Abstract

A simple expression for the magnetic filed of a highly focused radially polarized light is derived and the incorrect results for the time averaged Poynting vector and the trapping stability for a gold particle presented in the paper “Trapping metallic Rayleigh particles with radial polarization” by Zhan (Opt. Express 12, 3377–3382 (2004)) are corrected.

© 2009 Optical Society of America

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References

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  1. K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7(2), 77-87 (2000).
    [CrossRef] [PubMed]
  2. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "The focus of light-theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).
  3. R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91(23), 233901 (2003).
    [CrossRef] [PubMed]
  4. Y. Kozawa and S. Sato, "Sharper focal spot formed by higher-order radially polarized laser beams," J. Opt. Soc. Am. A 24(6), 1793-1798 (2007).
    [CrossRef]
  5. Y. Zhang, and J. Bai, "Improving the recording ability of a near-field optical storage system by higher-order radially polarized beams," Opt. Express 17(5), 3698-3706 (2009).
    [CrossRef] [PubMed]
  6. V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D 32(13), 1455-1461 (1999).
    [CrossRef]
  7. S. C. Tidwell, G. H. Kim, and W. D. Kimura, "Efficient radially polarized laser beam generation with a double interferometer," Appl. Opt. 32(27), 5222-5229 (1993).
    [CrossRef] [PubMed]
  8. Q. Zhan, "Trapping metallic Rayleigh particles with radial polarization," Opt. Express 12(15), 3377-3382 (2004).
    [CrossRef] [PubMed]
  9. B. Richards, and E. Wolf, "Electromagnetic diffraction in optical systes II. Structure of the image field in an aplanatic system," Proc. R. Soc. Lond. A 253(1274), 358-379 (1959).
    [CrossRef]
  10. Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124(5-6), 529-541 (1996).
    [CrossRef]

2009 (1)

2007 (1)

2004 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

2001 (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "The focus of light-theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

2000 (1)

1999 (1)

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D 32(13), 1455-1461 (1999).
[CrossRef]

1996 (1)

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124(5-6), 529-541 (1996).
[CrossRef]

1993 (1)

1959 (1)

B. Richards, and E. Wolf, "Electromagnetic diffraction in optical systes II. Structure of the image field in an aplanatic system," Proc. R. Soc. Lond. A 253(1274), 358-379 (1959).
[CrossRef]

Asakura, T.

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124(5-6), 529-541 (1996).
[CrossRef]

Bai, J.

Brown, T. G.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "The focus of light-theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "The focus of light-theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "The focus of light-theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Harada, Y.

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124(5-6), 529-541 (1996).
[CrossRef]

Kim, G. H.

Kimura, W. D.

Kozawa, Y.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "The focus of light-theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Nesterov, A. V.

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D 32(13), 1455-1461 (1999).
[CrossRef]

Niziev, V. G.

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D 32(13), 1455-1461 (1999).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "The focus of light-theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Richards, B.

B. Richards, and E. Wolf, "Electromagnetic diffraction in optical systes II. Structure of the image field in an aplanatic system," Proc. R. Soc. Lond. A 253(1274), 358-379 (1959).
[CrossRef]

Sato, S.

Tidwell, S. C.

Wolf, E.

B. Richards, and E. Wolf, "Electromagnetic diffraction in optical systes II. Structure of the image field in an aplanatic system," Proc. R. Soc. Lond. A 253(1274), 358-379 (1959).
[CrossRef]

Youngworth, K. S.

Zhan, Q.

Zhang, Y.

Appl. Opt. (1)

Appl. Phys. B (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "The focus of light-theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

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

J. Phys. D (1)

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D 32(13), 1455-1461 (1999).
[CrossRef]

Opt. Commun. (1)

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124(5-6), 529-541 (1996).
[CrossRef]

Opt. Express (3)

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A (1)

B. Richards, and E. Wolf, "Electromagnetic diffraction in optical systes II. Structure of the image field in an aplanatic system," Proc. R. Soc. Lond. A 253(1274), 358-379 (1959).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Ray-tracing model for focusing a radially polarized incoming light

Fig. 2
Fig. 2

The time averaged Poynting vector based on the exact magnetic field near the focal region of a highly focused radial polarized light beam. (a) 2-dimensional distribution in the xz plane; (b) line scan of (a) at the focal plane.

Fig. 3
Fig. 3

Calculated radiation forces on a 19.1 nm (radius) gold particle in the xz plane. (a) Transverse gradient force (Fgrad,x); (b) axial gradient force (Fgrad,z); (c) sum of transverse scattering and absorption forces (Fscat,x + Fabs,x); (d) sum of axial scattering and absorption forces (Fscat,z + Fabs,z). All radiation forces are in unit of pico-Newton (pN).

Equations (10)

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E = i k f 2 π 0 α d θ 0 2 π d ϕ sin θ cos θ A ( θ ) P e ( θ , ϕ ) exp [ i k r sin θ cos ( ϕ φ ) ] exp ( i k z cos θ ) ,
P e = [ cos θ cos ϕ cos θ sin ϕ sin θ ] .
E r ( r , z ) = η 0 α cos θ A ( θ ) sin 2 θ J 1 ( k r sin θ ) exp ( i k z cos θ ) d θ ,
E z ( r , z ) = 2 i η 0 α cos θ A ( θ ) sin 2 θ J 0 ( k r sin θ ) exp ( i k z cos θ ) d θ ,
H = i η n π μ 0 c 0 α d θ 0 2 π d ϕ cos θ sin θ A ( θ ) P m ( θ , ϕ ) exp [ i k r sin θ cos ( ϕ φ ) ] exp ( i k z cos θ ) ,
P m = [ sin ϕ cos ϕ 0 ] .
H ( r , z ) = H ϕ ( r , z ) e ^ ϕ = 2 η n μ 0 c 0 α cos θ A ( θ ) ) sin θ J 1 ( k r sin θ ) exp ( i k z cos θ ) d θ e ^ ϕ .
< S > = Re ( E × H * ) / 2 = Re ( E r H ϕ * ) e ^ z / 2 Re ( E z H ϕ * ) e ^ ρ / 2.
A ( θ ) = { E 0 , sin 1 ( NA 1 ) < θ < sin 1 ( NA / n ) 0 , otherwise
R = ( F grad , z ) max / [ ( F scat , z ) max + ( F abs , z ) max ] .

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