Abstract

A wave optics numerical analysis of the force and torque on a semicylindrical optical wing is presented. Comparisons with a recently reported ray optics analysis indicate good agreement when the radius is large compared with the wavelength of light, as expected. Surprisingly, we find that the dominant rotationally stable angle of attack at α15° is relatively invariant to changes in radius and refractive index. However, the torsional stiffness at the equilibrium point is found to increase, approximately, as the cubic power of the radius. Quasi-resonant internal modes of light produce complex size-dependent variations of the angle and magnitude of the optical lift force.

© 2012 Optical Society of America

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References

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  1. G. A. Swartzlander, T. J. Peterson, A. B. Artusio-Glimpse, and A. D. Raisanen, Nat. Photonics 5, 48 (2011).
    [CrossRef]
  2. M. Mishchenko, J. Quant. Spectrosc. Radiat. Transfer 101, 404 (2006).
    [CrossRef]
  3. R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. 13, 044017 (2011).
    [CrossRef]
  4. A. Gautesen, R. Ziolkowski, and R. McLeod, SIAM J. Appl. Math. 51, 1556 (1991).
    [CrossRef]
  5. C. Hafner, The Generalized Multipole Technique For Computational Electrodynamics (Artech House, 1990).
  6. F. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79, 775 (2003).
    [CrossRef]
  7. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1983).
  8. J. A. Stratton, Electromagnetic Theory (Adams, 2007).
  9. S. H. Simpson and S. Hanna, Phys. Rev. E 82, 031141 (2010).
    [CrossRef]
  10. S. H. Simpson, D. C. Benito, and S. Hanna, Phys. Rev. A 76, 043408 (2007).
    [CrossRef]
  11. S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Dover, 2005).

2011 (2)

G. A. Swartzlander, T. J. Peterson, A. B. Artusio-Glimpse, and A. D. Raisanen, Nat. Photonics 5, 48 (2011).
[CrossRef]

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. 13, 044017 (2011).
[CrossRef]

2010 (1)

S. H. Simpson and S. Hanna, Phys. Rev. E 82, 031141 (2010).
[CrossRef]

2007 (1)

S. H. Simpson, D. C. Benito, and S. Hanna, Phys. Rev. A 76, 043408 (2007).
[CrossRef]

2006 (1)

M. Mishchenko, J. Quant. Spectrosc. Radiat. Transfer 101, 404 (2006).
[CrossRef]

2003 (1)

F. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79, 775 (2003).
[CrossRef]

1991 (1)

A. Gautesen, R. Ziolkowski, and R. McLeod, SIAM J. Appl. Math. 51, 1556 (1991).
[CrossRef]

Artusio-Glimpse, A. B.

G. A. Swartzlander, T. J. Peterson, A. B. Artusio-Glimpse, and A. D. Raisanen, Nat. Photonics 5, 48 (2011).
[CrossRef]

Benito, D. C.

S. H. Simpson, D. C. Benito, and S. Hanna, Phys. Rev. A 76, 043408 (2007).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1983).

Gautesen, A.

A. Gautesen, R. Ziolkowski, and R. McLeod, SIAM J. Appl. Math. 51, 1556 (1991).
[CrossRef]

Hafner, C.

C. Hafner, The Generalized Multipole Technique For Computational Electrodynamics (Artech House, 1990).

Hanna, S.

S. H. Simpson and S. Hanna, Phys. Rev. E 82, 031141 (2010).
[CrossRef]

S. H. Simpson, D. C. Benito, and S. Hanna, Phys. Rev. A 76, 043408 (2007).
[CrossRef]

Heckenberg, N. R.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. 13, 044017 (2011).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1983).

Kahnert, F.

F. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79, 775 (2003).
[CrossRef]

Karrila, S. J.

S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Dover, 2005).

Kim, S.

S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Dover, 2005).

McLeod, R.

A. Gautesen, R. Ziolkowski, and R. McLeod, SIAM J. Appl. Math. 51, 1556 (1991).
[CrossRef]

Mishchenko, M.

M. Mishchenko, J. Quant. Spectrosc. Radiat. Transfer 101, 404 (2006).
[CrossRef]

Nieminen, T. A.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. 13, 044017 (2011).
[CrossRef]

Peterson, T. J.

G. A. Swartzlander, T. J. Peterson, A. B. Artusio-Glimpse, and A. D. Raisanen, Nat. Photonics 5, 48 (2011).
[CrossRef]

Pfeifer, R. N. C.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. 13, 044017 (2011).
[CrossRef]

Raisanen, A. D.

G. A. Swartzlander, T. J. Peterson, A. B. Artusio-Glimpse, and A. D. Raisanen, Nat. Photonics 5, 48 (2011).
[CrossRef]

Rubinsztein-Dunlop, H.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. 13, 044017 (2011).
[CrossRef]

Simpson, S. H.

S. H. Simpson and S. Hanna, Phys. Rev. E 82, 031141 (2010).
[CrossRef]

S. H. Simpson, D. C. Benito, and S. Hanna, Phys. Rev. A 76, 043408 (2007).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (Adams, 2007).

Swartzlander, G. A.

G. A. Swartzlander, T. J. Peterson, A. B. Artusio-Glimpse, and A. D. Raisanen, Nat. Photonics 5, 48 (2011).
[CrossRef]

Ziolkowski, R.

A. Gautesen, R. Ziolkowski, and R. McLeod, SIAM J. Appl. Math. 51, 1556 (1991).
[CrossRef]

J. Opt. (1)

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. 13, 044017 (2011).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

M. Mishchenko, J. Quant. Spectrosc. Radiat. Transfer 101, 404 (2006).
[CrossRef]

F. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79, 775 (2003).
[CrossRef]

Nat. Photonics (1)

G. A. Swartzlander, T. J. Peterson, A. B. Artusio-Glimpse, and A. D. Raisanen, Nat. Photonics 5, 48 (2011).
[CrossRef]

Phys. Rev. A (1)

S. H. Simpson, D. C. Benito, and S. Hanna, Phys. Rev. A 76, 043408 (2007).
[CrossRef]

Phys. Rev. E (1)

S. H. Simpson and S. Hanna, Phys. Rev. E 82, 031141 (2010).
[CrossRef]

SIAM J. Appl. Math. (1)

A. Gautesen, R. Ziolkowski, and R. McLeod, SIAM J. Appl. Math. 51, 1556 (1991).
[CrossRef]

Other (4)

C. Hafner, The Generalized Multipole Technique For Computational Electrodynamics (Artech House, 1990).

S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Dover, 2005).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1983).

J. A. Stratton, Electromagnetic Theory (Adams, 2007).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic showing the axes and angles used in the text. The angle of attack, α , and the angle at which the excess force acts, ϕ f , are measured counterclockwise from the positive x -axis.

Fig. 2.
Fig. 2.

Forces and torques experienced by lightfoils with n = 1.3 , L = 1 μm , and various radii, a . (a) Scaled axial torque, t z / L a 2 ( pN / μm 2 ), (b) scattering force, f x / L a , and (c) lift force, f y / L a ( pN / μm 2 ).

Fig. 3.
Fig. 3.

Stable equilibrium conditions for lightfoils of length 1 μm, with six distinct refractive indices, and 0.1 < a < 5 μm . (a) Angle of attack, α eqm , (b) lift angle ϕ f , (c) scaled force modulus, | f | / L a ( pN / μm 2 ), and (d) scaled torsional stiffness, K z r / L a 3 ( pN / deg . μm 3 ).

Fig. 4.
Fig. 4.

(a) Angle of attack at equilibrium, α eqm , (b) lift angle, ϕ f , (c) scaled force modulus, | f | / L a ( pN / μm 2 ), and (d) scaled torsional stiffness, K z r / L a 3 ( pN / deg . μm 3 ), as functions of n and a .

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