Abstract

An in situ separation system, cross-type optical chromatography, is developed theoretically, and an analytic solution of the retention distance is derived. Particle trajectories in the cross-type optical chromatography are calculated for various sizes and materials of the particles and for flow velocities. Further, cross-type optical chromatography assisted by a particle beam generation system is designed.

© 2006 Optical Society of America

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  1. A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
    [CrossRef]
  2. 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] [PubMed]
  3. S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
    [CrossRef] [PubMed]
  4. A. Ashkin, "Trapping of atoms by resonance radiation pressure," Phys. Rev. Lett. 40, 729-732 (1978).
    [CrossRef]
  5. W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
    [CrossRef]
  6. S. Chu, "The manipulation of neutral particles," Rev. Mod. Phys. 70, 685-706 (1998).
    [CrossRef]
  7. A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  11. J. Makihara, T. Kaneta, and T. Imasaka, "Optical chromatography size determination by eluting particles," Talanta 48, 551-557 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. R. C. Gauthier, "Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects," J. Opt. Soc. Am. B 14, 3323-3333 (1997).
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  26. W. C. Hinds, Aerosol Technology (Wiley, 1999).

2006

1999

J. Makihara, T. Kaneta, and T. Imasaka, "Optical chromatography size determination by eluting particles," Talanta 48, 551-557 (1999).
[CrossRef]

1998

W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
[CrossRef]

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

1997

1996

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

1995

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

T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, "Optical chromatography," Anal. Chem. 67, 1763-1765 (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]

1994

J. T. Finner, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics:picoNewton forces and nanometer steps," Nature (London) 368, 113-119 (1994).
[CrossRef]

1992

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 12, 569-582 (1992).
[CrossRef]

1989

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

1988

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam," J. Appl. Phys. 64, 1632-1639 (1988).
[CrossRef]

1987

1986

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] [PubMed]

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

1985

1983

1978

A. Ashkin, "Trapping of atoms by resonance radiation pressure," Phys. Rev. Lett. 40, 729-732 (1978).
[CrossRef]

1970

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

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam," J. Appl. Phys. 64, 1632-1639 (1988).
[CrossRef]

Ashkin, A.

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 12, 569-582 (1992).
[CrossRef]

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

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[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, 288-289 (1986).
[CrossRef] [PubMed]

A. Ashkin, "Trapping of atoms by resonance radiation pressure," Phys. Rev. Lett. 40, 729-732 (1978).
[CrossRef]

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

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam," J. Appl. Phys. 64, 1632-1639 (1988).
[CrossRef]

Bjorkholm, J. E.

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] [PubMed]

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

Buican, T. N.

Calbe, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

Chang, S.

Chu, S.

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] [PubMed]

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

Crissman, H. A.

Dziedzic, J. M.

Finner, J. T.

J. T. Finner, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics:picoNewton forces and nanometer steps," Nature (London) 368, 113-119 (1994).
[CrossRef]

Gauthier, R. C.

Hinds, W. C.

W. C. Hinds, Aerosol Technology (Wiley, 1999).

Imasaka, T.

J. Makihara, T. Kaneta, and T. Imasaka, "Optical chromatography size determination by eluting particles," Talanta 48, 551-557 (1999).
[CrossRef]

T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, "Theory of optical chromatography," Anal. Chem. 69, 2701-2710 (1997).
[CrossRef] [PubMed]

T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, "Optical chromatography," Anal. Chem. 67, 1763-1765 (1995).
[CrossRef]

Ishidzu, Y.

T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, "Theory of optical chromatography," Anal. Chem. 69, 2701-2710 (1997).
[CrossRef] [PubMed]

T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, "Optical chromatography," Anal. Chem. 67, 1763-1765 (1995).
[CrossRef]

Kaneta, T.

J. Makihara, T. Kaneta, and T. Imasaka, "Optical chromatography size determination by eluting particles," Talanta 48, 551-557 (1999).
[CrossRef]

T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, "Theory of optical chromatography," Anal. Chem. 69, 2701-2710 (1997).
[CrossRef] [PubMed]

T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, "Optical chromatography," Anal. Chem. 67, 1763-1765 (1995).
[CrossRef]

Kawabata, Y.

T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, "Optical chromatography," Anal. Chem. 67, 1763-1765 (1995).
[CrossRef]

Kim, J. S.

Kim, S. B.

Kim, S. S.

Koehler, D. R.

Lee, S. S.

Makihara, J.

J. Makihara, T. Kaneta, and T. Imasaka, "Optical chromatography size determination by eluting particles," Talanta 48, 551-557 (1999).
[CrossRef]

Martin, J. C.

Mishima, N.

T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, "Theory of optical chromatography," Anal. Chem. 69, 2701-2710 (1997).
[CrossRef] [PubMed]

Phillips, W. D.

W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
[CrossRef]

Salzeman, G. C.

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam," J. Appl. Phys. 64, 1632-1639 (1988).
[CrossRef]

Simmons, R. M.

J. T. Finner, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics:picoNewton forces and nanometer steps," Nature (London) 368, 113-119 (1994).
[CrossRef]

Smith, M. J.

Spudich, J. A.

J. T. Finner, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics:picoNewton forces and nanometer steps," Nature (London) 368, 113-119 (1994).
[CrossRef]

Stewart, C. C.

Wallace, S.

Anal. Chem.

T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, "Optical chromatography," Anal. Chem. 67, 1763-1765 (1995).
[CrossRef]

T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, "Theory of optical chromatography," Anal. Chem. 69, 2701-2710 (1997).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

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

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

Biophys. J.

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 12, 569-582 (1992).
[CrossRef]

J. Appl. Phys.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam," J. Appl. Phys. 64, 1632-1639 (1988).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Nature

J. T. Finner, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics:picoNewton forces and nanometer steps," Nature (London) 368, 113-119 (1994).
[CrossRef]

Opt. Laser Technol.

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

Opt. Lett.

Phys. Rev. Lett.

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

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

A. Ashkin, "Trapping of atoms by resonance radiation pressure," Phys. Rev. Lett. 40, 729-732 (1978).
[CrossRef]

Rev. Mod. Phys.

W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
[CrossRef]

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

Science

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

Talanta

J. Makihara, T. Kaneta, and T. Imasaka, "Optical chromatography size determination by eluting particles," Talanta 48, 551-557 (1999).
[CrossRef]

Other

W. C. Hinds, Aerosol Technology (Wiley, 1999).

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Figures (10)

Fig. 1
Fig. 1

Schematics of axial-type optical chromatography. Particles remain stationary when the drag force, F d , is equal to the radiation force, F r .

Fig. 2
Fig. 2

Schematics of cross-type optical chromatography. Light illuminates perpendicularly to the flow direction. As particles pass through the illuminating light, particles are separated continuously.

Fig. 3
Fig. 3

Geometry of a simplified system to derive the analytic solution of the retention distance. The radiation force and width of the illuminated light are assumed to be constant.

Fig. 4
Fig. 4

Particle trajectories for various particle sizes. As particles pass through the illuminated region, the trajectories of the particles deviate from the initial position due to the radiation force. After escaping from the illuminated region, the z-direction position of the particles remains constant. The retention distance increases as particle size increases.

Fig. 5
Fig. 5

Particle trajectories for different materials (PSL, PMMA and silica). Identical particle sizes with different materials are separated continuously.

Fig. 6
Fig. 6

Particle trajectories with different flow velocity and power of the illuminating light. By varying the flow velocity or light power, the resolution of cross-type optical chromatography can be controlled.

Fig. 7
Fig. 7

Comparison between the analytic solutions and detailed numerical calculations. The analytic solutions agree well with numerical calculations.

Fig. 8
Fig. 8

Particle beam generation system. As particles pass through the side flows, particles are focused at the center axis with a certain particle beam width.

Fig. 9
Fig. 9

Particle trajectories in the particle beam generation system. The calculation geometry and flow condition are as follows: D 1 = 1   mm , D 2 = 0.5   mm , U 1 = 10 μm / s , U 2 = 40 μm / s , and U 3 = 50 μm / s .

Fig. 10
Fig. 10

Particle trajectories in the combined cross-type optical chromatography and particle beam generation system. n 1 / n 0 is 1.2 (PSL suspended in water).

Equations (56)

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

F s = n 0 2 c 0 2 π 0 π / 2 I ( ρ , z ) [ 1 + R cos 2 θ 1 T 2 × cos 2 ( θ 1 θ 2 ) + R cos 2 θ 1 1 + R 2 + 2 R cos 2 θ 2 ] r p 2 sin 2 θ 1 d θ 1 d φ ,
F g = n 0 2 c 0 2 π 0 π / 2 I ( ρ , z ) [ R sin 2 θ 1 T 2 × sin 2 ( θ 1 θ 2 ) + R sin 2 θ 1 1 + R 2 + 2 R cos 2 θ 2 ] × r p 2 sin 2 θ 1   cos   φ d θ 1 d φ ,
I ( ρ , z )
n 0
r p
θ 1
θ 2
m p d 2 r d t 2 + 6 π μ r p ( U d r d t ) = F ,
m p
m p d 2 z d t 2 + 6 π μ r p d z d t = F s ,
m p d 2 y d t 2 + 6 π μ r p ( U d y d t ) = F g ,
m p d 2 z d t 2 + 6 π μ r p d z d t = F * , 0 t t 1 ,
m p d 2 z d t 2 + 6 π μ r p d z d t = 0 , t 1 < t ,
y = U t ,
F *
t 1
2 ω 0 / U
v z ( t = 0 ) = 0 , z ( t = 0 ) = 0 ,
z = F * τ m p [ t 1 τ e t / τ ( 1 e t 1 / τ ) ] ,
m p / 6 π μ r p
z r = lim t z = F * τ m t 1 = F * τ m 2 ω 0 U .
F *
F * = 1 2 ω 0 ω 0 ω 0 F s d y .
F s = n 0 2 c 0 2 π 0 π / 2 2 P π ω 0 2 exp ( 2 ρ 2 ω 0     2 ) Q ( θ ) r p 2 sin 2 θ d θ d φ ,
Q ( θ )
Q ( θ ) = 1 + R cos 2 θ 1 T 2 cos 2 ( θ 1 θ 2 ) + R cos 2 θ 1 1 + R 2 + 2 R cos 2 θ 2 ,
ρ = y 2 + r p     2 sin 2 θ 2 y r p sin θ cos φ .
r p / ω 1
F s = 2 n 0 P c ( r p ω 0 ) 2 Q * exp ( 2 y 2 ω 0     2 ) ,
Q *
Q * = 0 π / 2 Q ( θ ) sin 2 θ d θ .
F * = n 0 P c ( r p ω 0 ) 2 Q * π 2   erf ( 2 ) .
z r = n 0 P 3 π μ U c r p ω 0 Q * π 2   erf ( 2 ) .
P = 500   mW , ω 0 = 15   μm , λ = 488   nm , and
n 0 = 1.33 .
1   μm
10   μm
r p / ω
n 1 = 1.59
n 1 = 1.49
n 1 = 1.43
1   to   10   μm
300   μm
60   μm
10 8
10 6
1   μm
10   μm
F d
F r
D 1 = 1   mm
D 2 = 0.5   mm
U 1 = 10 μm / s
U 2 = 40 μm / s
U 3 = 50 μm / s
n 1 / n 0

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