Abstract

The photon stream method is used to derive the optical force on a pair of concentric spheres in a focused beam. The effects of the differences in refractive index and relative size between the inner and outer spheres on the optical force are evaluated. In addition, the effects of total internal reflection at the interface between the inner and outer spheres are examined. Computational results are compared with previous findings. The present method can be applied to arbitrary intensity distributions of the laser beam.

© 2012 Optical Society of America

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2012 (1)

K. H. Lee, S. B. Kim, S. Y. Yoon, K. S. Lee, J. H. Jung, and H. J. Sung, “Behavior of double emulsions in a cross-type optical separation system,” Langmuir 28, 7343–7349 (2012).
[CrossRef]

2011 (1)

K. Ariga, Y. M. Lvov, K. Kawakami, Q. Ji, and J. P. Hill, “Layer-by-layer self-assembled shells for drug delivery,” Adv. Drug Delivery Rev. 63, 762–771 (2011).
[CrossRef]

2009 (2)

2008 (4)

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008).
[CrossRef]

S. B. Kim, S. Y. Yoon, H. J. Sung, and S. S. Kim, “Cross-type optical particle separation in a microchannel,” Anal. Chem. 80, 2628–2630 (2008).
[CrossRef]

H. Maenaka, M. Yamada, M. Yasuda, and M. Seki, “Continuous and size-dependent sorting of emulsion droplets using hydrodynamics in pinched microchannels,” Anal. Chem. 24, 4405–4410 (2008).

2007 (1)

2006 (3)

2005 (2)

M. He, J. S. Edgar, G. D. M. Jefferies, R. M. Lorenz, J. P. Shelby, and D. T. Chu, “Selective encapsulation of single cells and subcellular organelles into picoliter- and femtoliter-volume droplets,” Anal. Chem. 77, 1539–1544 (2005).
[CrossRef]

R. C. Gauthier, “Computation of the optical trapping force using an FDTD based technique,” Opt. Express 13, 3707–3718 (2005).
[CrossRef]

2003 (2)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83, 5316–5318 (2003).
[CrossRef]

2002 (2)

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

W. Li, X. Sha, W. Dong, and Z. Wang, “Synthesis of stable hollow silica microspheres with mesoporous shell in nonionic W/O emulsion,” Chem. Commun.2434–2435 (2002).
[CrossRef]

2000 (1)

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

1998 (3)

S. Nemoto and H. Togo, “Axial force acting on a dielectric sphere in a focused laser beam,” Appl. Opt. 37, 6386–6394 (1998).
[CrossRef]

S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
[CrossRef]

S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
[CrossRef]

1997 (2)

R. C. Gauthier, “Optical trapping a tool to assist optical machining,” Opt. Laser Technol. 29, 389–399 (1997).
[CrossRef]

E. Sidick, S. D. Collins, and A. Knoesen, “Trapping forces in a multiple-beam fiber-optic trap,” Appl. Opt. 36, 6423–6433 (1997).
[CrossRef]

1996 (1)

R. C. Gauthier, “Theoretical model for an improved radiation pressure micromotor,” Appl. Phys. Lett. 69, 2015–2017 (1996).
[CrossRef]

1995 (2)

R. C. Gauthier and S. Wallace, “Optical levitation of spheres: analytical development and numerical computations of the force equations,” J. Opt. Soc. Am. B 12, 1680–1686 (1995).
[CrossRef]

R. C. Gauthier, “Ray optics model and numerical computations for radiation pressure micromotor,” Appl. Phys. Lett. 67, 2269–2271 (1995).
[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]

1991 (1)

H. Misawa, N. Kitamura, and H. Masuhara, “Laser manipulation and ablation of a single microcapsule in water,” J. Chem. Am. Soc. 113, 7856–7863 (1991).
[CrossRef]

1987 (2)

1986 (1)

1970 (1)

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

Agresti, J. J.

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

Ander, M.

Angile, F. E.

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

Arendt, J. T.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Ariga, K.

K. Ariga, Y. M. Lvov, K. Kawakami, Q. Ji, and J. P. Hill, “Layer-by-layer self-assembled shells for drug delivery,” Adv. Drug Delivery Rev. 63, 762–771 (2011).
[CrossRef]

Arnold, J.

S. J. Hart, A. Terray, T. A. Leski, J. Arnold, and R. Stroud, “Discovery of a significant optical chromatography difference between spores of Bacillus anthracis and its close relative, Bacillus thuringiensis,” Anal. Chem. 78, 3221–3225 (2006).
[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]

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef]

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, 288–289 (1986).
[CrossRef]

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

Backman, V.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Badizadegan, K.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Bjorkholm, J. E.

Borghese, F.

Bormuth, V.

Buican, T. N.

Chang, Y.

Chi, S.

Chu, D. T.

M. He, J. S. Edgar, G. D. M. Jefferies, R. M. Lorenz, J. P. Shelby, and D. T. Chu, “Selective encapsulation of single cells and subcellular organelles into picoliter- and femtoliter-volume droplets,” Anal. Chem. 77, 1539–1544 (2005).
[CrossRef]

Chu, S.

S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
[CrossRef]

S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
[CrossRef]

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, 288–289 (1986).
[CrossRef]

Collins, S. D.

Crissman, H. A.

Dasari, R. R.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Denti, P.

Dong, W.

W. Li, X. Sha, W. Dong, and Z. Wang, “Synthesis of stable hollow silica microspheres with mesoporous shell in nonionic W/O emulsion,” Chem. Commun.2434–2435 (2002).
[CrossRef]

Duan, H.

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

Dziedzic, J. M.

Edgar, J. S.

M. He, J. S. Edgar, G. D. M. Jefferies, R. M. Lorenz, J. P. Shelby, and D. T. Chu, “Selective encapsulation of single cells and subcellular organelles into picoliter- and femtoliter-volume droplets,” Anal. Chem. 77, 1539–1544 (2005).
[CrossRef]

Feld, M. S.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Gauthier, R. C.

R. C. Gauthier, “Computation of the optical trapping force using an FDTD based technique,” Opt. Express 13, 3707–3718 (2005).
[CrossRef]

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

R. C. Gauthier, “Optical trapping a tool to assist optical machining,” Opt. Laser Technol. 29, 389–399 (1997).
[CrossRef]

R. C. Gauthier, “Theoretical model for an improved radiation pressure micromotor,” Appl. Phys. Lett. 69, 2015–2017 (1996).
[CrossRef]

R. C. Gauthier, “Ray optics model and numerical computations for radiation pressure micromotor,” Appl. Phys. Lett. 67, 2269–2271 (1995).
[CrossRef]

R. C. Gauthier and S. Wallace, “Optical levitation of spheres: analytical development and numerical computations of the force equations,” J. Opt. Soc. Am. B 12, 1680–1686 (1995).
[CrossRef]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

Griffiths, A. D.

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

Gurjar, R.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Hammond, M.

Hart, S. J.

A. Terray, H. D. Ladouceur, M. Hammond, and S. J. Hart, “Numerical simulation of an optical chromatographic separator,” Opt. Express 17, 2024–2032 (2009).
[CrossRef]

S. J. Hart, A. Terray, T. A. Leski, J. Arnold, and R. Stroud, “Discovery of a significant optical chromatography difference between spores of Bacillus anthracis and its close relative, Bacillus thuringiensis,” Anal. Chem. 78, 3221–3225 (2006).
[CrossRef]

S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83, 5316–5318 (2003).
[CrossRef]

He, M.

M. He, J. S. Edgar, G. D. M. Jefferies, R. M. Lorenz, J. P. Shelby, and D. T. Chu, “Selective encapsulation of single cells and subcellular organelles into picoliter- and femtoliter-volume droplets,” Anal. Chem. 77, 1539–1544 (2005).
[CrossRef]

Hill, J. P.

K. Ariga, Y. M. Lvov, K. Kawakami, Q. Ji, and J. P. Hill, “Layer-by-layer self-assembled shells for drug delivery,” Adv. Drug Delivery Rev. 63, 762–771 (2011).
[CrossRef]

Howard, J.

Hsu, L.

Iatì, M. A.

Itzkan, I.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Jannasch, A.

Jefferies, G. D. M.

M. He, J. S. Edgar, G. D. M. Jefferies, R. M. Lorenz, J. P. Shelby, and D. T. Chu, “Selective encapsulation of single cells and subcellular organelles into picoliter- and femtoliter-volume droplets,” Anal. Chem. 77, 1539–1544 (2005).
[CrossRef]

Ji, Q.

K. Ariga, Y. M. Lvov, K. Kawakami, Q. Ji, and J. P. Hill, “Layer-by-layer self-assembled shells for drug delivery,” Adv. Drug Delivery Rev. 63, 762–771 (2011).
[CrossRef]

Jung, J. H.

K. H. Lee, S. B. Kim, S. Y. Yoon, K. S. Lee, J. H. Jung, and H. J. Sung, “Behavior of double emulsions in a cross-type optical separation system,” Langmuir 28, 7343–7349 (2012).
[CrossRef]

Kabani, S.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Kawakami, K.

K. Ariga, Y. M. Lvov, K. Kawakami, Q. Ji, and J. P. Hill, “Layer-by-layer self-assembled shells for drug delivery,” Adv. Drug Delivery Rev. 63, 762–771 (2011).
[CrossRef]

Kim, J. H.

Kim, S. B.

Kim, S. S.

Kitamura, N.

H. Misawa, N. Kitamura, and H. Masuhara, “Laser manipulation and ablation of a single microcapsule in water,” J. Chem. Am. Soc. 113, 7856–7863 (1991).
[CrossRef]

Kline, E.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Knoesen, A.

Köster, S.

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

Ladouceur, H. D.

Lee, K. H.

K. H. Lee, S. B. Kim, S. Y. Yoon, K. S. Lee, J. H. Jung, and H. J. Sung, “Behavior of double emulsions in a cross-type optical separation system,” Langmuir 28, 7343–7349 (2012).
[CrossRef]

Lee, K. S.

K. H. Lee, S. B. Kim, S. Y. Yoon, K. S. Lee, J. H. Jung, and H. J. Sung, “Behavior of double emulsions in a cross-type optical separation system,” Langmuir 28, 7343–7349 (2012).
[CrossRef]

Leski, T. A.

S. J. Hart, A. Terray, T. A. Leski, J. Arnold, and R. Stroud, “Discovery of a significant optical chromatography difference between spores of Bacillus anthracis and its close relative, Bacillus thuringiensis,” Anal. Chem. 78, 3221–3225 (2006).
[CrossRef]

Levin, H. S.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Li, W.

W. Li, X. Sha, W. Dong, and Z. Wang, “Synthesis of stable hollow silica microspheres with mesoporous shell in nonionic W/O emulsion,” Chem. Commun.2434–2435 (2002).
[CrossRef]

Lorenz, R. M.

M. He, J. S. Edgar, G. D. M. Jefferies, R. M. Lorenz, J. P. Shelby, and D. T. Chu, “Selective encapsulation of single cells and subcellular organelles into picoliter- and femtoliter-volume droplets,” Anal. Chem. 77, 1539–1544 (2005).
[CrossRef]

Lvov, Y. M.

K. Ariga, Y. M. Lvov, K. Kawakami, Q. Ji, and J. P. Hill, “Layer-by-layer self-assembled shells for drug delivery,” Adv. Drug Delivery Rev. 63, 762–771 (2011).
[CrossRef]

Maenaka, H.

H. Maenaka, M. Yamada, M. Yasuda, and M. Seki, “Continuous and size-dependent sorting of emulsion droplets using hydrodynamics in pinched microchannels,” Anal. Chem. 24, 4405–4410 (2008).

Martin, J. C.

Masuhara, H.

H. Misawa, N. Kitamura, and H. Masuhara, “Laser manipulation and ablation of a single microcapsule in water,” J. Chem. Am. Soc. 113, 7856–7863 (1991).
[CrossRef]

McGillican, T.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Merten, C. A.

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

Misawa, H.

H. Misawa, N. Kitamura, and H. Masuhara, “Laser manipulation and ablation of a single microcapsule in water,” J. Chem. Am. Soc. 113, 7856–7863 (1991).
[CrossRef]

Muller, M. G.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Nemoto, S.

Perelman, L. T.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Pisignano, D.

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

Rowat, A. C.

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

Saija, R.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics(Wiley, 1991).

Salzeman, G. C.

Schäffer, E.

Schmitz, C.

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

Seiler, M.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Seki, M.

H. Maenaka, M. Yamada, M. Yasuda, and M. Seki, “Continuous and size-dependent sorting of emulsion droplets using hydrodynamics in pinched microchannels,” Anal. Chem. 24, 4405–4410 (2008).

Sha, X.

W. Li, X. Sha, W. Dong, and Z. Wang, “Synthesis of stable hollow silica microspheres with mesoporous shell in nonionic W/O emulsion,” Chem. Commun.2434–2435 (2002).
[CrossRef]

Shapshay, S.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Shelby, J. P.

M. He, J. S. Edgar, G. D. M. Jefferies, R. M. Lorenz, J. P. Shelby, and D. T. Chu, “Selective encapsulation of single cells and subcellular organelles into picoliter- and femtoliter-volume droplets,” Anal. Chem. 77, 1539–1544 (2005).
[CrossRef]

Sidick, E.

Smith, M. J.

Stewart, C. C.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (IEEE, 2007).

Stroud, R.

S. J. Hart, A. Terray, T. A. Leski, J. Arnold, and R. Stroud, “Discovery of a significant optical chromatography difference between spores of Bacillus anthracis and its close relative, Bacillus thuringiensis,” Anal. Chem. 78, 3221–3225 (2006).
[CrossRef]

Sung, H. J.

K. H. Lee, S. B. Kim, S. Y. Yoon, K. S. Lee, J. H. Jung, and H. J. Sung, “Behavior of double emulsions in a cross-type optical separation system,” Langmuir 28, 7343–7349 (2012).
[CrossRef]

S. B. Kim, H. J. Sung, and S. S. Kim, “Nondimensional analysis of particle behavior during cross-type optical particle separation,” Appl. Opt. 48, 4291–4296 (2009).
[CrossRef]

S. B. Kim, S. Y. Yoon, H. J. Sung, and S. S. Kim, “Cross-type optical particle separation in a microchannel,” Anal. Chem. 80, 2628–2630 (2008).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics(Wiley, 1991).

Terray, A.

A. Terray, H. D. Ladouceur, M. Hammond, and S. J. Hart, “Numerical simulation of an optical chromatographic separator,” Opt. Express 17, 2024–2032 (2009).
[CrossRef]

S. J. Hart, A. Terray, T. A. Leski, J. Arnold, and R. Stroud, “Discovery of a significant optical chromatography difference between spores of Bacillus anthracis and its close relative, Bacillus thuringiensis,” Anal. Chem. 78, 3221–3225 (2006).
[CrossRef]

Terray, A. V.

S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83, 5316–5318 (2003).
[CrossRef]

Togo, H.

Valdez, T.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

van Blaaderen, A.

Van Dam, J.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

van Kats, C. M.

Wallace, M. B.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Wallace, S.

Wang, Z.

W. Li, X. Sha, W. Dong, and Z. Wang, “Synthesis of stable hollow silica microspheres with mesoporous shell in nonionic W/O emulsion,” Chem. Commun.2434–2435 (2002).
[CrossRef]

Weitz, D. A.

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

Wintner, A.

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

Yamada, M.

H. Maenaka, M. Yamada, M. Yasuda, and M. Seki, “Continuous and size-dependent sorting of emulsion droplets using hydrodynamics in pinched microchannels,” Anal. Chem. 24, 4405–4410 (2008).

Yasuda, M.

H. Maenaka, M. Yamada, M. Yasuda, and M. Seki, “Continuous and size-dependent sorting of emulsion droplets using hydrodynamics in pinched microchannels,” Anal. Chem. 24, 4405–4410 (2008).

Yoon, S. Y.

K. H. Lee, S. B. Kim, S. Y. Yoon, K. S. Lee, J. H. Jung, and H. J. Sung, “Behavior of double emulsions in a cross-type optical separation system,” Langmuir 28, 7343–7349 (2012).
[CrossRef]

S. B. Kim, S. Y. Yoon, H. J. Sung, and S. S. Kim, “Cross-type optical particle separation in a microchannel,” Anal. Chem. 80, 2628–2630 (2008).
[CrossRef]

Zhang, Q.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

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V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

Adv. Drug Delivery Rev. (1)

K. Ariga, Y. M. Lvov, K. Kawakami, Q. Ji, and J. P. Hill, “Layer-by-layer self-assembled shells for drug delivery,” Adv. Drug Delivery Rev. 63, 762–771 (2011).
[CrossRef]

Anal. Chem. (4)

M. He, J. S. Edgar, G. D. M. Jefferies, R. M. Lorenz, J. P. Shelby, and D. T. Chu, “Selective encapsulation of single cells and subcellular organelles into picoliter- and femtoliter-volume droplets,” Anal. Chem. 77, 1539–1544 (2005).
[CrossRef]

S. B. Kim, S. Y. Yoon, H. J. Sung, and S. S. Kim, “Cross-type optical particle separation in a microchannel,” Anal. Chem. 80, 2628–2630 (2008).
[CrossRef]

H. Maenaka, M. Yamada, M. Yasuda, and M. Seki, “Continuous and size-dependent sorting of emulsion droplets using hydrodynamics in pinched microchannels,” Anal. Chem. 24, 4405–4410 (2008).

S. J. Hart, A. Terray, T. A. Leski, J. Arnold, and R. Stroud, “Discovery of a significant optical chromatography difference between spores of Bacillus anthracis and its close relative, Bacillus thuringiensis,” Anal. Chem. 78, 3221–3225 (2006).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. Lett. (3)

S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83, 5316–5318 (2003).
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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).
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Chem. Commun. (1)

W. Li, X. Sha, W. Dong, and Z. Wang, “Synthesis of stable hollow silica microspheres with mesoporous shell in nonionic W/O emulsion,” Chem. Commun.2434–2435 (2002).
[CrossRef]

J. Chem. Am. Soc. (1)

H. Misawa, N. Kitamura, and H. Masuhara, “Laser manipulation and ablation of a single microcapsule in water,” J. Chem. Am. Soc. 113, 7856–7863 (1991).
[CrossRef]

J. Opt. Soc. Am. B (2)

Lab Chip (1)

S. Köster, F. E. Angile, H. Duan, J. J. Agresti, A. Wintner, C. Schmitz, A. C. Rowat, C. A. Merten, D. Pisignano, A. D. Griffiths, and D. A. Weitz, “Drop-based microfluidic devices for encapsulation of single cells,” Lab Chip 8, 1110–1115 (2008).
[CrossRef]

Langmuir (1)

K. H. Lee, S. B. Kim, S. Y. Yoon, K. S. Lee, J. H. Jung, and H. J. Sung, “Behavior of double emulsions in a cross-type optical separation system,” Langmuir 28, 7343–7349 (2012).
[CrossRef]

Nature (2)

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Műller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000).
[CrossRef]

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

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R. C. Gauthier, “Optical trapping a tool to assist optical machining,” Opt. Laser Technol. 29, 389–399 (1997).
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A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
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S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
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S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
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A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
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J. A. Stratton, Electromagnetic Theory (IEEE, 2007).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics(Wiley, 1991).

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Figures (14)

Fig. 1.
Fig. 1.

Schematics of the rotational transform: (a) the photon stream path is parallel to the beam axis and (b) normal to the wavefront.

Fig. 2.
Fig. 2.

Schematics of the optical force on a pair of concentric spheres: (a) photon stream path and (b) infinitesimal area.

Fig. 3.
Fig. 3.

Schematics for θh and θm: (a) photon stream never impinges on the inner sphere for θ>θh sphere, (b) photon stream never incidents on the outer sphere for θ>θm.

Fig. 4.
Fig. 4.

Optical force distribution for Case I in a loosely focused beam: (a) axial force and (b) radial force.

Fig. 5.
Fig. 5.

Optical force distribution for Case I in a tightly focused beam: (a) axial force and (b) radial force.

Fig. 6.
Fig. 6.

Optical force distribution for Case II in a loosely focused beam: (a) axial force and (b) radial force.

Fig. 7.
Fig. 7.

Optical force distribution for Case II in a tightly focused beam: (a) axial force and (b) radial force.

Fig. 8.
Fig. 8.

Schematic of the cross-type optical particle separation.

Fig. 9.
Fig. 9.

Comparison of the predicted trajectories with experimental data.

Fig. 10.
Fig. 10.

Optical force distributions for Case I in the cross-type optical particle separation: (a) axial force and (b) radial force.

Fig. 11.
Fig. 11.

Optical force distributions for Case II in the cross-type optical particle separation: (a) axial force and (b) radial force.

Fig. 12.
Fig. 12.

Trajectories of particles in cross-type optical particle separation for Case I: (a) trajectory of the sphere, (b) y-directional velocity variation of the sphere, (c) z-directional velocity variation of the sphere, and (d) y-directional position variation of the sphere.

Fig. 13.
Fig. 13.

Trajectories of particles in cross-type optical particle separation for Case II: (a) trajectory of the sphere, (b) y-directional velocity variation of the sphere, (c) z-directional velocity variation of the sphere, and (d) y-directional position variation of the sphere.

Fig. 14.
Fig. 14.

Schematics of the concentric sphere and the photon stream path through the sphere.

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

ps=Qpi,
dF=ΔpΔt=(pspi)Δt=pi(1Q)Δt,
Qy-z=QN,y-zQD,y-z,QN,y-z=(12R1)(12R2)exp[i2(θ1+θ2ϕ1ϕ2)]R1R2exp[i2(θ1ϕ2)]R2(12R1)exp[i2(θ1+θ2ϕ1)]R1exp[i2θ1],QD,y-z=1R1R2exp[i2(θ2ϕ1)]+R2exp[i2ϕ2]+R1(12R2)exp[i2(θ2ϕ1ϕ2)],
sinϕ1=n0n1sinθ1,sinθ2=rp1rp2n0n1sinθ1,sinϕ2=rp1rp2n1n2sinθ1,
dFy-z=exp(iα)dFy-z=pi[exp(iα)Qy-zexp(iα)]/Δt.
dFy-z=pi[(cosαRe{Qy-z})z^(sinαIm{Qy-z})y^]/Δt,Qy-z=Qy-zexp(iα)=QNQD,QN,y-z=(12R1)(12R2)exp[i2(θ1+θ2ϕ1ϕ2)],R1R2exp[i2(θ1ϕ2)]R2(12R1)exp[i2(θ1+θ2ϕ1)]R1exp[i2θ1],QD,y-z=1R1R2exp[i2(θ2ϕ1)]+R2exp[i2ϕ2]+R1(12R2)exp[i2(θ2ϕ1ϕ2)],
θ1=θ+α.
ρ=a2+rp12sin2θ2arp1sinθcosϕ,zp=zrp1cosθ,Rc=zp[1+(πω02λzp)],α=sin1(ρRc),θ1=θ+α,
Qh,y-z=R1exp[i(θ1+θ)]+T2exp[i(θ1+θ2ϕ1)]+Rexp[i(θ1+θ)]1+R2+2R1cosϕ1.
N=n0λhcI(ρ,z)ΔAΔt,I(ρ,z)=2Pπω2exp[2ρ2ω2],ω2=ω0[1+(λzpπω02)2]1/2,
dFz-r=NhλΔt[(cosαRe{Qy-z})z^(sinαIm{Qy-z})cosϕr^]=n0cI(ρ,z)[(cosαRe{Qy-z})z^(sinαIm{Qy-z})cosϕr^]rp12sinθcosθ1dθdφ,
pi=hλ,dA=rp12sinθcosθ1dθdφ.
θh=sin1(n1n0rp2rp1)α,θm=π2α.
Fz=n0crp1202π[θhθmI(ρ,z)[cosαRe{Qy-z}]sinθcosθ1dθ+0θhI(ρ,z)[cosαRe{Qh,y-z}]sinθdθcosθ1]dφ,
Fr=n0crp1202π[θhθmI(ρ,z)[sinαIm{Qy-z}]sinθcosθ1dθ+0θhI(ρ,z)[sinαIm{Qh,y-z}]sinθdθcosθ1]cosφdφ.
mpdrdt6πμrp(UVp)=FU=Uy^,Vp=vpy^+wpz^,F=Fry^+Fzz^,
prefl=p0Rexp(iΔθrefl),prefr=p0(1R)exp(iΔθrefr),
pi,1=pi,0(1R1)exp[i(θ1φ1)]+ps,1R1exp[i(π+2φ1)],ps,0=pi,0R1exp[i(π2θ1)]+ps,1(1R1)exp[i(θ1φ1)].
pi,0=pi,1exp[i(θ1φ1)](1R1)ps,1R1(1R1)exp[i(π+θ1+φ1)].
ps,0=pi,1R1(1R1)exp[i(θ1φ1)]ps,1R12(1R1)exp[i(θ1+φ1)]+ps,1(1R1)exp[i(θ1+φ1)],
[pi,0ps,0]=[exp[i(θ1φ1)]1R1R1exp[i(θ1+φ1)]1R1R1exp[i(θ1+φ1)]1R1(12R1)exp[i(θ1φ1)]1R1][pi,1ps,1].
[pi,1ps,1]=[exp[i(θ2φ2)]1R2R2exp[i(θ2+φ2)]1R2R2exp[i(θ2+φ2)]1R2(12R2)exp[i(θ2φ2)]1R2][pi,2ps,2].
R1=12[sin2(θ1ϕ1)sin2(θ1+ϕ1)+]tann2(θ1ϕ1)tan2(θ1+ϕ1),R2=12[sin2(θ2ϕ2)sin2(θ2+ϕ2)+]tann2(θ2ϕ2)tan2(θ2+ϕ2).
[pi,0ps,0]=[exp[i(θ1φ1)]1R1R1exp[i(θ1+φ1)]1R1R1exp[i(θ1+φ1)]1R1(12R1)exp[i(θ1φ1)]1R1]×[exp[i(θ2φ2)]1R2R2exp[i(θ2+φ2)]1R2R2exp[i(θ2+φ2)]1R2(12R2)exp[i(θ2φ2)]1R2][pp],=[M11M12M21M22][pp].
ps,0=M21+M22M11+M12pi,0=Qpi,0.

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