Abstract

The capabilities of optical tweezers to trap DNG (double negative) spherical particles, with both negative permittivity and permeability, are explored in detail by analyzing some interesting theoretical features not seeing in conventional DPS (double positive) particles possessing positive refractive index. The ray optics regime is adopted and, although this regime is quite simple and limited, its validity is already known and tested for DPS particles such as biological cells and molecules trapped by highly focused beams. Simulation results confirm that even for ray optics, DNG particles present unusual and interesting trapping characteristics.

© 2009 Optical Society of America

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  1. A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
    [CrossRef]
  2. A. Ashkin, "Atomic-beam deflection by resonance-radiation pressure," Phys. Rev. Lett. 24, 1321-1324 (1970).
    [CrossRef]
  3. A. Ashkin and J. M. Dziedzic "Optical levitation by radiation pressure," Appl. Phys. Lett. 19, 283-285 (1971).
    [CrossRef]
  4. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
    [CrossRef] [PubMed]
  5. A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
    [CrossRef] [PubMed]
  6. R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap," Cytometry 12, 505-510 (1991).
    [CrossRef] [PubMed]
  7. M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, and R. J. Walter, "Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
    [CrossRef]
  8. V. Emiliani et al., "Wave front engineering for microscopy of living cells," Opt. Express 13, 1395-1405 (2005).
    [CrossRef] [PubMed]
  9. V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  10. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite Medium with Simultaneously Negative Permeability and permittivity," Phys. Rev. Lett. 84, 18 (2000).
    [CrossRef]
  11. J. B. Pendry, "Negative Refraction Makes Perfect Lens," Phys. Rev. Lett. 85, 18 (2000).
    [CrossRef]
  12. N. Engheta and R. W. Ziolkowski, Metamaterials - Physics and Engineering Explorations, (IEEE Press, Wiley-Interscience, 2006).
  13. N. Engheta and R. W. Ziolkowski, "A positive future for Double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53(4), (part II), 1535-1556 (2005).
  14. A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
    [CrossRef] [PubMed]

2005 (2)

V. Emiliani et al., "Wave front engineering for microscopy of living cells," Opt. Express 13, 1395-1405 (2005).
[CrossRef] [PubMed]

N. Engheta and R. W. Ziolkowski, "A positive future for Double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53(4), (part II), 1535-1556 (2005).

2000 (2)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite Medium with Simultaneously Negative Permeability and permittivity," Phys. Rev. Lett. 84, 18 (2000).
[CrossRef]

J. B. Pendry, "Negative Refraction Makes Perfect Lens," Phys. Rev. Lett. 85, 18 (2000).
[CrossRef]

1992 (1)

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

1991 (1)

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

1989 (1)

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, and R. J. Walter, "Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
[CrossRef]

1987 (1)

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef] [PubMed]

1986 (1)

1971 (1)

A. Ashkin and J. M. Dziedzic "Optical levitation by radiation pressure," Appl. Phys. Lett. 19, 283-285 (1971).
[CrossRef]

1970 (2)

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

A. Ashkin, "Atomic-beam deflection by resonance-radiation pressure," Phys. Rev. Lett. 24, 1321-1324 (1970).
[CrossRef]

1968 (1)

V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Andrews, J. J.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, and R. J. Walter, "Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
[CrossRef]

Ashkin, A.

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic "Optical levitation by radiation pressure," Appl. Phys. Lett. 19, 283-285 (1971).
[CrossRef]

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

A. Ashkin, "Atomic-beam deflection by resonance-radiation pressure," Phys. Rev. Lett. 24, 1321-1324 (1970).
[CrossRef]

Berns, M. W.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, and R. J. Walter, "Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
[CrossRef]

Bjorkholm, J. E.

Cheng, S.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

Chu, S.

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic "Optical levitation by radiation pressure," Appl. Phys. Lett. 19, 283-285 (1971).
[CrossRef]

Emiliani, V.

Engheta, N.

N. Engheta and R. W. Ziolkowski, "A positive future for Double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53(4), (part II), 1535-1556 (2005).

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite Medium with Simultaneously Negative Permeability and permittivity," Phys. Rev. Lett. 84, 18 (2000).
[CrossRef]

Numajiri, Y.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite Medium with Simultaneously Negative Permeability and permittivity," Phys. Rev. Lett. 84, 18 (2000).
[CrossRef]

Pendry, J. B.

J. B. Pendry, "Negative Refraction Makes Perfect Lens," Phys. Rev. Lett. 85, 18 (2000).
[CrossRef]

Profeta, G. A.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, and R. J. Walter, "Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite Medium with Simultaneously Negative Permeability and permittivity," Phys. Rev. Lett. 84, 18 (2000).
[CrossRef]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite Medium with Simultaneously Negative Permeability and permittivity," Phys. Rev. Lett. 84, 18 (2000).
[CrossRef]

Steubing, R. W.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

Tromberg, B. J.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, and R. J. Walter, "Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite Medium with Simultaneously Negative Permeability and permittivity," Phys. Rev. Lett. 84, 18 (2000).
[CrossRef]

Walter, R. J.

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, and R. J. Walter, "Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
[CrossRef]

Wright, W. H.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, and R. J. Walter, "Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
[CrossRef]

Ziolkowski, R. W.

N. Engheta and R. W. Ziolkowski, "A positive future for Double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53(4), (part II), 1535-1556 (2005).

Appl. Phys. Lett. (1)

A. Ashkin and J. M. Dziedzic "Optical levitation by radiation pressure," Appl. Phys. Lett. 19, 283-285 (1971).
[CrossRef]

Biophys. J. (1)

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

Cytometry (1)

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

IEEE Trans. Microwave Theory Tech. (1)

N. Engheta and R. W. Ziolkowski, "A positive future for Double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53(4), (part II), 1535-1556 (2005).

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (4)

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

A. Ashkin, "Atomic-beam deflection by resonance-radiation pressure," Phys. Rev. Lett. 24, 1321-1324 (1970).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite Medium with Simultaneously Negative Permeability and permittivity," Phys. Rev. Lett. 84, 18 (2000).
[CrossRef]

J. B. Pendry, "Negative Refraction Makes Perfect Lens," Phys. Rev. Lett. 85, 18 (2000).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, and R. J. Walter, "Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle," Proc. Natl. Acad. Sci. U.S.A. 86, 7914-7918 (1989).
[CrossRef]

Science (1)

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (1)

N. Engheta and R. W. Ziolkowski, Metamaterials - Physics and Engineering Explorations, (IEEE Press, Wiley-Interscience, 2006).

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Figures (5)

Fig. 1.
Fig. 1.

Geometric optics when (a) the medium possesses an refractive index n1 higher than the modulus of the refractive index of the sphere, |n 2|, and (b) the inverse case. In (a), transmitted angles are greater than the incident ones, whereas for (b) those angles are smaller. Stronger forces act on the particle when it is DNG, due to a more intense variation of the momentum of the ray. In (c), a series of infinite rays appears when the incident ray, with power P, hits the DNG particle (n 1>|n 2| or vice-versa).

Fig. 2.
Fig. 2.

Normalized (over n 1 P/c) values of Fg (solid) and FS (dashed), for both conventional case ((a) and (c)) and DNG case ((b) and (d)) with n 1=1.33. The refractive indexes are: (a) n 2=1.62; (b) n 2=-1.62; (c) n 2=1.21 and (d) n 2=-1.21.

Fig. 3.
Fig. 3.

(a). The total scattering and gradient forces for a focused collimated beam will depend on the angle γ between the z-axis and the distance vector r, directed from the focus f of the beam to the centre O of the sphere of radius a. (b). A tridimensional view of the problem. The incident cone and the sphere were cut for clearness.

Fig. 4.
Fig. 4.

Scattering (dashed) and gradient (solid) total forces as functions of the angle γ for n 1=1.33. (a) n 2=1.62; (b) n 2=-1.62; (c) n 2=1.21 and (d) n 2=-1.21.

Fig. 5.
Fig. 5.

Scattering (dashed) and gradient (solid) total forces for a DNG particle as functions of r, for (a) and (d) γ=0°; (b) and (e) γ=90°; (c) and (f) γ=180°. For (a)–(c), |n 2|=1.62 and n 1=1.33. For (d)–(f), |n 2|=1.21 and n 1=1.33. Both components of the total force F are inverted when |n 2| becomes lower than n 1. Compared to the conventional case, the inversion of the total forces does not occur, while new behaviors – that did not exist for conventional particles – can be seen.

Equations (7)

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

F g = n 1 P c { R sin 2 θ i T 2 [ sin ( 2 θ i + 2 θ i ) + R sin 2 θ i ] 1 + R 2 + 2 R cos 2 θ t }
F s = n 1 P c { 1 + R cos 2 θ i T 2 [ cos ( 2 θ i + 2 θ t ) + R cos 2 θ i ] 1 + R 2 + 2 R cos 2 θ t } ,
F = A F i d A A d A ,
r = ( r sin γ , 0 , r cos γ )
d = r [ sin θ cos ϕ sin γ + cos θ cos γ ] +
a 2 ( 1 r d ) 2 + r 2 ( sin θ cos ϕ sin γ + cos θ cos γ ) 2 ,
θ i = cos 1 [ a 2 d ( 1 + d a ) 2 ( r a ) 2 ]

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