Abstract

Sub-micron polystyrene spheres spontaneously assemble into twodimensional arrays in the evanescent field of counterpropagating laser beams at the silica–water interface. The symmetry and dynamics of these arrays depends on the particle size and the polarization of the two laser beams. Here we describe the polarization effects for particles with diameters of 390–520 nm, which are small enough to form regular 2-D arrays yet large enough to be readily observed with an optical microscope. We report the observation of rectangular arrays, three different types of hexagonal arrays and a defective array in which every third row is missing. The structure of the arrays is determined by both optical trapping and optical binding. Optical binding can overwhelm optical trapping and give rise to an array that is incommensurate with the interference fringes formed by two laser beams of the same polarization.

© 2006 Optical Society of America

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  1. S. Kawata and T. Sugiura, "Movement of micrometer-sized particles in the evanescent field of a laser beam," Opt. Lett. 17, 772-774 (1992).
    [CrossRef] [PubMed]
  2. C. D. Mellor, C. D. Bain and J. Lekner, "Pattern formation in evanescent wave optical traps," in Optical Trapping and Optical Micromanipulation II, K. Dholakia, and G. C. Spalding, eds. Proc. SPIE 5930, 352-361 (2005).
  3. C. D. Mellor and C. D. Bain, "Array formation in evanescent waves," ChemPhysChem,  7, 329-332 (2006).
    [CrossRef]
  4. P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B. 42, 035422 (2001).
    [CrossRef]
  5. M. M. Burns, J.-M. Fournier and J. E. Golovchenko, "Optical Matter: Crystallization and Binding in Intense Optical Fields," Science 249, 749-754 (1990)
    [CrossRef] [PubMed]
  6. J. Lekner, "Force on a scatterer in counter-propagating coherent beams," J. Opt. A: Pure Appl. Opt. 7, 238-248 (2005).
    [CrossRef]
  7. V. Garcés-Chávez, K. Dholakia and G. C. Spalding, "Extended-area optically induced organization of microparticles on a surface," Appl. Phys. Lett. 86,031106 (2005).
    [CrossRef]
  8. S. Chang, J. J. Jo and S. S. Lee, "Theoretical calculations of the optical force exerted on a dielectric sphere in the evanescent field generated with a totally internally reflected focused Gaussian beam," Opt. Commun. 108, 133-143 (1994).
    [CrossRef]
  9. E. Almaas and I. Brevik, "Radiation forces on a micrometer-sized sphere in an evanescent field," J. Opt. Soc. Am. B. 12, 2429-2438 (1995).
    [CrossRef]
  10. M. Lester and M. Nieto-Vesperinas, "Optical forces on microparticles in an evanescent laser field" Opt. Lett. 24, 936-938 (1999).
    [CrossRef]
  11. J.Y. Walz, "Ray optics calculation of the radiation forces exerted on a dielectric sphere in an evanescent field," Appl. Optics 38, 5319-5330 (1999).
    [CrossRef]
  12. M. M. Burns, J.-M. Fournier and J. E. Golovchenko, "Optical Binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
    [CrossRef] [PubMed]
  13. J. Ng, Z. F. Lin, C. T. Chan and P. Sheng, "Photonic clusters formed by dielectric microspheres: numerical simulations," Phys. Rev. E 72, 085130 (2005).
  14. D. S. Bradshaw and D. L. Andrews, "Optically induced forces and torques: interactions between nanoparticles in a laser beam," Phys. Rev. A 72, 033816 (2005).
    [CrossRef]
  15. T. M. Grzegorczyk, B. A. Kemp and J. A. Kong, "Stable optical trapping based on optical binding forces," Phys. Rev. Lett. 96, 113903 (2006).
    [CrossRef] [PubMed]
  16. J. Ng and C. T. Chan, private communication.

2006

C. D. Mellor and C. D. Bain, "Array formation in evanescent waves," ChemPhysChem,  7, 329-332 (2006).
[CrossRef]

T. M. Grzegorczyk, B. A. Kemp and J. A. Kong, "Stable optical trapping based on optical binding forces," Phys. Rev. Lett. 96, 113903 (2006).
[CrossRef] [PubMed]

2005

J. Ng, Z. F. Lin, C. T. Chan and P. Sheng, "Photonic clusters formed by dielectric microspheres: numerical simulations," Phys. Rev. E 72, 085130 (2005).

D. S. Bradshaw and D. L. Andrews, "Optically induced forces and torques: interactions between nanoparticles in a laser beam," Phys. Rev. A 72, 033816 (2005).
[CrossRef]

J. Lekner, "Force on a scatterer in counter-propagating coherent beams," J. Opt. A: Pure Appl. Opt. 7, 238-248 (2005).
[CrossRef]

V. Garcés-Chávez, K. Dholakia and G. C. Spalding, "Extended-area optically induced organization of microparticles on a surface," Appl. Phys. Lett. 86,031106 (2005).
[CrossRef]

2001

P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B. 42, 035422 (2001).
[CrossRef]

1999

M. Lester and M. Nieto-Vesperinas, "Optical forces on microparticles in an evanescent laser field" Opt. Lett. 24, 936-938 (1999).
[CrossRef]

J.Y. Walz, "Ray optics calculation of the radiation forces exerted on a dielectric sphere in an evanescent field," Appl. Optics 38, 5319-5330 (1999).
[CrossRef]

1995

E. Almaas and I. Brevik, "Radiation forces on a micrometer-sized sphere in an evanescent field," J. Opt. Soc. Am. B. 12, 2429-2438 (1995).
[CrossRef]

1994

S. Chang, J. J. Jo and S. S. Lee, "Theoretical calculations of the optical force exerted on a dielectric sphere in the evanescent field generated with a totally internally reflected focused Gaussian beam," Opt. Commun. 108, 133-143 (1994).
[CrossRef]

1992

1990

M. M. Burns, J.-M. Fournier and J. E. Golovchenko, "Optical Matter: Crystallization and Binding in Intense Optical Fields," Science 249, 749-754 (1990)
[CrossRef] [PubMed]

1989

M. M. Burns, J.-M. Fournier and J. E. Golovchenko, "Optical Binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

Almaas, E.

E. Almaas and I. Brevik, "Radiation forces on a micrometer-sized sphere in an evanescent field," J. Opt. Soc. Am. B. 12, 2429-2438 (1995).
[CrossRef]

Andrews, D. L.

D. S. Bradshaw and D. L. Andrews, "Optically induced forces and torques: interactions between nanoparticles in a laser beam," Phys. Rev. A 72, 033816 (2005).
[CrossRef]

Bain, C. D.

C. D. Mellor and C. D. Bain, "Array formation in evanescent waves," ChemPhysChem,  7, 329-332 (2006).
[CrossRef]

Bradshaw, D. S.

D. S. Bradshaw and D. L. Andrews, "Optically induced forces and torques: interactions between nanoparticles in a laser beam," Phys. Rev. A 72, 033816 (2005).
[CrossRef]

Brevik, I.

E. Almaas and I. Brevik, "Radiation forces on a micrometer-sized sphere in an evanescent field," J. Opt. Soc. Am. B. 12, 2429-2438 (1995).
[CrossRef]

Burns, M. M.

M. M. Burns, J.-M. Fournier and J. E. Golovchenko, "Optical Matter: Crystallization and Binding in Intense Optical Fields," Science 249, 749-754 (1990)
[CrossRef] [PubMed]

M. M. Burns, J.-M. Fournier and J. E. Golovchenko, "Optical Binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

Chan, C. T.

J. Ng, Z. F. Lin, C. T. Chan and P. Sheng, "Photonic clusters formed by dielectric microspheres: numerical simulations," Phys. Rev. E 72, 085130 (2005).

Chang, S.

S. Chang, J. J. Jo and S. S. Lee, "Theoretical calculations of the optical force exerted on a dielectric sphere in the evanescent field generated with a totally internally reflected focused Gaussian beam," Opt. Commun. 108, 133-143 (1994).
[CrossRef]

Chaumet, P. C.

P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B. 42, 035422 (2001).
[CrossRef]

Dholakia, K.

V. Garcés-Chávez, K. Dholakia and G. C. Spalding, "Extended-area optically induced organization of microparticles on a surface," Appl. Phys. Lett. 86,031106 (2005).
[CrossRef]

Fournier, J.-M.

M. M. Burns, J.-M. Fournier and J. E. Golovchenko, "Optical Matter: Crystallization and Binding in Intense Optical Fields," Science 249, 749-754 (1990)
[CrossRef] [PubMed]

M. M. Burns, J.-M. Fournier and J. E. Golovchenko, "Optical Binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

Garcés-Chávez, V.

V. Garcés-Chávez, K. Dholakia and G. C. Spalding, "Extended-area optically induced organization of microparticles on a surface," Appl. Phys. Lett. 86,031106 (2005).
[CrossRef]

Golovchenko, J. E.

M. M. Burns, J.-M. Fournier and J. E. Golovchenko, "Optical Matter: Crystallization and Binding in Intense Optical Fields," Science 249, 749-754 (1990)
[CrossRef] [PubMed]

M. M. Burns, J.-M. Fournier and J. E. Golovchenko, "Optical Binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

Grzegorczyk, T. M.

T. M. Grzegorczyk, B. A. Kemp and J. A. Kong, "Stable optical trapping based on optical binding forces," Phys. Rev. Lett. 96, 113903 (2006).
[CrossRef] [PubMed]

Jo, J. J.

S. Chang, J. J. Jo and S. S. Lee, "Theoretical calculations of the optical force exerted on a dielectric sphere in the evanescent field generated with a totally internally reflected focused Gaussian beam," Opt. Commun. 108, 133-143 (1994).
[CrossRef]

Kawata, S.

Kemp, B. A.

T. M. Grzegorczyk, B. A. Kemp and J. A. Kong, "Stable optical trapping based on optical binding forces," Phys. Rev. Lett. 96, 113903 (2006).
[CrossRef] [PubMed]

Kong, J. A.

T. M. Grzegorczyk, B. A. Kemp and J. A. Kong, "Stable optical trapping based on optical binding forces," Phys. Rev. Lett. 96, 113903 (2006).
[CrossRef] [PubMed]

Lee, S. S.

S. Chang, J. J. Jo and S. S. Lee, "Theoretical calculations of the optical force exerted on a dielectric sphere in the evanescent field generated with a totally internally reflected focused Gaussian beam," Opt. Commun. 108, 133-143 (1994).
[CrossRef]

Lekner, J.

J. Lekner, "Force on a scatterer in counter-propagating coherent beams," J. Opt. A: Pure Appl. Opt. 7, 238-248 (2005).
[CrossRef]

Lester, M.

Lin, Z. F.

J. Ng, Z. F. Lin, C. T. Chan and P. Sheng, "Photonic clusters formed by dielectric microspheres: numerical simulations," Phys. Rev. E 72, 085130 (2005).

Mellor, C. D.

C. D. Mellor and C. D. Bain, "Array formation in evanescent waves," ChemPhysChem,  7, 329-332 (2006).
[CrossRef]

Ng, J.

J. Ng, Z. F. Lin, C. T. Chan and P. Sheng, "Photonic clusters formed by dielectric microspheres: numerical simulations," Phys. Rev. E 72, 085130 (2005).

Nieto-Vesperinas, M.

P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B. 42, 035422 (2001).
[CrossRef]

M. Lester and M. Nieto-Vesperinas, "Optical forces on microparticles in an evanescent laser field" Opt. Lett. 24, 936-938 (1999).
[CrossRef]

Sheng, P.

J. Ng, Z. F. Lin, C. T. Chan and P. Sheng, "Photonic clusters formed by dielectric microspheres: numerical simulations," Phys. Rev. E 72, 085130 (2005).

Spalding, G. C.

V. Garcés-Chávez, K. Dholakia and G. C. Spalding, "Extended-area optically induced organization of microparticles on a surface," Appl. Phys. Lett. 86,031106 (2005).
[CrossRef]

Sugiura, T.

Walz, J.Y.

J.Y. Walz, "Ray optics calculation of the radiation forces exerted on a dielectric sphere in an evanescent field," Appl. Optics 38, 5319-5330 (1999).
[CrossRef]

Appl. Optics

J.Y. Walz, "Ray optics calculation of the radiation forces exerted on a dielectric sphere in an evanescent field," Appl. Optics 38, 5319-5330 (1999).
[CrossRef]

Appl. Phys. Lett.

V. Garcés-Chávez, K. Dholakia and G. C. Spalding, "Extended-area optically induced organization of microparticles on a surface," Appl. Phys. Lett. 86,031106 (2005).
[CrossRef]

ChemPhysChem

C. D. Mellor and C. D. Bain, "Array formation in evanescent waves," ChemPhysChem,  7, 329-332 (2006).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

J. Lekner, "Force on a scatterer in counter-propagating coherent beams," J. Opt. A: Pure Appl. Opt. 7, 238-248 (2005).
[CrossRef]

J. Opt. Soc. Am. B.

E. Almaas and I. Brevik, "Radiation forces on a micrometer-sized sphere in an evanescent field," J. Opt. Soc. Am. B. 12, 2429-2438 (1995).
[CrossRef]

Opt. Commun.

S. Chang, J. J. Jo and S. S. Lee, "Theoretical calculations of the optical force exerted on a dielectric sphere in the evanescent field generated with a totally internally reflected focused Gaussian beam," Opt. Commun. 108, 133-143 (1994).
[CrossRef]

Opt. Lett.

Phys. Rev. A

D. S. Bradshaw and D. L. Andrews, "Optically induced forces and torques: interactions between nanoparticles in a laser beam," Phys. Rev. A 72, 033816 (2005).
[CrossRef]

Phys. Rev. B.

P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B. 42, 035422 (2001).
[CrossRef]

Phys. Rev. E

J. Ng, Z. F. Lin, C. T. Chan and P. Sheng, "Photonic clusters formed by dielectric microspheres: numerical simulations," Phys. Rev. E 72, 085130 (2005).

Phys. Rev. Lett.

M. M. Burns, J.-M. Fournier and J. E. Golovchenko, "Optical Binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

T. M. Grzegorczyk, B. A. Kemp and J. A. Kong, "Stable optical trapping based on optical binding forces," Phys. Rev. Lett. 96, 113903 (2006).
[CrossRef] [PubMed]

Science

M. M. Burns, J.-M. Fournier and J. E. Golovchenko, "Optical Matter: Crystallization and Binding in Intense Optical Fields," Science 249, 749-754 (1990)
[CrossRef] [PubMed]

Other

C. D. Mellor, C. D. Bain and J. Lekner, "Pattern formation in evanescent wave optical traps," in Optical Trapping and Optical Micromanipulation II, K. Dholakia, and G. C. Spalding, eds. Proc. SPIE 5930, 352-361 (2005).

J. Ng and C. T. Chan, private communication.

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Figures (11)

Fig. 1.
Fig. 1.

Schematic of optical path for the trapping of particle arrays in an evanescent field.

Fig. 2.
Fig. 2.

Close-up illustration of the prism and thin film used for trapping. The quarter-wave plate is used to control the relative polarization of the incident and reflected beams.

Fig. 3.
Fig. 3.

Array of 460-nm diameter spheres with s-polarized light. A centred rectangular unit cell is shown, with lattice parameters a and b perpendicular and parallel to the fringes, respectively

Fig. 4.
Fig. 4.

Hexagonal array formed by 520 nm particles in s-polarized light with 5 µm NaCl

Fig. 5.
Fig. 5.

Arrays formed by 520 nm particles in p-polarized light: (A) hex 2 structure in which every second fringe is occupied; (B) broken hex 2 structure in which every third fringe is unoccupied. Spacing of interference fringes is shown by red lines.

Fig. 6.
Fig. 6.

Square array formed by 390-nm diameter particles in p-polarized light.

Fig. 7.
Fig. 7.

Pseudohexagonal array formed by 460 nm particles in orthogonally polarized laser beams.

Fig. 8.
Fig. 8.

Sequence of video frames of an array of 520 nm particles as a quarter-wave plate is rotated to change the polarization of the retro-reflected beam from s (ϕ=0°) to p (ϕ=45°)

Fig. 9.
Fig. 9.

Arrays of 390 nm particles with (A) and without (B) interference fringes, showing the different types of defects that arise in the presence of interference fringes. a–missing row, b–vacancy, c–twin plane. The vacancies in (B) healed after a few seconds by diffusion to the edge of the array.

Fig. 10.
Fig. 10.

Three coexisting arrays of 460 nm particles in s-polarized light.

Fig. 11.
Fig. 11.

Commensurate lattices formed in s-polarized fields. B is a square lattice. A is a hexagonal lattice formed by expansion of unit cell in b direction. C is a hexagonal lattice formed by contraction of unit cell in b direction. Centered rectangular unit cell shown in red; primitive hexagonal unit cells in blue dashes.

Tables (1)

Tables Icon

Table 1. Mean lattice parameters for three particle sizes in 5 µM NaCl. Errors in a and b are ±5 nm.

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