Abstract

Experimental observations suggest that there are differences between the behavior of particles optically trapped in air and trapped in a liquid phase. We have modified the Mie–Debye spherical aberration theory to numerically simulate an aerosol optical trap in an attempt to explain and predict the differences. The model incorporates Mie scattering and a trapping beam focused through media of stratified refractive index. We show that geometrical optics cannot correctly describe the aerosol optical trap and that spherical aberration must be included. We qualitatively explain the observed phenomena before discussing the limits of the experimental techniques and methods to improve it. We conclude that the system does not behave as a true “optical tweezers,” varying between levitation and single beam gradient force trapping, depending on particle and beam parameters.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2010

D. R. Burnham, P. J. Reece, and D. McGloin, “Parameter exploration of optically trapped liquid aerosols,” Phys. Rev. E 82, 051123 (2010).
[CrossRef]

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673-1675 (2010).
[CrossRef] [PubMed]

P. F. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
[CrossRef] [PubMed]

2009

2008

Y. Zhao, G. Milne, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

D. McGloin, D. R. Burnham, M. D. Summers, D. Rudd, N. Dewar, and S. Anand, “Optical manipulation of airborne particles: techniques and applications,” Faraday Discuss. Chem. Soc. 137, 335-350 (2008).
[CrossRef]

L. Mitchem and J. P. Reid, “Optical manipulation and characterisation of aerosol particles using a single-beam gradient force optical trap,” Chem. Soc. Rev. 37, 756-769 (2008).
[CrossRef] [PubMed]

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, “Direct measurement of critical Casimir forces,” Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

A. B. Stilgoe, T. A. Nieminen, G. Knoner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039-15051 (2008).
[CrossRef] [PubMed]

2007

R. Di Leonardo, G. Ruocco, J. Leach, M. J. Padgett, A. J. Wright, J. M. Girkin, D. R. Burnham, and D. McGloin, “Parametric resonance of optically trapped aerosols,” Phys. Rev. Lett. 99, 010601 (2007).
[CrossRef] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196-S203(2007).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezer,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemanek, “Transverse particle dynamics in a Bessel beam,” Opt. Express 15, 13972-13987 (2007).
[CrossRef] [PubMed]

K. J. Knox, J. P. Reid, K. L. Hanford, A. J. Hudson, and L. Mitchem, “Direct measurements of the axial displacement and evolving size of optically trapped aerosol droplets,” J. Opt. A 9, S180-S188 (2007).
[CrossRef]

S. Keen, J. Leach, G. Gibson, and M. J. Padgett, “Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers,” J. Opt. A 9, S264-S266 (2007).
[CrossRef]

R. S. Dutra, N. B. Viana, P. A. Maia Neto, and H. M. Nussenzveig, “Polarization effects in optical tweezers,” J. Opt. A 9, S221-S227(2007).
[CrossRef]

2006

D. R. Burnham and D. McGloin, “Holographic optical trapping of aerosol droplets,” Opt. Express 14, 4175-4181 (2006).
[CrossRef] [PubMed]

N. K. Metzger, E. M. Wright, and K. Dholakia, “Theory and simulation of the bistable behaviour of optically bound particles in the Mie size regime,” New J. Phys. 8, 139 (2006).
[CrossRef]

G. Knoner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

D. McGloin, “Optical tweezers: 20 years on,” Phil. Trans. R. Soc. A 364, 3521-3537 (2006).
[CrossRef] [PubMed]

2005

J. Joykutty, V. Mathur, V. Venkataraman, and V. Natarajan, “Direct measurement of the oscillation frequency in an optical-tweezers trap by parametric excitation,” Phys. Rev. Lett. 95, 193902 (2005).
[CrossRef] [PubMed]

2004

R. Symes, R. M. Sayer, and J. P. Reid, “Cavity enhanced droplet spectroscopy: principles, perspectives and prospects,” Phys. Chem. Chem. Phys. 6, 474-487 (2004).
[CrossRef]

E. Theofanidou, L. Wilson, W. J. Hossack, and J. Arlt, “Spherical aberration correction for optical tweezers,” Opt. Commun. 236, 145-150 (2004).
[CrossRef]

R. J. Hopkins, L. Mitchem, A. D. Ward, and J. P. Reid, “Control and characterisation of a single aerosol droplet in a single-beam gradient-force optical trap,” Phys. Chem. Chem. Phys. 6, 4924-4927 (2004).
[CrossRef]

2003

N. R. Labiris and M. B. Dolovich, “Pulmonary drug delivery. Part I: physiological factors affecting therapeutic effectiveness of aerosolized medications,” Br. J. Clin. Pharmacol. 56, 588-599(2003).
[CrossRef] [PubMed]

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. A 459, 3021-3041 (2003).
[CrossRef]

2002

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two dimensional optical force clamp for single molecule studies,” Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

2000

P. A. Maia Neto and H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

1999

L. I. McCann, M. Dykman, and B. Golding, “Thermally activated transitions in a bistable three-dimensional optical trap,” Nature 402, 785-787 (1999).
[CrossRef]

1997

1996

O. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108-130 (1996).
[CrossRef]

1995

1992

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]

1977

G. Roosen, “Theoretical and experimental-study of stable equilibrium positions of spheres levitated by 2 horizontal laser-beams,” Opt. Commun. 21, 189-194 (1977).
[CrossRef]

1959

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358-379 (1959).
[CrossRef]

Anand, S.

D. McGloin, D. R. Burnham, M. D. Summers, D. Rudd, N. Dewar, and S. Anand, “Optical manipulation of airborne particles: techniques and applications,” Faraday Discuss. Chem. Soc. 137, 335-350 (2008).
[CrossRef]

Arlt, J.

E. Theofanidou, L. Wilson, W. J. Hossack, and J. Arlt, “Spherical aberration correction for optical tweezers,” Opt. Commun. 236, 145-150 (2004).
[CrossRef]

Asbury, C. L.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two dimensional optical force clamp for single molecule studies,” Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

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]

Barker, P. F.

P. F. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
[CrossRef] [PubMed]

Bechinger, C.

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, “Direct measurement of critical Casimir forces,” Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

Block, S. M.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two dimensional optical force clamp for single molecule studies,” Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

Booker, G. R.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1980).

Branczyk, A. M.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196-S203(2007).
[CrossRef]

Burnham, D. R.

D. R. Burnham, P. J. Reece, and D. McGloin, “Parameter exploration of optically trapped liquid aerosols,” Phys. Rev. E 82, 051123 (2010).
[CrossRef]

D. McGloin, D. R. Burnham, M. D. Summers, D. Rudd, N. Dewar, and S. Anand, “Optical manipulation of airborne particles: techniques and applications,” Faraday Discuss. Chem. Soc. 137, 335-350 (2008).
[CrossRef]

R. Di Leonardo, G. Ruocco, J. Leach, M. J. Padgett, A. J. Wright, J. M. Girkin, D. R. Burnham, and D. McGloin, “Parametric resonance of optically trapped aerosols,” Phys. Rev. Lett. 99, 010601 (2007).
[CrossRef] [PubMed]

D. R. Burnham and D. McGloin, “Holographic optical trapping of aerosol droplets,” Opt. Express 14, 4175-4181 (2006).
[CrossRef] [PubMed]

D. R. Burnham, “Microscopic applications of holographic beam shaping and studies of optically trapped aerosols,” Ph.D. thesis (University of St. Andrews, 2009).

Chiu, D. T.

Y. Zhao, G. Milne, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

Dewar, N.

D. McGloin, D. R. Burnham, M. D. Summers, D. Rudd, N. Dewar, and S. Anand, “Optical manipulation of airborne particles: techniques and applications,” Faraday Discuss. Chem. Soc. 137, 335-350 (2008).
[CrossRef]

Dholakia, K.

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemanek, “Transverse particle dynamics in a Bessel beam,” Opt. Express 15, 13972-13987 (2007).
[CrossRef] [PubMed]

N. K. Metzger, E. M. Wright, and K. Dholakia, “Theory and simulation of the bistable behaviour of optically bound particles in the Mie size regime,” New J. Phys. 8, 139 (2006).
[CrossRef]

Di Leonardo, R.

R. Di Leonardo, G. Ruocco, J. Leach, M. J. Padgett, A. J. Wright, J. M. Girkin, D. R. Burnham, and D. McGloin, “Parametric resonance of optically trapped aerosols,” Phys. Rev. Lett. 99, 010601 (2007).
[CrossRef] [PubMed]

Dietrich, S.

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, “Direct measurement of critical Casimir forces,” Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

Dolovich, M. B.

N. R. Labiris and M. B. Dolovich, “Pulmonary drug delivery. Part I: physiological factors affecting therapeutic effectiveness of aerosolized medications,” Br. J. Clin. Pharmacol. 56, 588-599(2003).
[CrossRef] [PubMed]

Dutra, R. S.

R. S. Dutra, N. B. Viana, P. A. Maia Neto, and H. M. Nussenzveig, “Polarization effects in optical tweezers,” J. Opt. A 9, S221-S227(2007).
[CrossRef]

Dykman, M.

L. I. McCann, M. Dykman, and B. Golding, “Thermally activated transitions in a bistable three-dimensional optical trap,” Nature 402, 785-787 (1999).
[CrossRef]

Edgar, J. S.

Y. Zhao, G. Milne, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

Farsund, O.

O. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108-130 (1996).
[CrossRef]

Felderhof, B. U.

O. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108-130 (1996).
[CrossRef]

Gambassi, A.

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, “Direct measurement of critical Casimir forces,” Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

Gibson, G.

S. Keen, J. Leach, G. Gibson, and M. J. Padgett, “Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers,” J. Opt. A 9, S264-S266 (2007).
[CrossRef]

Girkin, J. M.

R. Di Leonardo, G. Ruocco, J. Leach, M. J. Padgett, A. J. Wright, J. M. Girkin, D. R. Burnham, and D. McGloin, “Parametric resonance of optically trapped aerosols,” Phys. Rev. Lett. 99, 010601 (2007).
[CrossRef] [PubMed]

Golding, B.

L. I. McCann, M. Dykman, and B. Golding, “Thermally activated transitions in a bistable three-dimensional optical trap,” Nature 402, 785-787 (1999).
[CrossRef]

Grier, D. G.

Hanford, K. L.

K. J. Knox, J. P. Reid, K. L. Hanford, A. J. Hudson, and L. Mitchem, “Direct measurements of the axial displacement and evolving size of optically trapped aerosol droplets,” J. Opt. A 9, S180-S188 (2007).
[CrossRef]

Heckenberg, N. R.

T. A. Nieminen, A. B. Stilgoe, V. L. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers: reply,” Opt. Express 17, 2661-2662(2009).
[CrossRef]

A. B. Stilgoe, T. A. Nieminen, G. Knoner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039-15051 (2008).
[CrossRef] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196-S203(2007).
[CrossRef]

G. Knoner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

Helden, L.

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, “Direct measurement of critical Casimir forces,” Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

Hertlein, C.

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, “Direct measurement of critical Casimir forces,” Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

Hopkins, R. J.

R. J. Hopkins, L. Mitchem, A. D. Ward, and J. P. Reid, “Control and characterisation of a single aerosol droplet in a single-beam gradient-force optical trap,” Phys. Chem. Chem. Phys. 6, 4924-4927 (2004).
[CrossRef]

Hossack, W. J.

E. Theofanidou, L. Wilson, W. J. Hossack, and J. Arlt, “Spherical aberration correction for optical tweezers,” Opt. Commun. 236, 145-150 (2004).
[CrossRef]

Hudson, A. J.

K. J. Knox, J. P. Reid, K. L. Hanford, A. J. Hudson, and L. Mitchem, “Direct measurements of the axial displacement and evolving size of optically trapped aerosol droplets,” J. Opt. A 9, S180-S188 (2007).
[CrossRef]

Jacobson, M. Z.

M. Z. Jacobson, Atmospheric Pollution: History, Science, and Regulation (Cambridge University, 2002).

Jeffries, G. D. M.

Y. Zhao, G. Milne, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

Joykutty, J.

J. Joykutty, V. Mathur, V. Venkataraman, and V. Natarajan, “Direct measurement of the oscillation frequency in an optical-tweezers trap by parametric excitation,” Phys. Rev. Lett. 95, 193902 (2005).
[CrossRef] [PubMed]

Keen, S.

S. Keen, J. Leach, G. Gibson, and M. J. Padgett, “Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers,” J. Opt. A 9, S264-S266 (2007).
[CrossRef]

Kheifets, S.

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673-1675 (2010).
[CrossRef] [PubMed]

Knoner, G.

A. B. Stilgoe, T. A. Nieminen, G. Knoner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039-15051 (2008).
[CrossRef] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196-S203(2007).
[CrossRef]

G. Knoner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

Knox, K. J.

K. J. Knox, J. P. Reid, K. L. Hanford, A. J. Hudson, and L. Mitchem, “Direct measurements of the axial displacement and evolving size of optically trapped aerosol droplets,” J. Opt. A 9, S180-S188 (2007).
[CrossRef]

Kwamena, N.-O. A.

N.-O. A. Kwamena and J. P. Reid, “Aerosols,” in Colloid Science: Principles, Methods and Applications, T.Cosgrove, ed. (Wiley-Blackwell, 2005), Vol. 10, pp. 219-244.

Labiris, N. R.

N. R. Labiris and M. B. Dolovich, “Pulmonary drug delivery. Part I: physiological factors affecting therapeutic effectiveness of aerosolized medications,” Br. J. Clin. Pharmacol. 56, 588-599(2003).
[CrossRef] [PubMed]

Laczik, Z.

Lang, M. J.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two dimensional optical force clamp for single molecule studies,” Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

Leach, J.

S. Keen, J. Leach, G. Gibson, and M. J. Padgett, “Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers,” J. Opt. A 9, S264-S266 (2007).
[CrossRef]

R. Di Leonardo, G. Ruocco, J. Leach, M. J. Padgett, A. J. Wright, J. M. Girkin, D. R. Burnham, and D. McGloin, “Parametric resonance of optically trapped aerosols,” Phys. Rev. Lett. 99, 010601 (2007).
[CrossRef] [PubMed]

Li, T.

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673-1675 (2010).
[CrossRef] [PubMed]

Loke, V. L.

Loke, V. L. Y.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196-S203(2007).
[CrossRef]

Maia Neto, P. A.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezer,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

R. S. Dutra, N. B. Viana, P. A. Maia Neto, and H. M. Nussenzveig, “Polarization effects in optical tweezers,” J. Opt. A 9, S221-S227(2007).
[CrossRef]

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. A 459, 3021-3041 (2003).
[CrossRef]

P. A. Maia Neto and H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

Mathur, V.

J. Joykutty, V. Mathur, V. Venkataraman, and V. Natarajan, “Direct measurement of the oscillation frequency in an optical-tweezers trap by parametric excitation,” Phys. Rev. Lett. 95, 193902 (2005).
[CrossRef] [PubMed]

Mazolli, A.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezer,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. A 459, 3021-3041 (2003).
[CrossRef]

McCann, L. I.

L. I. McCann, M. Dykman, and B. Golding, “Thermally activated transitions in a bistable three-dimensional optical trap,” Nature 402, 785-787 (1999).
[CrossRef]

McGloin, D.

D. R. Burnham, P. J. Reece, and D. McGloin, “Parameter exploration of optically trapped liquid aerosols,” Phys. Rev. E 82, 051123 (2010).
[CrossRef]

D. McGloin, D. R. Burnham, M. D. Summers, D. Rudd, N. Dewar, and S. Anand, “Optical manipulation of airborne particles: techniques and applications,” Faraday Discuss. Chem. Soc. 137, 335-350 (2008).
[CrossRef]

Y. Zhao, G. Milne, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

R. Di Leonardo, G. Ruocco, J. Leach, M. J. Padgett, A. J. Wright, J. M. Girkin, D. R. Burnham, and D. McGloin, “Parametric resonance of optically trapped aerosols,” Phys. Rev. Lett. 99, 010601 (2007).
[CrossRef] [PubMed]

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemanek, “Transverse particle dynamics in a Bessel beam,” Opt. Express 15, 13972-13987 (2007).
[CrossRef] [PubMed]

D. R. Burnham and D. McGloin, “Holographic optical trapping of aerosol droplets,” Opt. Express 14, 4175-4181 (2006).
[CrossRef] [PubMed]

D. McGloin, “Optical tweezers: 20 years on,” Phil. Trans. R. Soc. A 364, 3521-3537 (2006).
[CrossRef] [PubMed]

Medellin, D.

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673-1675 (2010).
[CrossRef] [PubMed]

Mesquita, O. N.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezer,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

Metzger, N. K.

N. K. Metzger, E. M. Wright, and K. Dholakia, “Theory and simulation of the bistable behaviour of optically bound particles in the Mie size regime,” New J. Phys. 8, 139 (2006).
[CrossRef]

Milne, G.

Y. Zhao, G. Milne, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemanek, “Transverse particle dynamics in a Bessel beam,” Opt. Express 15, 13972-13987 (2007).
[CrossRef] [PubMed]

Mitchem, L.

L. Mitchem and J. P. Reid, “Optical manipulation and characterisation of aerosol particles using a single-beam gradient force optical trap,” Chem. Soc. Rev. 37, 756-769 (2008).
[CrossRef] [PubMed]

K. J. Knox, J. P. Reid, K. L. Hanford, A. J. Hudson, and L. Mitchem, “Direct measurements of the axial displacement and evolving size of optically trapped aerosol droplets,” J. Opt. A 9, S180-S188 (2007).
[CrossRef]

R. J. Hopkins, L. Mitchem, A. D. Ward, and J. P. Reid, “Control and characterisation of a single aerosol droplet in a single-beam gradient-force optical trap,” Phys. Chem. Chem. Phys. 6, 4924-4927 (2004).
[CrossRef]

Natarajan, V.

J. Joykutty, V. Mathur, V. Venkataraman, and V. Natarajan, “Direct measurement of the oscillation frequency in an optical-tweezers trap by parametric excitation,” Phys. Rev. Lett. 95, 193902 (2005).
[CrossRef] [PubMed]

Nieminen, T. A.

T. A. Nieminen, A. B. Stilgoe, V. L. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers: reply,” Opt. Express 17, 2661-2662(2009).
[CrossRef]

A. B. Stilgoe, T. A. Nieminen, G. Knoner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039-15051 (2008).
[CrossRef] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196-S203(2007).
[CrossRef]

G. Knoner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

Nussenzveig, H. M.

R. S. Dutra, N. B. Viana, P. A. Maia Neto, and H. M. Nussenzveig, “Polarization effects in optical tweezers,” J. Opt. A 9, S221-S227(2007).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezer,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. A 459, 3021-3041 (2003).
[CrossRef]

P. A. Maia Neto and H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

Padgett, M. J.

S. Keen, J. Leach, G. Gibson, and M. J. Padgett, “Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers,” J. Opt. A 9, S264-S266 (2007).
[CrossRef]

R. Di Leonardo, G. Ruocco, J. Leach, M. J. Padgett, A. J. Wright, J. M. Girkin, D. R. Burnham, and D. McGloin, “Parametric resonance of optically trapped aerosols,” Phys. Rev. Lett. 99, 010601 (2007).
[CrossRef] [PubMed]

Parkin, S.

G. Knoner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

Raizen, M. G.

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673-1675 (2010).
[CrossRef] [PubMed]

Reece, P. J.

D. R. Burnham, P. J. Reece, and D. McGloin, “Parameter exploration of optically trapped liquid aerosols,” Phys. Rev. E 82, 051123 (2010).
[CrossRef]

Reid, J. P.

L. Mitchem and J. P. Reid, “Optical manipulation and characterisation of aerosol particles using a single-beam gradient force optical trap,” Chem. Soc. Rev. 37, 756-769 (2008).
[CrossRef] [PubMed]

K. J. Knox, J. P. Reid, K. L. Hanford, A. J. Hudson, and L. Mitchem, “Direct measurements of the axial displacement and evolving size of optically trapped aerosol droplets,” J. Opt. A 9, S180-S188 (2007).
[CrossRef]

R. J. Hopkins, L. Mitchem, A. D. Ward, and J. P. Reid, “Control and characterisation of a single aerosol droplet in a single-beam gradient-force optical trap,” Phys. Chem. Chem. Phys. 6, 4924-4927 (2004).
[CrossRef]

R. Symes, R. M. Sayer, and J. P. Reid, “Cavity enhanced droplet spectroscopy: principles, perspectives and prospects,” Phys. Chem. Chem. Phys. 6, 474-487 (2004).
[CrossRef]

N.-O. A. Kwamena and J. P. Reid, “Aerosols,” in Colloid Science: Principles, Methods and Applications, T.Cosgrove, ed. (Wiley-Blackwell, 2005), Vol. 10, pp. 219-244.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358-379 (1959).
[CrossRef]

Rocha, M. S.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezer,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

Roosen, G.

G. Roosen, “Theoretical and experimental-study of stable equilibrium positions of spheres levitated by 2 horizontal laser-beams,” Opt. Commun. 21, 189-194 (1977).
[CrossRef]

Rubinsztein-Dunlop, H.

T. A. Nieminen, A. B. Stilgoe, V. L. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers: reply,” Opt. Express 17, 2661-2662(2009).
[CrossRef]

A. B. Stilgoe, T. A. Nieminen, G. Knoner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039-15051 (2008).
[CrossRef] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196-S203(2007).
[CrossRef]

G. Knoner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

Rudd, D.

D. McGloin, D. R. Burnham, M. D. Summers, D. Rudd, N. Dewar, and S. Anand, “Optical manipulation of airborne particles: techniques and applications,” Faraday Discuss. Chem. Soc. 137, 335-350 (2008).
[CrossRef]

Ruocco, G.

R. Di Leonardo, G. Ruocco, J. Leach, M. J. Padgett, A. J. Wright, J. M. Girkin, D. R. Burnham, and D. McGloin, “Parametric resonance of optically trapped aerosols,” Phys. Rev. Lett. 99, 010601 (2007).
[CrossRef] [PubMed]

Sayer, R. M.

R. Symes, R. M. Sayer, and J. P. Reid, “Cavity enhanced droplet spectroscopy: principles, perspectives and prospects,” Phys. Chem. Chem. Phys. 6, 474-487 (2004).
[CrossRef]

Shaevitz, J. W.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two dimensional optical force clamp for single molecule studies,” Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

Stilgoe, A. B.

Summers, M. D.

D. McGloin, D. R. Burnham, M. D. Summers, D. Rudd, N. Dewar, and S. Anand, “Optical manipulation of airborne particles: techniques and applications,” Faraday Discuss. Chem. Soc. 137, 335-350 (2008).
[CrossRef]

Sun, B.

Symes, R.

R. Symes, R. M. Sayer, and J. P. Reid, “Cavity enhanced droplet spectroscopy: principles, perspectives and prospects,” Phys. Chem. Chem. Phys. 6, 474-487 (2004).
[CrossRef]

Theofanidou, E.

E. Theofanidou, L. Wilson, W. J. Hossack, and J. Arlt, “Spherical aberration correction for optical tweezers,” Opt. Commun. 236, 145-150 (2004).
[CrossRef]

Török, P.

Varga, P.

Venkataraman, V.

J. Joykutty, V. Mathur, V. Venkataraman, and V. Natarajan, “Direct measurement of the oscillation frequency in an optical-tweezers trap by parametric excitation,” Phys. Rev. Lett. 95, 193902 (2005).
[CrossRef] [PubMed]

Viana, N. B.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezer,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

R. S. Dutra, N. B. Viana, P. A. Maia Neto, and H. M. Nussenzveig, “Polarization effects in optical tweezers,” J. Opt. A 9, S221-S227(2007).
[CrossRef]

Volke-Sepulveda, K.

Ward, A. D.

R. J. Hopkins, L. Mitchem, A. D. Ward, and J. P. Reid, “Control and characterisation of a single aerosol droplet in a single-beam gradient-force optical trap,” Phys. Chem. Chem. Phys. 6, 4924-4927 (2004).
[CrossRef]

Wilson, L.

E. Theofanidou, L. Wilson, W. J. Hossack, and J. Arlt, “Spherical aberration correction for optical tweezers,” Opt. Commun. 236, 145-150 (2004).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358-379 (1959).
[CrossRef]

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1980).

Wright, A. J.

R. Di Leonardo, G. Ruocco, J. Leach, M. J. Padgett, A. J. Wright, J. M. Girkin, D. R. Burnham, and D. McGloin, “Parametric resonance of optically trapped aerosols,” Phys. Rev. Lett. 99, 010601 (2007).
[CrossRef] [PubMed]

Wright, E. M.

N. K. Metzger, E. M. Wright, and K. Dholakia, “Theory and simulation of the bistable behaviour of optically bound particles in the Mie size regime,” New J. Phys. 8, 139 (2006).
[CrossRef]

Zemanek, P.

Zhao, Y.

Y. Zhao, G. Milne, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

Y. Zhao, G. Milne, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett. 92, 161111 (2008).
[CrossRef]

Biophys. J.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two dimensional optical force clamp for single molecule studies,” Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

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]

Br. J. Clin. Pharmacol.

N. R. Labiris and M. B. Dolovich, “Pulmonary drug delivery. Part I: physiological factors affecting therapeutic effectiveness of aerosolized medications,” Br. J. Clin. Pharmacol. 56, 588-599(2003).
[CrossRef] [PubMed]

Chem. Soc. Rev.

L. Mitchem and J. P. Reid, “Optical manipulation and characterisation of aerosol particles using a single-beam gradient force optical trap,” Chem. Soc. Rev. 37, 756-769 (2008).
[CrossRef] [PubMed]

Europhys. Lett.

P. A. Maia Neto and H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

Faraday Discuss. Chem. Soc.

D. McGloin, D. R. Burnham, M. D. Summers, D. Rudd, N. Dewar, and S. Anand, “Optical manipulation of airborne particles: techniques and applications,” Faraday Discuss. Chem. Soc. 137, 335-350 (2008).
[CrossRef]

J. Opt. A

S. Keen, J. Leach, G. Gibson, and M. J. Padgett, “Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers,” J. Opt. A 9, S264-S266 (2007).
[CrossRef]

R. S. Dutra, N. B. Viana, P. A. Maia Neto, and H. M. Nussenzveig, “Polarization effects in optical tweezers,” J. Opt. A 9, S221-S227(2007).
[CrossRef]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196-S203(2007).
[CrossRef]

K. J. Knox, J. P. Reid, K. L. Hanford, A. J. Hudson, and L. Mitchem, “Direct measurements of the axial displacement and evolving size of optically trapped aerosol droplets,” J. Opt. A 9, S180-S188 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Nature

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, “Direct measurement of critical Casimir forces,” Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

L. I. McCann, M. Dykman, and B. Golding, “Thermally activated transitions in a bistable three-dimensional optical trap,” Nature 402, 785-787 (1999).
[CrossRef]

New J. Phys.

N. K. Metzger, E. M. Wright, and K. Dholakia, “Theory and simulation of the bistable behaviour of optically bound particles in the Mie size regime,” New J. Phys. 8, 139 (2006).
[CrossRef]

Opt. Commun.

G. Roosen, “Theoretical and experimental-study of stable equilibrium positions of spheres levitated by 2 horizontal laser-beams,” Opt. Commun. 21, 189-194 (1977).
[CrossRef]

E. Theofanidou, L. Wilson, W. J. Hossack, and J. Arlt, “Spherical aberration correction for optical tweezers,” Opt. Commun. 236, 145-150 (2004).
[CrossRef]

Opt. Express

Phil. Trans. R. Soc. A

D. McGloin, “Optical tweezers: 20 years on,” Phil. Trans. R. Soc. A 364, 3521-3537 (2006).
[CrossRef] [PubMed]

Phys. Chem. Chem. Phys.

R. Symes, R. M. Sayer, and J. P. Reid, “Cavity enhanced droplet spectroscopy: principles, perspectives and prospects,” Phys. Chem. Chem. Phys. 6, 474-487 (2004).
[CrossRef]

R. J. Hopkins, L. Mitchem, A. D. Ward, and J. P. Reid, “Control and characterisation of a single aerosol droplet in a single-beam gradient-force optical trap,” Phys. Chem. Chem. Phys. 6, 4924-4927 (2004).
[CrossRef]

Phys. Rev. E

D. R. Burnham, P. J. Reece, and D. McGloin, “Parameter exploration of optically trapped liquid aerosols,” Phys. Rev. E 82, 051123 (2010).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezer,” Phys. Rev. E 75, 021914 (2007).
[CrossRef]

Phys. Rev. Lett.

G. Knoner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

P. F. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
[CrossRef] [PubMed]

J. Joykutty, V. Mathur, V. Venkataraman, and V. Natarajan, “Direct measurement of the oscillation frequency in an optical-tweezers trap by parametric excitation,” Phys. Rev. Lett. 95, 193902 (2005).
[CrossRef] [PubMed]

R. Di Leonardo, G. Ruocco, J. Leach, M. J. Padgett, A. J. Wright, J. M. Girkin, D. R. Burnham, and D. McGloin, “Parametric resonance of optically trapped aerosols,” Phys. Rev. Lett. 99, 010601 (2007).
[CrossRef] [PubMed]

Physica A

O. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108-130 (1996).
[CrossRef]

Proc. R. Soc. A

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. A 459, 3021-3041 (2003).
[CrossRef]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358-379 (1959).
[CrossRef]

Science

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673-1675 (2010).
[CrossRef] [PubMed]

Other

N.-O. A. Kwamena and J. P. Reid, “Aerosols,” in Colloid Science: Principles, Methods and Applications, T.Cosgrove, ed. (Wiley-Blackwell, 2005), Vol. 10, pp. 219-244.

M. Z. Jacobson, Atmospheric Pollution: History, Science, and Regulation (Cambridge University, 2002).

D. R. Burnham, “Microscopic applications of holographic beam shaping and studies of optically trapped aerosols,” Ph.D. thesis (University of St. Andrews, 2009).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1980).

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Figures (14)

Fig. 1
Fig. 1

(Inset) Beam of waist w enters objective lens of focal length f with back aperture radius ρ. It is focused to a point f p having propagated through two mismatched refractive index interfaces. The first interface is glass to water and the second is water to air. n g , n w , and n a are the refractive indices of glass, water, and air, respectively. Without interfaces the light would be focused to point r f . (Left) Expanded view of focal region. Light is incident on the first interface, z 1 , at θ g and refracted to θ w , and is incident on the second interface z 2 , a distance Δ h away where it is refracted to θ a and focused to its paraxial focus point f p . The height of the paraxial focus above the second and first interfaces is L 2 and L 1 , respectively. The droplet is trapped a distance h above the first interface, z above the paraxial focus, and z f below the point r f .

Fig. 2
Fig. 2

Intensity profile of a focused 532 nm Gaussian beam taken from a y - z slice through the beam axis. (a) The beam is focused into water ( n w = 1.33 ). (b) The beam is focused into water having crossed a glass ( n g = 1.517 )-to-water ( n w = 1.33 ) interface after the objective lens. (c) The beam is focused into air ( n a = 1.00 ) across glass-to-water ( n w = 1.342 ) and water-to-air interfaces. The objective displacement X = 40 μm , the water layer is 10 μm thick, γ = 1 and θ 0 = 41.23 ° . Zero on the axial axis is the position of the paraxial focus had there been no interfaces.

Fig. 3
Fig. 3

(a) Axial trapping efficiencies calculated through Mie scattering for a 5 μm (purple dashed) water droplet ( n p = 1.342 ) and through GO (black solid). (b) Axial trapping efficiencies for Mie calculation of 250 nm (blue dashed) and 1 μm (red solid) water droplets. All are trapped with 532 nm light in air ( n m = 1.000 ) with γ = 1 and θ 0 = 41.23 ° in a system like Fig. 1 with no refractive index interfaces. The four curves are plotted on two separate graphs for clarity.

Fig. 4
Fig. 4

Axial efficiency curves for 1 and 5 μm water droplets ( n p = 1.342 ) trapped in air ( n a = 1.000 ) above a glass coverslip ( n g = 1.517 ) and thin water layer ( n w = 1.342 ) as depicted in Fig. 1. X = 40 μm , Δ h = 10 μm , γ = 1 and θ 0 = 41.23 ° . (a) For a 1 μm sphere the blue solid line is without aberration and the purple dashed line with aberration. (b) For a 5 μm sphere the red solid line is without aberration and the black dashed line with aberration.

Fig. 5
Fig. 5

Axial efficiency curves as a function of z / R for 1 and 5 μm water droplets ( n p = 1.342 ) trapped in air ( n a = 1.000 ) above a glass coverslip ( n g = 1.517 ) with and without a thin water layer ( n w = 1.342 ). X = 40 μm , γ = 1 , θ 0 = 41.23 ° , and if present when the thin water layer is 10 μm thick. In (a) the blue solid and purple dashed curves are calculated without and with the thin water layer, respectively. In (b) the red solid and black dashed curves are calculated without and with the thin water layer, respectively.

Fig. 6
Fig. 6

(a) Variation of axial force for a 4 μm water droplet ( n p = 1.342 ) trapped in air ( n a = 1.000 ) at trapping powers of 10 mW (blue dotted–dashed), 20 mW (green dotted), 50 mW (purple dashed), and 200 mW (red solid). The force has been normalized to unity for clarity. (b) Height variation above the water layer droplets of radius 2 μm (blue dotted), 3 μm (red dotted–dashed), 4 μm (purple dashed), and 5.5 μm (black solid) are trapped as a function of power. All but the 5.5 μm droplet curve stop due to the loss of axial equilibrium position at high powers as in (a). X = 40 μm , Δ h = 10 μm ( n w = 1.342 ), γ = 1 , θ 0 = 41.23 ° , and the coverslip refractive index n g = 1.517 for both (a) and (b).

Fig. 7
Fig. 7

Variation of axial force for a 4 μm water droplet ( n p = 1.342 ) trapped in air ( n a = 1.000 ) with 8 mW of power for microscope objective displacements of 25 μm (red dotted–dashed), 30 μm (solid black), and 35 μm (dashed blue). The water layer ( n w = 1.342 ) is 10 μm thick, γ = 1 , θ 0 = 41.23 ° , and the coverslip refractive index n g = 1.517 .

Fig. 8
Fig. 8

Plot of the height a water droplet ( n p = 1.342 ) in air ( n a = 1.000 ) that is trapped above the underlying water layer ( n w = 1.342 ) as a function of radius. X = 25 μm , Δ h = 10 μm , γ = 1 , θ 0 = 41.23 ° , the coverslip refractive index n g = 1.517 , and the trap power is 10 mW .

Fig. 9
Fig. 9

Q z , max as a function of relative refractive index and radius for spheres trapped in a water medium ( n w = 1.33 ). X = 40 μm , γ = 1 , θ 0 = 61.25 ° , and the coverslip refractive index n g = 1.517 .

Fig. 10
Fig. 10

Q z , max as a function of relative refractive index and radius for spheres trapped in an air medium ( n a = 1.000 ). X = 40 μm , Δ h = 10 μm ( n w = 1.342 ), γ = 1 , θ 0 = 41.23 ° , and the coverslip refractive index n g = 1.517 .

Fig. 11
Fig. 11

F z , max as a function of relative refractive index and radius for spheres trapped in an air medium ( n a = 1.000 ). X = 40 μm , Δ h = 10 μm ( n w = 1.342 ), γ = 1 , θ 0 = 41.23 ° , and the coverslip refractive index n g = 1.517 .

Fig. 12
Fig. 12

Superposition of Figs. 10, 11 highlighting the areas of parameter space as a function of relative refractive index and radius, where water droplets are truly optically tweezed (high R, low n rel , gray), only trapped with the assistance of gravity (high R, high n rel , red), and optically tweezed if the droplet had neutral buoyancy (low R, low n rel , blue). The white area represents areas where neither optical tweezing nor levitation occurs. The parameters for these plots are the same as the respective figures.

Fig. 13
Fig. 13

Q z , max as a function of relative refractive index and radius for spheres trapped in an air medium ( n a = 1.00 ) with an additional spherical aberration placed on the Gaussian beam entering the objective back aperture of magnitude 0.08 λ . X = 40 μm , Δ h = 10 μm ( n w = 1.342 ), γ = 1 , θ 0 = 41.23 ° , and the coverslip refractive index n g = 1.517 .

Fig. 14
Fig. 14

Q z , max as a function of relative refractive index and radius for spheres trapped in an air medium ( n a = 1.000 ) with a Gaussian beam entering the back aperture of the microscope objective with 57% of its central area removed. The objective axial displacement, X = 40 μm , Δ h = 10 μm ( n w = 1.342 ), γ = 1 , θ 0 = 41.23 ° , and the coverslip refractive index n g = 1.517 .

Equations (2)

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L 2 = ( X n w n g Δ h ) n a n w ,
Ψ = k 0 ( ( n g N 1 Δ h + n g N 1 N 2 L 2 ) cos θ g + n w Δ h cos θ w + n a ( L 2 + z ) cos θ a ) .

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