Abstract

We have developed and implemented a numerical scheme to compute optical forces in two-dimensional (2D) structures based on the boundary integral equations, which are solved by the numerical boundary element method. We demonstrate the efficiency of this method by calculating the optical scattering and radiation pressures exerted on 2D objects under the illumination of both plane wave and cylindrical Gaussian beams. The results are validated by comparing to analytical Mie scattering results on circular cylinders. In the framework of this approach the object can be of arbitrary shape with dimensions either far larger, comparable, or much less than the wavelength concerned, and the constituent components can be either dielectric or metallic. We applied the method to study the resonance enhancement of optical forces and the effect of surface roughness on such enhancement. Surprisingly, we found that a cylinder with “controlled roughness” can give a stronger optical force than a smooth surface at resonance.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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  4. M. Guillon, O. Moine, and B. Stout, “Longitudinal optical binding of high optical contrast microdroplets in air,” Phys. Rev. Lett. 96, 143902 (2006).
    [CrossRef] [PubMed]
  5. J. Ng and C. T. Chan, “Localized vibrational modes in optically bound structures,” Opt. Lett. 31, 2583-2585 (2006).
    [CrossRef] [PubMed]
  6. J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: numerical simulations,” Phys. Rev. B 72, 085130 (2005).
    [CrossRef]
  7. M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, “Near-field photonic forces,” Philos. Trans. R. Soc. London, Ser. A 362, 719-737 (2004).
    [CrossRef]
  8. F. J. García de Abajo, T. Brixner, and W. Pfeiffer, “Nanoscale force manipulation in the vicinity of a metal nanostructure,” J. Phys. B 40, S249-S258 (2007).
    [CrossRef]
  9. M. Righini, A. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys. 3, 477-480 (2007).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  31. For a point not on a smooth surface, and instead right at a sharp corner with an inside angle θΓ, this CPV correction takes the value of θΓ/2π. In practice, we may also smooth a sharp corner first.
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  35. We implement a regularization by the “add-subtract scheme” and do the singular integral anaytically while employing a Gaussian quadrature for the nonsingular part.
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    [CrossRef]
  37. There are also implementions of the indirect BEM method for EM scattering calculations. See, for example, F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett. 80, 5180-5183 (1998).
    [CrossRef]
  38. F. J. García de Abajo and A. Howie,“Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 75, 115418 (2002); See .
    [CrossRef]
  39. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
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    [CrossRef]
  42. T. M. Grzegorczyk and J. A. Kong, “Analytical expression of the force due to multiple TM plane-wave incidences on an infinite lossless dielectric circular cylinder of arbitrary size,” J. Opt. Soc. Am. B 24, 644-652 (2007).
    [CrossRef]
  43. T. M. Grzegorczyk and J. A. Kong, “Analytical prediction of stable optical trapping in optical vortices created by three TE or TM plane waves,” Opt. Express 13, 8010-8020 (2007).
    [CrossRef]
  44. M. Ohki, K. Shimizu, and S. Kozaki, “Scattering of Gaussian beam by a dielectric rectangular cylinder,” IEEE Trans. Electromagn. Compat. 42, 164-171 (2000).
    [CrossRef]
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    [CrossRef]
  47. A. V. Itagi and W. A. Challener, “Optics of photonic nanojets,” J. Opt. Soc. Am. A 22, 2847-2858 (2005).
    [CrossRef]
  48. Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1215-1220 (2004).
    [CrossRef]

2008 (2)

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

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008).
[CrossRef] [PubMed]

2007 (9)

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416-422 (2007).
[CrossRef]

A. Rodriguez, M. Ibanescu, D. Iannuzzi, J. D. Joannopoulos, and S. G. Johnson, “Virtual photons in imaginary time: computing exact Casimir forces via standard numerical electromagnetism techniques,” Phys. Rev. A 76, 032106 (2007).
[CrossRef]

A. Mendoza-Suárez, F. Villa-Villa, and J. A. Gaspar-Armenta, “Band structure of two-dimensional photonic crystals that include dispersive left-handed materials and dielectrics in the unit cell,” J. Opt. Soc. Am. B 24, 3091-3098 (2007).
[CrossRef]

F. J. García de Abajo, T. Brixner, and W. Pfeiffer, “Nanoscale force manipulation in the vicinity of a metal nanostructure,” J. Phys. B 40, S249-S258 (2007).
[CrossRef]

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

A. S. Zelenina, R. Quidant, and M. Nieto-Vesperinas, “Enhanced optical forces between coupled resonant metal nanoparticles,” Opt. Lett. 32, 1156-1158 (2007).
[CrossRef] [PubMed]

E. Pone, A. Hassani, S. Lacroix, A. Kabashin, and M. Skorobogatiy, “Boundary integral method for the challenging problems in bandgap guiding, plasmonics and sensing,” Opt. Express 15, 10231-10246 (2007).
[CrossRef] [PubMed]

T. M. Grzegorczyk and J. A. Kong, “Analytical expression of the force due to multiple TM plane-wave incidences on an infinite lossless dielectric circular cylinder of arbitrary size,” J. Opt. Soc. Am. B 24, 644-652 (2007).
[CrossRef]

T. M. Grzegorczyk and J. A. Kong, “Analytical prediction of stable optical trapping in optical vortices created by three TE or TM plane waves,” Opt. Express 13, 8010-8020 (2007).
[CrossRef]

2006 (5)

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, “Lorentz force on dielectric and magnetic particles,” J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

F. Zhou, X. Gan, W. Xu, and F. Gan, “Comment on: computation of the optical trapping force using an fdtd based technique,” Opt. Express 14, 12494-12496 (2006).
[CrossRef] [PubMed]

K. Dholakia and P. Reece, “Optical micromanipulation takes hold,” Nanotoday 1, 18-27 (2006).

M. Guillon, O. Moine, and B. Stout, “Longitudinal optical binding of high optical contrast microdroplets in air,” Phys. Rev. Lett. 96, 143902 (2006).
[CrossRef] [PubMed]

J. Ng and C. T. Chan, “Localized vibrational modes in optically bound structures,” Opt. Lett. 31, 2583-2585 (2006).
[CrossRef] [PubMed]

2005 (3)

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: numerical simulations,” Phys. Rev. B 72, 085130 (2005).
[CrossRef]

T. Nobis and M. Grundmann, “Low-order optical whispering-gallery modes in hexagonal nanocavities,” Phys. Rev. A 72, 063806 (2005).
[CrossRef]

A. V. Itagi and W. A. Challener, “Optics of photonic nanojets,” J. Opt. Soc. Am. A 22, 2847-2858 (2005).
[CrossRef]

2004 (9)

Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1215-1220 (2004).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Spectral shift and Q change of circular and square-shaped optical microcavity modes due to periodic sidewall surface roughness,” J. Opt. Soc. Am. B 21, 1792-1796 (2004).
[CrossRef]

J. Lindberg, K. Lindfors, T. Setälä, M. Kaivola, and A. T. Friberg, “Spectral analysis of resonant transmission of light through a single sub-wavelength slit,” Opt. Express 12, 623-632 (2004).
[CrossRef] [PubMed]

H. Schomerus, J. Wiersig, and M. Hentschel, “Optomechanical probes of resonances in amplifying microresonators,” Phys. Rev. A 70, 012703 (2004).
[CrossRef]

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393-402 (2004).
[CrossRef]

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

H. Cheng, W. Y. Crutchfield, M. Doery, and L. Greengard, “Fast, accurate integral equation methods for the analysis of photonic crystal fibers I: theory,” Opt. Express 12, 3791-3805 (2004).
[CrossRef] [PubMed]

D. Zhang, X.-C. Yuan, S. C. Tjin, and S. Krishnan, “Rigorous time domain simulation of momentum transfer between light and microscopic particles in optical trapping,” Opt. Express 12, 2220-2230 (2004).
[CrossRef] [PubMed]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, “Near-field photonic forces,” Philos. Trans. R. Soc. London, Ser. A 362, 719-737 (2004).
[CrossRef]

2003 (5)

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

D. R. Fredkin and I. D. Mayergoyz, “Resonant behavior of dielectric objects (electromagnetic resonances),” Phys. Rev. Lett. 91, 253902 (2003).
[CrossRef]

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A, Pure Appl. Opt. 5, 53-60 (2003).
[CrossRef]

N. Guan, S. Habu, K. Takenaga, K. Himeno, and A. Wada, “Boundary element method for analysis of holey optical fibers,” J. Lightwave Technol. 21, 1787-1792 (2003).
[CrossRef]

T. Lu and D. Yevick, “A vectorial boundary element method analysis of integrated optical waveguides,” J. Lightwave Technol. 21, 1793-1807 (2003).
[CrossRef]

2002 (2)

F. J. García de Abajo and A. Howie,“Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 75, 115418 (2002); See .
[CrossRef]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, “Optical trapping and manipulation of nano-objects with an apertureless probe,” Phys. Rev. Lett. 88, 123601 (2002).
[CrossRef] [PubMed]

2000 (1)

M. Ohki, K. Shimizu, and S. Kozaki, “Scattering of Gaussian beam by a dielectric rectangular cylinder,” IEEE Trans. Electromagn. Compat. 42, 164-171 (2000).
[CrossRef]

1998 (1)

There are also implementions of the indirect BEM method for EM scattering calculations. See, for example, F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett. 80, 5180-5183 (1998).
[CrossRef]

1997 (1)

1996 (1)

P. A. Knipp and T. L. Reinecke, “Boundary-element method for the calculation of electronic states in semiconductor nanostructures,” Phys. Rev. B 54, 1880-1891 (1996).
[CrossRef]

Backman, V.

Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1215-1220 (2004).
[CrossRef]

Benson, T. M.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Boriskina, S. V.

Brixner, T.

F. J. García de Abajo, T. Brixner, and W. Pfeiffer, “Nanoscale force manipulation in the vicinity of a metal nanostructure,” J. Phys. B 40, S249-S258 (2007).
[CrossRef]

Challener, W. A.

Chan, C. T.

J. Ng and C. T. Chan, “Localized vibrational modes in optically bound structures,” Opt. Lett. 31, 2583-2585 (2006).
[CrossRef] [PubMed]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: numerical simulations,” Phys. Rev. B 72, 085130 (2005).
[CrossRef]

Chaumet, P. C.

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, “Near-field photonic forces,” Philos. Trans. R. Soc. London, Ser. A 362, 719-737 (2004).
[CrossRef]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, “Optical trapping and manipulation of nano-objects with an apertureless probe,” Phys. Rev. Lett. 88, 123601 (2002).
[CrossRef] [PubMed]

Chen, Z.

Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1215-1220 (2004).
[CrossRef]

Cheng, H.

Chew, W. C.

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

Crutchfield, W. Y.

Dholakia, K.

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

K. Dholakia and P. Reece, “Optical micromanipulation takes hold,” Nanotoday 1, 18-27 (2006).

Doery, M.

Eichenfield, M.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416-422 (2007).
[CrossRef]

Fredkin, D. R.

D. R. Fredkin and I. D. Mayergoyz, “Resonant behavior of dielectric objects (electromagnetic resonances),” Phys. Rev. Lett. 91, 253902 (2003).
[CrossRef]

Friberg, A. T.

Gan, F.

Gan, X.

García de Abajo, F. J.

F. J. García de Abajo, T. Brixner, and W. Pfeiffer, “Nanoscale force manipulation in the vicinity of a metal nanostructure,” J. Phys. B 40, S249-S258 (2007).
[CrossRef]

F. J. García de Abajo and A. Howie,“Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 75, 115418 (2002); See .
[CrossRef]

There are also implementions of the indirect BEM method for EM scattering calculations. See, for example, F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett. 80, 5180-5183 (1998).
[CrossRef]

Gaspar-Armenta, J. A.

Girard, C.

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

Greengard, L.

Grier, D. G.

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

Grundmann, M.

T. Nobis and M. Grundmann, “Low-order optical whispering-gallery modes in hexagonal nanocavities,” Phys. Rev. A 72, 063806 (2005).
[CrossRef]

Grzegorczyk, T. M.

T. M. Grzegorczyk and J. A. Kong, “Analytical expression of the force due to multiple TM plane-wave incidences on an infinite lossless dielectric circular cylinder of arbitrary size,” J. Opt. Soc. Am. B 24, 644-652 (2007).
[CrossRef]

T. M. Grzegorczyk and J. A. Kong, “Analytical prediction of stable optical trapping in optical vortices created by three TE or TM plane waves,” Opt. Express 13, 8010-8020 (2007).
[CrossRef]

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, “Lorentz force on dielectric and magnetic particles,” J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

Gu, M.

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

Guan, N.

Guillon, M.

M. Guillon, O. Moine, and B. Stout, “Longitudinal optical binding of high optical contrast microdroplets in air,” Phys. Rev. Lett. 96, 143902 (2006).
[CrossRef] [PubMed]

Habu, S.

Hackbush, W.

W. Hackbush and B. Verlag, Integral Equations: Theory and Numerical Treatment (Birkhauser Verlag, 1995).

Hassani, A.

Hentschel, M.

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008).
[CrossRef] [PubMed]

H. Schomerus, J. Wiersig, and M. Hentschel, “Optomechanical probes of resonances in amplifying microresonators,” Phys. Rev. A 70, 012703 (2004).
[CrossRef]

Himeno, K.

Howie, A.

F. J. García de Abajo and A. Howie,“Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 75, 115418 (2002); See .
[CrossRef]

There are also implementions of the indirect BEM method for EM scattering calculations. See, for example, F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett. 80, 5180-5183 (1998).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Iannuzzi, D.

A. Rodriguez, M. Ibanescu, D. Iannuzzi, J. D. Joannopoulos, and S. G. Johnson, “Virtual photons in imaginary time: computing exact Casimir forces via standard numerical electromagnetism techniques,” Phys. Rev. A 76, 032106 (2007).
[CrossRef]

Ibanescu, M.

A. Rodriguez, M. Ibanescu, D. Iannuzzi, J. D. Joannopoulos, and S. G. Johnson, “Virtual photons in imaginary time: computing exact Casimir forces via standard numerical electromagnetism techniques,” Phys. Rev. A 76, 032106 (2007).
[CrossRef]

Itagi, A. V.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Jin, J.-M.

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

Joannopoulos, J. D.

A. Rodriguez, M. Ibanescu, D. Iannuzzi, J. D. Joannopoulos, and S. G. Johnson, “Virtual photons in imaginary time: computing exact Casimir forces via standard numerical electromagnetism techniques,” Phys. Rev. A 76, 032106 (2007).
[CrossRef]

Johnson, S. G.

A. Rodriguez, M. Ibanescu, D. Iannuzzi, J. D. Joannopoulos, and S. G. Johnson, “Virtual photons in imaginary time: computing exact Casimir forces via standard numerical electromagnetism techniques,” Phys. Rev. A 76, 032106 (2007).
[CrossRef]

Kabashin, A.

Kaivola, M.

Kemp, B. A.

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, “Lorentz force on dielectric and magnetic particles,” J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

Kim, C.-M.

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Knipp, P. A.

P. A. Knipp and T. L. Reinecke, “Boundary-element method for the calculation of electronic states in semiconductor nanostructures,” Phys. Rev. B 54, 1880-1891 (1996).
[CrossRef]

Kong, J. A.

T. M. Grzegorczyk and J. A. Kong, “Analytical prediction of stable optical trapping in optical vortices created by three TE or TM plane waves,” Opt. Express 13, 8010-8020 (2007).
[CrossRef]

T. M. Grzegorczyk and J. A. Kong, “Analytical expression of the force due to multiple TM plane-wave incidences on an infinite lossless dielectric circular cylinder of arbitrary size,” J. Opt. Soc. Am. B 24, 644-652 (2007).
[CrossRef]

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, “Lorentz force on dielectric and magnetic particles,” J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

Kozaki, S.

M. Ohki, K. Shimizu, and S. Kozaki, “Scattering of Gaussian beam by a dielectric rectangular cylinder,” IEEE Trans. Electromagn. Compat. 42, 164-171 (2000).
[CrossRef]

Krishnan, S.

Kurdoglyan, M. S.

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Lacroix, S.

Lee, S.-Y.

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Lin, Z. F.

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: numerical simulations,” Phys. Rev. B 72, 085130 (2005).
[CrossRef]

Lindberg, J.

Lindfors, K.

Lu, T.

Mait, J. N.

Mayergoyz, I. D.

D. R. Fredkin and I. D. Mayergoyz, “Resonant behavior of dielectric objects (electromagnetic resonances),” Phys. Rev. Lett. 91, 253902 (2003).
[CrossRef]

Mendoza-Suárez, A.

Michael, C. P.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416-422 (2007).
[CrossRef]

Michielssen, E.

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

Mirotznik, M. S.

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Moine, O.

M. Guillon, O. Moine, and B. Stout, “Longitudinal optical binding of high optical contrast microdroplets in air,” Phys. Rev. Lett. 96, 143902 (2006).
[CrossRef] [PubMed]

Ng, J.

J. Ng and C. T. Chan, “Localized vibrational modes in optically bound structures,” Opt. Lett. 31, 2583-2585 (2006).
[CrossRef] [PubMed]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: numerical simulations,” Phys. Rev. B 72, 085130 (2005).
[CrossRef]

Nieto-Vesperinas, M.

A. S. Zelenina, R. Quidant, and M. Nieto-Vesperinas, “Enhanced optical forces between coupled resonant metal nanoparticles,” Opt. Lett. 32, 1156-1158 (2007).
[CrossRef] [PubMed]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, “Near-field photonic forces,” Philos. Trans. R. Soc. London, Ser. A 362, 719-737 (2004).
[CrossRef]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, “Optical trapping and manipulation of nano-objects with an apertureless probe,” Phys. Rev. Lett. 88, 123601 (2002).
[CrossRef] [PubMed]

Nobis, T.

T. Nobis and M. Grundmann, “Low-order optical whispering-gallery modes in hexagonal nanocavities,” Phys. Rev. A 72, 063806 (2005).
[CrossRef]

Nosich, A. I.

Ohki, M.

M. Ohki, K. Shimizu, and S. Kozaki, “Scattering of Gaussian beam by a dielectric rectangular cylinder,” IEEE Trans. Electromagn. Compat. 42, 164-171 (2000).
[CrossRef]

Painter, O.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416-422 (2007).
[CrossRef]

Perahia, R.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416-422 (2007).
[CrossRef]

Pfeiffer, W.

F. J. García de Abajo, T. Brixner, and W. Pfeiffer, “Nanoscale force manipulation in the vicinity of a metal nanostructure,” J. Phys. B 40, S249-S258 (2007).
[CrossRef]

Pone, E.

Pozrikidis, C.

C. Pozrikidis, A Practical Guide to Boundary Element Methods with the Software Library BEMLIB (CRC, 2002).
[CrossRef]

Prather, D. W.

Quidant, R.

A. S. Zelenina, R. Quidant, and M. Nieto-Vesperinas, “Enhanced optical forces between coupled resonant metal nanoparticles,” Opt. Lett. 32, 1156-1158 (2007).
[CrossRef] [PubMed]

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

Rahmani, A.

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, “Near-field photonic forces,” Philos. Trans. R. Soc. London, Ser. A 362, 719-737 (2004).
[CrossRef]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, “Optical trapping and manipulation of nano-objects with an apertureless probe,” Phys. Rev. Lett. 88, 123601 (2002).
[CrossRef] [PubMed]

Reece, P.

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

K. Dholakia and P. Reece, “Optical micromanipulation takes hold,” Nanotoday 1, 18-27 (2006).

Reinecke, T. L.

P. A. Knipp and T. L. Reinecke, “Boundary-element method for the calculation of electronic states in semiconductor nanostructures,” Phys. Rev. B 54, 1880-1891 (1996).
[CrossRef]

Righini, M.

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

Rim, S.

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Rodriguez, A.

A. Rodriguez, M. Ibanescu, D. Iannuzzi, J. D. Joannopoulos, and S. G. Johnson, “Virtual photons in imaginary time: computing exact Casimir forces via standard numerical electromagnetism techniques,” Phys. Rev. A 76, 032106 (2007).
[CrossRef]

Schomerus, H.

H. Schomerus, J. Wiersig, and M. Hentschel, “Optomechanical probes of resonances in amplifying microresonators,” Phys. Rev. A 70, 012703 (2004).
[CrossRef]

Setälä, T.

Sewell, P.

Sheng, P.

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: numerical simulations,” Phys. Rev. B 72, 085130 (2005).
[CrossRef]

Shimizu, K.

M. Ohki, K. Shimizu, and S. Kozaki, “Scattering of Gaussian beam by a dielectric rectangular cylinder,” IEEE Trans. Electromagn. Compat. 42, 164-171 (2000).
[CrossRef]

Skorobogatiy, M.

Sladek, J.

V. Sladek and J. Sladek, Singular Integrals in Boundary Element Methods (Computational Mechanics Publications, 1998).

Sladek, V.

V. Sladek and J. Sladek, Singular Integrals in Boundary Element Methods (Computational Mechanics Publications, 1998).

Song, J.

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

Stout, B.

M. Guillon, O. Moine, and B. Stout, “Longitudinal optical binding of high optical contrast microdroplets in air,” Phys. Rev. Lett. 96, 143902 (2006).
[CrossRef] [PubMed]

Taflove, A.

Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1215-1220 (2004).
[CrossRef]

Takenaga, K.

Tjin, S. C.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Verlag, B.

W. Hackbush and B. Verlag, Integral Equations: Theory and Numerical Treatment (Birkhauser Verlag, 1995).

Villa-Villa, F.

Wada, A.

Wiersig, J.

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008).
[CrossRef] [PubMed]

H. Schomerus, J. Wiersig, and M. Hentschel, “Optomechanical probes of resonances in amplifying microresonators,” Phys. Rev. A 70, 012703 (2004).
[CrossRef]

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A, Pure Appl. Opt. 5, 53-60 (2003).
[CrossRef]

Xu, W.

Yevick, D.

Yuan, X.-C.

Zelenina, A.

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

Zelenina, A. S.

Zhang, D.

Zhou, F.

Chem. Soc. Rev. (1)

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

IEEE Trans. Electromagn. Compat. (1)

M. Ohki, K. Shimizu, and S. Kozaki, “Scattering of Gaussian beam by a dielectric rectangular cylinder,” IEEE Trans. Electromagn. Compat. 42, 164-171 (2000).
[CrossRef]

J. Electromagn. Waves Appl. (1)

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, “Lorentz force on dielectric and magnetic particles,” J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. A, Pure Appl. Opt. (1)

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A, Pure Appl. Opt. 5, 53-60 (2003).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (3)

J. Phys. B (1)

F. J. García de Abajo, T. Brixner, and W. Pfeiffer, “Nanoscale force manipulation in the vicinity of a metal nanostructure,” J. Phys. B 40, S249-S258 (2007).
[CrossRef]

Nanotoday (1)

K. Dholakia and P. Reece, “Optical micromanipulation takes hold,” Nanotoday 1, 18-27 (2006).

Nat. Photonics (1)

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416-422 (2007).
[CrossRef]

Nat. Phys. (1)

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

Nature (1)

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

Opt. Express (7)

Opt. Lett. (2)

Philos. Trans. R. Soc. London, Ser. A (1)

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, “Near-field photonic forces,” Philos. Trans. R. Soc. London, Ser. A 362, 719-737 (2004).
[CrossRef]

Phys. Rev. A (4)

A. Rodriguez, M. Ibanescu, D. Iannuzzi, J. D. Joannopoulos, and S. G. Johnson, “Virtual photons in imaginary time: computing exact Casimir forces via standard numerical electromagnetism techniques,” Phys. Rev. A 76, 032106 (2007).
[CrossRef]

H. Schomerus, J. Wiersig, and M. Hentschel, “Optomechanical probes of resonances in amplifying microresonators,” Phys. Rev. A 70, 012703 (2004).
[CrossRef]

T. Nobis and M. Grundmann, “Low-order optical whispering-gallery modes in hexagonal nanocavities,” Phys. Rev. A 72, 063806 (2005).
[CrossRef]

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Phys. Rev. B (3)

P. A. Knipp and T. L. Reinecke, “Boundary-element method for the calculation of electronic states in semiconductor nanostructures,” Phys. Rev. B 54, 1880-1891 (1996).
[CrossRef]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: numerical simulations,” Phys. Rev. B 72, 085130 (2005).
[CrossRef]

F. J. García de Abajo and A. Howie,“Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 75, 115418 (2002); See .
[CrossRef]

Phys. Rev. Lett. (5)

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, “Optical trapping and manipulation of nano-objects with an apertureless probe,” Phys. Rev. Lett. 88, 123601 (2002).
[CrossRef] [PubMed]

M. Guillon, O. Moine, and B. Stout, “Longitudinal optical binding of high optical contrast microdroplets in air,” Phys. Rev. Lett. 96, 143902 (2006).
[CrossRef] [PubMed]

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008).
[CrossRef] [PubMed]

D. R. Fredkin and I. D. Mayergoyz, “Resonant behavior of dielectric objects (electromagnetic resonances),” Phys. Rev. Lett. 91, 253902 (2003).
[CrossRef]

There are also implementions of the indirect BEM method for EM scattering calculations. See, for example, F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett. 80, 5180-5183 (1998).
[CrossRef]

Other (9)

For a point not on a smooth surface, and instead right at a sharp corner with an inside angle θΓ, this CPV correction takes the value of θΓ/2π. In practice, we may also smooth a sharp corner first.

V. Sladek and J. Sladek, Singular Integrals in Boundary Element Methods (Computational Mechanics Publications, 1998).

W. Hackbush and B. Verlag, Integral Equations: Theory and Numerical Treatment (Birkhauser Verlag, 1995).

We implement a regularization by the “add-subtract scheme” and do the singular integral anaytically while employing a Gaussian quadrature for the nonsingular part.

C. Pozrikidis, A Practical Guide to Boundary Element Methods with the Software Library BEMLIB (CRC, 2002).
[CrossRef]

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

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

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Figures (12)

Fig. 1
Fig. 1

Definition of the geometry of the 2D problem where × represents the vertexes of boundary element while the solid circle is a representative point for the particular boundary element. The inset shows the divergency and oscillations of the Green’s function g ( r , r ) when r r : the solid curve is the real part and dashed red curve is the imaginary part.

Fig. 2
Fig. 2

Percent error of the total cross section as a function of the boundary element number for several size parameters.

Fig. 3
Fig. 3

Comparing BEM results with MST results for (a) one cylinder, (b), (c) cylinder pairs under longitudinal and transverse plane wave illumination, respectively. The wavelength is λ = a .

Fig. 4
Fig. 4

Boundary field solutions near the WG resonances (a) TE 15 , 1 ( λ 0.515 a ) , (b) TE 14 , 1 ( λ 0.548 a ) , and (c) TE 13 , 1 ( λ 0.587 a ) under the illumination of a plane wave and a tapered cylindrical Gaussian beam.

Fig. 5
Fig. 5

WG mode TE 15 , 1 excited by a plane wave exp ( i k x ) propagating towards the + x ̂ direction.

Fig. 6
Fig. 6

Optical force on a circular cylinder by a plane wave exp ( i k x ) propagating towards the + x ̂ direction.

Fig. 7
Fig. 7

Optical force on a circular cylinder by a plane wave and various cylindrical Gaussian beams propagating towards + x ̂ direction, calculated by the BEM.

Fig. 8
Fig. 8

Random roughness effect on the optical force for both (a), (c) resonant and (b) off-resonant cases. Inset in (b) shows a randomly rough surface with x-axis mirror symmetry.

Fig. 9
Fig. 9

Near fields for scattering of a plane wave λ = 0.515 a on a cylinder with different surface random roughness strengths. Here n = 1.5 and R = a .

Fig. 10
Fig. 10

DSCS of several cylinders with different modulation strength h and at various wavelengths λ.

Fig. 11
Fig. 11

Near fields for scattering of a plane wave λ = 0.515 a by various cookies. Here n = 1.5 , R = a , and N e = 700 .

Fig. 12
Fig. 12

Radiation force on circular and cookie cylinders of the same area, by a plane wave exp ( i k x ) propagating towards the + x ̂ direction. The Grzegorczyk and Kong results are for a circular cylinder [42]. The cookie cylinders are calculated with BEM with N e = 700 .

Tables (1)

Tables Icon

Table 1 Resonant Wavelength and Quality Factor Q for Whispering Gallery Modes TE ( m , l ) in the Frequency Range of Fig. 6 for a Circular Cylinder of n = 1.5 a

Equations (22)

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

( 2 + k j 2 ) ϕ ( r ) = 0 ,
( 2 + k j 2 ) g j ( r , r ) = δ ( r r ) , r , r Ω j ,
ϕ ( r ) = Ω j { g j ( s , r ) [ n ̂ j ( s ) s ϕ ( s ) ] ϕ ( s ) [ n ̂ j ( s ) s g j ( s , r ) ] } d s ,
1 2 ϕ ( s ) = Ω j g j ( s , s ) [ n ̂ j ( s ) s ϕ ( s ) ] d s Ω j ( PV ) ϕ ( s ) [ n ̂ j ( s ) s g j ( s , s ) ] d s .
ϕ ( s ) = t = 1 p ϕ t α θ t α ( s ) , ψ ( s ) = t = 1 p ψ t α θ t α ( s ) ,
β = 1 N j ( H j , α β ϕ β + G j , α β ψ β ) = 0 ( j = 1 , 2 , , J ) ,
G j , α β = S β g j ( s α , s ) d s ,
H j , α β = 1 2 δ α β + S β n ̂ j ( s ) s g j ( s α , s ) d s .
ϕ ( r ) ϕ in ( r ) = Ω 0 d s { n ̂ 0 ( s ) [ g 0 ( s , r ) s ϕ ( s ) ϕ ( s ) s g 0 ( s , r ) ] } ,
β = 1 N e ( H 0 , α β ϕ β + G 0 , α β ψ β ) = β = 1 N e δ α β ϕ β in .
[ H 0 G 0 H int G int ] [ Φ Ψ ] = [ Φ in 0 ] ,
G int = [ G 1 0 G 2 0 G J ] .
Φ 0 = ( Φ 1 , Φ 2 , , Φ J ) T ,
Ψ 0 = ( Ψ 1 p 1 , Ψ 2 p 2 , , Ψ J p J ) T ,
[ H 0 G 0 H int G int ] [ Φ Ψ ] = M ( ω ) [ Φ Ψ ] = 0 .
Err ( N e ) = [ σ ( k ) σ ( Mie ) ( k ) σ ( Mie ) ( k ) ] × 100 ( % ) .
F = Ω > Ω j n ̂ T ( r ) d l ,
n ̂ T ( r ) = ϵ 0 2 R ( E n ̂ ) E * + μ 0 2 R ( H n ̂ ) H * ϵ 0 4 E E * n ̂ μ 0 4 H H * n ̂ ,
F n ̂ inc = 1 c I inc [ C ext 0 2 π d r ̂ n ̂ inc r ̂ d C sca d θ ] ,
r ( θ ) r c = R [ 1 + i = 1 M h i R cos ( δ i θ ) ] ,
r ( θ ) r c = R [ 1 + h cos ( δ θ ) ] ,
n J m 1 ( k a ) H m ( 1 ) ( k 0 a ) J m ( k a ) H m 1 ( 1 ) ( k 0 a ) = 0 ,

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