## Calculation of the optical force on an infinite cylinder with arbitrary cross section by the boundary element method

JOSA B, Vol. 25, Issue 9, pp. 1553-1561 (2008)

http://dx.doi.org/10.1364/JOSAB.25.001553

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### 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

**OCIS Codes**

(020.7010) Atomic and molecular physics : Laser trapping

(140.4780) Lasers and laser optics : Optical resonators

(260.2110) Physical optics : Electromagnetic optics

(290.5850) Scattering : Scattering, particles

**ToC Category:**

Physical Optics

**History**

Original Manuscript: April 4, 2008

Revised Manuscript: July 7, 2008

Manuscript Accepted: July 8, 2008

Published: August 26, 2008

**Citation**

J. J. Xiao and C. T. Chan, "Calculation of the optical force on an infinite cylinder with arbitrary cross section by the boundary element method," J. Opt. Soc. Am. B **25**, 1553-1561 (2008)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-25-9-1553

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### References

- D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810-816 (2003). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- 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]
- 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]
- K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37, 42-55 (2008). [CrossRef] [PubMed]
- 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]
- W. C. Chew, J.-M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics (Artech, 2001).
- 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]
- 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]
- C. Pozrikidis, A Practical Guide to Boundary Element Methods with the Software Library BEMLIB (CRC, 2002). [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]
- D. W. Prather, M. S. Mirotznik, and J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34-43 (1997). [CrossRef]
- 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]
- T. Nobis and M. Grundmann, “Low-order optical whispering-gallery modes in hexagonal nanocavities,” Phys. Rev. A 72, 063806 (2005). [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]
- 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. 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]
- 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]
- 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]
- 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]
- 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.
- 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]
- 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.
- 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]
- 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]
- 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]
- 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).
- 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]
- 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]
- 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]
- M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).
- 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]
- A. V. Itagi and W. A. Challener, “Optics of photonic nanojets,” J. Opt. Soc. Am. A 22, 2847-2858 (2005). [CrossRef]
- 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]

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