via Enhancing the Wedge Plasmon Polariton Modes with Tapered Cusps,” ACS Photonics 4(5), 1108–1113 (2017).
[Crossref]

M. Samadi, S. Darbari, and M. K. Moravvej-Farshi, “Numerical Investigation of Tunable Plasmonic Tweezers based on Graphene Stripes,” Sci. Rep. 7(1), 14533 (2017).
[Crossref] [PubMed]

S. M. Mousavi, S. N. S. Reihani, G. Anvari, M. Anvari, H. G. Alinezhad, and M. R. R. Tabar, “Stochastic analysis of time series for the spatial positions of particles trapped in optical tweezers,” Sci. Rep. 7(1), 4832 (2017).
[Crossref] [PubMed]

2016 (3)

P. Mestres, J. Berthelot, S. S. Aćimović, and R. Quidant, “Unraveling the optomechanical nature of plasmonic trapping,” Light Sci. Appl. 5(7), e16092 (2016).
[Crossref] [PubMed]

M. Ghorbanzadeh, S. Darbari, and M. Moravvej-Farshi, “Graphene-based plasmonic force switch,” Appl. Phys. Lett. 108(11), 111105 (2016).
[Crossref]

J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Towards nano-optical tweezers with graphene plasmons: Numerical investigation of trapping 10-nm particles with mid-infrared light,” Sci. Rep. 6(1), 38086 (2016).
[Crossref] [PubMed]

2015 (1)

M. Ghorbanzadeh, M. K. Moravvej-Farshi, and S. Darbari, “Designing a plasmonic optophoresis system for trapping and simultaneous sorting/counting of micro-and nano-particles,” J. Lightwave Technol. 33(16), 3453–3460 (2015).
[Crossref]

2014 (1)

T. Shoji and Y. Tsuboi, “Plasmonic optical tweezers toward molecular manipulation: tailoring plasmonic nanostructure, light source, and resonant trapping,” J. Phys. Chem. Lett. 5(17), 2957–2967 (2014).
[Crossref] [PubMed]

2013 (2)

X. Wang, K. Xiao, C. Min, Q. Zou, Y. Hua, and X.-C. Yuan, “Theoretical and experimental study of surface plasmon radiation force on micrometer-sized spheres,” Plasmonics 8(2), 637–643 (2013).
[Crossref]

A. Cuche, A. Canaguier-Durand, E. Devaux, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Sorting nanoparticles with intertwined plasmonic and thermo-hydrodynamical forces,” Nano Lett. 13(9), 4230–4235 (2013).
[Crossref] [PubMed]

2012 (3)

O. A. Yeshchenko, I. M. Dmitruk, A. A. Alexeenko, A. V. Kotko, J. Verdal, and A. O. Pinchuk, “Size and temperature effects on the surface plasmon resonance in silver nanoparticles,” Plasmonics 7(4), 685–694 (2012).
[Crossref]

B. J. Roxworthy, K. D. Ko, A. Kumar, K. H. Fung, E. K. Chow, G. L. Liu, N. X. Fang, and K. C. Toussaint, “Application of plasmonic bowtie nanoantenna arrays for optical trapping, stacking, and sorting,” Nano Lett. 12(2), 796–801 (2012).
[Crossref] [PubMed]

M. Ploschner, T. Čižmár, M. Mazilu, A. Di Falco, and K. Dholakia, “Bidirectional optical sorting of gold nanoparticles,” Nano Lett. 12(4), 1923–1927 (2012).
[Crossref] [PubMed]

2011 (2)

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
[Crossref]

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat. Commun. 2(1), 469 (2011).
[Crossref] [PubMed]

2010 (1)

Y. Tsuboi, T. Shoji, N. Kitamura, M. Takase, K. Murakoshi, Y. Mizumoto, and H. Ishihara, “Optical trapping of quantum dots based on gap-mode-excitation of localized surface plasmon,” J. Phys. Chem. Lett. 1(15), 2327–2333 (2010).
[Crossref]

2009 (3)

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
[Crossref]

L. Huang, S. J. Maerkl, and O. J. Martin, “Integration of plasmonic trapping in a microfluidic environment,” Opt. Express 17(8), 6018–6024 (2009).
[Crossref] [PubMed]

K. Wang, E. Schonbrun, and K. B. Crozier, “Propulsion of gold nanoparticles with surface plasmon polaritons: evidence of enhanced optical force from near-field coupling between gold particle and gold film,” Nano Lett. 9(7), 2623–2629 (2009).
[Crossref] [PubMed]

2008 (3)

A. Grigorenko, N. Roberts, M. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
[Crossref]

M. Righini, C. Girard, and R. Quidant, “Light-induced manipulation with surface plasmons,” J. Opt. A, Pure Appl. Opt. 10(9), 093001 (2008).
[Crossref]

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett. 100(18), 186804 (2008).
[Crossref] [PubMed]

2007 (2)

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys. 3(7), 477–480 (2007).
[Crossref]

J. Hong, C. K. Hong, and S. E. Shim, “Synthesis of polystyrene microspheres by dispersion polymerization using poly (vinyl alcohol) as a steric stabilizer in aqueous alcohol media,” Colloids Surf. A Physicochem. Eng. Asp. 302(1-3), 225–233 (2007).
[Crossref]

2006 (1)

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett. 96(23), 238101 (2006).
[Crossref] [PubMed]

2004 (3)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[Crossref]

Y. Zheng, S. Chua, C. Huan, and Z. Miao, “Selective growth of GaAs quantum dots on the triangle nanocavities bounded by SiO2 mask on Si substrate by MBE,” J. Cryst. Growth 268(3-4), 369–374 (2004).
[Crossref]

2003 (2)

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003).
[Crossref]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

2002 (1)

C. L. Haynes, A. D. McFarland, M. T. Smith, J. C. Hulteen, and R. P. J. T. J. P. C. B. Van Duyne, “Angle-resolved nanosphere lithography: manipulation of nanoparticle size, shape, and interparticle spacing,” J. Phys. Chem. B 106(8), 1898–1902 (2002).
[Crossref]

2001 (1)

P. A. Kralchevsky and N. D. Denkov, “Capillary forces and structuring in layers of colloid particles,” Curr. Opin. Colloid Interface Sci. 6(4), 383–401 (2001).
[Crossref]

1997 (1)

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 4853–4860 (1997).
[Crossref] [PubMed]

1986 (1)

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986).
[Crossref] [PubMed]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

Acimovic, S. S.

P. Mestres, J. Berthelot, S. S. Aćimović, and R. Quidant, “Unraveling the optomechanical nature of plasmonic trapping,” Light Sci. Appl. 5(7), e16092 (2016).
[Crossref] [PubMed]

Alexeenko, A. A.

Alinezhad, H. G.

Anvari, G.

Anvari, M.

Ashkin, A.

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 4853–4860 (1997).
[Crossref] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

Badenes, G.

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett. 96(23), 238101 (2006).
[Crossref] [PubMed]

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[Crossref]

Berthelot, J.

P. Mestres, J. Berthelot, S. S. Aćimović, and R. Quidant, “Unraveling the optomechanical nature of plasmonic trapping,” Light Sci. Appl. 5(7), e16092 (2016).
[Crossref] [PubMed]

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

Canaguier-Durand, A.

Chow, E. K.

Chu, S.

Chua, S.

Cižmár, T.

M. Ploschner, T. Čižmár, M. Mazilu, A. Di Falco, and K. Dholakia, “Bidirectional optical sorting of gold nanoparticles,” Nano Lett. 12(4), 1923–1927 (2012).
[Crossref] [PubMed]

Coronado, E.

Crozier, K. B.

Cuche, A.

Darbari, S.

M. Samadi, S. Darbari, and M. K. Moravvej-Farshi, “Numerical Investigation of Tunable Plasmonic Tweezers based on Graphene Stripes,” Sci. Rep. 7(1), 14533 (2017).
[Crossref] [PubMed]

M. Ghorbanzadeh, S. Darbari, and M. Moravvej-Farshi, “Graphene-based plasmonic force switch,” Appl. Phys. Lett. 108(11), 111105 (2016).
[Crossref]

Denkov, N. D.

P. A. Kralchevsky and N. D. Denkov, “Capillary forces and structuring in layers of colloid particles,” Curr. Opin. Colloid Interface Sci. 6(4), 383–401 (2001).
[Crossref]

Devaux, E.

Dholakia, K.

M. Ploschner, T. Čižmár, M. Mazilu, A. Di Falco, and K. Dholakia, “Bidirectional optical sorting of gold nanoparticles,” Nano Lett. 12(4), 1923–1927 (2012).
[Crossref] [PubMed]

Di Falco, A.

M. Ploschner, T. Čižmár, M. Mazilu, A. Di Falco, and K. Dholakia, “Bidirectional optical sorting of gold nanoparticles,” Nano Lett. 12(4), 1923–1927 (2012).
[Crossref] [PubMed]

Dickinson, M.

A. Grigorenko, N. Roberts, M. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
[Crossref]

Dmitruk, I. M.

Dziedzic, J. M.

Ebbesen, T. W.

Eftekhari, F.

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
[Crossref]

Fang, N. X.

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[Crossref]

Fung, K. H.

Genet, C.

Ghorbanzadeh, M.

M. Ghorbanzadeh, S. Darbari, and M. Moravvej-Farshi, “Graphene-based plasmonic force switch,” Appl. Phys. Lett. 108(11), 111105 (2016).
[Crossref]

Girard, C.

M. Righini, C. Girard, and R. Quidant, “Light-induced manipulation with surface plasmons,” J. Opt. A, Pure Appl. Opt. 10(9), 093001 (2008).
[Crossref]

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys. 3(7), 477–480 (2007).
[Crossref]

Gordon, R.

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
[Crossref]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Grigorenko, A.

A. Grigorenko, N. Roberts, M. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
[Crossref]

Haynes, C. L.

Hong, C. K.

Hong, J.

Hua, Y.

Huan, C.

Huang, L.

L. Huang, S. J. Maerkl, and O. J. Martin, “Integration of plasmonic trapping in a microfluidic environment,” Opt. Express 17(8), 6018–6024 (2009).
[Crossref] [PubMed]

Hulteen, J. C.

Hutchison, J. A.

Ishihara, H.

Jones, S.

Juan, M. L.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
[Crossref]

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
[Crossref]

Kelly, K. L.

Kitamura, N.

Ko, K. D.

Kotko, A. V.

Kralchevsky, P. A.

P. A. Kralchevsky and N. D. Denkov, “Capillary forces and structuring in layers of colloid particles,” Curr. Opin. Colloid Interface Sci. 6(4), 383–401 (2001).
[Crossref]

Kumar, A.

Liu, G. L.

Liu, W.

Maerkl, S. J.

L. Huang, S. J. Maerkl, and O. J. Martin, “Integration of plasmonic trapping in a microfluidic environment,” Opt. Express 17(8), 6018–6024 (2009).
[Crossref] [PubMed]

Martin, O. J.

L. Huang, S. J. Maerkl, and O. J. Martin, “Integration of plasmonic trapping in a microfluidic environment,” Opt. Express 17(8), 6018–6024 (2009).
[Crossref] [PubMed]

Mazilu, M.

M. Ploschner, T. Čižmár, M. Mazilu, A. Di Falco, and K. Dholakia, “Bidirectional optical sorting of gold nanoparticles,” Nano Lett. 12(4), 1923–1927 (2012).
[Crossref] [PubMed]

McFarland, A. D.

Mestres, P.

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Appl. Phys. Lett. (1)

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Fig. 1 (a) PS particles, spread on a glass substrate and dried under a uniform vertical flow of N₂. SEM images of the resulting HCP monolayer (b) in a large scale area (~200 × 200 μm²), and (c) in a magnified view. (d) Deposition of an Au layer on top of the HCP monolayer by thermal evaporation with an incident angle of θ. SEM images of the fabricated hexagonal gold array, obtained from different deposition angles (e) θ = 0°, (f) θ = 15°, (g) θ = 25°, (h) θ = 35°, (i) θ = 45°. (j) Variation of the achieved feature sizes versus θ. The error bars present the corresponding size deviations.

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Fig. 2 (a) 2D and (b) 3D AFM images of the achieved gold hexagonal array, (c) the thickness profile along AAʹ, shown in part (a).

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Fig. 3 The measured extinction spectra for the hexagonal array of gold triangles prepared at different deposition angles (θ = 0°, 15°, and 25°); in the (a) visible and (b) near IR wavelength ranges.

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Fig. 4 (a) Scattering spectra calculated for a single gold triangle with three different feature sizes, l = 300, 280, 230 nm, corresponding to the deposition angles of θ = 0°, 15°, 25°, respectively. Inset: Schematic diagram of a single gold triangle with feature size l and thickness h. Field distribution above a single gold triangle at z₀ = 10 nm for: (b) λ₁ = 650 nm, and (c) λ₂ = 1250 nm.

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Fig. 5 (a) Schematic diagram of a hexagonal array of gold triangles with l = 300 nm and h = 50 nm, and d = 300 nm. (b) The scattering spectra calculated for a single gold triangle (dashes-dots), a pair of gold triangles (dots), and a hexagonal array of gold triangles (solid). The normalized plasmonic field distributions monitored at z₀ = 10 nm above the hexagonal array, calculated for the incident wavelength (c) λ₁≈650 nm and (d) λ₂≈1250 nm.

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Fig. 6 (a) Schematic of a PS particle of radius r = 650 nm, moving along x-direction above the hexagonal array of gold triangles (inset) at a height of z₀ = 10 nm; (b) F_x (solid curve) and F_z (dashes) represent the components of the plasmonic force exerted on the PS particle. (c) Comparison of the corresponding potentials versus x, (solid curves) with those sensed by the PS particle when passing above the pair of triangles (dashes) (Fig. 5(a)). The thin and thick curves represent the data obtained for the incident laser beams (λ_S1≈633 nm, I_S1 = 3.6 mW/μm²) and (λ_S2≈1064 nm, I_S2 = 560 μW/μm²).

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Fig. 7 The magnified schematic cross-section view of the focused laser beam with respect to (a) the bare glass and (b) the sample with plasmonic structure in the optical tweezers configuration. PS microsphere trapped by optical tweezers with λ_S2≈1064 nm, and laser power of 80mW (c) on the bare glass, and (d) on the hexagonal arrangement of gold triangles.

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Fig. 8 The power spectra of the PS particle trapped by an 80-mW Nd: YAG laser beam (a), (b): in the absence of the hexagonal arrays along x- and y-direction; and (c), (d): in the presence of the hexagonal arrays along the x- and y-directions. The time series x(t) for the spatial positions were recorded with a sampling rate of 22 kHz. The solid lines represent Lorentzian fits to the experimental data.

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Tables (1)

Table 1 Values of f_C and k extracted from the curves fitted to the experimental data of all four cases shown in Fig. 8

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Equations (3)

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p (f) = \frac{k_{B} T}{2 π^{2} γ (f^{2} + f_{c}^{2})},

〈 F 〉 = \frac{1}{2} Re \oint_{Ω}^{} T (r, t) \cdot \hat{n} ​ d s

T (r, t) = ε E (r) \otimes E^{*} (r) + µ H (r) \otimes H^{*} (r) - \frac{1}{2} (ε {| E (r) |}^{2} + µ {| H (r) |}^{2})

	Tweezers Configuration
Direction	Bare Glass Slide		Hexagonal Arrays		∆f_c/f_c(%) = ∆k/k(%)
Direction	f_c(Hz)	k(fN∙nm⁻¹)	f_c(Hz)	k(fN∙nm⁻¹)	∆f_c/f_c(%) = ∆k/k(%)
x	387 ± 8.0	26.5 ± 0.5	556.2 ± 10.0	38.1 ± 0.7	43.7 ± 5.5
y	446.8 ± 8.6	30.6 ± 0.6	606 ± 10.8	41.5 ± 0.7	35.6 ± 5