Abstract

We report what is to our knowledge the first experimental demonstration and theoretical analysis of an optical laser trap that uses a pair of mutually phase-conjugate beams. A primary trapping beam derived from an argon laser (514.5 nm) together with its counterpropagating phase-conjugate beam creates a self-aligned dual-beam laser trap that provides stable three-dimensional confinement for micrometer-sized dielectric particles. The transverse trapping efficiency, experimentally measured for low-numerical-aperture (N.A. 0.40–0.85) objective lenses, is found to be comparable with that produced by a single-beam gradient force trap. A theoretical analysis, which compares the performance of the self-aligned dual-beam trap against that of single-beam gradient force and conventional counterpropagating dual-beam laser traps, shows that phase-conjugate trapping provides a slight improvement in axial trapping efficiency over the other trapping geometries. The advantages of combining laser trapping with photorefractive optical phase conjugation for simultaneous sample micromanipulation and optical image processing are discussed.

© 1997 Optical Society of America

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References

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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, 288–290 (1986).
    [CrossRef] [PubMed]
  3. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
    [CrossRef] [PubMed]
  4. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biomol. Struct. 23, 247–285 (1994).
    [PubMed]
  5. A. E. Chiou, J. Hong, G. J. Sonek, Y. Liu, and M. W. Berns, “Image processing and trapping of microscopic objects using a phase conjugate Michelson interferometer,” in Biomedical Fiber Optic Instrumentation, J. A. Harrington, D. M. Harris, A. Katair, and F. P. Milanovich, eds., Proc. SPIE 2131, 406–416 (1994).
    [CrossRef]
  6. R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
  7. P. Gunter and J.-P. Huignard, in Photorefractive Materials and Their Applications I: Fundamental Phenomena, P. Gunter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 7–23.
  8. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  9. R. S. Cudney, R. M. Pierce, and J. Feinberg, “The transient detection microscope,” Nature (London) 332, 424–426 (1988).
    [CrossRef]
  10. A. E. Chiou, P. Yeh, and M. Khoshnevisan, “Nonlinear optical image subtraction for potential industrial applications,” Opt. Eng. 27, 385–392 (1988).
    [CrossRef]
  11. J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7, 486–488 (1982).
    [CrossRef] [PubMed]
  12. A. Chiou, T. Y. Chang, and M. Khoshnevisan, “High-speed photorefractive phase conjugator with large dynamic range and wide field of view,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 40.
  13. P. Yeh and A. Chiou, in Real-Time Optical Information Processing, B. Javidi and J. L. Horner, eds. (Academic, Boston, Mass., 1994).
  14. W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
    [CrossRef] [PubMed]
  15. 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]
  16. A. Ashkin and J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by alternating light beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
    [CrossRef] [PubMed]

1994 (2)

A. E. Chiou, J. Hong, G. J. Sonek, Y. Liu, and M. W. Berns, “Image processing and trapping of microscopic objects using a phase conjugate Michelson interferometer,” in Biomedical Fiber Optic Instrumentation, J. A. Harrington, D. M. Harris, A. Katair, and F. P. Milanovich, eds., Proc. SPIE 2131, 406–416 (1994).
[CrossRef]

W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

1992 (1)

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

1988 (2)

R. S. Cudney, R. M. Pierce, and J. Feinberg, “The transient detection microscope,” Nature (London) 332, 424–426 (1988).
[CrossRef]

A. E. Chiou, P. Yeh, and M. Khoshnevisan, “Nonlinear optical image subtraction for potential industrial applications,” Opt. Eng. 27, 385–392 (1988).
[CrossRef]

1987 (1)

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

1986 (1)

1985 (1)

A. Ashkin and J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by alternating light beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
[CrossRef] [PubMed]

1982 (1)

1970 (1)

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

Ashkin, A.

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

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

A. Ashkin and J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by alternating light beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
[CrossRef] [PubMed]

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

Berns, M. W.

A. E. Chiou, J. Hong, G. J. Sonek, Y. Liu, and M. W. Berns, “Image processing and trapping of microscopic objects using a phase conjugate Michelson interferometer,” in Biomedical Fiber Optic Instrumentation, J. A. Harrington, D. M. Harris, A. Katair, and F. P. Milanovich, eds., Proc. SPIE 2131, 406–416 (1994).
[CrossRef]

W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

Bjorkholm, J. E.

Chiou, A. E.

A. E. Chiou, J. Hong, G. J. Sonek, Y. Liu, and M. W. Berns, “Image processing and trapping of microscopic objects using a phase conjugate Michelson interferometer,” in Biomedical Fiber Optic Instrumentation, J. A. Harrington, D. M. Harris, A. Katair, and F. P. Milanovich, eds., Proc. SPIE 2131, 406–416 (1994).
[CrossRef]

A. E. Chiou, P. Yeh, and M. Khoshnevisan, “Nonlinear optical image subtraction for potential industrial applications,” Opt. Eng. 27, 385–392 (1988).
[CrossRef]

Chu, S.

Cudney, R. S.

R. S. Cudney, R. M. Pierce, and J. Feinberg, “The transient detection microscope,” Nature (London) 332, 424–426 (1988).
[CrossRef]

Dziedzic, J. M.

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

A. Ashkin and J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by alternating light beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
[CrossRef] [PubMed]

Feinberg, J.

R. S. Cudney, R. M. Pierce, and J. Feinberg, “The transient detection microscope,” Nature (London) 332, 424–426 (1988).
[CrossRef]

J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7, 486–488 (1982).
[CrossRef] [PubMed]

Hong, J.

A. E. Chiou, J. Hong, G. J. Sonek, Y. Liu, and M. W. Berns, “Image processing and trapping of microscopic objects using a phase conjugate Michelson interferometer,” in Biomedical Fiber Optic Instrumentation, J. A. Harrington, D. M. Harris, A. Katair, and F. P. Milanovich, eds., Proc. SPIE 2131, 406–416 (1994).
[CrossRef]

Khoshnevisan, M.

A. E. Chiou, P. Yeh, and M. Khoshnevisan, “Nonlinear optical image subtraction for potential industrial applications,” Opt. Eng. 27, 385–392 (1988).
[CrossRef]

Liu, Y.

A. E. Chiou, J. Hong, G. J. Sonek, Y. Liu, and M. W. Berns, “Image processing and trapping of microscopic objects using a phase conjugate Michelson interferometer,” in Biomedical Fiber Optic Instrumentation, J. A. Harrington, D. M. Harris, A. Katair, and F. P. Milanovich, eds., Proc. SPIE 2131, 406–416 (1994).
[CrossRef]

Pierce, R. M.

R. S. Cudney, R. M. Pierce, and J. Feinberg, “The transient detection microscope,” Nature (London) 332, 424–426 (1988).
[CrossRef]

Sonek, G. J.

A. E. Chiou, J. Hong, G. J. Sonek, Y. Liu, and M. W. Berns, “Image processing and trapping of microscopic objects using a phase conjugate Michelson interferometer,” in Biomedical Fiber Optic Instrumentation, J. A. Harrington, D. M. Harris, A. Katair, and F. P. Milanovich, eds., Proc. SPIE 2131, 406–416 (1994).
[CrossRef]

W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

Wright, W. H.

Yeh, P.

A. E. Chiou, P. Yeh, and M. Khoshnevisan, “Nonlinear optical image subtraction for potential industrial applications,” Opt. Eng. 27, 385–392 (1988).
[CrossRef]

Appl. Opt. (1)

Biophys. J. (1)

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

Nature (London) (1)

R. S. Cudney, R. M. Pierce, and J. Feinberg, “The transient detection microscope,” Nature (London) 332, 424–426 (1988).
[CrossRef]

Opt. Eng. (1)

A. E. Chiou, P. Yeh, and M. Khoshnevisan, “Nonlinear optical image subtraction for potential industrial applications,” Opt. Eng. 27, 385–392 (1988).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (2)

A. Ashkin and J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by alternating light beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
[CrossRef] [PubMed]

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

Proc. SPIE (1)

A. E. Chiou, J. Hong, G. J. Sonek, Y. Liu, and M. W. Berns, “Image processing and trapping of microscopic objects using a phase conjugate Michelson interferometer,” in Biomedical Fiber Optic Instrumentation, J. A. Harrington, D. M. Harris, A. Katair, and F. P. Milanovich, eds., Proc. SPIE 2131, 406–416 (1994).
[CrossRef]

Science (1)

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

Other (6)

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biomol. Struct. 23, 247–285 (1994).
[PubMed]

R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).

P. Gunter and J.-P. Huignard, in Photorefractive Materials and Their Applications I: Fundamental Phenomena, P. Gunter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 7–23.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

A. Chiou, T. Y. Chang, and M. Khoshnevisan, “High-speed photorefractive phase conjugator with large dynamic range and wide field of view,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 40.

P. Yeh and A. Chiou, in Real-Time Optical Information Processing, B. Javidi and J. L. Horner, eds. (Academic, Boston, Mass., 1994).

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Figures (8)

Fig. 1
Fig. 1

Schematic showing three different optical trapping configurations: (a) counterpropagating dual-beam trap, (b) single-beam gradient force trap, and (c) mutually phase-conjugate dual-beam trap that uses a phase-conjugate mirror (PCM).

Fig. 2
Fig. 2

Experimental system for the demonstration of optical laser trapping microscopy combined with photorefractive phase conjugation. A BaTiO3 crystal is used to generate a counter-propagating phase-conjugate beam that is combined with a primary beam to form a self-aligned dual-beam trap. M's, mirrors; BS's beam splitters.

Fig. 3
Fig. 3

Transverse escape velocity as a function of the relative axial trapping position (sz) for a 2.8-µm-diameter polystyrene bead confined by a single beam gradient force trap (filled circles) or a self-aligned dual-beam phase-conjugate trap (filled squares) measured with a 40×(0.65-N.A.) microscope objective.

Fig. 4
Fig. 4

Two different dual-beam trapping geometries: (a) a phase-conjugate dual-beam trap and (b) a confocal dual-beam trap. The latter is a special case of the counterpropagating dual-beam trap in which two beams are focused to the same point f in the absence of the particle.

Fig. 5
Fig. 5

Geometries for calculating the force that is due to (a) a single ray aI of power P and (b) the phase-conjugate ray aϕ of power P.

Fig. 6
Fig. 6

Comparison of (a) scattering efficiency (Qs) and (b) gradient efficiency (Qg) for a single-beam gradient force trap, a phase-conjugate dual-beam trap, and a confocal dual-beam trap. The maximum convergence angle is taken to be ϕmax=20°. Refractive indices of n1=1.33 (water) and n2=1.59 (latex microsphere), and a relative refractive index n=1.2 have been used. The microsphere radius is taken to be 1.

Fig. 7
Fig. 7

Comparison of the total trapping efficiency (Qt) for the three trap configurations when the relative refractive index is n=1.2 and (a) ϕmax=20°, (b) ϕmax=60°.

Fig. 8
Fig. 8

(a) Comparison of trapping efficiency (Qt) for single-beam, phase-conjugate beam, and confocal dual-beam traps for different values of beam power ratio γ=P/P with ϕmax=20° and n=1.2. (b) Comparison of Qt values for a counterpropagating dual-beam trap for different separations d between the foci of the two beams (d>0 in far-field region) with ϕmax =20° and n=1.2.

Tables (1)

Tables Icon

Table 1 Summary of Optical Parameters and Transverse Trapping Efficiencies for Single-Beam and Phase-Conjugate Dual-Beam Laser Traps

Equations (14)

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FIζ=FIs=n1Pc1+R cos 2θ-n=0 T2Rn×cos(α+nβ)=n1Pc1+R cos 2θ-T2cos(2θ-2r)+R cos 2θ1+R2+2R cos 2r,
FIη=FIg=n1Pc[0+R sin 2θ-n=0 T2Rn×sin(α+nβ)]=n1PcR sin 2θ-T2[sin(2θ-2r)+R sin 2θ]1+R2+2R cos 2r,
QIζ=QIs=1+R cos 2θ-T2[cos(2θ-2r)+R cos 2θ]1+R2+2R cos 2r,
QIη=QIg=R sin 2θ-T2[sin(2θ-2r)+R sin 2θ]1+R2+2R cos 2r.
FTϕζ=FTϕs=FIs-γ(FIs cos α+FIg sin α),
FTϕη=FTϕg=FIg-γ(FIs sin α-FIg cos α),
QTϕs=QIs-γ(QIs cos α+QIg sin α)1+γ,
QTϕg=QIg-γ(QIs sin α-QIg cos α)1+γ,
Fcs(sz)=FIs(-sz)=FIs(sz),
Fcg(sz)=FIg(-sz)=-FIg(sz).
FTcs=(1-γ)FIs,
FTcg=(1+γ)FIg.
QTcs=1-γ1+γQIs,
QTcg=QIg,

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