Abstract

The hybrid of finite element and boundary integral (FE-BI) method is employed to predict nano-optical trapping forces of arbitrarily shaped metallic nanostructures. A preconditioning strategy is proposed to improve the convergence of the iterative solution. Skeletonization is employed to speed up the design and optimization where iteration has to be repeated for each beam configuration. The radiation pressure force (RPF) is computed by vector flux of the Maxwell’s stress tensor. Numerical simulations are performed to validate the developed method in analyzing the plasmonic effects as well as the optical trapping forces. It is shown that the proposed method is capable of predicting the trapping forces of complex metallic nanostructures accurately and efficiently.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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  32. E. Liberty, F. Woolfe, P. G. Martinsson, V. Rokhlin, and M. Tygert, “Randomized algorithms for the low-rank approximation of matrices,” Proc. Natl. Acad. Sci. USA 104, 20167–20172 (2007).
    [Crossref] [PubMed]
  33. X. M. Pan, M. J. Gou, and X. Q. Sheng, “Prediction of radiation pressure force exerted on moving particles by the two-level skeletonization,” Opt. Express 22, 10032–10045 (2014).
    [Crossref] [PubMed]
  34. H. W. Gao, J. W. Hao, X. M. Pan, and X. Q. Sheng, “Application of interpolative decomposition to FE-BI-MLFMA for fast computation of monostatic scattering from 3-d complex composite objects,” Antennas and Wireless Propagation Letters”, IEEE 13, 1490–1493 (2014).
  35. X. M. Pan, J. G. Wei, Z. Peng, and X. Q. Sheng, “A fast algorithm for multiscale electromagnetic problems using interpolative decomposition and multilevel fast multipole algorithm,” Radio Sci. 47, RS1011 (2012).
    [Crossref]
  36. X. M. Pan and X. Q. Sheng, “Improved algebraic preconditioning for MoM solutions of large-scale electromagnetic problems,” IEEE Antennas Wireless Propag. Lett. 13, 106–109 (2014).
    [Crossref]
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    [Crossref]
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    [Crossref]

2014 (6)

D. M. Solis, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8, 7559–7570 (2014).
[Crossref] [PubMed]

A. Ji, T. V. Raziman, J. Butet, R. P. Sharma, and O. J. F. Martin, “Optical forces and torques on realistic plasmonic nanostructures: a surface integral approach,” Opt. Lett. 39, 4699–4702 (2014).
[Crossref] [PubMed]

X. M. Pan and X. Q. Sheng, “Accurate and efficient evaluation of spatial electromagnetic responses of large scale targets,” IEEE Trans. Antennas Propag. 62, 4746–4753 (2014).
[Crossref]

X. M. Pan, M. J. Gou, and X. Q. Sheng, “Prediction of radiation pressure force exerted on moving particles by the two-level skeletonization,” Opt. Express 22, 10032–10045 (2014).
[Crossref] [PubMed]

H. W. Gao, J. W. Hao, X. M. Pan, and X. Q. Sheng, “Application of interpolative decomposition to FE-BI-MLFMA for fast computation of monostatic scattering from 3-d complex composite objects,” Antennas and Wireless Propagation Letters”, IEEE 13, 1490–1493 (2014).

X. M. Pan and X. Q. Sheng, “Improved algebraic preconditioning for MoM solutions of large-scale electromagnetic problems,” IEEE Antennas Wireless Propag. Lett. 13, 106–109 (2014).
[Crossref]

2013 (4)

M. L. Yang, K. F. Ren, M. J. Gou, and X. Q. Sheng, “Computation of radiation pressure force on arbitrary shaped homogenous particles by multilevel fast multipole algorithm,” Opt. Lett. 38, 1784–1786 (2013).
[Crossref] [PubMed]

X. M. Pan and X. Q. Sheng, “Preconditioning technique in the interpolative decomposition multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 61, 3373–3377 (2013).
[Crossref]

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

O. Ergul and L. Gurel, “Fast and accurate analysis of large-scale composite structures with the parallel multilevel fast multipole algorithm,” J. Opt. Soc. Am. A 30, 509–517 (2013).
[Crossref]

2012 (6)

X. M. Pan, L. Cai, and X. Q. Sheng, “An efficient high order multilevel fast multipole algorithm for electromagnetic scattering analysis,” Progr. Electromagn. Res. 126, 85–100 (2012).
[Crossref]

C. Forestiere, G. Iadarola, G. Rubinacci, A. Tamburrino, L. D. Negro, and G. Miano, “Surface integral formulations for the design of plasmonic nanostructures,” J. Opt. Soc. Am. A 29, 2314–2327 (2012).
[Crossref]

X. M. Pan, W. C. Pi, M. L. Yang, Z. Peng, and X. Q. Sheng, “Solving problems with over one billion unknowns by the MLFMA,” IEEE Trans. Antennas Propag. 60, 2571–2574 (2012).
[Crossref]

M. G. Araujo, J. M. Taboada, D. M. Solis, J. Rivero, L. Landesa, and F. Obelleiro, “Comparison of surface integral equation formulations for electromagnetic analysis of plasmonic nanoscatterers,” Opt. Express 20, 9161–9171 (2012).
[Crossref] [PubMed]

L. Landesa, M. G. Araujo, J. M. Taboada, L. Bote, and F. Obelleiro, “Improving condition number and convergence of the surface integral-equation method of moments for penetrable bodies,” Opt. Express 20, 17237–17249 (2012).
[Crossref]

X. M. Pan, J. G. Wei, Z. Peng, and X. Q. Sheng, “A fast algorithm for multiscale electromagnetic problems using interpolative decomposition and multilevel fast multipole algorithm,” Radio Sci. 47, RS1011 (2012).
[Crossref]

2010 (3)

G. K. Christopher, J. N. Stephen, and V.-D. Tuan, “Investigating the plasmonics of a dipole-excited silver nanoshell: Mie theory versus finite element method,” Nanotechnology 21, 315203 (2010).
[Crossref]

G. Miano, G. Rubinacci, and A. Tamburrino, “Numerical modeling for the analysis of plasmon oscillations in metallic nanoparticles,” IEEE Trans. Antennas Propag. 58, 2920–2933 (2010).
[Crossref]

G. Benjamin and O. J. Martin, “Scattering on plasmonic nanostructures arrays modeled with a surface integral formulation,” Photonics and Nanostructures - Fundamentals and Applications 8, 278–284 (2010).
[Crossref]

2009 (2)

2007 (3)

W.-B. Ewe, H.-S. Chu, and E.-P. Li, “Volume integral equation analysis of surface plasmon resonance of nanoparticles,” Opt. Express 15, 18200–18208 (2007).
[Crossref] [PubMed]

F. Xu, K.-F. Ren, G. Gouesbet, X.-S. Cai, and G. Grehan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[Crossref]

E. Liberty, F. Woolfe, P. G. Martinsson, V. Rokhlin, and M. Tygert, “Randomized algorithms for the low-rank approximation of matrices,” Proc. Natl. Acad. Sci. USA 104, 20167–20172 (2007).
[Crossref] [PubMed]

2003 (1)

Stephen K. Gray and T. Kupka, “Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders,” Phys. Rev. B 68, 045,415 (2003).
[Crossref]

2002 (2)

E. Moreno, D. Erni, C. Hafner, and R. Vahldieck, “Multiple multipole method with automatic multipole setting applied to the simulation of surface plasmons in metallic nanostructures,” J. Opt. Soc. Am. A 19, 101–111 (2002).
[Crossref]

X. Q. Sheng and E. K.-N. Yung, “Implementation and experiments of a hybrid algorithm of the mlfma-enhanced FE-BI method for open-region inhomogeneous electromagnetic problems,” IEEE Trans. Antennas Propag. 50, 163–167 (2002).
[Crossref]

2001 (1)

M. I. Mishchenko, “Radiation force caused by scattering, absorption, and emission of light by nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 70, 811–816 (2001).
[Crossref]

2000 (1)

Y. Ji and T. H. Hubing, “Emap5: A 3d hybrid FEM/MoM code,” Appl. Computat. Electromagn. Soc. J. 15, 1–12 (2000).

1998 (1)

X. Q. Sheng, J. M. Jin, J. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral method for 3d scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[Crossref]

1996 (1)

1994 (2)

1989 (1)

J. P. Barton and D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Alexander, D. R.

J. P. Barton and D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[Crossref]

Araujo, M. G.

Barton, J. P.

J. P. Barton and D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[Crossref]

Benjamin, G.

G. Benjamin and O. J. Martin, “Scattering on plasmonic nanostructures arrays modeled with a surface integral formulation,” Photonics and Nanostructures - Fundamentals and Applications 8, 278–284 (2010).
[Crossref]

Block, S. M.

Bote, L.

Butet, J.

Cai, L.

X. M. Pan, L. Cai, and X. Q. Sheng, “An efficient high order multilevel fast multipole algorithm for electromagnetic scattering analysis,” Progr. Electromagn. Res. 126, 85–100 (2012).
[Crossref]

Cai, X.-S.

F. Xu, K.-F. Ren, G. Gouesbet, X.-S. Cai, and G. Grehan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[Crossref]

Chew, W. C.

X. Q. Sheng, J. M. Jin, J. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral method for 3d scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[Crossref]

W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast Efficient Algorithms in Computational Electromagnetics (Artech House, Boston, MA, 2001).

Christopher, G. K.

G. K. Christopher, J. N. Stephen, and V.-D. Tuan, “Investigating the plasmonics of a dipole-excited silver nanoshell: Mie theory versus finite element method,” Nanotechnology 21, 315203 (2010).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Chu, H.-S.

Draine, B. T.

Ergul, O.

Erni, D.

Ewe, W.-B.

Ferrari, A. C.

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

Flatau, P. J.

Forestiere, C.

Gao, H. W.

H. W. Gao, J. W. Hao, X. M. Pan, and X. Q. Sheng, “Application of interpolative decomposition to FE-BI-MLFMA for fast computation of monostatic scattering from 3-d complex composite objects,” Antennas and Wireless Propagation Letters”, IEEE 13, 1490–1493 (2014).

Garcia de Abajo, F. J.

D. M. Solis, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8, 7559–7570 (2014).
[Crossref] [PubMed]

Gou, M. J.

Gouesbet, G.

F. Xu, K.-F. Ren, G. Gouesbet, X.-S. Cai, and G. Grehan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[Crossref]

K. F. Ren, G. Grehan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized lorenz-mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[Crossref] [PubMed]

Gray, Stephen K.

Stephen K. Gray and T. Kupka, “Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders,” Phys. Rev. B 68, 045,415 (2003).
[Crossref]

Grehan, G.

F. Xu, K.-F. Ren, G. Gouesbet, X.-S. Cai, and G. Grehan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[Crossref]

K. F. Ren, G. Grehan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized lorenz-mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[Crossref] [PubMed]

Gucciardi, P. G.

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

Gurel, L.

Hafner, C.

Hao, J. W.

H. W. Gao, J. W. Hao, X. M. Pan, and X. Q. Sheng, “Application of interpolative decomposition to FE-BI-MLFMA for fast computation of monostatic scattering from 3-d complex composite objects,” Antennas and Wireless Propagation Letters”, IEEE 13, 1490–1493 (2014).

Hubing, T. H.

Y. Ji and T. H. Hubing, “Emap5: A 3d hybrid FEM/MoM code,” Appl. Computat. Electromagn. Soc. J. 15, 1–12 (2000).

Iadarola, G.

Ji, A.

Ji, Y.

Y. Ji and T. H. Hubing, “Emap5: A 3d hybrid FEM/MoM code,” Appl. Computat. Electromagn. Soc. J. 15, 1–12 (2000).

Jin, J. M.

X. Q. Sheng, J. M. Jin, J. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral method for 3d scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[Crossref]

W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast Efficient Algorithms in Computational Electromagnetics (Artech House, Boston, MA, 2001).

J. M. Jin, The Finite Element Method in Electromagnetics (Wiley-IEEE Press, New York, 2002), 2nd ed.

J. M. Jin, Theory and Computation of Electromagnetic Fields (Wiley-IEEE Press, 2010).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Jones, P. H.

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

Kern, A. M.

Kupka, T.

Stephen K. Gray and T. Kupka, “Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders,” Phys. Rev. B 68, 045,415 (2003).
[Crossref]

Landesa, L.

Li, E.-P.

Liberty, E.

E. Liberty, F. Woolfe, P. G. Martinsson, V. Rokhlin, and M. Tygert, “Randomized algorithms for the low-rank approximation of matrices,” Proc. Natl. Acad. Sci. USA 104, 20167–20172 (2007).
[Crossref] [PubMed]

Liz-Marzan, L. M.

D. M. Solis, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8, 7559–7570 (2014).
[Crossref] [PubMed]

Lu, C. C.

X. Q. Sheng, J. M. Jin, J. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral method for 3d scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[Crossref]

Marago, O. M.

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

Martin, O. J.

G. Benjamin and O. J. Martin, “Scattering on plasmonic nanostructures arrays modeled with a surface integral formulation,” Photonics and Nanostructures - Fundamentals and Applications 8, 278–284 (2010).
[Crossref]

Martin, O. J. F.

Martinsson, P. G.

E. Liberty, F. Woolfe, P. G. Martinsson, V. Rokhlin, and M. Tygert, “Randomized algorithms for the low-rank approximation of matrices,” Proc. Natl. Acad. Sci. USA 104, 20167–20172 (2007).
[Crossref] [PubMed]

Miano, G.

C. Forestiere, G. Iadarola, G. Rubinacci, A. Tamburrino, L. D. Negro, and G. Miano, “Surface integral formulations for the design of plasmonic nanostructures,” J. Opt. Soc. Am. A 29, 2314–2327 (2012).
[Crossref]

G. Miano, G. Rubinacci, and A. Tamburrino, “Numerical modeling for the analysis of plasmon oscillations in metallic nanoparticles,” IEEE Trans. Antennas Propag. 58, 2920–2933 (2010).
[Crossref]

Michielssen, E.

W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast Efficient Algorithms in Computational Electromagnetics (Artech House, Boston, MA, 2001).

Mishchenko, M. I.

M. I. Mishchenko, “Radiation force caused by scattering, absorption, and emission of light by nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 70, 811–816 (2001).
[Crossref]

Moreno, E.

Negro, L. D.

Obelleiro, F.

Pan, X. M.

X. M. Pan and X. Q. Sheng, “Accurate and efficient evaluation of spatial electromagnetic responses of large scale targets,” IEEE Trans. Antennas Propag. 62, 4746–4753 (2014).
[Crossref]

X. M. Pan, M. J. Gou, and X. Q. Sheng, “Prediction of radiation pressure force exerted on moving particles by the two-level skeletonization,” Opt. Express 22, 10032–10045 (2014).
[Crossref] [PubMed]

X. M. Pan and X. Q. Sheng, “Improved algebraic preconditioning for MoM solutions of large-scale electromagnetic problems,” IEEE Antennas Wireless Propag. Lett. 13, 106–109 (2014).
[Crossref]

H. W. Gao, J. W. Hao, X. M. Pan, and X. Q. Sheng, “Application of interpolative decomposition to FE-BI-MLFMA for fast computation of monostatic scattering from 3-d complex composite objects,” Antennas and Wireless Propagation Letters”, IEEE 13, 1490–1493 (2014).

X. M. Pan and X. Q. Sheng, “Preconditioning technique in the interpolative decomposition multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 61, 3373–3377 (2013).
[Crossref]

X. M. Pan, L. Cai, and X. Q. Sheng, “An efficient high order multilevel fast multipole algorithm for electromagnetic scattering analysis,” Progr. Electromagn. Res. 126, 85–100 (2012).
[Crossref]

X. M. Pan, W. C. Pi, M. L. Yang, Z. Peng, and X. Q. Sheng, “Solving problems with over one billion unknowns by the MLFMA,” IEEE Trans. Antennas Propag. 60, 2571–2574 (2012).
[Crossref]

X. M. Pan, J. G. Wei, Z. Peng, and X. Q. Sheng, “A fast algorithm for multiscale electromagnetic problems using interpolative decomposition and multilevel fast multipole algorithm,” Radio Sci. 47, RS1011 (2012).
[Crossref]

Peng, Z.

X. M. Pan, J. G. Wei, Z. Peng, and X. Q. Sheng, “A fast algorithm for multiscale electromagnetic problems using interpolative decomposition and multilevel fast multipole algorithm,” Radio Sci. 47, RS1011 (2012).
[Crossref]

X. M. Pan, W. C. Pi, M. L. Yang, Z. Peng, and X. Q. Sheng, “Solving problems with over one billion unknowns by the MLFMA,” IEEE Trans. Antennas Propag. 60, 2571–2574 (2012).
[Crossref]

Pi, W. C.

X. M. Pan, W. C. Pi, M. L. Yang, Z. Peng, and X. Q. Sheng, “Solving problems with over one billion unknowns by the MLFMA,” IEEE Trans. Antennas Propag. 60, 2571–2574 (2012).
[Crossref]

Raziman, T. V.

Ren, K. F.

Ren, K.-F.

F. Xu, K.-F. Ren, G. Gouesbet, X.-S. Cai, and G. Grehan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[Crossref]

Rivero, J.

Rokhlin, V.

E. Liberty, F. Woolfe, P. G. Martinsson, V. Rokhlin, and M. Tygert, “Randomized algorithms for the low-rank approximation of matrices,” Proc. Natl. Acad. Sci. USA 104, 20167–20172 (2007).
[Crossref] [PubMed]

Rubinacci, G.

C. Forestiere, G. Iadarola, G. Rubinacci, A. Tamburrino, L. D. Negro, and G. Miano, “Surface integral formulations for the design of plasmonic nanostructures,” J. Opt. Soc. Am. A 29, 2314–2327 (2012).
[Crossref]

G. Miano, G. Rubinacci, and A. Tamburrino, “Numerical modeling for the analysis of plasmon oscillations in metallic nanoparticles,” IEEE Trans. Antennas Propag. 58, 2920–2933 (2010).
[Crossref]

Sendur, K.

Sharma, R. P.

Sheng, X. Q.

X. M. Pan, M. J. Gou, and X. Q. Sheng, “Prediction of radiation pressure force exerted on moving particles by the two-level skeletonization,” Opt. Express 22, 10032–10045 (2014).
[Crossref] [PubMed]

X. M. Pan and X. Q. Sheng, “Accurate and efficient evaluation of spatial electromagnetic responses of large scale targets,” IEEE Trans. Antennas Propag. 62, 4746–4753 (2014).
[Crossref]

H. W. Gao, J. W. Hao, X. M. Pan, and X. Q. Sheng, “Application of interpolative decomposition to FE-BI-MLFMA for fast computation of monostatic scattering from 3-d complex composite objects,” Antennas and Wireless Propagation Letters”, IEEE 13, 1490–1493 (2014).

X. M. Pan and X. Q. Sheng, “Improved algebraic preconditioning for MoM solutions of large-scale electromagnetic problems,” IEEE Antennas Wireless Propag. Lett. 13, 106–109 (2014).
[Crossref]

M. L. Yang, K. F. Ren, M. J. Gou, and X. Q. Sheng, “Computation of radiation pressure force on arbitrary shaped homogenous particles by multilevel fast multipole algorithm,” Opt. Lett. 38, 1784–1786 (2013).
[Crossref] [PubMed]

X. M. Pan and X. Q. Sheng, “Preconditioning technique in the interpolative decomposition multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 61, 3373–3377 (2013).
[Crossref]

X. M. Pan, L. Cai, and X. Q. Sheng, “An efficient high order multilevel fast multipole algorithm for electromagnetic scattering analysis,” Progr. Electromagn. Res. 126, 85–100 (2012).
[Crossref]

X. M. Pan, W. C. Pi, M. L. Yang, Z. Peng, and X. Q. Sheng, “Solving problems with over one billion unknowns by the MLFMA,” IEEE Trans. Antennas Propag. 60, 2571–2574 (2012).
[Crossref]

X. M. Pan, J. G. Wei, Z. Peng, and X. Q. Sheng, “A fast algorithm for multiscale electromagnetic problems using interpolative decomposition and multilevel fast multipole algorithm,” Radio Sci. 47, RS1011 (2012).
[Crossref]

X. Q. Sheng and E. K.-N. Yung, “Implementation and experiments of a hybrid algorithm of the mlfma-enhanced FE-BI method for open-region inhomogeneous electromagnetic problems,” IEEE Trans. Antennas Propag. 50, 163–167 (2002).
[Crossref]

X. Q. Sheng, J. M. Jin, J. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral method for 3d scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[Crossref]

Solis, D. M.

Song, J.

X. Q. Sheng, J. M. Jin, J. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral method for 3d scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[Crossref]

W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast Efficient Algorithms in Computational Electromagnetics (Artech House, Boston, MA, 2001).

Stephen, J. N.

G. K. Christopher, J. N. Stephen, and V.-D. Tuan, “Investigating the plasmonics of a dipole-excited silver nanoshell: Mie theory versus finite element method,” Nanotechnology 21, 315203 (2010).
[Crossref]

Svoboda, K.

Taboada, J. M.

Tamburrino, A.

C. Forestiere, G. Iadarola, G. Rubinacci, A. Tamburrino, L. D. Negro, and G. Miano, “Surface integral formulations for the design of plasmonic nanostructures,” J. Opt. Soc. Am. A 29, 2314–2327 (2012).
[Crossref]

G. Miano, G. Rubinacci, and A. Tamburrino, “Numerical modeling for the analysis of plasmon oscillations in metallic nanoparticles,” IEEE Trans. Antennas Propag. 58, 2920–2933 (2010).
[Crossref]

Tuan, V.-D.

G. K. Christopher, J. N. Stephen, and V.-D. Tuan, “Investigating the plasmonics of a dipole-excited silver nanoshell: Mie theory versus finite element method,” Nanotechnology 21, 315203 (2010).
[Crossref]

Tygert, M.

E. Liberty, F. Woolfe, P. G. Martinsson, V. Rokhlin, and M. Tygert, “Randomized algorithms for the low-rank approximation of matrices,” Proc. Natl. Acad. Sci. USA 104, 20167–20172 (2007).
[Crossref] [PubMed]

Vahldieck, R.

Volpe, G.

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

Wei, J. G.

X. M. Pan, J. G. Wei, Z. Peng, and X. Q. Sheng, “A fast algorithm for multiscale electromagnetic problems using interpolative decomposition and multilevel fast multipole algorithm,” Radio Sci. 47, RS1011 (2012).
[Crossref]

Woolfe, F.

E. Liberty, F. Woolfe, P. G. Martinsson, V. Rokhlin, and M. Tygert, “Randomized algorithms for the low-rank approximation of matrices,” Proc. Natl. Acad. Sci. USA 104, 20167–20172 (2007).
[Crossref] [PubMed]

Xu, F.

F. Xu, K.-F. Ren, G. Gouesbet, X.-S. Cai, and G. Grehan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[Crossref]

Yang, M. L.

M. L. Yang, K. F. Ren, M. J. Gou, and X. Q. Sheng, “Computation of radiation pressure force on arbitrary shaped homogenous particles by multilevel fast multipole algorithm,” Opt. Lett. 38, 1784–1786 (2013).
[Crossref] [PubMed]

X. M. Pan, W. C. Pi, M. L. Yang, Z. Peng, and X. Q. Sheng, “Solving problems with over one billion unknowns by the MLFMA,” IEEE Trans. Antennas Propag. 60, 2571–2574 (2012).
[Crossref]

Yung, E. K.-N.

X. Q. Sheng and E. K.-N. Yung, “Implementation and experiments of a hybrid algorithm of the mlfma-enhanced FE-BI method for open-region inhomogeneous electromagnetic problems,” IEEE Trans. Antennas Propag. 50, 163–167 (2002).
[Crossref]

ACS Nano (1)

D. M. Solis, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8, 7559–7570 (2014).
[Crossref] [PubMed]

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Appl. Opt. (1)

IEEE (1)

H. W. Gao, J. W. Hao, X. M. Pan, and X. Q. Sheng, “Application of interpolative decomposition to FE-BI-MLFMA for fast computation of monostatic scattering from 3-d complex composite objects,” Antennas and Wireless Propagation Letters”, IEEE 13, 1490–1493 (2014).

IEEE Antennas Wireless Propag. Lett. (1)

X. M. Pan and X. Q. Sheng, “Improved algebraic preconditioning for MoM solutions of large-scale electromagnetic problems,” IEEE Antennas Wireless Propag. Lett. 13, 106–109 (2014).
[Crossref]

IEEE Trans. Antennas Propag. (6)

X. Q. Sheng and E. K.-N. Yung, “Implementation and experiments of a hybrid algorithm of the mlfma-enhanced FE-BI method for open-region inhomogeneous electromagnetic problems,” IEEE Trans. Antennas Propag. 50, 163–167 (2002).
[Crossref]

X. M. Pan and X. Q. Sheng, “Accurate and efficient evaluation of spatial electromagnetic responses of large scale targets,” IEEE Trans. Antennas Propag. 62, 4746–4753 (2014).
[Crossref]

X. M. Pan and X. Q. Sheng, “Preconditioning technique in the interpolative decomposition multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 61, 3373–3377 (2013).
[Crossref]

X. Q. Sheng, J. M. Jin, J. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral method for 3d scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[Crossref]

G. Miano, G. Rubinacci, and A. Tamburrino, “Numerical modeling for the analysis of plasmon oscillations in metallic nanoparticles,” IEEE Trans. Antennas Propag. 58, 2920–2933 (2010).
[Crossref]

X. M. Pan, W. C. Pi, M. L. Yang, Z. Peng, and X. Q. Sheng, “Solving problems with over one billion unknowns by the MLFMA,” IEEE Trans. Antennas Propag. 60, 2571–2574 (2012).
[Crossref]

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[Crossref]

J. Opt. Soc. Am. A (5)

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M. I. Mishchenko, “Radiation force caused by scattering, absorption, and emission of light by nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 70, 811–816 (2001).
[Crossref]

Nanotechnology (1)

G. K. Christopher, J. N. Stephen, and V.-D. Tuan, “Investigating the plasmonics of a dipole-excited silver nanoshell: Mie theory versus finite element method,” Nanotechnology 21, 315203 (2010).
[Crossref]

Nature Nanotech. (1)

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

Opt. Express (5)

Opt. Lett. (3)

Photonics and Nanostructures - Fundamentals and Applications (1)

G. Benjamin and O. J. Martin, “Scattering on plasmonic nanostructures arrays modeled with a surface integral formulation,” Photonics and Nanostructures - Fundamentals and Applications 8, 278–284 (2010).
[Crossref]

Phys. Rev. B (2)

Stephen K. Gray and T. Kupka, “Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders,” Phys. Rev. B 68, 045,415 (2003).
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[Crossref]

Phys. Rev. E (1)

F. Xu, K.-F. Ren, G. Gouesbet, X.-S. Cai, and G. Grehan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

E. Liberty, F. Woolfe, P. G. Martinsson, V. Rokhlin, and M. Tygert, “Randomized algorithms for the low-rank approximation of matrices,” Proc. Natl. Acad. Sci. USA 104, 20167–20172 (2007).
[Crossref] [PubMed]

Progr. Electromagn. Res. (1)

X. M. Pan, L. Cai, and X. Q. Sheng, “An efficient high order multilevel fast multipole algorithm for electromagnetic scattering analysis,” Progr. Electromagn. Res. 126, 85–100 (2012).
[Crossref]

Radio Sci. (1)

X. M. Pan, J. G. Wei, Z. Peng, and X. Q. Sheng, “A fast algorithm for multiscale electromagnetic problems using interpolative decomposition and multilevel fast multipole algorithm,” Radio Sci. 47, RS1011 (2012).
[Crossref]

Other (3)

W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast Efficient Algorithms in Computational Electromagnetics (Artech House, Boston, MA, 2001).

J. M. Jin, The Finite Element Method in Electromagnetics (Wiley-IEEE Press, New York, 2002), 2nd ed.

J. M. Jin, Theory and Computation of Electromagnetic Fields (Wiley-IEEE Press, 2010).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Arbitrarily shaped nanostructures illuminated by the optical beam (Einc,Hinc).
Fig. 2
Fig. 2 Distribution of equivalent surface electric current on the brick when illuminated by the plane wave with the wavelength λ = 1024 nm at the orientation (θ = 135°,ϕ = 270°). The size of the brick is (0.4, 0.2, 0.6) λ. The center of the block is at the origin of the coordinate. The magnitude of the current is scaled for a nice view. (a): the full view; (b)-(e): viewed from the −y direction for the cases with different meshes.
Fig. 3
Fig. 3 The iteration history and RPF data for the Au particle simulation. The wavelength (λ) and the waist (wo) of the incident beam is 1064 nm and 1.029 λ. The beam propagates along −y direction. (a): iteration history when the bean center is at (0, 0, 0). The residual, an indicator of the error, is evaluated by computing the L2-norm of the residual vector in GMRES. (b): The y-component of the RPF. ”Fy-FE-BI” and ”Fy-no-skel”, respectively, denotes the data obtained by FE-BI with and without skeletonization. ”Fy-JMCFIE” represents the data obtained by JMCFIE. The beam center moves along y-axis from -21280 nm to 21280 nm at the step of 106.4 nm. The unit of force is 10−9N/W.
Fig. 4
Fig. 4 The variation of the z-component of the RPF exerted on the Au sphere located at (0, 0, 0) when the center of the vertical polarized incident Gaussian beam varying. The wavelength and waist of the Gaussian is, respectively, 532 nm and 1.029 λ. The beam propagates along −z direction. The unit of force is 109N/W.
Fig. 5
Fig. 5 The field distribution on the X-Z plane for different d’s when the center of the vertical polarized Gaussian beam is at (0, 0, 0). (a): the one-sphere case; (b-d): the the three-sphere cases with different d’s. The wavelength and waist of the Gaussian is, respectively, 532 nm and 1.029 λ. The beam propagates along −z direction. The unit of the electric field is 10−9V/m.
Fig. 6
Fig. 6 The geometry configuration of the system consisting of multiple nanoparticles.
Fig. 7
Fig. 7 Variation of the x-component of the RPF exerted on the Au sphere (see Fig. 6) when the orientation and center of the vertical polarized Gaussian beam varying simultaneously. The wavelength and waist of the Gaussian is, respectively, 879.88 nm and 1.029 λ. The unit of force is 10−9N/W.

Tables (2)

Tables Icon

Table 1 Statistics of computations on the Au sphere with radius 74.712 nm. The error is computed by Σ ( E Mie E c ) / L max ( E Mie ), where EMie and Ec is the far fields corresponding to Mie’s series and each computation. L, the number of samplings along θ, is equal to 181 for the angle range of 0°–180°.

Tables Icon

Table 2 Statistics of computations on the Au particle as shown Fig. 3a. Iteration counts and time are averaged for 3 skeleton incident beams.

Equations (28)

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f = S T ¯ ( r ) n ^ d S ,
T ¯ = 1 2 [ ε 0 E ( r ) E * ( r ) + μ 0 H ( r ) H * ( r ) 1 2 ( ε 0 | E ( r ) | 2 + μ 0 | H ( r ) | 2 ) I ¯ ] ,
E sca ( r ) + E inc = { 0 , if r V i E 0 , if r V 0
H sca ( r ) + H inc = { 0 , if r V i H 0 , if r V 0
E sca ( r ) = i [ η 0 ( J i ) K ( M i ) ] , and , H sca ( r ) = i [ η 0 1 ( M i ) + K ( J i ) ] ,
{ x } ( r ) = j k 0 S d S [ I + 1 k 2 ] X ( r ) g ( r , r ) ,
K { x } ( r ) = Ω ( r ) 4 π X ( r ) + × S d S g ( r , r ) X ( r ) ,
F ( E i ) = 1 2 V i [ 1 μ i ( × E i ) ( × E i ) k 0 2 ε i E i E i ] d V + j k 0 S i ( E i × H ˜ i ) n ^ d S ,
n ^ i 0 × ( E 0 E i ) | S i = 0 , and n ^ i 0 × ( H 0 H i ) | S i = 0.
α EFIE + ( 1 α ) η 0 n ^ i 0 × MFIE ,
E i = k N i I ( x e ) k N k I + p N i S ( x e ) p N p S ,
H ˜ i = k N i S ( x h ) k N k S ,
[ K II K IS 0 K SI K SS B ] [ x e I x e S x h S ] = [ 0 0 ] , x e I = { ( x e ) 1 , ( x e ) 2 , , ( x e ) N I } T , x e S = { ( x e ) 1 , ( x e ) 2 , , ( x e ) N S } T , x h S = { ( x h ) 1 , ( x h ) 2 , , ( x h ) N S } T ,
K m n II = V i [ 1 μ i ( × N m I ) ( × N n I ) k 0 2 ε i N m I N n I ] d V , K m n IS = V i [ 1 μ i ( × N m I ) ( × N n S ) k 0 2 ε i N m I N n S ] d v , K m n SI = V i [ 1 μ i ( × N m S ) ( × N n I ) k 0 2 ε i N m S N n I ] d V , K m n SS = V i [ 1 μ i ( × N m S ) ( × N n S ) k 0 2 ε i N m S N n S ] d V , B m n j k 0 S i [ n ^ i 0 ( N m S × N n S ) ] d S ,
η 0 J i = n ^ i 0 × H ˜ i ( r ) = k N i S ( x h ) k n ^ i 0 × N k S = k N i S ( x h ) k g k , M i = n ^ i 0 × E i ( r ) = k N i S ( x e ) k n ^ i 0 × N k S = k N i S ( x e ) k g k ,
[ P ] x e S + [ Q ] x h S = y ,
P m n = S i S i [ α g m ( r ) K ( g n ( r ) ) + ( 1 α ) g m ( r ) n ^ i 0 × ( g n ( r ) ) ] d S d S Q m n = S i S i [ α g m ( r ) ( g n ( r ) ) + ( 1 α ) g m ( r ) n ^ i 0 × K ( g n ( r ) ) ] d S d S .
y n = S i [ α g m ( r ) E inc + ( 1 α ) g m ( r ) n ^ i 0 × H inc ] d S .
[ K II K IS 0 K SI K SS B 0 P Q ] [ x e I x e S x h S ] = [ 0 0 y ] , or , Z x = y .
M = [ K II K IS K SI K SS ] 1 [ 0 B ] .
( P M + Q ) x h S = y .
[ K 1 II K 1 IS 0 0 0 0 0 0 0 K 1 SI K 1 SS B 1 0 0 0 0 0 0 0 P 11 Q 11 0 P 12 Q 12 0 P 13 Q 13 0 0 0 K 2 II K 2 IS 0 0 0 0 0 0 0 K 2 SI K 2 SS B 2 0 0 0 0 P 21 Q 21 0 P 22 Q 22 0 P 23 Q 23 ¯ 0 0 0 0 0 0 K 3 II K 3 IS 0 0 0 0 0 0 0 K 3 SI K 3 SS B 3 0 P 31 Q 31 0 P 32 Q 32 0 P 33 Q 33 ¯ ] [ x e , 1 I x e , 1 S x h , 1 S x e , 2 I x e , 2 S x e , 2 S x e , 3 I x e , 3 S x e , 3 S ] = [ 0 0 y 1 0 0 y 2 0 0 y 3 ] ,
[ Z 11 0 0 0 Z 22 0 0 0 Z 33 ] [ x 1 x 2 x 3 ] + [ 0 Z 12 Z 13 Z 21 0 Z 23 Z 31 Z 32 0 ] [ x 1 x 2 x 3 ] = [ y ˜ 1 y ˜ 2 y ˜ 3 ] ,
Z i i = [ K i II K i IS 0 K i SI K i SS B i 0 P i i Q i i ] , Z i l | i l = [ 0 0 0 0 0 0 0 P i l Q i l ] , x i = [ x e , i I x e , i S x h , i S ] , y ˜ i = [ 0 0 y i ] , i , l = 1 , 2 , 3.
( I + [ Z 11 1 0 0 0 Z 22 1 0 0 0 Z 33 1 ] [ 0 Z 12 Z 13 Z 21 0 Z 23 Z 31 Z 32 0 ] ) [ x 1 x 2 x 3 ] = [ Z 11 1 y ˜ 1 Z 22 1 y ˜ 2 Z 33 1 y ˜ 3 ] .
Z X ( κ ) = Y ( κ ) , or , X ( κ ) = Z 1 Y ( κ ) ,
Y ( κ ) = Y s ( κ ) R ( κ ) ,
X ( κ ) = Z 1 Y s ( κ ) R ( κ ) = X s ( κ ) R ( κ ) , with , X s ( κ ) = Z 1 Y s ( κ ) ,

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