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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 3 — Jan. 30, 2012
  • pp: 2832–2834
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Light spin forces in optical traps: comment on “Trapping metallic Rayleigh particles with radial polarization”

Ignacio Iglesias and Juan José Sáenz  »View Author Affiliations


Optics Express, Vol. 20, Issue 3, pp. 2832-2834 (2012)
http://dx.doi.org/10.1364/OE.20.002832


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Abstract

An incomplete modeling of the scattering forces on a Rayleigh particle without taking into account the light spin forces in “Trapping metallic Rayleigh particles with radial polarization” by Q. Zhan, leads to erroneous statements on the advantages of using radial polarization to trap metallic particles.

© 2012 OSA

The trapping of Rayleigh metallic particles has been experimentally demonstrated in a conventional optical trap [1

1. K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19(13), 930–932 (1994). [CrossRef] [PubMed]

] using a microscope objective illuminated with a Gaussian beam. In these experiments, in order to have a significant prevalence of the trapping forces over the scattering forces, given that the scattering forces are proportional to the imaginary part of the metal polarizability, long wavelengths are needed.

To improve the trapping efficiency of metallic particles by minimizing the scattering forces, Zhan [2

2. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-15-3377. [CrossRef] [PubMed]

, 3

3. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009). [CrossRef]

] proposed the use of radial polarized beams in optical tweezers. These papers have had a large impact in the field of optical forces and trapping. The underlying idea of the abovementioned work is to take advantage of that the radial polarization generates a force field in the focal volume of a high numerical aperture (NA) microscope objective in which the equilibrium location of the conservative forces responsible for the particle trapping is on axis and spatially delocalized respecting the radiation pressure. This is because the radial polarization generates a tight intensity distribution around the focal point whereas the axial component of the radiation pressure, proportional to the time average Poynting vector, surrounds the optical axis. Then, in this picture, a metallic particle close to the focal point would be only significantly affected by the trapping force relaxing to a great extend the need of a small imaginary part of the polarizability.

Unfortunately, the description of the forces acting on a Rayleigh particle in the Zhan’s paper [2

2. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-15-3377. [CrossRef] [PubMed]

] is not complete.

It has been shown recently, that the force exerted by a light field on a small particle can be decomposed in three terms [4

4. S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009). [CrossRef] [PubMed]

],
F=n22(αε02|E|2+αk0c0{E×H*}+αε0×{E×E*})
(1)
where α=α+iα is the complex polarizability, ε0, k0=2π/λ0and c0are the dielectric constant, the wavenumber and the speed of light respectively in the vacuum and n is the host medium refraction index. In Eq. (1) the first term is the gradient force responsible for the particle trapping, the second term is the radiation pressure proportional to the Poynting vector and the third is a scattering force proportional to the curl of the time averaged spin density of the light field.

The first two terms in Eq. (1) follow the spatial distribution of forces mentioned before. The third term is small when the NA is low but when the NA increases it becomes significant altering the trapping potential structure, even in the case of a linear polarized beam [5

5. I. Iglesias and J. J. Sáenz, “Scattering forces in the focal volume of high numerical aperture microscope objectives,” Opt. Commun. 284(10-11), 2430–2436 (2011). [CrossRef]

].

Whereas in the linear uniform polarization case, the third term in Eq. (1) can be considered as a small correction (except for the case of large NA), in the case of a radial polarized beam is fundamental. Must be noticed that here, given that the non-zero electrical field components are radial, and an axial component appears after the refraction by the lens, the spin density is azimuthal and consequently the curl force is axial (parallel to the optical axis) on the focal plane.

In conclusion we have shown that when modeling the scattering forces acting on a Rayleigh particle in full, the radial polarization does not provide a spatial distribution of scattering forces in the focal volume of microscope objective advantageous to minimize its effects in optical trapping.

Acknowledgment

This work has been supported by the Spanish MICINN Consolider NanoLight (CSD2007-00046), FIS2009-13430-C02, as well as by the Comunidad de Madrid Microseres-CM (S2009/TIC- 1476).

References and links

1.

K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19(13), 930–932 (1994). [CrossRef] [PubMed]

2.

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-15-3377. [CrossRef] [PubMed]

3.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009). [CrossRef]

4.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009). [CrossRef] [PubMed]

5.

I. Iglesias and J. J. Sáenz, “Scattering forces in the focal volume of high numerical aperture microscope objectives,” Opt. Commun. 284(10-11), 2430–2436 (2011). [CrossRef]

6.

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

OCIS Codes
(020.7010) Atomic and molecular physics : Laser trapping
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation
(260.5430) Physical optics : Polarization

ToC Category:
Optical Trapping and Manipulation

History
Original Manuscript: December 2, 2011
Revised Manuscript: January 13, 2012
Manuscript Accepted: January 16, 2012
Published: January 23, 2012

Virtual Issues
Vol. 7, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Ignacio Iglesias and Juan José Sáenz, "Light spin forces in optical traps: comment on “Trapping metallic Rayleigh particles with radial polarization”," Opt. Express 20, 2832-2834 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-2832


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References

  1. K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett.19(13), 930–932 (1994). [CrossRef] [PubMed]
  2. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express12(15), 3377–3382 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-15-3377 . [CrossRef] [PubMed]
  3. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon.1(1), 1–57 (2009). [CrossRef]
  4. S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett.102(11), 113602 (2009). [CrossRef] [PubMed]
  5. I. Iglesias and J. J. Sáenz, “Scattering forces in the focal volume of high numerical aperture microscope objectives,” Opt. Commun.284(10-11), 2430–2436 (2011). [CrossRef]
  6. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).

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