Abstract

We analyze the forces on a small dipolar particle and the electromagnetic momentum density in a configuration consisting in two perpendicular circularly polarized stationary waves. The field distribution shows regions in which the electric and magnetic fields are parallel corresponding to a null Poynting vector. Although the average value of the momentum density, proportional to the Poynting vector, is zero in these regions, there are scattering forces acting on small particles due to light’s spin force. The total scattering force suggests a new definition of the average value of the momentum density for free propagating electromagnetic fields.

© 2012 Optical Society of America

Full Article  |  PDF Article

Corrections

Manuel I. Marqués and Juan José Saénz, "Scattering forces and electromagnetic momentum density in crossed circularly polarized standing waves: erratum," Opt. Lett. 37, 4470-4470 (2012)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-37-21-4470

References

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    [CrossRef]
  2. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, Opt. Lett. 11, 288 (1986).
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    [CrossRef]
  5. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
    [CrossRef]
  6. R. Gómez-Medina, and J. J. Sáenz, Phys. Rev. Lett. 93, 243602 (2004).
    [CrossRef]
  7. K. Dholakia and P. Zemánek, Rev. Mod. Phys. 82, 1767 (2010).
    [CrossRef]
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    [CrossRef]
  9. J. J. Sáenz, Nat. Photonics 5, 514 (2011).
    [CrossRef]
  10. A. Novitsky, C.-W. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, Opt. Express 18, 11428 (2010).
    [CrossRef]
  18. I. Iglesias and J. J. Sáenz, Opt. Commun. 284, 2430 (2011).
    [CrossRef]
  19. I. Iglesias and J. J. Sáenz, Opt. Express 20, 2832 (2012).
    [CrossRef]
  20. Q. Zhan, Opt. Express 20, 6058 (2012).
    [CrossRef]
  21. A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
    [CrossRef]
  22. A. Hemmerich and T. W. Hänsch, Phys. Rev. Lett. 68, 1492 (1992).
    [CrossRef]
  23. S. Albaladejo, M. I. Marqués, F. Scheffold, and J. J. Sáenz, Nano Lett. 9, 3527 (2009).
    [CrossRef]
  24. I. Zapata, S. Albaladejo, J. M. R. Parrondo, J. J. Sáenz, and F. Sols, Phys. Rev. Lett. 103, 130601 (2009).
    [CrossRef]
  25. S. Albaladejo, M. I. Marqués, and J. J. Sáenz, Opt. Express 19, 11471 (2011).
    [CrossRef]

2012 (2)

2011 (8)

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

J. J. Sáenz, Nat. Photonics 5, 514 (2011).
[CrossRef]

A. Novitsky, C.-W. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef]

S. Sukhov and A. Dogariu, Phys. Rev. Lett. 107, 203602 (2011).
[CrossRef]

A. Salandrino and D. N. Christodoulides, Opt. Lett. 36, 3103 (2011).
[CrossRef]

I. Iglesias and J. J. Sáenz, Opt. Commun. 284, 2430 (2011).
[CrossRef]

S. Albaladejo, M. I. Marqués, and J. J. Sáenz, Opt. Express 19, 11471 (2011).
[CrossRef]

2010 (2)

2009 (3)

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef]

S. Albaladejo, M. I. Marqués, F. Scheffold, and J. J. Sáenz, Nano Lett. 9, 3527 (2009).
[CrossRef]

I. Zapata, S. Albaladejo, J. M. R. Parrondo, J. J. Sáenz, and F. Sols, Phys. Rev. Lett. 103, 130601 (2009).
[CrossRef]

2006 (1)

V. Wong and M. Ratner, Phys. Rev. B 73, 075416 (2006).
[CrossRef]

2004 (3)

R. Gómez-Medina, and J. J. Sáenz, Phys. Rev. Lett. 93, 243602 (2004).
[CrossRef]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Phil. Trans. R. Soc. A 362, 719 (2004).
[CrossRef]

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

2003 (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

1992 (1)

A. Hemmerich and T. W. Hänsch, Phys. Rev. Lett. 68, 1492 (1992).
[CrossRef]

1989 (1)

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef]

1986 (1)

1970 (1)

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Albaladejo, S.

S. Albaladejo, M. I. Marqués, and J. J. Sáenz, Opt. Express 19, 11471 (2011).
[CrossRef]

I. Zapata, S. Albaladejo, J. M. R. Parrondo, J. J. Sáenz, and F. Sols, Phys. Rev. Lett. 103, 130601 (2009).
[CrossRef]

S. Albaladejo, M. I. Marqués, F. Scheffold, and J. J. Sáenz, Nano Lett. 9, 3527 (2009).
[CrossRef]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef]

Ashkin, A.

Bekshaev, A.

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

Bjorkholm, J. E.

Bliokh, K. Y.

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

Block, S. M.

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

Burns, M. M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef]

Chan, C. T.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

Chantada, L.

Chaumet, P. C.

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Phil. Trans. R. Soc. A 362, 719 (2004).
[CrossRef]

Chen, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

Christodoulides, D. N.

Chu, S.

Dholakia, K.

K. Dholakia and P. Zemánek, Rev. Mod. Phys. 82, 1767 (2010).
[CrossRef]

Dogariu, A.

S. Sukhov and A. Dogariu, Phys. Rev. Lett. 107, 203602 (2011).
[CrossRef]

Dziedzic, J. M.

Fournier, J.-M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef]

Golovchenko, J. A.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef]

Gómez-Medina, R.

Grier, D. G.

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Hänsch, T. W.

A. Hemmerich and T. W. Hänsch, Phys. Rev. Lett. 68, 1492 (1992).
[CrossRef]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006).

Hemmerich, A.

A. Hemmerich and T. W. Hänsch, Phys. Rev. Lett. 68, 1492 (1992).
[CrossRef]

Iglesias, I.

I. Iglesias and J. J. Sáenz, Opt. Express 20, 2832 (2012).
[CrossRef]

I. Iglesias and J. J. Sáenz, Opt. Commun. 284, 2430 (2011).
[CrossRef]

Laroche, M.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef]

Lin, Z.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

Marqués, M. I.

S. Albaladejo, M. I. Marqués, and J. J. Sáenz, Opt. Express 19, 11471 (2011).
[CrossRef]

S. Albaladejo, M. I. Marqués, F. Scheffold, and J. J. Sáenz, Nano Lett. 9, 3527 (2009).
[CrossRef]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef]

Neuman, K. C.

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

Ng, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, Opt. Express 18, 11428 (2010).
[CrossRef]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Phil. Trans. R. Soc. A 362, 719 (2004).
[CrossRef]

Novitsky, A.

A. Novitsky, C.-W. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006).

Parrondo, J. M. R.

I. Zapata, S. Albaladejo, J. M. R. Parrondo, J. J. Sáenz, and F. Sols, Phys. Rev. Lett. 103, 130601 (2009).
[CrossRef]

Qiu, C.-W.

A. Novitsky, C.-W. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef]

Rahmani, A.

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Phil. Trans. R. Soc. A 362, 719 (2004).
[CrossRef]

Ratner, M.

V. Wong and M. Ratner, Phys. Rev. B 73, 075416 (2006).
[CrossRef]

Sáenz, J. J.

I. Iglesias and J. J. Sáenz, Opt. Express 20, 2832 (2012).
[CrossRef]

I. Iglesias and J. J. Sáenz, Opt. Commun. 284, 2430 (2011).
[CrossRef]

S. Albaladejo, M. I. Marqués, and J. J. Sáenz, Opt. Express 19, 11471 (2011).
[CrossRef]

J. J. Sáenz, Nat. Photonics 5, 514 (2011).
[CrossRef]

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, Opt. Express 18, 11428 (2010).
[CrossRef]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef]

S. Albaladejo, M. I. Marqués, F. Scheffold, and J. J. Sáenz, Nano Lett. 9, 3527 (2009).
[CrossRef]

I. Zapata, S. Albaladejo, J. M. R. Parrondo, J. J. Sáenz, and F. Sols, Phys. Rev. Lett. 103, 130601 (2009).
[CrossRef]

R. Gómez-Medina, and J. J. Sáenz, Phys. Rev. Lett. 93, 243602 (2004).
[CrossRef]

Salandrino, A.

Scheffold, F.

S. Albaladejo, M. I. Marqués, F. Scheffold, and J. J. Sáenz, Nano Lett. 9, 3527 (2009).
[CrossRef]

Sols, F.

I. Zapata, S. Albaladejo, J. M. R. Parrondo, J. J. Sáenz, and F. Sols, Phys. Rev. Lett. 103, 130601 (2009).
[CrossRef]

Soskin, M.

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

Sukhov, S.

S. Sukhov and A. Dogariu, Phys. Rev. Lett. 107, 203602 (2011).
[CrossRef]

Wang, H.

A. Novitsky, C.-W. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef]

Wong, V.

V. Wong and M. Ratner, Phys. Rev. B 73, 075416 (2006).
[CrossRef]

Zapata, I.

I. Zapata, S. Albaladejo, J. M. R. Parrondo, J. J. Sáenz, and F. Sols, Phys. Rev. Lett. 103, 130601 (2009).
[CrossRef]

Zemánek, P.

K. Dholakia and P. Zemánek, Rev. Mod. Phys. 82, 1767 (2010).
[CrossRef]

Zhan, Q.

J. Opt. (1)

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

Nano Lett. (1)

S. Albaladejo, M. I. Marqués, F. Scheffold, and J. J. Sáenz, Nano Lett. 9, 3527 (2009).
[CrossRef]

Nat. Photonics (2)

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

J. J. Sáenz, Nat. Photonics 5, 514 (2011).
[CrossRef]

Nature (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Opt. Commun. (1)

I. Iglesias and J. J. Sáenz, Opt. Commun. 284, 2430 (2011).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phil. Trans. R. Soc. A (1)

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Phil. Trans. R. Soc. A 362, 719 (2004).
[CrossRef]

Phys. Rev. B (1)

V. Wong and M. Ratner, Phys. Rev. B 73, 075416 (2006).
[CrossRef]

Phys. Rev. Lett. (8)

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef]

R. Gómez-Medina, and J. J. Sáenz, Phys. Rev. Lett. 93, 243602 (2004).
[CrossRef]

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

A. Novitsky, C.-W. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef]

S. Sukhov and A. Dogariu, Phys. Rev. Lett. 107, 203602 (2011).
[CrossRef]

I. Zapata, S. Albaladejo, J. M. R. Parrondo, J. J. Sáenz, and F. Sols, Phys. Rev. Lett. 103, 130601 (2009).
[CrossRef]

A. Hemmerich and T. W. Hänsch, Phys. Rev. Lett. 68, 1492 (1992).
[CrossRef]

Rev. Mod. Phys. (1)

K. Dholakia and P. Zemánek, Rev. Mod. Phys. 82, 1767 (2010).
[CrossRef]

Rev. Sci. Instrum. (1)

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

Other (1)

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006).

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Figures (2)

Fig. 1.
Fig. 1.

Intensity map for the configuration consisting in two perpendicular, circularly polarized, stationary waves with wavelength λ propagating in the XY plane and with a difference on the phase ϕ=π/2. Values are normalized to the maximum intensity value. The map also shows the time-averaged scattering forces induced by the electromagnetic radiation.

Fig. 2.
Fig. 2.

(a) Time-averaged scattering forces in the XY plane coming from the average value of the Poynting vector and (b) from the curl of the average value of the spin angular momentum of light. The modulus of the forces (normalized to the maximum value of the forces coming from the Poynting vector) is also shown in the color map.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

F=α{U}+σ{1cS}+σ{c×LS},
U=ϵ0|E|2/4,
S=Re{E×H*}/2,
LS=ϵ0{E×E*}/(4ωi).
E1=(eikxeikx)(1,0,i),
E2=(eikyeiky)(1,0,i)eiϕ.
Sx=ϵ0c[cos(kx)sin(ky)+sin(kx)cos(ky)],
Sy=Sx,
Sz=0.
y=x±mλ2,
Fx=αk[cos(kx)sin(ky)],
Fy=αk[cos(ky)sin(kx)],
Fz=0.
x=±m1λ2,y=±m2λ2,
Ssc2=Sc2+×LS.
Ssc2=iϵ04ωi=x,y,z(EiEi*Ei*Ei),
p=i2(ΨΨ*Ψ*Ψ).

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