Abstract

Optical forces on a micro-bubble were computed using the Finite Difference Time Domain method. Non-paraxial Gaussian beam equation was used to represent the incident laser with high numerical aperture, common in optical tweezers. The electromagnetic field distribution around a micro-bubble was computed using FDTD method and the electromagnetic stress tensor on the surface of a micro-bubble was used to compute the optical forces. By the analysis of the computational results, interesting relations between the radius of the circular trapping ring and the corresponding stability of the trap were found.

© 2008 Optical Society of America

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  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and Steven Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
    [CrossRef] [PubMed]
  2. S. Chu, "Laser manipulation and atoms and particles," Science 253, 861-866 (1991).
    [CrossRef] [PubMed]
  3. A. Ashkin, J. M. Dziedzic, and T. Yamane, "Optical trapping and manipulation of single cells using infrared laser beams," Nature 330, 769-771 (1987).
    [CrossRef] [PubMed]
  4. I.-Y. Park, S.-Y. Sung, J.-H. Lee, and Y.-G. Lee, "Manufacturing micro-scale structures by an optical tweezers system controlled by five finger tips," J. Micromech. Microeng. 17, 82-89 (2007).
    [CrossRef]
  5. Peter John Rodrigo, Lóránd Kelemen, Carlo Amadeo Alonzo, Ivan R. Perch-Nielsen, Jeppe Seidelin Dam, Pál Ormos, and Jesper Glückstad, "2D optical manipulation and assembly of shape complementary planar microstructures," Opt. Express 15, 9009-9014 (2007).
    [CrossRef] [PubMed]
  6. A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
    [CrossRef] [PubMed]
  7. Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
    [CrossRef]
  8. W. Sun, S. Pan, and Y. Jiang, "Computation of the optical trapping force on small particles illuminated with a focused light beam using a FDTD method," J. Mod. Opt. 53, 2691-2700, (2006).
    [CrossRef]
  9. J. A. Stratton, Electromagnetic Theory (McGraw-Hill Inc., New York and London, 1941), Chap. 2.
  10. G. Zhou, R. Chen, and J. Chen, "Propagation of non-paraxial nonsymmetrical vector Gaussian beam," Opt. Commun. 259, 32-39 (2006).
    [CrossRef]
  11. K. S. Yee, "Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).
  12. A. Taflove and S. C. Hangess, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Third Edition (Artech House Inc., Norwood, MA, 2005).
  13. P. H. Jones, E. Stride, and N. Saffari, "Trapping and manipulation of microscopic bubbles with a scanning optical tweezer," Appl. Phys. Lett. 89, 081113 (2006).
    [CrossRef]
  14. N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
    [CrossRef]
  15. S. K. Mohanty, R. S. Verma, and P. K. Gupta, "Trapping and controlled rotation of low-refractive-index particles using dual line optical tweezers," Appl. Phys. B 87, 211-216 (2007).
    [CrossRef]

2007 (3)

S. K. Mohanty, R. S. Verma, and P. K. Gupta, "Trapping and controlled rotation of low-refractive-index particles using dual line optical tweezers," Appl. Phys. B 87, 211-216 (2007).
[CrossRef]

I.-Y. Park, S.-Y. Sung, J.-H. Lee, and Y.-G. Lee, "Manufacturing micro-scale structures by an optical tweezers system controlled by five finger tips," J. Micromech. Microeng. 17, 82-89 (2007).
[CrossRef]

Peter John Rodrigo, Lóránd Kelemen, Carlo Amadeo Alonzo, Ivan R. Perch-Nielsen, Jeppe Seidelin Dam, Pál Ormos, and Jesper Glückstad, "2D optical manipulation and assembly of shape complementary planar microstructures," Opt. Express 15, 9009-9014 (2007).
[CrossRef] [PubMed]

2006 (3)

P. H. Jones, E. Stride, and N. Saffari, "Trapping and manipulation of microscopic bubbles with a scanning optical tweezer," Appl. Phys. Lett. 89, 081113 (2006).
[CrossRef]

W. Sun, S. Pan, and Y. Jiang, "Computation of the optical trapping force on small particles illuminated with a focused light beam using a FDTD method," J. Mod. Opt. 53, 2691-2700, (2006).
[CrossRef]

G. Zhou, R. Chen, and J. Chen, "Propagation of non-paraxial nonsymmetrical vector Gaussian beam," Opt. Commun. 259, 32-39 (2006).
[CrossRef]

1998 (1)

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

1996 (1)

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

1992 (1)

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

1991 (1)

S. Chu, "Laser manipulation and atoms and particles," Science 253, 861-866 (1991).
[CrossRef] [PubMed]

1987 (1)

A. Ashkin, J. M. Dziedzic, and T. Yamane, "Optical trapping and manipulation of single cells using infrared laser beams," Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

1986 (1)

1966 (1)

K. S. Yee, "Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

Allen, L.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

Ashkin, A.

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

A. Ashkin, J. M. Dziedzic, and T. Yamane, "Optical trapping and manipulation of single cells using infrared laser beams," Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

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

Bjorkholm, J. E.

Chen, J.

G. Zhou, R. Chen, and J. Chen, "Propagation of non-paraxial nonsymmetrical vector Gaussian beam," Opt. Commun. 259, 32-39 (2006).
[CrossRef]

Chen, R.

G. Zhou, R. Chen, and J. Chen, "Propagation of non-paraxial nonsymmetrical vector Gaussian beam," Opt. Commun. 259, 32-39 (2006).
[CrossRef]

Chu, S.

S. Chu, "Laser manipulation and atoms and particles," Science 253, 861-866 (1991).
[CrossRef] [PubMed]

Dholakia, K.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, and T. Yamane, "Optical trapping and manipulation of single cells using infrared laser beams," Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

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

Gupta, P. K.

S. K. Mohanty, R. S. Verma, and P. K. Gupta, "Trapping and controlled rotation of low-refractive-index particles using dual line optical tweezers," Appl. Phys. B 87, 211-216 (2007).
[CrossRef]

Jiang, Y.

W. Sun, S. Pan, and Y. Jiang, "Computation of the optical trapping force on small particles illuminated with a focused light beam using a FDTD method," J. Mod. Opt. 53, 2691-2700, (2006).
[CrossRef]

Jones, P. H.

P. H. Jones, E. Stride, and N. Saffari, "Trapping and manipulation of microscopic bubbles with a scanning optical tweezer," Appl. Phys. Lett. 89, 081113 (2006).
[CrossRef]

McGloin, D.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

Mohanty, S. K.

S. K. Mohanty, R. S. Verma, and P. K. Gupta, "Trapping and controlled rotation of low-refractive-index particles using dual line optical tweezers," Appl. Phys. B 87, 211-216 (2007).
[CrossRef]

Padgett, M. J.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

Pan, S.

W. Sun, S. Pan, and Y. Jiang, "Computation of the optical trapping force on small particles illuminated with a focused light beam using a FDTD method," J. Mod. Opt. 53, 2691-2700, (2006).
[CrossRef]

Saffari, N.

P. H. Jones, E. Stride, and N. Saffari, "Trapping and manipulation of microscopic bubbles with a scanning optical tweezer," Appl. Phys. Lett. 89, 081113 (2006).
[CrossRef]

Simpson, N. B.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

Stride, E.

P. H. Jones, E. Stride, and N. Saffari, "Trapping and manipulation of microscopic bubbles with a scanning optical tweezer," Appl. Phys. Lett. 89, 081113 (2006).
[CrossRef]

Sun, W.

W. Sun, S. Pan, and Y. Jiang, "Computation of the optical trapping force on small particles illuminated with a focused light beam using a FDTD method," J. Mod. Opt. 53, 2691-2700, (2006).
[CrossRef]

Verma, R. S.

S. K. Mohanty, R. S. Verma, and P. K. Gupta, "Trapping and controlled rotation of low-refractive-index particles using dual line optical tweezers," Appl. Phys. B 87, 211-216 (2007).
[CrossRef]

Yamane, T.

A. Ashkin, J. M. Dziedzic, and T. Yamane, "Optical trapping and manipulation of single cells using infrared laser beams," Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

Yee, K. S.

K. S. Yee, "Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

Zhou, G.

G. Zhou, R. Chen, and J. Chen, "Propagation of non-paraxial nonsymmetrical vector Gaussian beam," Opt. Commun. 259, 32-39 (2006).
[CrossRef]

Appl. Phys. B (1)

S. K. Mohanty, R. S. Verma, and P. K. Gupta, "Trapping and controlled rotation of low-refractive-index particles using dual line optical tweezers," Appl. Phys. B 87, 211-216 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

P. H. Jones, E. Stride, and N. Saffari, "Trapping and manipulation of microscopic bubbles with a scanning optical tweezer," Appl. Phys. Lett. 89, 081113 (2006).
[CrossRef]

Biophys. J. (1)

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

IEEE Trans. Antennas Propag. (1)

K. S. Yee, "Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

J. Micromech. Microeng. (1)

I.-Y. Park, S.-Y. Sung, J.-H. Lee, and Y.-G. Lee, "Manufacturing micro-scale structures by an optical tweezers system controlled by five finger tips," J. Micromech. Microeng. 17, 82-89 (2007).
[CrossRef]

J. Mod. Opt. (2)

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

W. Sun, S. Pan, and Y. Jiang, "Computation of the optical trapping force on small particles illuminated with a focused light beam using a FDTD method," J. Mod. Opt. 53, 2691-2700, (2006).
[CrossRef]

Nature (1)

A. Ashkin, J. M. Dziedzic, and T. Yamane, "Optical trapping and manipulation of single cells using infrared laser beams," Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

Opt. Commun. (2)

G. Zhou, R. Chen, and J. Chen, "Propagation of non-paraxial nonsymmetrical vector Gaussian beam," Opt. Commun. 259, 32-39 (2006).
[CrossRef]

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Science (1)

S. Chu, "Laser manipulation and atoms and particles," Science 253, 861-866 (1991).
[CrossRef] [PubMed]

Other (2)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill Inc., New York and London, 1941), Chap. 2.

A. Taflove and S. C. Hangess, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Third Edition (Artech House Inc., Norwood, MA, 2005).

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Figures (9)

Fig. 1.
Fig. 1.

Solid and medium under an incident field.

Fig. 2.
Fig. 2.

Computational domain.

Fig. 3.
Fig. 3.

Circular trapping ring (CTR).

Fig. 4.
Fig. 4.

Radial and axial force on a micro-bubble.

Fig. 5.
Fig. 5.

The axial (z) sum of optical force and buoyant force for inverted geometry.

Fig. 6.
Fig. 6.

The axial (z) sum of optical force and buoyant force for upright geometry.

Fig. 7.
Fig. 7.

Radial forces.

Fig. 8.
Fig. 8.

Total force vector of a micro-bubble under a circular trap (10mW) and buoyant force.

Fig. 9.
Fig. 9.

The axial (z) sum of optical force and buoyant force for inverted geometry under different laser powers.

Equations (16)

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F = S [ ε ( E · n ) E + μ ( H · n ) H 1 2 ( ε E 2 + μ H 2 ) n ] da 1 c 2 d dt v E × H dv .
F = s [ ε ( E · n ) E + μ ( H · n ) H 1 2 ( ε E 2 + μ H 2 ) n ] da 1 c 2 d dt v E × H dv
= 1 T T s [ ε ( E · n ) E + μ ( H · n ) H 1 2 ( ε E 2 + μ H 2 ) n ] da .
E ( x , y , z ) = exp ( i ω t ) 0 2 π A E ( r , θ ) λ 2
× exp [ i k ( xr cos θ + yr sin θ + z 1 r 2 ) ] rdrd θ ,
H ( x , y , z ) = exp ( i ω t ) 0 2 π A H ( r , θ ) λ 2
× exp [ i k ( xr cos θ + yr sin θ + z 1 r 2 ) ] rdrd θ .
b = 2 π 2 ω 0 x 2 λ 2 ,   c = 2 π 2 ω 0 y 2 λ 2 ,
A E ( r , θ ) = π { a ω 0 x 2 exp ( br 2 2 ) i + ω 0 y 2 exp ( cr 2 2 ) j [ ar cos θ ω 0 x 2 exp ( br 2 2 ) + r sin θ ω 0 y 2 exp ( cr 2 2 ) ] k 1 r 2 } ,
A H ( r , θ ) = ε μ π { [ ω 0 y 2 exp ( cr 2 2 ) ar 2 sin θ cos θ ω 0 x 2 exp ( br 2 2 ) + r 2 cos 2 θ ω 0 y 2 exp ( cr 2 2 ) ] i 1 r 2
+ [ a ω 0 x 2 exp ( br 2 2 ) ar 2 sin 2 θ ω 0 x 2 exp ( br 2 2 ) + r 2 sin θ cos θ ω 0 y 2 exp ( cr 2 2 ) ] j 1 r 2
+ [ r cos θ ω 0 y 2 exp ( cr 2 2 ) ar sin θ ω 0 x 2 exp ( br 2 2 ) ] k } .
P = S z d x d y
= ε μ π 3 λ 2 0 1 [ a 2 ω 0 x 4 exp ( br 2 ) + ω 0 y 4 exp ( cr 2 ) ] 2 r r 3 1 r 2 d r ,
ε E scat t + σ E scat = × H scat σ E inc ( ε ε 0 ) E inc t
{ E inc = electric incident field E scat = electric   scattered field H scat = magnetic scattered field .

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