FDTD simulations of forces on particles
during holographic assembly

doi:10.1364/OE.16.002942

FDTD simulations of forces on particles during holographic assembly

David C. Benito, Stephen H. Simpson, and Simon Hanna »View Author Affiliations

Optics Express, Vol. 16, Issue 5, pp. 2942-2957 (2008)
http://dx.doi.org/10.1364/OE.16.002942

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Abstract

We present finite-difference time-domain (FDTD) calculations of the forces and torques on dielectric particles of various shapes, held in one or many Gaussian optical traps, as part of a study of the physical limitations involved in the construction of micro- and nanostructures using a dynamic holographic assembler (DHA). We employ a full 3-dimensional FDTD implementation, which includes a complete treatment of optical anisotropy. The Gaussian beams are sourced using a multipole expansion of a fifth order Davis beam. Force and torques are calculated for pairs of silica spheres in adjacent traps, for silica cylinders trapped by multiple beams and for oblate silica spheroids and calcite spheres in both linearly and circularly polarized beams. Comparisons are drawn between the magnitudes of the optical forces and the Van der Waals forces acting on the systems. The paper also considers the limitations of the FDTD approach when applied to optical trapping.

OCIS Codes
(090.5694) Holography : Real-time holography
(290.5825) Scattering : Scattering theory

ToC Category:
Trapping

History
Original Manuscript: January 4, 2008
Revised Manuscript: February 8, 2008
Manuscript Accepted: February 13, 2008
Published: February 19, 2008

Virtual Issues
Vol. 3, Iss. 4 Virtual Journal for Biomedical Optics

Citation
David C. Benito, Stephen H. Simpson, and Simon Hanna, "FDTD simulations of forces on particles during holographic assembly," Opt. Express 16, 2942-2957 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-5-2942

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References

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970). [CrossRef]
E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72, 1810-1816 (2001). [CrossRef]
J. E. Curtis, B. A. Koss and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002). [CrossRef]
Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005). [CrossRef] [PubMed]
J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003). [CrossRef] [PubMed]
C. H. J. Schmitz, K. Uhrig, J. P. Spatz and J. E. Curtis, "Tuning the orbital angular momentum in optical vortex beams," Opt. Express 14, 6604-6612 (2006). [CrossRef] [PubMed]
D. A. White, "Vector finite element modeling of optical tweezers," Comput. Phys. Commun. 128, 558-564 (2000). [CrossRef]
N. V. Voshchinnikov and V. G. Farafonov, "Optical properties of spheroidal particles," Astrophys. Space Sci. 204, 19-86 (1993). [CrossRef]
M. I. Mishchenko, L. D. Travis and D.W. Mackowski, "T-matrix computations of light scattering by nonspherical particles: A review," J. Quant. Spectrosc. Radiat. Transfer 55, 535-575 (1996). [CrossRef]
T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg and A. I. Bishop, "Numerical modelling of optical trapping," Comput. Phys. Commun. 142, 468-471 (2001). [CrossRef]
S. H. Simpson and S. Hanna, "Numerical calculation of interparticle forces arising in association with holographic assembly," J. Opt. Soc. Am. A 23, 1419-1431 (2006). [CrossRef]
S. H. Simpson and S. Hanna, "Optical trapping of spheroidal particles in Gaussian beams," J. Opt. Soc. Am. A 24, 430-443 (2007). [CrossRef]
S. H. Simpson, D. C. Benito and S. Hanna, "Polarization-induced torque in optical traps," Phys. Rev. A 76, 408 (2007). [CrossRef]
D. W. 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]
A. R. Zakharian, M. Mansuripur and J. V. Moloney, "Radiation pressure and the distribution of electromagnetic force in dielectric media," Opt. Express 13, 2321-2336 (2005). [CrossRef] [PubMed]
R. C. Gauthier, "Computation of the optical trapping force using an FDTD based technique," Opt. Express 13, 3707-3718 (2005). [CrossRef] [PubMed]
K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. Mag. 14, 302-307 (1966). [CrossRef]
A. Taflove and S. C. Hagness, Computational Electrodynamics The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, Inc, Norwood, MA, 2005).
S. A. Schelkunoff, Electromagnetic Waves (Van Nostrand, New York, 1943).
P. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields, vol. 12 of International Series of Monographs in Electromagnetic Waves, 1st ed. (Pergamon Press, London, 1966).
L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (John Wiley & Sons, New York, 1985).
O. Moine and B. Stout, "Optical force calculations in arbitrary beams by use of the vector addition theorem," J. Opt. Soc. Am. B 22, 1620-1631 (2005). [CrossRef]
J. A. Pereda, A. Vegas, and A. Prieto, "An improved compact 2D fullwave FDFD method for general guided wave structures," Microwave Opt. Technol. Lett. 38, 331-335 (2003). [CrossRef]
S. H. Simpson and S. Hanna, "Analysis of the effects arising from the near-field optical microscopy of homogeneous dielectric slabs," Opt. Commun. 196, 17-31 (2001). [CrossRef]
S. H. Simpson and S. Hanna, "Scanning near-field optical microscopy of metallic features," Opt. Commun. 256, 476-488 (2005). [CrossRef]
R. Agarwal, K. Ladavac, Y. Roichman, G. H. 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]
M. K. Liu, N. Ji, Z. F. Lin, and S. T. Chui, "Radiation torque on a birefringent sphere caused by an electromagnetic wave," Phys. Rev. E 72, 610 (2005). [CrossRef]
V. L. Y. Loke, T. A. Nieminen, S. J. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "FDFD/T-matrix hybrid method," J. Quant. Spectrosc. Radiat. Transfer 106, 274-284 (2007). [CrossRef]

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[1] A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970). [CrossRef]

[2] E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72, 1810-1816 (2001). [CrossRef]

[3] J. E. Curtis, B. A. Koss and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002). [CrossRef]

[4] Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005). [CrossRef] [PubMed]

[5] J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003). [CrossRef] [PubMed]

[6] C. H. J. Schmitz, K. Uhrig, J. P. Spatz and J. E. Curtis, "Tuning the orbital angular momentum in optical vortex beams," Opt. Express 14, 6604-6612 (2006). [CrossRef] [PubMed]

[7] D. A. White, "Vector finite element modeling of optical tweezers," Comput. Phys. Commun. 128, 558-564 (2000). [CrossRef]

[8] N. V. Voshchinnikov and V. G. Farafonov, "Optical properties of spheroidal particles," Astrophys. Space Sci. 204, 19-86 (1993). [CrossRef]

[9] M. I. Mishchenko, L. D. Travis and D.W. Mackowski, "T-matrix computations of light scattering by nonspherical particles: A review," J. Quant. Spectrosc. Radiat. Transfer 55, 535-575 (1996). [CrossRef]

[10] T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg and A. I. Bishop, "Numerical modelling of optical trapping," Comput. Phys. Commun. 142, 468-471 (2001). [CrossRef]

[11] S. H. Simpson and S. Hanna, "Numerical calculation of interparticle forces arising in association with holographic assembly," J. Opt. Soc. Am. A 23, 1419-1431 (2006). [CrossRef]

[12] S. H. Simpson and S. Hanna, "Optical trapping of spheroidal particles in Gaussian beams," J. Opt. Soc. Am. A 24, 430-443 (2007). [CrossRef]

[13] S. H. Simpson, D. C. Benito and S. Hanna, "Polarization-induced torque in optical traps," Phys. Rev. A 76, 408 (2007). [CrossRef]

[14] D. W. 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]

[15] A. R. Zakharian, M. Mansuripur and J. V. Moloney, "Radiation pressure and the distribution of electromagnetic force in dielectric media," Opt. Express 13, 2321-2336 (2005). [CrossRef] [PubMed]

[16] R. C. Gauthier, "Computation of the optical trapping force using an FDTD based technique," Opt. Express 13, 3707-3718 (2005). [CrossRef] [PubMed]

[17] K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. Mag. 14, 302-307 (1966). [CrossRef]

[18] A. Taflove and S. C. Hagness, Computational Electrodynamics The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, Inc, Norwood, MA, 2005).

[19] S. A. Schelkunoff, Electromagnetic Waves (Van Nostrand, New York, 1943).

[20] P. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields, vol. 12 of International Series of Monographs in Electromagnetic Waves, 1st ed. (Pergamon Press, London, 1966).

[21] L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (John Wiley & Sons, New York, 1985).

[22] O. Moine and B. Stout, "Optical force calculations in arbitrary beams by use of the vector addition theorem," J. Opt. Soc. Am. B 22, 1620-1631 (2005). [CrossRef]

[23] J. A. Pereda, A. Vegas, and A. Prieto, "An improved compact 2D fullwave FDFD method for general guided wave structures," Microwave Opt. Technol. Lett. 38, 331-335 (2003). [CrossRef]

[24] S. H. Simpson and S. Hanna, "Analysis of the effects arising from the near-field optical microscopy of homogeneous dielectric slabs," Opt. Commun. 196, 17-31 (2001). [CrossRef]

[25] S. H. Simpson and S. Hanna, "Scanning near-field optical microscopy of metallic features," Opt. Commun. 256, 476-488 (2005). [CrossRef]

[26] R. Agarwal, K. Ladavac, Y. Roichman, G. H. 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]

[27] M. K. Liu, N. Ji, Z. F. Lin, and S. T. Chui, "Radiation torque on a birefringent sphere caused by an electromagnetic wave," Phys. Rev. E 72, 610 (2005). [CrossRef]

[28] V. L. Y. Loke, T. A. Nieminen, S. J. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "FDFD/T-matrix hybrid method," J. Quant. Spectrosc. Radiat. Transfer 106, 274-284 (2007). [CrossRef]

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FDTD simulations of forces on particles during holographic assembly