Abstract

The computation details related to computing the optical radiation pressure force on various objects using a 2-D grid FDTD algorithm are presented. The technique is based on propagating the electric and magnetic fields through the grid and determining the changes in the optical energy flow with and without the trap object(s) in the system. Traces displayed indicate that the optical forces and FDTD predicted object behavior are in agreement with published experiments and also determined through other computation techniques. We show computation results for a high and low dielectric disc and thin walled shell. The FDTD technique for computing the light-particle force interaction may be employed in all regimes relating particle dimensions to source wavelength. The algorithm presented here can be easily extended to 3-D and include torque computation algorithms, thus providing a highly flexible and universally useable computation engine.

© 2005 Optical Society of America

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References

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  27. S. Nemoto and H. Togo, �??Axial force acting on a dielectric sphere in a focus laser beam,�?? Appl. Opt. 37, 6386-6394 (1998).
    [CrossRef]
  28. R. C. Gauthier, �??Laser-trapping properties of dual component spheres,�?? Appl. Opt. 41, 7135-7144 (2002).
    [CrossRef] [PubMed]
  29. G. Roosen, �??A theoretical and experimental study of the stable equilibrium positions of spheres levitated by two horizontal laser beams,�?? Opt. Commun. 21, 189-194 (1977).
    [CrossRef]
  30. A. Constable, J. K. Kim, J. Mervis, F. Zarinetchi and M. Prentiss, �??Demonstration of a fiber-optic light-force trap,�?? Opt. Lett. 18, 1867-1869 (1993).
    [CrossRef] [PubMed]
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Appl. Opt. (9)

M. Goksor, J. Enger and D. Hanstrop, �??Optical manipulation in combination with multiphoton microscopy for single-cell studies,�?? Appl. Opt. 43, 4831-4837 (2004).
[CrossRef] [PubMed]

K. F. Ren, G. Grehan and G. Gouesbet, �??Prediction of reverse radiation pressure by generalized Lorentz-Mie theory,�?? Appl. Opt. 35, 2702-2710 (1996).
[CrossRef] [PubMed]

J. Lock, �??Calculation of the radiation trapping force for laser tweezers by use of generalized Lorentz-Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberrations,�?? Appl. Opt. 43, 2532-2544 (2004).
[CrossRef] [PubMed]

R. C. Gauthier and A. Frangioudakis, �??Theoretical investigation of the optical trapping properties of a micro-optic cube glass structure,�?? Appl. Opt. 39, 3060-3070 (2000).
[CrossRef]

R. C. Gauthier, �??Optical levitation and trapping of a micro-optic inclined end-surface cylindrical spinner,�?? Appl. Opt. 40, 1961-1973 (2001).
[CrossRef]

R. C. Gauthier, M. Friesen, T. Gerrard, W. Hassouneh, P. Koziorowski, D. Moore, K. Oprea and S. Uttamalingam, �??Self-centering of a ball lens by laser trapping: fiber-to-fiber coupling analysis,�?? Appl. Opt. 42, 1610-1619 (2002).
[CrossRef]

R. C. Gauthier and M. Ashman, �??Simulated dynamic behavior of single and multiple spheres in a trap region of focused laser beams,�?? Appl. Opt. 37, 6421-6431 (1998).
[CrossRef]

S. Nemoto and H. Togo, �??Axial force acting on a dielectric sphere in a focus laser beam,�?? Appl. Opt. 37, 6386-6394 (1998).
[CrossRef]

R. C. Gauthier, �??Laser-trapping properties of dual component spheres,�?? Appl. Opt. 41, 7135-7144 (2002).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

W. L. Collett, C. A. Ventrice and S. M. Mahajan, �??Electromagnetic wave technique to determine radiation torque on micromachines driven by light,�?? Appl. Phys. Lett. 82, 2730-2732 (2003).
[CrossRef]

E. Higurashi, H. Ukita, H. Tanaka and O. Ohguchi, �??Optically indiced rotation of anisotropic micro-objects fabricated by surface micromachining,�?? Appl. Phys. Lett. 64, 2209-2210 (1994).
[CrossRef]

IEEE Press Series on RF and Microwave Te (1)

D. Sullivan, Electromagnetic simulation using the FDTD method, IEEE Press Series on RF and Microwave Technology, New York, 2000.

IEEE Trans. Antennas and Propagat. (1)

K. S. Yee, �??Numerical solution of initial boundary value problems involving Maxwell�??s equations in isotropic media,�?? IEEE Trans. Antennas and Propagat. 14, 302-307 (1966).
[CrossRef]

J. Biophys. (1)

A. Ashkin, �??Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,�?? J. Biophys. 61, 569-582 (1992).
[CrossRef]

J. Comput. Phys. (1)

J.-P. Berenger, �??A perfectly matched layer for the absorption of electromagnetic waves,�?? J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

J. Opt. Soc. Am B (1)

R. Goussgard and T. Lindmo, �??Calculation of the trapping force in a strongly focused laser beam,�?? J. Opt. Soc. Am B 9, 1922-1930 (1992).
[CrossRef]

Opt. Commun. (1)

G. Roosen, �??A theoretical and experimental study of the stable equilibrium positions of spheres levitated by two horizontal laser beams,�?? Opt. Commun. 21, 189-194 (1977).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, �??Observation of a single-beam gradient force optical trap for dielectric particles,�?? Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

R. C. Gauthier, R. N. Tait, M. Ubriaco, �??Activation of microcomponents with light for micro-electro-mechanical systems and micro-optical-electro-mechanical systems applications,�?? Opt. Lett. 41, 2361-2367 (2002).

A. Constable, J. K. Kim, J. Mervis, F. Zarinetchi and M. Prentiss, �??Demonstration of a fiber-optic light-force trap,�?? Opt. Lett. 18, 1867-1869 (1993).
[CrossRef] [PubMed]

E. Sidick, S. D. Collins and A. Knoesen, �??Trapping forces in a multiple-beam fiber- optic trap,�?? Opt. Lett. 36, 6423-6433 (1997).

Optik (2)

K. Visscher and G. J. Brakenhoff, �??Theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatterers,�?? Optik 89, 174-180 (1992).

K. Visscher and G. J. Brakenhoff, �??Theoretical study of optically induced forces on spherical particles in a single beam trap II: Mie scatterers,�?? Optik 90, 57-60 (1992).

Phys. Rev A (1)

S. J. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, �??Optical measurement of torque exerted on an elongated object by a noncircular laser beam,�?? Phys. Rev A 70, 023816 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

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

Rev. Sci. Inst. (1)

F. Qian, S. Ermilov, D. Murdock, W. E. Brownell and B. Anvari, �??Combining optical tweezers and patch clamp for studies of cell membrane electromechanics,�?? Rev. Sci. Inst. 75, 2937-2942 (2004).
[CrossRef]

Other (1)

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain, Boston: Artech House, 1995.

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Figures (8)

Fig. 1.
Fig. 1.

(X, Y) computation domain showing a single sphere axially offset and displaced in the divergent region of the source plane. The computation domain is discretized into an (I, J) grid. The boundary is composed of a perfectly matched layer 15 grid points wide.

Fig. 2.
Fig. 2.

(a)Efficiency factor Qx for radial force on a high dielectric sphere in water. (square-1 µm, circle-4 µm from minimum waist). (b)Efficiency factor Qy for the axial force on the same sphere. Sphere and beam parameters defined in text. The FDTD analysis predicts that axial trapping is expected and that the sphere is pushed in the direction of beam propagation.

Fig. 3.
Fig. 3.

(a) Efficiency factor Qx for radial force on a low dielectric sphere in water. (square-1 µm, circle-4 µm from minimum waist). (b) Efficiency factor Qy for the axial force on the same sphere. Sphere and beam parameters defined in text. The FDTD analysis correctly predicts that the sphere is pushed out of the beam and along the beam propagation direction.

Fig. 4.
Fig. 4.

FDTD computation domain traces. Center trace is a gray scale representation of the electric field plotted for each (I, J) grid point. White represents high electric field values. In this trace a plane wave is incident from the left onto a positive lens (large circle) and is focused before diverging. The top trace shows the electric field profile down the Y-axis centerline. The envelope maximum of the E field profile corresponds to the focal point of the lens and can be quantified knowing the grid dimensions or source wavelength in the various mediums. The lower trace is a top plot of the E field profile through the focal region. From this trace the minimum waist can be determined as well the level of aberrations present in the optical trap system.

Fig. 5.
Fig. 5.

Efficiency factor Qy for the high dielectric disc axially aligned with the beam center and propagated through the focal region of the beam. Focusing system and E field profile shown in figure 4. In the minimum waist region Qy is less than zero indicating that laser trapping can be accomplished with these beam-object-focusing-system parameters.

Fig. 6.
Fig. 6.

Radial trapping efficiency (Qx) for the thick walled dielectric shell. The central region has 1.00 index, the shell has 1.45, and the ambient index is 1.33. The shell is pushed out of axial alignment with the beam but may be axially trapped, offset from the beam axis as indicated in the figure.

Fig. 7.
Fig. 7.

(a) FDTD field profile for the dual beam counter-propagating trap configuration. Left and right Gaussian beams have been propagated a short distance in the system. Beam on the left is focusing after passing through the lens while the beam on the right is still diverging. (b) Axial force profile obtained when the beam separation corresponds to 4F. The mid point axial location corresponds to an unstable equilibrium for this sphere between these beams. (c) Axial force profile obtained when the beam separation corresponds to 6F. The mid point axial location corresponds to a stable equilibrium for this sphere between these beams.

Fig. 8.
Fig. 8.

FDTD E-field trace of the fiber-to-fiber coupling through a dual beam trapped ball lens. The FDTD trapping computation engine developed permits the optical system to be modeled, the field and beams propagated and the resultant E fields permit the determination of the coupling efficiency.

Equations (6)

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F x = Δ S x c L , Δ S x = S xo S x
F y = Δ S y c L , Δ S y = S yo S y
A xy = exp [ 2 ( x x c W 0 ) 2 ]
E z ( x , y c ) = E z ( x , y c ) + A xy sin ( ω t )
H x ( x , y c ) = H x ( x , y c ) + A xy sin ( ω t )
Q x , y = c F x , y n s P

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