Abstract

At the microscopic level, light-matter interactions can organize colloidal matter via a process known as optical binding. Optical binding refers to the creation of arrays of microparticles formed in the presence of laser fields, the inter-particle spacing being determined by the refocusing and/or scattering of the laser fields by the microparticles. In this paper we investigate one-dimensional optically bound arrays of microparticles using a femtosecond dual-beam optical fiber trap, and develop a means to visualize the field intensity distributions responsible for the optical binding using two-photon fluoresence imaging from fluorescein added to the host medium. The experimental intensity distributions are shown to be in good agreement with numerical simulations, thereby validating our new approach to visualizing the fields responsible for optical binding, and the physical model of optical binding as due to refocusing of the fields by the microparticles.

© 2006 Optical Society of America

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2006

K. Dholakia, and P. Reece, "Optical micromanipulation takes hold," Nano Today,  1, 18 (2006).
[CrossRef]

N. K. Metzger, K. Dholakia and E.M. Wright, "Observation of bistability and hysteresis in optical binding of two dielectric spheres," Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

2005

2004

2003

2002

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296,1101-1103 (2002).
[CrossRef] [PubMed]

S. Tatarkova, A. E. Carruthers and K. Dholakia, "One dimensional optical bound arrays of microscopic particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

2001

1995

1993

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]

1990

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical matter: Crystallization and binding in intense optical fields," Science 249, 749-754 (1990).
[CrossRef] [PubMed]

1987

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

1986

1984

1961

W. Kaiser and C. G. B. Garret, "Two-photon excitation in CaF2:Eu2+," Phys. Rev. Lett. 7, 229-331 (1961).
[CrossRef]

Agate, B.

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Physics 6, 13 (2004).
[CrossRef]

B. Agate, C. T. A. Brown, W. Sibbett and K. Dholakia, "Femtosecond optical tweezers for in-situ control of two-photon fluorescence," Opt. Express 12, 3011-3017 (2004), http://www.opticsexpress.org/abstract.cfm?id=80322
[CrossRef] [PubMed]

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296,1101-1103 (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]

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

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

Bernet, S.

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman and S. M. Block, "Optical Trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Brown, C. T. A.

B. Agate, C. T. A. Brown, W. Sibbett and K. Dholakia, "Femtosecond optical tweezers for in-situ control of two-photon fluorescence," Opt. Express 12, 3011-3017 (2004), http://www.opticsexpress.org/abstract.cfm?id=80322
[CrossRef] [PubMed]

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Physics 6, 13 (2004).
[CrossRef]

Burns, M. M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical matter: Crystallization and binding in intense optical fields," Science 249, 749-754 (1990).
[CrossRef] [PubMed]

Carruthers, A. E.

D. McGloin, A. E. Carruthers, K. Dholakia and E.M. Wright, "Optically bound microscopic particles in one dimension," Phys. Rev. E 69, 021403 (2004).
[CrossRef]

S. Tatarkova, A. E. Carruthers and K. Dholakia, "One dimensional optical bound arrays of microscopic particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Chin, S L.

Chu, S.

Cizmar, T.

T. Cizmar, V. Garces-Chavez, K. Dholakia and P. Zemanek, "Optical conveyor belt for delivery of submicron particles," Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Constable, A.

Cooper, J.

Courtial, J.

Cremer, C.

Cronin-Golomb, M.

Daria, V. R.

P. J. Rodrigo, V. R. Daria, J. Glueckstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

Dholakia, K.

N. K. Metzger, K. Dholakia and E.M. Wright, "Observation of bistability and hysteresis in optical binding of two dielectric spheres," Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

K. Dholakia, and P. Reece, "Optical micromanipulation takes hold," Nano Today,  1, 18 (2006).
[CrossRef]

T. Cizmar, V. Garces-Chavez, K. Dholakia and P. Zemanek, "Optical conveyor belt for delivery of submicron particles," Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

B. Agate, C. T. A. Brown, W. Sibbett and K. Dholakia, "Femtosecond optical tweezers for in-situ control of two-photon fluorescence," Opt. Express 12, 3011-3017 (2004), http://www.opticsexpress.org/abstract.cfm?id=80322
[CrossRef] [PubMed]

D. McGloin, A. E. Carruthers, K. Dholakia and E.M. Wright, "Optically bound microscopic particles in one dimension," Phys. Rev. E 69, 021403 (2004).
[CrossRef]

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Physics 6, 13 (2004).
[CrossRef]

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia and D. McGloin,"Creation and manipulation of three-dimensional optically trapped structures," Opt. Express 11, 3562 (2003), http://www.opticsexpress.org/abstract.cfm?id=78220
[CrossRef] [PubMed]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296,1101-1103 (2002).
[CrossRef] [PubMed]

S. Tatarkova, A. E. Carruthers and K. Dholakia, "One dimensional optical bound arrays of microscopic particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Domachuk, P.

Dziedzic, J.-M.

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

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

Eggleton, B.

Fischer, A.

Fournier, J.-M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical matter: Crystallization and binding in intense optical fields," Science 249, 749-754 (1990).
[CrossRef] [PubMed]

Frick, M.

Garces-Chavez, V.

T. Cizmar, V. Garces-Chavez, K. Dholakia and P. Zemanek, "Optical conveyor belt for delivery of submicron particles," Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Garret, C. G. B.

W. Kaiser and C. G. B. Garret, "Two-photon excitation in CaF2:Eu2+," Phys. Rev. Lett. 7, 229-331 (1961).
[CrossRef]

Glueckstad, J.

P. J. Rodrigo, V. R. Daria, J. Glueckstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

Golovchenko, J. A.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical matter: Crystallization and binding in intense optical fields," Science 249, 749-754 (1990).
[CrossRef] [PubMed]

Greenhalgh, D. A.

Grier, D. G.

Jordan, P.

Kaiser, W.

W. Kaiser and C. G. B. Garret, "Two-photon excitation in CaF2:Eu2+," Phys. Rev. Lett. 7, 229-331 (1961).
[CrossRef]

Kelman, J. B.

Kim, J.

Laczik, Z.

Leach, J.

Li, R.

Little, H.

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Physics 6, 13 (2004).
[CrossRef]

Liu, J.

MacDonald, M. P.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296,1101-1103 (2002).
[CrossRef] [PubMed]

McGloin, D

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Physics 6, 13 (2004).
[CrossRef]

McGloin, D.

Melville, H.

Mervis, J.

Metzger, N. K.

N. K. Metzger, K. Dholakia and E.M. Wright, "Observation of bistability and hysteresis in optical binding of two dielectric spheres," Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

Milne, G. F.

Mitchell, A.

Mutzenich, S.

Neuman, K. C.

K. C. Neuman and S. M. Block, "Optical Trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Padgett, M.

Paterson, L.

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Physics 6, 13 (2004).
[CrossRef]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296,1101-1103 (2002).
[CrossRef] [PubMed]

Prentiss, M.

Ramsay, E.

Reece, P.

K. Dholakia, and P. Reece, "Optical micromanipulation takes hold," Nano Today,  1, 18 (2006).
[CrossRef]

Reid, D. T.

Ritsch-Marte, M.

Rodrigo, P. J.

P. J. Rodrigo, V. R. Daria, J. Glueckstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

Roichman, Y.

Rosengarten, G.

Schroeder, H.

Shank, C. V.

Sibbett, W.

B. Agate, C. T. A. Brown, W. Sibbett and K. Dholakia, "Femtosecond optical tweezers for in-situ control of two-photon fluorescence," Opt. Express 12, 3011-3017 (2004), http://www.opticsexpress.org/abstract.cfm?id=80322
[CrossRef] [PubMed]

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Physics 6, 13 (2004).
[CrossRef]

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia and D. McGloin,"Creation and manipulation of three-dimensional optically trapped structures," Opt. Express 11, 3562 (2003), http://www.opticsexpress.org/abstract.cfm?id=78220
[CrossRef] [PubMed]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296,1101-1103 (2002).
[CrossRef] [PubMed]

Sinclair, G.

Singer, W.

Spalding, G. C.

Stelzer, E. H. K.

Stolen, R. H.

Tatarkova, S.

S. Tatarkova, A. E. Carruthers and K. Dholakia, "One dimensional optical bound arrays of microscopic particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Tomlinson, W. J.

Volke-Sepulveda, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296,1101-1103 (2002).
[CrossRef] [PubMed]

Wright, E.M.

N. K. Metzger, K. Dholakia and E.M. Wright, "Observation of bistability and hysteresis in optical binding of two dielectric spheres," Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

D. McGloin, A. E. Carruthers, K. Dholakia and E.M. Wright, "Optically bound microscopic particles in one dimension," Phys. Rev. E 69, 021403 (2004).
[CrossRef]

Xiao, D.

Xu, Z.

Yamane, T.

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

Zarinetchi, F.

Zemanek, P.

T. Cizmar, V. Garces-Chavez, K. Dholakia and P. Zemanek, "Optical conveyor belt for delivery of submicron particles," Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

T. Cizmar, V. Garces-Chavez, K. Dholakia and P. Zemanek, "Optical conveyor belt for delivery of submicron particles," Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

P. J. Rodrigo, V. R. Daria, J. Glueckstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

Biophys. J.

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]

J. Opt. Soc. Am. B

Nano Today

K. Dholakia, and P. Reece, "Optical micromanipulation takes hold," Nano Today,  1, 18 (2006).
[CrossRef]

Nature

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

New J. Physics

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Physics 6, 13 (2004).
[CrossRef]

Opt. Express

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia and D. McGloin,"Creation and manipulation of three-dimensional optically trapped structures," Opt. Express 11, 3562 (2003), http://www.opticsexpress.org/abstract.cfm?id=78220
[CrossRef] [PubMed]

J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. Laczik, "3D manipulation of particles into crystal structures using holographic optical tweezers," Opt. Express 12,220-226 (2004), http://www.opticsexpress.org/abstract.cfm?id=78450
[CrossRef] [PubMed]

9. Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005), http://www.opticsexpress.org/abstract.cfm?id=84909
[CrossRef] [PubMed]

J. Liu, H. Schroeder, S L. Chin, R. Li, and Z. Xu, "Nonlinear propagation of fs laser pulses in liquids and evolution of supercontinuum generation," Opt. Express 13, 10248-10259 (2005), http://www.opticsexpress.org/abstract.cfm?id=86467
[CrossRef] [PubMed]

P. Domachuk, M. Cronin-Golomb, B. Eggleton, S. Mutzenich, G. Rosengarten and A. Mitchell, "Application of optical trapping to beam manipulation in optofluidics, " Opt. Express 13, 7265-7275 (2005), http://www.opticsexpress.org/abstract.cfm?id=85429
[CrossRef] [PubMed]

B. Agate, C. T. A. Brown, W. Sibbett and K. Dholakia, "Femtosecond optical tweezers for in-situ control of two-photon fluorescence," Opt. Express 12, 3011-3017 (2004), http://www.opticsexpress.org/abstract.cfm?id=80322
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. E

D. McGloin, A. E. Carruthers, K. Dholakia and E.M. Wright, "Optically bound microscopic particles in one dimension," Phys. Rev. E 69, 021403 (2004).
[CrossRef]

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Supplementary Material (2)

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Figures (5)

Fig. 1.
Fig. 1.

Fiber optical trap setup: Light at 800 nm from a Ti:Sa femtosecond laser is coupled via ND filters into fiber F1 and F2 to ensure equal power distribution. Inset shows fiber trap side view: The array is formed in the gap between the two fibers (F1 and F2) with D being the separation of the spheres and Df the fiber separation. A second helper tweezers is coupled into the observation microscope via dichroic beam splitter to hold a sphere in the beam or to initiate the array. Images were taken through the microscope via the CCD camera in front of which a lens could be flipped to achieve varying image magnification.

Fig. 2.
Fig. 2.

[1.38MB] Diffraction pattern of a 5.17 μm silica sphere being scanned along the y-axis by an optical tweezers. The sphere position (overlaid white circle) is at approximately 50±1 μm from the beam waist. The movie shows the experimental images and the theoretical simulation. The insert on the right shows the intensity distribution along the y-axis from a to b at 8±1 μm after the sphere which has an offset from the beam axis of 3±0.5 μm (experiment: blue dots; theory: red line). Light is diffracted away from the beam path creating a valley of low intensity light.

Fig. 3.
Fig. 3.

Diffraction pattern of a 5.17 μm silica sphere which is held by optical tweezers at 54±1 μm from the beam waist in a single beam, originating from the left side of images. Comparison between different refractive index mismatches Δn: Δn = 0.07. 1) On-axis intensity distribution (blue – experimental data; red – theoretical prediction). 2) Theoretical simulation of diffraction pattern, and 3) False color images of two-photon fluorescence.Δn = 0.05. 1) On-axis intensity, 2) Theoretical simulation, and 3) False color images of two-photon fluorescence.

Fig. 4.
Fig. 4.

Optically bound arrays: Array of two 3 μm spheres with a separation of 8 μm with Δn = 0.06. 1) On-axis intensity distribution showing the full waist separation of 72 μm (blue – experimental data; red – theoretical prediction). 2) Theoretical simulation of diffraction pattern in a 2 sphere array, 3) False color image of two-photon fluorescence.Same array as in A) with left propagating field blocked, and for a time such that the sphere separation is 9 μm. 2) Theoretical simulation of the diffraction pattern, 3) false color image of two-photon fluorescence beam coming from left side of picture.Array of three 3 μm spheres with a separation of 5 μm with Δn = 0.05 and a waist separation of 100 μm. 1) On-axis intensity comparison between theory and experiment which is being cut off at 60 μm. 2) and 3) theoretical and experimental images of diffraction pattern.Array of four 3 μm sphere array with a separation of 12 μm with Δn = 0.01 with a waist separation of 85 μm. 1) On-axis intensity plot, 2) Theoretical image matching, 3) experimental false color image of two-photon fluorescence with right and left hand side of beam being partly cut off.

Fig. 5.
Fig. 5.

[1.31MB] On-axis intensity distribution of two 2.3 μm sphere array exhibiting bistability with a separation of a) 5 μm, and B) 16 μm with Δn = 0.065 and a waist separation of 90 μm. The respective on-axis intensity plots show a slight disagreement for a separation of 16 μm in B1) which is caused by sphere size variation within the sample batch. Respective intensity planes are shown in A2) and B2) for the simulations and A3) and B3) from the experiment. The movie shows an array of two 2.3 μm spheres having a separation of 16 μm, which are being guided to the right fiber facet. After the left propagating beam is reintroduced, they exhibit a separation of 5 μm. To get a clearer image of the spheres the microscope illumination was used, but the two-photon signal of the beam in the medium can still be observed.

Equations (5)

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E r t = x ̂ 2 [ ( ε + ( r ) e ikz + ε ( r ) e ikz ) e iωt + c . c ] ,
ε + x y z = 0 = ε x y z = D f = 4 P 0 n h c ε 0 π e r 2 / w 0 2 ,
n 2 ( r ) = n h 2 + ( n s 2 n h 2 ) j = 1 N θ ( R r r j ) ,
± ε ± z = i 2 k 2 ε ± + i k 0 ( n 2 ( r ) n h 2 ) 2 n h ε ± ,
S two photon ( y , z ) I field 2 x y z d x

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