Abstract

An experiment is described, where an ultra-weak force of 25 femtoNewtons (fN = 10-15 N) displaces a 0.53μm latex bead captured in a soft optical trap. The displacement is measured by exploiting the phase anomaly of the trapping beam, resulting in a small phase shift of the scattered light. The 25fN force stems from the radiation pressure of a nearly collimated second laser beam, which is switched by an accousto-optical modulator. To the best of my knowledge, this is the smallest switchable force which has ever been directly measured.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. R. A. Millikan, "A new modification of the cloud method of. determining the elementary electric charge and the most probable value of that charge," Philosophical Magazine 19, 209-228 (1910).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. G. M. Wang, E. M. Sevick, E. Mittag, D. J. Searles, and D. J. Evans, "Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales," Phys. Rev. Lett. 89, - (2002).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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Ann. Biomed. Eng.

J. Y. Shao, "Finite element analysis of imposing femtonewton forces with micropipette aspiration," Ann. Biomed. Eng. 30, 546-554 (2002).
[CrossRef] [PubMed]

Appl. Opt.

J. Appl. Phys.

A. Rohrbach, and E. H. K. Stelzer, "Three-dimensional position detection of optically trapped dielectric particles," J. Appl. Phys. 91, 5474-5488 (2002b).
[CrossRef]

J. Phys.: Condens. Matter

D. Rudhardt, C. Bechinger, and P. Leiderer, "Repulsive depletion interactions in colloid–polymer mixtures," J. Phys.: Condens. Matter 11, 10073–10078 (1999).
[CrossRef]

Journal of Applied Physics

Y. Matsuo, H. Takasaki, J. Hotta, and K. Sasaki, "Absorption analysis of a single microparticle by optical force measurement," Journal of Applied Physics 89, 5438-5441 (2001).
[CrossRef]

Microscopy Research and Techniques

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, "Three-dimensional position tracking for optical tweezers by forward scattered light," Microscopy Research and Techniques 44, 378-386 (1999).
[CrossRef]

Opt. Lett.

Philosophical Magazine

R. A. Millikan, "A new modification of the cloud method of. determining the elementary electric charge and the most probable value of that charge," Philosophical Magazine 19, 209-228 (1910).

Phys. Rev. Lett.

J. C. Meiners, and S. R. Quake, "Femtonewton force spectroscopy of single extended DNA molecules," Phys. Rev. Lett. 84, 5014-5017 (2000).
[CrossRef] [PubMed]

G. M. Wang, E. M. Sevick, E. Mittag, D. J. Searles, and D. J. Evans, "Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales," Phys. Rev. Lett. 89, - (2002).
[CrossRef] [PubMed]

A. Rohrbach, "Stiffness of optical traps: Quantitative agreement between experiment and electromagnetic theory," Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

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

Physica

H. A. Kramers, "Brownian motion in a field of force and the diffusion model of chemical reactions," Physica VII, 284-304 (1940).
[CrossRef]

Rev. Sci. Instr.

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

Rev. Sci. Instrum.

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, "Trapping and tracking a local probe with a Photonic Force Microscope," Rev. Sci. Instrum. 75, 2197-2210 (2004b).
[CrossRef]

Other

C. Bohren, and D. R. Huffman, Absorption and scattering of light by small particles (Wiley Science Paperback, New York, 1998).
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, Inc., Leiden, 1957).

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup. A collimated IR beam (1064nm) is focused by NA = 1.2 water immersion lens. A 535nm latex sphere is trapped weakly and scatters the incident IR light coherently. The detection lens dipping into the fluid droplet collects both the scattered and unscattered light, which have a phase difference of Δϕ to each other. A quadrant photo diode (QPD) records the interference pattern, which changes with Δϕ. The fluid droplet consists of a fluorescein solution. A 488nm laser is switched on, resulting in an axial displacement of the trapped bead by Δz and an phase shift Δϕ(Δz) of the IR light due to radiation pressure. The fluorescence light emitted along the 488nm beam profile is recorded by the imaging system.

Fig. 2.
Fig. 2.

Axial bead displacements and histograms. (a) The 535nm latex bead fluctuates inside the weak optical trap. By switching on an additional radiation pressure after about 5 sec, the mean position of the bead changes by 70nm. (b) The histograms illustrate the ratio between the mean displacements due to thermal noise and due to the ultra-weak external force. The widths of the histograms σsz are nearly the same in both cases. (c) The radiation force can also be obtained from the difference in the corresponding potentials.

Fig. 3.
Fig. 3.

The Gaussian profile of the weakly focused laser beam is visible due to fluorescence emission in the fluorescein solution (left image). The intensity profile reveals a beam waist of 2s = 14μm at a 1/e decay. Right: A bead trapped in the center of visible laser beam produces an increase in electric field density behind the bead due to scattering. In this region the fluorescence intensity is increased by 70% as indicated by the profile and the photo. Integration time was 20ms.

Equations (7)

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F rad = I 0 · n / Q pr · ( a 2 π )
S z ( Z ) g z · Z = σ sz · [ γ / ( τ z · k B T ) ] 1 / 2 · Z .
F rad = F trap ( Δz ) = κ z · Δz = κ z · Δ S z / g z = Δ S z / σ sz · ( κ z · k B T ) 1 / 2
Δ S z = S on S off = 1 Δ T on Δ T on S z , on ( t ) dt 1 Δ T off Δ T off S z , off ( t ) dt
S z ( z ) = E i + E s ( z ) 2 dA = ( E i 2 + E s ( z ) 2 + E i E s ( z ) cos ( ϕ i ϕ s ( z ) ) ) dA
P 488 = 0 I ( r ) · 2 πr dr = I 0 2 π 0 exp ( r 2 / s 2 ) · r dr = I 0 · s 2 · π
Q pr = Q abs + Q sca Q sca n 2 k 0 2 a 2 0 π 1 2 ( T 1 ( θ ) 2 + T 2 ( θ ) 2 ) cos θ sin θ

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