Abstract

It is well known that a circularly polarized Gaussian beam carries spin angular momentum, but not orbital angular momentum. This paper demonstrates that focusing a beam carrying spin angular momentum can induce an orbital angular momentum which we used to drive the orbital motion of a micron-sized metal particle that is trapped off the beam axis. The direction of the orbital motion is controlled by the handedness of the circular polarization. The orbiting dynamics of the trapped particle, which acted as an optical micro-detector, were quantitatively measured and found to be in excellent agreement with the theoretical predictions.

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References

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  1. R. E. Beth, “Mechanical Detection and Measurement of the Angular Momentum of Light,” Phys. Rev. 50(2), 115–125 (1936).
    [CrossRef]
  2. A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
    [CrossRef] [PubMed]
  3. T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused Gaussian beam,” J. Opt. A, Pure Appl. Opt. 10(11), 115005 (2008).
    [CrossRef]
  4. Q. Zhan, “Properties of circularly polarized vortex beams,” Opt. Lett. 31(7), 867–869 (2006).
    [CrossRef] [PubMed]
  5. Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital Angular Momentum Conversion in a Strongly Focused Optical Beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
    [CrossRef] [PubMed]
  6. V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the Transfer of the Local Angular Momentum Density of a Multiringed Light Beam to an Optically Trapped Particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
    [CrossRef] [PubMed]
  7. H. Adachi, S. Akahoshi, and K. Miyakawa, “Orbital motion of spherical microparticles trapped in diffraction patterns of circularly polarized light,” Phys. Rev. A 75(6), 063409 (2007).
    [CrossRef]
  8. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
    [CrossRef] [PubMed]
  9. S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, “Influence of geometric shape of optically trapped particles on the optical rotation induced by vortex beams,” J. Appl. Phys. 100(4), 043105 (2006).
    [CrossRef]
  10. A. T. O’Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185(1-3), 139–143 (2000).
    [CrossRef]
  11. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
    [CrossRef]
  12. A. Boivin and E. Wolf, “Electromagnetic field in the neighborhood of the focus of a coherent beam,” Phys. Rev. 138(6B), B1561–B1565 (1965).
    [CrossRef]

2008 (1)

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused Gaussian beam,” J. Opt. A, Pure Appl. Opt. 10(11), 115005 (2008).
[CrossRef]

2007 (2)

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital Angular Momentum Conversion in a Strongly Focused Optical Beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[CrossRef] [PubMed]

H. Adachi, S. Akahoshi, and K. Miyakawa, “Orbital motion of spherical microparticles trapped in diffraction patterns of circularly polarized light,” Phys. Rev. A 75(6), 063409 (2007).
[CrossRef]

2006 (2)

Q. Zhan, “Properties of circularly polarized vortex beams,” Opt. Lett. 31(7), 867–869 (2006).
[CrossRef] [PubMed]

S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, “Influence of geometric shape of optically trapped particles on the optical rotation induced by vortex beams,” J. Appl. Phys. 100(4), 043105 (2006).
[CrossRef]

2003 (1)

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the Transfer of the Local Angular Momentum Density of a Multiringed Light Beam to an Optically Trapped Particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[CrossRef] [PubMed]

2002 (1)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[CrossRef] [PubMed]

2000 (1)

A. T. O’Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185(1-3), 139–143 (2000).
[CrossRef]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef] [PubMed]

1965 (1)

A. Boivin and E. Wolf, “Electromagnetic field in the neighborhood of the focus of a coherent beam,” Phys. Rev. 138(6B), B1561–B1565 (1965).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

1936 (1)

R. E. Beth, “Mechanical Detection and Measurement of the Angular Momentum of Light,” Phys. Rev. 50(2), 115–125 (1936).
[CrossRef]

Adachi, H.

H. Adachi, S. Akahoshi, and K. Miyakawa, “Orbital motion of spherical microparticles trapped in diffraction patterns of circularly polarized light,” Phys. Rev. A 75(6), 063409 (2007).
[CrossRef]

Akahoshi, S.

H. Adachi, S. Akahoshi, and K. Miyakawa, “Orbital motion of spherical microparticles trapped in diffraction patterns of circularly polarized light,” Phys. Rev. A 75(6), 063409 (2007).
[CrossRef]

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[CrossRef] [PubMed]

Beth, R. E.

R. E. Beth, “Mechanical Detection and Measurement of the Angular Momentum of Light,” Phys. Rev. 50(2), 115–125 (1936).
[CrossRef]

Boivin, A.

A. Boivin and E. Wolf, “Electromagnetic field in the neighborhood of the focus of a coherent beam,” Phys. Rev. 138(6B), B1561–B1565 (1965).
[CrossRef]

Chiu, D. T.

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital Angular Momentum Conversion in a Strongly Focused Optical Beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[CrossRef] [PubMed]

Dholakia, K.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the Transfer of the Local Angular Momentum Density of a Multiringed Light Beam to an Optically Trapped Particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[CrossRef] [PubMed]

Dultz, W.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the Transfer of the Local Angular Momentum Density of a Multiringed Light Beam to an Optically Trapped Particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[CrossRef] [PubMed]

Edgar, J. S.

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital Angular Momentum Conversion in a Strongly Focused Optical Beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[CrossRef] [PubMed]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef] [PubMed]

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the Transfer of the Local Angular Momentum Density of a Multiringed Light Beam to an Optically Trapped Particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[CrossRef] [PubMed]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused Gaussian beam,” J. Opt. A, Pure Appl. Opt. 10(11), 115005 (2008).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef] [PubMed]

Jeffries, G. D.

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital Angular Momentum Conversion in a Strongly Focused Optical Beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[CrossRef] [PubMed]

Lin, J.

S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, “Influence of geometric shape of optically trapped particles on the optical rotation induced by vortex beams,” J. Appl. Phys. 100(4), 043105 (2006).
[CrossRef]

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[CrossRef] [PubMed]

McGloin, D.

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital Angular Momentum Conversion in a Strongly Focused Optical Beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the Transfer of the Local Angular Momentum Density of a Multiringed Light Beam to an Optically Trapped Particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[CrossRef] [PubMed]

Miyakawa, K.

H. Adachi, S. Akahoshi, and K. Miyakawa, “Orbital motion of spherical microparticles trapped in diffraction patterns of circularly polarized light,” Phys. Rev. A 75(6), 063409 (2007).
[CrossRef]

Nieminen, T. A.

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused Gaussian beam,” J. Opt. A, Pure Appl. Opt. 10(11), 115005 (2008).
[CrossRef]

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[CrossRef] [PubMed]

A. T. O’Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185(1-3), 139–143 (2000).
[CrossRef]

Padgett, M. J.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the Transfer of the Local Angular Momentum Density of a Multiringed Light Beam to an Optically Trapped Particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[CrossRef] [PubMed]

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[CrossRef] [PubMed]

A. T. O’Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185(1-3), 139–143 (2000).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Rubinsztein-Dunlop, H.

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused Gaussian beam,” J. Opt. A, Pure Appl. Opt. 10(11), 115005 (2008).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef] [PubMed]

Schmitzer, H.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the Transfer of the Local Angular Momentum Density of a Multiringed Light Beam to an Optically Trapped Particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[CrossRef] [PubMed]

Stilgoe, A. B.

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused Gaussian beam,” J. Opt. A, Pure Appl. Opt. 10(11), 115005 (2008).
[CrossRef]

Sun, Y. Y.

S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, “Influence of geometric shape of optically trapped particles on the optical rotation induced by vortex beams,” J. Appl. Phys. 100(4), 043105 (2006).
[CrossRef]

Tao, S. H.

S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, “Influence of geometric shape of optically trapped particles on the optical rotation induced by vortex beams,” J. Appl. Phys. 100(4), 043105 (2006).
[CrossRef]

Wolf, E.

A. Boivin and E. Wolf, “Electromagnetic field in the neighborhood of the focus of a coherent beam,” Phys. Rev. 138(6B), B1561–B1565 (1965).
[CrossRef]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Yuan, X.-C.

S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, “Influence of geometric shape of optically trapped particles on the optical rotation induced by vortex beams,” J. Appl. Phys. 100(4), 043105 (2006).
[CrossRef]

Zhan, Q.

Zhao, Y.

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital Angular Momentum Conversion in a Strongly Focused Optical Beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, “Influence of geometric shape of optically trapped particles on the optical rotation induced by vortex beams,” J. Appl. Phys. 100(4), 043105 (2006).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused Gaussian beam,” J. Opt. A, Pure Appl. Opt. 10(11), 115005 (2008).
[CrossRef]

Opt. Commun. (1)

A. T. O’Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185(1-3), 139–143 (2000).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (2)

R. E. Beth, “Mechanical Detection and Measurement of the Angular Momentum of Light,” Phys. Rev. 50(2), 115–125 (1936).
[CrossRef]

A. Boivin and E. Wolf, “Electromagnetic field in the neighborhood of the focus of a coherent beam,” Phys. Rev. 138(6B), B1561–B1565 (1965).
[CrossRef]

Phys. Rev. A (1)

H. Adachi, S. Akahoshi, and K. Miyakawa, “Orbital motion of spherical microparticles trapped in diffraction patterns of circularly polarized light,” Phys. Rev. A 75(6), 063409 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef] [PubMed]

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[CrossRef] [PubMed]

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital Angular Momentum Conversion in a Strongly Focused Optical Beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the Transfer of the Local Angular Momentum Density of a Multiringed Light Beam to an Optically Trapped Particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Successive frames of a video recording that show the orbital motion of a ~3µm spherical gold particle three-dimensionally confined by a focused Gaussian beam with right (right column) and left (left column) circular polarization. The laser power measured after the objective for both circular polarizations is 19mW. The scale bar represents 5µm, and the circular arrow denotes the orbital rotational direction.

Fig. 2
Fig. 2

(color online). Trajectories of the trapped gold particle as a function of time in the x (a) and y (b) directions. (c) The trajectories of the particle by overlaying 60 seconds of a video recording. Here, red circles and blue squares show the trajectories of the rotating particle driven by right () and left () circular polarization respectively. RCP: right circular polarization; LCP: left circular polarization. The positions are determined as the center of mass of the trapped particle in each frame using custom particle tracking software.

Fig. 3
Fig. 3

(color online). Orbital rotational radius (a) and frequency (b) versus trapping laser power driven by right (○) and left (□) circular polarization, respectively. The dash lines in (a) (and “+” in (c)) and (b) (and “×” in (c)) is the average value of clockwise and counter-clockwise orbital motions, which is combined in (c) to show that the orbital rotational radius increased and the frequency decreased as the laser power is increased.

Tables (1)

Tables Icon

Table 1 The velocity of a trapped particle rotating around the beam axis as a function of laser powers

Equations (1)

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N A e f f e c t i v e = N A o b j n a i r n w a t e r = 0.9 / 1.33 = 0.68.

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