Abstract

This paper aims to maximize optical force or torque on arbitrary micro- and nanoscale objects using numerically optimized structured illumination. By developing a numerical framework for computer-automated design of 3d vector-field illumination, we demonstrate a 20-fold enhancement in optical torque per intensity over circularly polarized plane wave on a model plasmonic particle. The nonconvex optimization is efficiently performed by combining a compact cylindrical Bessel basis representation with a fast boundary element method and a standard derivative-free, local optimization algorithm. We analyze the optimization results for 2000 random initial configurations, discuss the tradeoff between robustness and enhancement, and compare the different effects of multipolar plasmon resonances on enhancing force or torque. All results are obtained using open-source computational software available online.

© 2017 Optical Society of America

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References

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    [Crossref]

2016 (2)

2015 (2)

M. T. Reid and S. G. Johnson, “Efficient computation of power, force, and torque in BEM scattering calculations,” IEEE Trans. Antennas Propag. 63, 3588–3598 (2015).
[Crossref]

C.-F. Chen, C.-T. Ku, Y.-H. Tai, P.-K. Wei, H.-N. Lin, and C.-B. Huang, “Creating Optical Near-Field Orbital Angular Momentum in a Gold Metasurface,” Nano Lett. 15, 2746–2750 (2015).
[Crossref] [PubMed]

2014 (5)

J. Chen, J. Ng, K. Ding, K. H. Fung, Z. Lin, and C. T. Chan, “Negative Optical Torque,” Sci. Rep. 406386 (2014).
[Crossref]

A. Lehmuskero, Y. Li, P. Johansson, and M. Käll, “Plasmonic particles set into fast orbital motion by an optical vortex beam,” Opt. Express 22, 4349–4356 (2014).
[Crossref] [PubMed]

I. Liberal, Y. Ra’di, R. Gonzalo, I. Ederra, S. A. Tretyakov, and R. W. Ziolkowski, “Least Upper Bounds of the Powers Extracted and Scattered by Bi-anisotropic Particles,” IEEE Trans. Antennas Propag. 62, 4726–4735 (2014).
[Crossref]

Y. E. Lee, K. H. Fung, D. Jin, and N. X. Fang, “Optical torque from enhanced scattering by multipolar plasmonic resonance,” Nanophotonics 3, 343–440 (2014).
[Crossref]

O. Miller, C. Hsu, M. Reid, W. Qiu, B. DeLacy, J. Joannopoulos, M. Soljačić, and S. Johnson, “Fundamental Limits to Extinction by Metallic Nanoparticles,” Phys. Rev. Lett. 112123903 (2014).
[Crossref] [PubMed]

2013 (3)

S. A. Schulz, T. Machula, E. Karimi, and R. W. Boyd, “Integrated multi vector vortex beam generator,” Opt. Express 21, 16130–16141 (2013).
[Crossref] [PubMed]

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] [PubMed]

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 42374 (2013).
[Crossref] [PubMed]

2012 (1)

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012).
[Crossref] [PubMed]

2011 (6)

2010 (4)

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181, 1444–1448 (2010).
[Crossref]

T. Čižmár, O. Brzobohaty, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2010).
[Crossref]

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

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nature Nanotechnol. 5, 570–573 (2010).
[Crossref]

2009 (4)

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
[Crossref]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009).
[Crossref]

A. Mutapcic, S. Boyd, A. Farjadpour, S. G. Johnson, and Y. Avniel, “Robust design of slow-light tapers in periodic waveguides,” Eng. Optimiz. 41, 365–384 (2009).
[Crossref]

D.-H. Kwon and D. M. Pozar, “Optimal characteristics of an arbitrary receive antenna,” IEEE Trans. Antennas Propag. 57, 3720–3727 (2009).
[Crossref]

2008 (2)

W. C. Chew, M. S. Tong, and B. Hu, “Integral equation methods for electromagnetic and elastic waves,” Synthesis Lectures on Computational Electromagnetics 3, 1–241 (2008).
[Crossref]

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37, 42–55 (2008).
[Crossref] [PubMed]

2007 (4)

R. Di Leonardo, F. Ianni, and G. Ruocco, “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15, 1913–1922 (2007).
[Crossref] [PubMed]

E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. Soc. Am. A 9, S267–S277 (2007).

R. E. Hamam, A. Karalis, J. Joannopoulos, and M. Soljačić, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
[Crossref]

A. Jesacher, A. Schwaighofer, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15, 5801–5808 (2007).
[Crossref] [PubMed]

2005 (4)

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. Grier, “Optimized holographic optical traps,” Opt. Express 13, 5831–5845 (2005).
[Crossref] [PubMed]

M. Liu, N. Ji, Z. Lin, and S. Chui, “Radiation torque on a birefringent sphere caused by an electromagnetic wave,” Phys. Rev. E 72056610 (2005).
[Crossref]

R. Agarwal, K. Ladavac, Y. Roichman, G. Yu, C. M. Lieber, and D. G. Grier, “Manipulation and assembly of nanowires with holographic optical traps,” Opt. Express 13, 8906–8912 (2005).
[Crossref] [PubMed]

Y. Xia and N. J. Halas, “Shape-controlled synthesis and surface plasmonic properties of metallic nanostructures,” MRS Bulletin 30, 338–348 (2005).
[Crossref]

2004 (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]

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, 668–677 (2003).
[Crossref]

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

2002 (2)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclass. Opt. 4, S82–S89 (2002).
[Crossref]

2000 (1)

W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, “Three-dimensional force calibration of optical tweezers,” J. Mod. Opt. 47, 2921–2931 (2000).
[Crossref]

1998 (1)

1997 (1)

1995 (1)

1992 (1)

1984 (1)

P. L. Marston and J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508 (1984).
[Crossref]

1971 (1)

J. H. Bruning and Y. T. Lo, “Multiple scattering of EM waves by spheres part I–Multipole expansion and ray-optical solutions,” IEEE Trans. Antennas Propag. 19, 378–390 (1971).
[Crossref]

Agarwal, R.

Allen, L.

Andilla, J.

E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. Soc. Am. A 9, S267–S277 (2007).

Arie, A.

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012).
[Crossref] [PubMed]

Arita, Y.

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 42374 (2013).
[Crossref] [PubMed]

Arlt, J.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclass. Opt. 4, S82–S89 (2002).
[Crossref]

Avniel, Y.

A. Mutapcic, S. Boyd, A. Farjadpour, S. G. Johnson, and Y. Avniel, “Robust design of slow-light tapers in periodic waveguides,” Eng. Optimiz. 41, 365–384 (2009).
[Crossref]

Bartal, G.

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nature Nanotechnol. 5, 570–573 (2010).
[Crossref]

Berg-Sørensen, K.

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]

Bernet, S.

Bertsekas, D. P.

D. P. Bertsekas, Nonlinear Programming (Athena Scientific Belmont, 1999).

Bianchi, S.

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181, 1444–1448 (2010).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH Verlag GmbH & Co. KGaA, 2004).

Boyd, R. W.

Boyd, S.

A. Mutapcic, S. Boyd, A. Farjadpour, S. G. Johnson, and Y. Avniel, “Robust design of slow-light tapers in periodic waveguides,” Eng. Optimiz. 41, 365–384 (2009).
[Crossref]

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge university press, 2004).
[Crossref]

Bruning, J. H.

J. H. Bruning and Y. T. Lo, “Multiple scattering of EM waves by spheres part I–Multipole expansion and ray-optical solutions,” IEEE Trans. Antennas Propag. 19, 378–390 (1971).
[Crossref]

Brzobohaty, O.

T. Čižmár, O. Brzobohaty, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2010).
[Crossref]

Carnicer, A.

E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. Soc. Am. A 9, S267–S277 (2007).

Chan, C. T.

J. Chen, J. Ng, K. Ding, K. H. Fung, Z. Lin, and C. T. Chan, “Negative Optical Torque,” Sci. Rep. 406386 (2014).
[Crossref]

Chávez-Cerda, S.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclass. Opt. 4, S82–S89 (2002).
[Crossref]

Chen, C.-F.

C.-F. Chen, C.-T. Ku, Y.-H. Tai, P.-K. Wei, H.-N. Lin, and C.-B. Huang, “Creating Optical Near-Field Orbital Angular Momentum in a Gold Metasurface,” Nano Lett. 15, 2746–2750 (2015).
[Crossref] [PubMed]

Chen, H.

Chen, J.

J. Chen, N. Wang, L. Cui, X. Li, Z. Lin, and J. Ng, “Optical Twist Induced by Plasmonic Resonance,” Sci. Rep. 6, 27927 (2016).
[Crossref] [PubMed]

J. Chen, J. Ng, K. Ding, K. H. Fung, Z. Lin, and C. T. Chan, “Negative Optical Torque,” Sci. Rep. 406386 (2014).
[Crossref]

Chew, W. C.

W. C. Chew, M. S. Tong, and B. Hu, “Integral equation methods for electromagnetic and elastic waves,” Synthesis Lectures on Computational Electromagnetics 3, 1–241 (2008).
[Crossref]

Chui, S.

M. Liu, N. Ji, Z. Lin, and S. Chui, “Radiation torque on a birefringent sphere caused by an electromagnetic wave,” Phys. Rev. E 72056610 (2005).
[Crossref]

Cižmár, T.

T. Čižmár, O. Brzobohaty, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2010).
[Crossref]

Coronado, E.

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, 668–677 (2003).
[Crossref]

Crichton, J. H.

P. L. Marston and J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508 (1984).
[Crossref]

Cui, L.

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Figures (6)

Fig. 1
Fig. 1

Schematic of a structured vector-field illumination, analytically represented with a vector Bessel basis. The right inset shows the distributions for electric field (color) and polarization (black arrows) of the vector Bessel basis. The illumination can be optimized to produce maximum mechanical force or torque on an example target particle. The gold nanotriangle in the left inset has edge length 400nm, thickness 40nm, and rounding diameter 30nm. The scanning electron microscope (SEM) image shows an experimental sample fabricated using electron-beam lithography. This demonstrates that such particles can be made, but all results presented in this paper are purely computational.

Fig. 2
Fig. 2

Distribution of FOM for 2000 randomly chosen incident field configurations at 1028nm, before (black) and after (blue) optimization. Red marks on the x-axis indicate the initial (triangle) and final (circle) FOM when the optimization starts from a circularly polarized plane wave. Representative incident fields are plotted in the right.

Fig. 3
Fig. 3

Distribution of FOM for 2000 randomly chosen incident field configurations at 625nm. Top inset shows four different field patterns with a near-identical FOM near the median, and the bottom inset shows the field with the best FOM.

Fig. 4
Fig. 4

Force spectrum for two different target wavelengths (vertical green line), (a) 1028nm and (b) 625nm. The spectra for the best (blue line) and the median (red dashed line) optimized field configurations are each labeled with the factor of enhancement, with respect to CP planewave reference (black dashed line).

Fig. 5
Fig. 5

Torque spectrum for three different target wavelengths (vertical green line), (a) 1028nm, (b) 805nm, and (c) 625nm. The spectra for the best (blue line) and the median (red dashed line) optimized field configurations are each labeled with the factor of enhancement, with respect to CP planewave reference (black dashed line). (d): Total-field distributions of initial random field (left) and final optimized field (right) for the best optimized field configurations at three target wavelengths. Scalebar is 400nm.

Fig. 6
Fig. 6

Robustness of the optimized incident fields, quantified by the decrease in FOMT with respect to fractional random error added to the best (blue) and the median (red) optimized fields, at λdip (right) and λquad (left). The error bar represents the standard deviation for 100 samples.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

ψ m ( r , φ , z ) = J m ( k t r ) exp ( i m φ + i k z z ) ,
M i = × ( ψ i u z ) , ( azimuthal polarization )
N i = 1 k × M i , ( radial polarization )
E inc ( r , ϕ , z ) = i = 0 N a i M i + b i N i ,
M fixed BEM matrix c output current = f rapidly updated input field
FOM F = F z I avg ( π c 3 λ 2 ) ,
FOM T = T z I avg ( 4 π 2 c 3 λ 3 ) ,
E w = i = 0 m ( a i + δ a i ) M i + ( b i + δ b i ) N i , ( | δ | w | a , b | ) ,

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