Abstract

Many applications use a focused Gaussian laser beam to manipulate spherical dielectric particles. The axial trapping efficiency of this process is a function of (i) the particle radius r, (ii) the ratio of the refractive index of particle over the medium, and (iii) the numerical aperture of the delivered light beam. During what we believe is the first comprehensive simulation of its kind, we uncovered optical trapping regions in the three-dimensional (3D) parameter space forming an iso-surface landscape with ridge-like contours. Using specific points in the parameter space, we drew attention to difficulties in using the trapping efficiency and stiffness metrics in defining how well particles are drawn into and held in the trap. We have proposed an alternative calculation based on the maximum forward and restoration values of the trapping efficiency in the axial sense, called the trapping quality. We also discuss the manner in which the ridge regions may be harnessed for effective particle sorting, how the optical trapping blind spots can be used in applications that seek to eschew photothermal damage, and how trapping can proceed when many parameters change, such as when swelling occurs.

© 2013 Optical Society of America

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2012 (6)

2010 (2)

2009 (5)

2008 (6)

T. W. Ng, A. Neild, and P. Heeraman, “Continuous and fast sorting of Brownian particles,” Opt. Lett. 33, 584–586 (2008).
[Crossref]

P. Jákl, T. Čižmár, M. Šerý, and P. Zemánek, “Static optical sorting in a laser interference field,” Appl. Phys. Lett. 92, 161110 (2008).
[Crossref]

G.-B. Liao, P. B. Bareil, Y. Sheng, and A. Chiou, “One-dimensional jumping optical tweezers for optical stretching of bi-concave human red blood cells,” Opt. Express 16, 1996–2004 (2008).
[Crossref]

Y. N. Dai, P. Li, J. P. Zhang, A. Q. Wang, and Q. Wei, “Swelling characteristics and drug delivery properties of nifedipine-loaded pH sensitive alginate-chitosan hydrogel beads,” J. Biomed. Mater. Res. B Appl. Biomater. 86, 493–500 (2008).
[Crossref]

M. Polin, Y. Roichman, and D. G. Grier, “Autocalibrated colloidal interaction measurements with extended optical traps,” Phys. Rev. E 77, 051401 (2008).
[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]

2007 (3)

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]

D. DiCarlo, D. Irimia, R. G. Tompkins, and M. Toner, “Continuous inertial focusing, ordering, and separation of particles in microchannels,” Proc. Natl. Acad. Sci. USA. 104, 18892–18897 (2007).
[Crossref]

K. Dholakia, M. P. MacDonald, P. Zemánek, and T. Cizmár, “Cellular and colloidal separation using optical forces,” Methods Cell Biol. 82, 467–495 (2007).
[Crossref]

2004 (1)

J.-P. Matas, J. F. Morris, and E. Guazzelli, “Inertial migration of rigid spherical particles in Poiseuille flow,” J. Fluid Mech. 515, 171–195 (2004).
[Crossref]

2003 (2)

J. Koo and C. Kleinstreuer, “Liquid flow in microchannels: experimental observations and computational analyses of microfluidics effects,” J. Micromech. Microeng. 13, 568–579 (2003).
[Crossref]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421–424 (2003).
[Crossref]

2000 (1)

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

1999 (1)

M. Bier, I. Derenyi, M. Kostur, and R. D. Astumian, “Intrawell relaxation of overdamped Brownian particles,” Phys. Rev. E 59, 6422–6432 (1999).
[Crossref]

1996 (2)

1992 (2)

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, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[Crossref]

1989 (1)

1986 (1)

1970 (1)

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

Alonso, M. A.

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, “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, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[Crossref]

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

Astumian, R. D.

M. Bier, I. Derenyi, M. Kostur, and R. D. Astumian, “Intrawell relaxation of overdamped Brownian particles,” Phys. Rev. E 59, 6422–6432 (1999).
[Crossref]

Bareil, P. B.

Beckley, A. M.

Berns, M. W.

N. Hyun, C. Chandsawangbhuwana, Q. Zhu, L. Z. Shi, C. Yang-Wong, and M. W. Berns, “Effects of viscosity on sperm motility studied with optical tweezers,” J. Biomed. Opt. 17, 025005 (2012).
[Crossref]

K. Konig, H. Liang, M. W. Berns, and B. J. Tromberg, “Cell damage in near-infrared multimode optical traps as a result of multiphoton absorption,” Opt. Lett. 21, 1090–1092 (1996).
[Crossref]

Bier, M.

M. Bier, I. Derenyi, M. Kostur, and R. D. Astumian, “Intrawell relaxation of overdamped Brownian particles,” Phys. Rev. E 59, 6422–6432 (1999).
[Crossref]

Bjorkholm, J. E.

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]

Brown, T. G.

Burnham, D. R.

Chandsawangbhuwana, C.

N. Hyun, C. Chandsawangbhuwana, Q. Zhu, L. Z. Shi, C. Yang-Wong, and M. W. Berns, “Effects of viscosity on sperm motility studied with optical tweezers,” J. Biomed. Opt. 17, 025005 (2012).
[Crossref]

Cheraghian, M.

Chiou, A.

Chiu, W. S.-Y.

Chu, S.

Chýlek, P.

Cizmár, T.

K. Dholakia, M. P. MacDonald, P. Zemánek, and T. Cizmár, “Cellular and colloidal separation using optical forces,” Methods Cell Biol. 82, 467–495 (2007).
[Crossref]

Cižmár, T.

P. Jákl, T. Čižmár, M. Šerý, and P. Zemánek, “Static optical sorting in a laser interference field,” Appl. Phys. Lett. 92, 161110 (2008).
[Crossref]

Dai, Y. N.

Y. N. Dai, P. Li, J. P. Zhang, A. Q. Wang, and Q. Wei, “Swelling characteristics and drug delivery properties of nifedipine-loaded pH sensitive alginate-chitosan hydrogel beads,” J. Biomed. Mater. Res. B Appl. Biomater. 86, 493–500 (2008).
[Crossref]

Dam, J. S.

I. Perch-Nielsen, D. Palima, J. S. Dam, and J. Gluckstad, “Parallel particle identification and separation for active optical sorting,” J. Opt. A 11, 034013 (2009).
[Crossref]

Derenyi, I.

M. Bier, I. Derenyi, M. Kostur, and R. D. Astumian, “Intrawell relaxation of overdamped Brownian particles,” Phys. Rev. E 59, 6422–6432 (1999).
[Crossref]

Dholakia, K.

K. Dholakia, M. P. MacDonald, P. Zemánek, and T. Cizmár, “Cellular and colloidal separation using optical forces,” Methods Cell Biol. 82, 467–495 (2007).
[Crossref]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421–424 (2003).
[Crossref]

DiCarlo, D.

D. DiCarlo, D. Irimia, R. G. Tompkins, and M. Toner, “Continuous inertial focusing, ordering, and separation of particles in microchannels,” Proc. Natl. Acad. Sci. USA. 104, 18892–18897 (2007).
[Crossref]

Dziedzic, J. M.

Fenollosa, R.

E. Xifré-Pérez, F. J. García de Abajo, R. Fenollosa, and F. Meseguer, “Photonic binding in silicon-colloid microcavities,” Phys. Rev. Lett. 103, 103902 (2009).
[Crossref]

García de Abajo, F. J.

E. Xifré-Pérez, F. J. García de Abajo, R. Fenollosa, and F. Meseguer, “Photonic binding in silicon-colloid microcavities,” Phys. Rev. Lett. 103, 103902 (2009).
[Crossref]

Gluckstad, J.

I. Perch-Nielsen, D. Palima, J. S. Dam, and J. Gluckstad, “Parallel particle identification and separation for active optical sorting,” J. Opt. A 11, 034013 (2009).
[Crossref]

Gorodetsky, M. L.

Grier, D. G.

B. Sun and D. G. Grier, “The effect of Mie resonances on trapping in optical tweezers: comment,” Opt. Express 17, 2658–2660 (2009).
[Crossref]

M. Polin, Y. Roichman, and D. G. Grier, “Autocalibrated colloidal interaction measurements with extended optical traps,” Phys. Rev. E 77, 051401 (2008).
[Crossref]

Guazzelli, E.

J.-P. Matas, J. F. Morris, and E. Guazzelli, “Inertial migration of rigid spherical particles in Poiseuille flow,” J. Fluid Mech. 515, 171–195 (2004).
[Crossref]

Heckenberg, N. R.

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]

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]

Heeraman, P.

Hyun, N.

N. Hyun, C. Chandsawangbhuwana, Q. Zhu, L. Z. Shi, C. Yang-Wong, and M. W. Berns, “Effects of viscosity on sperm motility studied with optical tweezers,” J. Biomed. Opt. 17, 025005 (2012).
[Crossref]

Ilchenko, V. S.

Irimia, D.

D. DiCarlo, D. Irimia, R. G. Tompkins, and M. Toner, “Continuous inertial focusing, ordering, and separation of particles in microchannels,” Proc. Natl. Acad. Sci. USA. 104, 18892–18897 (2007).
[Crossref]

Jákl, P.

P. Jákl, T. Čižmár, M. Šerý, and P. Zemánek, “Static optical sorting in a laser interference field,” Appl. Phys. Lett. 92, 161110 (2008).
[Crossref]

Kendrick, M. J.

Kleinstreuer, C.

J. Koo and C. Kleinstreuer, “Liquid flow in microchannels: experimental observations and computational analyses of microfluidics effects,” J. Micromech. Microeng. 13, 568–579 (2003).
[Crossref]

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]

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]

Knox, K. J.

Konig, K.

Koo, J.

J. Koo and C. Kleinstreuer, “Liquid flow in microchannels: experimental observations and computational analyses of microfluidics effects,” J. Micromech. Microeng. 13, 568–579 (2003).
[Crossref]

Kostur, M.

M. Bier, I. Derenyi, M. Kostur, and R. D. Astumian, “Intrawell relaxation of overdamped Brownian particles,” Phys. Rev. E 59, 6422–6432 (1999).
[Crossref]

Lau, C. Y.

Le, T.

Li, P.

Y. N. Dai, P. Li, J. P. Zhang, A. Q. Wang, and Q. Wei, “Swelling characteristics and drug delivery properties of nifedipine-loaded pH sensitive alginate-chitosan hydrogel beads,” J. Biomed. Mater. Res. B Appl. Biomater. 86, 493–500 (2008).
[Crossref]

Li, Y.-M.

Liang, H.

Liao, G.-B.

Liew, O. W.

Liu, Z.

Y. Zhang, Z. Liu, J. Yang, and L. Yuan, “A non-contact single optical fiber multi-optical tweezers probe: design and fabrication,” Opt. Commun. 285, 4068–4071 (2012).
[Crossref]

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]

MacDonald, M. P.

K. Dholakia, M. P. MacDonald, P. Zemánek, and T. Cizmár, “Cellular and colloidal separation using optical forces,” Methods Cell Biol. 82, 467–495 (2007).
[Crossref]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421–424 (2003).
[Crossref]

Madadi, E.

Matas, J.-P.

J.-P. Matas, J. F. Morris, and E. Guazzelli, “Inertial migration of rigid spherical particles in Poiseuille flow,” J. Fluid Mech. 515, 171–195 (2004).
[Crossref]

McCann, L. I.

McGloin, D.

McIntyre, D. H.

Meseguer, F.

E. Xifré-Pérez, F. J. García de Abajo, R. Fenollosa, and F. Meseguer, “Photonic binding in silicon-colloid microcavities,” Phys. Rev. Lett. 103, 103902 (2009).
[Crossref]

Morris, J. F.

J.-P. Matas, J. F. Morris, and E. Guazzelli, “Inertial migration of rigid spherical particles in Poiseuille flow,” J. Fluid Mech. 515, 171–195 (2004).
[Crossref]

Muradoglu, M.

Murphy, S. L.

Neild, A.

Neto, P. A. M.

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

Ng, T. W.

Nieminen, T. A.

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]

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]

Nussenzveig, H. M.

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

Ostroverkhova, O.

Palima, D.

I. Perch-Nielsen, D. Palima, J. S. Dam, and J. Gluckstad, “Parallel particle identification and separation for active optical sorting,” J. Opt. A 11, 034013 (2009).
[Crossref]

Perch-Nielsen, I.

I. Perch-Nielsen, D. Palima, J. S. Dam, and J. Gluckstad, “Parallel particle identification and separation for active optical sorting,” J. Opt. A 11, 034013 (2009).
[Crossref]

Polin, M.

M. Polin, Y. Roichman, and D. G. Grier, “Autocalibrated colloidal interaction measurements with extended optical traps,” Phys. Rev. E 77, 051401 (2008).
[Crossref]

Reid, J. P.

Reihani, S. N. S.

Ren, Y.-X.

Roichman, Y.

M. Polin, Y. Roichman, and D. G. Grier, “Autocalibrated colloidal interaction measurements with extended optical traps,” Phys. Rev. E 77, 051401 (2008).
[Crossref]

Rubinsztein-Dunlop, H.

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]

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]

Samadi, A.

Savchenkov, A. A.

Šerý, M.

P. Jákl, T. Čižmár, M. Šerý, and P. Zemánek, “Static optical sorting in a laser interference field,” Appl. Phys. Lett. 92, 161110 (2008).
[Crossref]

Sheng, Y.

Shi, L. Z.

N. Hyun, C. Chandsawangbhuwana, Q. Zhu, L. Z. Shi, C. Yang-Wong, and M. W. Berns, “Effects of viscosity on sperm motility studied with optical tweezers,” J. Biomed. Opt. 17, 025005 (2012).
[Crossref]

Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421–424 (2003).
[Crossref]

Stilgoe, A. B.

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]

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]

Sun, B.

Tompkins, R. G.

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Other (1)

Simulator for the optical trapping of spherical dielectric particles. www.biofuturex.com/LOAM/index-resource.html .

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Figures (11)

Fig. 1.
Fig. 1.

Efficiency in trapping a spherical particle using a focusing laser beam is dependent on its radius r and refractive index n1, the refractive index of the medium n2, and the NA of the light beam, which is a function of the half-angle.

Fig. 2.
Fig. 2.

Three field components |Ex|, |Ey| and |Ez| of an x-polarized Gaussian beam with a NA=1.0 when recovered by expanding its beam coefficients with VSWF in the focal plane xy. The fields are normalized to the maximum of |Ex| and lengths are in units of wavelength, λ.

Fig. 3.
Fig. 3.

Iso-surface of Qz,RFmin=1×10(10) representing the ability to conduct optical trapping calculated in relation to NA, particle refractive index ratio (n1), and radius (r) values. The volume space above the distribution represents those parameters that do not lead to optical trapping.

Fig. 4.
Fig. 4.

Example slice plots from Fig. 3 obtained by keeping the (a) refractive index ratio, (b) normalized radius, and (c) NA fixed. Finger landscapes are observed in all three cases. The white areas correspond to Qz,RFmin=0, which indicates a nontrap condition.

Fig. 5.
Fig. 5.

Optical force efficiency, Qz calculated on particles trapped under parameter conditions pA and pB placed at positions along the beam axis z. For both particles, the radiation pattern at different locations corresponding to the maximum forward restoration force, equilibrium point and maximum reverse restoration force also are shown.

Fig. 6.
Fig. 6.

Optical force efficiency, Qz, calculated on particles trapped under parameter conditons pC and pD placed at positions along the beam axis z. For both particles, the radiation pattern at different locations corresponding to the maximum forward restoration force, focal point, and z=1.0μm also are shown.

Fig. 7.
Fig. 7.

Zoomed-in region for Fig. 3, (2.0μmr2.5μm and 2.5n13.0) with smaller parameter value intervals, which show that the fingers form smoothly before they are thinned out and eventually vanish. Two lines, L1 and L2, indicate that particles with a radius ratio between 2.115 and 2.135 would be selectively trapped, which illustrates the ability for sorting.

Fig. 8.
Fig. 8.

Potential energy wells corresponding to a particle located in the safe region and on a trapping finger, depicted under conditions pE and pB, respectively.

Fig. 9.
Fig. 9.

Trapping strength and its gradient along the lines (a) L1 and (b) L2 as depicted in Fig. 7.

Fig. 10.
Fig. 10.

Schematic description of situation where a spherical of volume Vo of refractive index n1 undergoes swelling by absorbing material from the surrounding media of refractive index n2 such that its volume increases by ΔV.

Fig. 11.
Fig. 11.

Trajectory of a swelling dielectric sphere with an original radius ro=2.095μm and refractive index n1=2.506, placed in a medium with refractive index n2=1.33 for: (a) NA=1.2248 and (b) NA=1.33. The growth rate, α, was linearly increased from 0 to 2.0.

Equations (3)

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TQ={0Qz,RFmin0abs(Qz,RFminQz,RFmax)Qz,RFmin<0,
n1=Von1+ΔVn2Vo+ΔV=Von1+αVon2Vo+αVo=n1+αn21+α.
r=ro(1+α3).

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