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. Steven 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. In-Yong Park, Seung-Yong Sung, Jong-Hyun Lee, and Yong-Gu 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. Yasuhiro Harada and Toshimitsu Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
    [Crossref]
  8. Wei Sun, Shi Pan, and Yuchi 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. Guoquan Zhou, Ruipin Chen, and Junlang Chen, “Propagation of non-paraxial nonsymmetrical vector Gaussian beam,” Opt. Commun. 259, 32–39 (2006).
    [Crossref]
  11. Kane 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. Allen Taflove and Suans 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. B87, 211–216 (2007).
    [Crossref]

2007 (2)

In-Yong Park, Seung-Yong Sung, Jong-Hyun Lee, and Yong-Gu 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)

Wei Sun, Shi Pan, and Yuchi 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]

Guoquan Zhou, Ruipin Chen, and Junlang Chen, “Propagation of non-paraxial nonsymmetrical vector Gaussian beam,” Opt. Commun. 259, 32–39 (2006).
[Crossref]

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]

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)

Yasuhiro Harada and Toshimitsu 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)

Steven 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)

Kane 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]

Alonzo, Carlo Amadeo

Asakura, Toshimitsu

Yasuhiro Harada and Toshimitsu Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
[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, Junlang

Guoquan Zhou, Ruipin Chen, and Junlang Chen, “Propagation of non-paraxial nonsymmetrical vector Gaussian beam,” Opt. Commun. 259, 32–39 (2006).
[Crossref]

Chen, Ruipin

Guoquan Zhou, Ruipin Chen, and Junlang Chen, “Propagation of non-paraxial nonsymmetrical vector Gaussian beam,” Opt. Commun. 259, 32–39 (2006).
[Crossref]

Chu, Steven

Dam, Jeppe Seidelin

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]

Glückstad, Jesper

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. B87, 211–216 (2007).
[Crossref]

Hangess, Suans C.

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

Harada, Yasuhiro

Yasuhiro Harada and Toshimitsu Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
[Crossref]

Jiang, Yuchi

Wei Sun, Shi Pan, and Yuchi 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]

Kelemen, Lóránd

Lee, Jong-Hyun

In-Yong Park, Seung-Yong Sung, Jong-Hyun Lee, and Yong-Gu Lee, “Manufacturing micro-scale structures by an optical tweezers system controlled by five finger tips,” J. Micromech. Microeng. 17, 82–89 (2007).
[Crossref]

Lee, Yong-Gu

In-Yong Park, Seung-Yong Sung, Jong-Hyun Lee, and Yong-Gu Lee, “Manufacturing micro-scale structures by an optical tweezers system controlled by five finger tips,” J. Micromech. Microeng. 17, 82–89 (2007).
[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. B87, 211–216 (2007).
[Crossref]

Ormos, Pál

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, Shi

Wei Sun, Shi Pan, and Yuchi 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]

Park, In-Yong

In-Yong Park, Seung-Yong Sung, Jong-Hyun Lee, and Yong-Gu Lee, “Manufacturing micro-scale structures by an optical tweezers system controlled by five finger tips,” J. Micromech. Microeng. 17, 82–89 (2007).
[Crossref]

Perch-Nielsen, Ivan R.

Rodrigo, Peter John

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]

Stratton, J. A.

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

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, Wei

Wei Sun, Shi Pan, and Yuchi 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]

Sung, Seung-Yong

In-Yong Park, Seung-Yong Sung, Jong-Hyun Lee, and Yong-Gu Lee, “Manufacturing micro-scale structures by an optical tweezers system controlled by five finger tips,” J. Micromech. Microeng. 17, 82–89 (2007).
[Crossref]

Taflove, Allen

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

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. B87, 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, Kane S.

Kane 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, Guoquan

Guoquan Zhou, Ruipin Chen, and Junlang Chen, “Propagation of non-paraxial nonsymmetrical vector Gaussian beam,” Opt. Commun. 259, 32–39 (2006).
[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)

Kane 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)

In-Yong Park, Seung-Yong Sung, Jong-Hyun Lee, and Yong-Gu 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)

Wei Sun, Shi Pan, and Yuchi 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]

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]

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)

Guoquan Zhou, Ruipin Chen, and Junlang Chen, “Propagation of non-paraxial nonsymmetrical vector Gaussian beam,” Opt. Commun. 259, 32–39 (2006).
[Crossref]

Yasuhiro Harada and Toshimitsu 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)

Steven Chu, “Laser manipulation and atoms and particles,” Science 253, 861–866 (1991).
[Crossref] [PubMed]

Other (3)

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

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

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. B87, 211–216 (2007).
[Crossref]

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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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