Abstract

We show that the optical trapping of dielectric particles by a single focused beam in front of a weakly reflective surface is considerably affected by interference of the incident and reflected beams, which creates a standing-wave component of the total field. We use the two-photon-excited fluorescence from a trapped dyed probe to detect changes in the distance between the trapped beam focus as the focus approaches the reflective surface. This procedure enables us to determine the relative strengths of the single-beam and the standing-wave trapping forces. We demonstrate that, even for reflection from a glass–water interface, standing-wave trapping dominates, as far as 5 μm from the surface.

© 2001 Optical Society of America

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  1. K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
    [CrossRef] [PubMed]
  2. J. Y. Walz and D. C. Prieve, Langmuir 8, 3073–3082 (1992).
    [CrossRef]
  3. E.-L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, J. Struct. Biol. 119, 202 (1997).
    [CrossRef] [PubMed]
  4. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, Opt. Lett. 11, 288 (1986).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. E.-L. Florin, J. K. H. Hörber, and E. H. K. Stelzer, Appl. Phys. Lett. 69, 446 (1996).
    [CrossRef]
  10. J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
    [CrossRef]
  11. J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
    [CrossRef]

1999 (1)

1998 (2)

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, Opt. Commun. 151, 273 (1998).
[CrossRef]

E. R. Dufresne and D. G. Grier, Rev. Sci. Instrum. 69, 1974 (1998).
[CrossRef]

1997 (2)

E.-L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, J. Struct. Biol. 119, 202 (1997).
[CrossRef] [PubMed]

K. Sasaki, M. Tsukima, and H. Masuhara, Appl. Phys. Lett. 71, 37 (1997).
[CrossRef]

1996 (1)

E.-L. Florin, J. K. H. Hörber, and E. H. K. Stelzer, Appl. Phys. Lett. 69, 446 (1996).
[CrossRef]

1993 (1)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

1992 (1)

J. Y. Walz and D. C. Prieve, Langmuir 8, 3073–3082 (1992).
[CrossRef]

1989 (2)

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

1986 (1)

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

Ashkin, A.

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Chu, S.

Dufresne, E. R.

E. R. Dufresne and D. G. Grier, Rev. Sci. Instrum. 69, 1974 (1998).
[CrossRef]

Dziedzic, J. M.

Florin, E.-L.

E.-L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, J. Struct. Biol. 119, 202 (1997).
[CrossRef] [PubMed]

E.-L. Florin, J. K. H. Hörber, and E. H. K. Stelzer, Appl. Phys. Lett. 69, 446 (1996).
[CrossRef]

Grier, D. G.

E. R. Dufresne and D. G. Grier, Rev. Sci. Instrum. 69, 1974 (1998).
[CrossRef]

Hörber, J. K. H.

E.-L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, J. Struct. Biol. 119, 202 (1997).
[CrossRef] [PubMed]

E.-L. Florin, J. K. H. Hörber, and E. H. K. Stelzer, Appl. Phys. Lett. 69, 446 (1996).
[CrossRef]

Jonáš, A.

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, Opt. Lett. 24, 1448 (1999).
[CrossRef]

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, Opt. Commun. 151, 273 (1998).
[CrossRef]

Liška, M.

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, Opt. Lett. 24, 1448 (1999).
[CrossRef]

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, Opt. Commun. 151, 273 (1998).
[CrossRef]

Masuhara, H.

K. Sasaki, M. Tsukima, and H. Masuhara, Appl. Phys. Lett. 71, 37 (1997).
[CrossRef]

Pralle, A.

E.-L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, J. Struct. Biol. 119, 202 (1997).
[CrossRef] [PubMed]

Prieve, D. C.

J. Y. Walz and D. C. Prieve, Langmuir 8, 3073–3082 (1992).
[CrossRef]

Sasaki, K.

K. Sasaki, M. Tsukima, and H. Masuhara, Appl. Phys. Lett. 71, 37 (1997).
[CrossRef]

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

Schmidt, C. F.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Šrámek, L.

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, Opt. Lett. 24, 1448 (1999).
[CrossRef]

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, Opt. Commun. 151, 273 (1998).
[CrossRef]

Stelzer, E. H. K.

E.-L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, J. Struct. Biol. 119, 202 (1997).
[CrossRef] [PubMed]

E.-L. Florin, J. K. H. Hörber, and E. H. K. Stelzer, Appl. Phys. Lett. 69, 446 (1996).
[CrossRef]

Svoboda, K.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Tsukima, M.

K. Sasaki, M. Tsukima, and H. Masuhara, Appl. Phys. Lett. 71, 37 (1997).
[CrossRef]

Walz, J. Y.

J. Y. Walz and D. C. Prieve, Langmuir 8, 3073–3082 (1992).
[CrossRef]

Zemánek, P.

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, Opt. Lett. 24, 1448 (1999).
[CrossRef]

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, Opt. Commun. 151, 273 (1998).
[CrossRef]

Appl. Phys. Lett. (2)

K. Sasaki, M. Tsukima, and H. Masuhara, Appl. Phys. Lett. 71, 37 (1997).
[CrossRef]

E.-L. Florin, J. K. H. Hörber, and E. H. K. Stelzer, Appl. Phys. Lett. 69, 446 (1996).
[CrossRef]

J. Appl. Phys. (2)

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

J. Struct. Biol. (1)

E.-L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, J. Struct. Biol. 119, 202 (1997).
[CrossRef] [PubMed]

Langmuir (1)

J. Y. Walz and D. C. Prieve, Langmuir 8, 3073–3082 (1992).
[CrossRef]

Nature (1)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Opt. Commun. (1)

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, Opt. Commun. 151, 273 (1998).
[CrossRef]

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

E. R. Dufresne and D. G. Grier, Rev. Sci. Instrum. 69, 1974 (1998).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Experimental setup: PMT, photomultiplier tube; F, filter; DMs, dichroic mirrors; E, expander; SM, scanning mirror; SL, scan lens; TL, tube lens; PA, piezoactuator; O, objective; S, sample chamber; C, condenser; I, illumination. (b) Detail of the sample chamber.

Fig. 2
Fig. 2

Theoretical profiles of the trapping force (thicker solid curves) and the trapping potential (dashed curves) of the SBT modulated by the reflection from a glass–water interface at three distances zfocus of the beam focus from the reflective surface. The trapped probe is located at zpeq (places of zero force and potential minima). The diameter of the circles corresponds to the actual probe size (216  nm) used in simulations and experiments. The other parameters are surface reflectivity, 0.4% (calculated from the refractive indices of glass, 1.51, and water, 1.33); focal spot size, 0.475 μm (estimated from a Gaussian fit to the two-photon fluorescence intensity profile obtained by scanning of a stationary probe fixed to a coverslip across the incident beam); and trapping power, 80  mW. Under these conditions the average contribution of the GSW component to the total intensity is less than 3%. For comparison, thinner solid curves show the pure SBT force profile (i.e., without reflection) for the same parameters.

Fig. 3
Fig. 3

Comparison of experimentally recorded TPS (top) with theoretical simulation (middle) for reflection from a glass–water interface. The simulation parameters are identical to those in Fig.  2 and correspond to experimental conditions. Bottom, calculated distance of the trapped probe from the beam focus. To show clearly the detailed features of signals, we display only a narrow interval of beam-focus-to-slide distances. Arrows indicate the transition between smooth modulation of the probe position and abrupt jumps.

Fig. 4
Fig. 4

Experimentally recorded TPS as a function of the distance of the beam focus from the reflective slide for three slide reflectivities. Initially the probe was brought into contact with the coverslip at the bottom of the sample chamber; then the beam focus was moved toward the reflective slide. Dashed arrows, first appearance of the TPS modulation; solid arrows, transition between smooth modulation and abrupt jumps. The overall slope of the TPS is caused by the spherical aberration that is due to refractive-index mismatch between glass and water.

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