Abstract

At large NAs a micro-Fresnel zone plate produces a focal spot that is more elliptical than that produced by an objective lens with the same NA. Using this anisotropy we demonstrate a method for modulating the spring constant of an optical trap by rotating the linear input polarization. The focal spot ellipticity is enhanced by the apodization factor of the zone plate and its extremely high NA. By measuring the positions of trapped particles we obtain two-dimensional histograms of particle position. These indicate that the trap spring constant is 2.75 times larger perpendicular to the incident polarization than along it. The elliptical focal spot distribution can be rotated by rotating the incident polarization, allowing the spring constant along a given direction to be modulated.

© 2008 Optical Society of America

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References

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2008 (1)

E. Schonbrun, C. Rinzler, and K. B. Crozier, Appl. Phys. Lett. 92, 071112 (2008).
[CrossRef]

2007 (1)

2006 (1)

2005 (1)

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

2004 (2)

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

N. Davidson and N. Bokor, Opt. Lett. 29, 1318 (2004).
[CrossRef] [PubMed]

1998 (1)

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1943 (1998).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

1986 (1)

1979 (1)

J. E. Harvey, Am. J. Phys. 47, 974 (1979).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Allen, L.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1943 (1998).
[CrossRef]

Ashkin, A.

Bjorkholm, J. E.

Block, S. M.

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

Bokor, N.

Brevik, I.

Burns, M. W.

Chu, S.

Constable, A.

Crozier, K. B.

E. Schonbrun, C. Rinzler, and K. B. Crozier, Appl. Phys. Lett. 92, 071112 (2008).
[CrossRef]

Davidson, N.

Dholakia, K.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1943 (1998).
[CrossRef]

Dziezic, J. M.

Fournier, J.

Gussgard, R.

Halvorsen, K.

Harvey, J. E.

J. E. Harvey, Am. J. Phys. 47, 974 (1979).
[CrossRef]

Kim, J.

Lindmo, T.

McGloin, D.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1943 (1998).
[CrossRef]

Merenda, F.

Mervis, J.

Neuman, K. C.

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

Padgett, M. J.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1943 (1998).
[CrossRef]

Prentiss, M.

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Rinzler, C.

E. Schonbrun, C. Rinzler, and K. B. Crozier, Appl. Phys. Lett. 92, 071112 (2008).
[CrossRef]

Rohner, J.

Rohrbach, A.

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

Salathe, R.

Schonbrun, E.

E. Schonbrun, C. Rinzler, and K. B. Crozier, Appl. Phys. Lett. 92, 071112 (2008).
[CrossRef]

Simpson, N. B.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1943 (1998).
[CrossRef]

Sonek, G. J.

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Wong, W. P.

Wright, W. H.

Zarinetchi, F.

Am. J. Phys. (1)

J. E. Harvey, Am. J. Phys. 47, 974 (1979).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

E. Schonbrun, C. Rinzler, and K. B. Crozier, Appl. Phys. Lett. 92, 071112 (2008).
[CrossRef]

J. Mod. Opt. (1)

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1943 (1998).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Rev. Sci. Instrum. (1)

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

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Figures (5)

Fig. 1
Fig. 1

Fresnel zone plate schematic and focal spot size. (a) Illustration of zone plate illumination and maximum focusing angle. (b) FWHM of a zone plate in perpendicular (lower curve) and parallel (upper curve) cross sections through the focus. At small NAs, the focus is circular, and then becomes increasingly elliptical at larger NAs. Inset, expanded plot for NA ranging from 0.8 to 1.0.

Fig. 2
Fig. 2

Field distributions of the zone plate focal spot. (a)–(c) show the magnitude of the y, z, and total electric field distributions, respectively. The incident field is polarized in y and propagates in z.

Fig. 3
Fig. 3

Fabricated zone plate and the zone plate optical tweezer. (a) Scanning electron micrograph of the gold on glass zone plate. (b) Microscope image of a 1.1 μ m latex sphere trapped 2.9 μ m ( = 4 λ 0 n water ) above the substrate.

Fig. 4
Fig. 4

Histograms showing positions of trapped particle at 1000 instants in time. Particle positions are plotted over a 33 s duration at 30 Hz to map out the trapping potential of the elliptical focus for a laser power of 40 mW . Each position is convolved with a Gaussian half-width ( 2.5 nm half-width) representing measurement uncertainty. The orientation of the incident linear polarization is changed by rotating a half-wave plate.

Fig. 5
Fig. 5

Polarization modulation of the spring constant. The black and gray data points represent the motion blur corrected spring constants k x x and k y y , respectively, where the polarization angle is measured with respect to y. The solid curves show a least-squares fit obtained with the rotation matrix model.

Equations (1)

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[ F x F y ] = [ k x x k x y k y x k y y ] [ x y ] = [ cos θ sin θ sin θ cos θ ] [ k perp 0 0 k par ] [ cos θ sin θ sin θ cos θ ] [ x y ] ,

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