Abstract

A one-dimensional array of dipoles, optically trapped and bound in a fringe, is considered. The coupling with the incident field is studied as a function of the number of interacting dipoles. This coupling exhibits an enhancement which collapses when the chain is too long. Two possibilities are explored to keep enhancement: shrinking the coherence and spatially phase modulating the trapping light.

© 2006 Optical Society of America

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References

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  1. V.A. Markel, "Divergence of dipole sums and the nature of non-Lorentzian exponentially narrow resonances in one-dimensional periodic arrays of nanospheres," Let. Ed., J. Phys. B: At. Mol. Phys. 38,7, L115-L121 (2005).
    [CrossRef]
  2. M. Burns, J.-M. Fournier, J.A. Golovchenko, "Optical matter: crystallization and binding in intense optical fields," Science 249,749-754 (Aug. 1990).
    [CrossRef] [PubMed]
  3. S.A. Tatarkova, A.E. Carruthers, K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89,283901, 1-4 (2002).
    [CrossRef]
  4. V. Garcés-Chávez, K. Dholakia, G.C. Spalding, "Extended-area optically induced organization of microparticles on a surface," Appl. Phys. Lett. 86,031106 (2005).
    [CrossRef]
  5. V. Garcés-Chávez, R. Quidant, P.J. Reece, G. Badenes, L. Torner, K. Dholakia, "Extended organization of colloidal microparticles by surface plasmon polariton excitation," Phys. Rev. B 73,085417 (2006).
    [CrossRef]
  6. D. Rogovin, R. McGraw, P. Yeh, "Harmonic phase conjugation in liquid suspensions of microparticles via higherorder gratings," Phys. Rev. Lett. 55,2864-2867 (1985).
    [CrossRef] [PubMed]
  7. P.W. Smith, A. Ashkin, J.E. Bjorkholm, D.J. Eilenberger, "Studies of self-focusing bistable devices using liquid suspensions of dielectric particles," Opt. Lett. 10,131-133 (1984).
    [CrossRef]
  8. C.D. Mellor, C.D. Bain, "Array formation in evanescent wave," ChemPhysChem 7,329-332 (2005).
    [CrossRef] [PubMed]
  9. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63,12, 1233-1236 (1989).
    [CrossRef] [PubMed]
  10. W. Singer, M. Frick, S. Bernet, M Ritsch-Marte, "Self-organized array of regularly spaced microbeads in a fiberoptical trap," J. Opt. Soc. Am. B 20,7, 1568-1574 (2003).
    [CrossRef]
  11. M. Guillon, "Optical trapping in rarefied media: towards laser-trapped space telescopes," in Optical Trapping and Optical Micromanipulation II, K. Dholakia and G.C. Spalding, eds., Proc. SPIE, 59301T, 1-7 (2005).
  12. F. Depasse, J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D: Appl. Phys. 27,914-919 (1994).
    [CrossRef]
  13. P. C. Chaumet,M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64,035422, 1-7 (2001).
    [CrossRef]
  14. V. Garcés-Chávez, D. Roskey, M.D. Summers, H. Melville, D. McGloin, E.M. Wright, K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 85,4001-4003 (2004).
    [CrossRef]
  15. J.D. Jackson, "Classical electrodynamics," second edition, New York, John Wiley & Son, Chpt 9.
  16. Mufei Xiao and Sergey I. Bozhevolnyi, "Resonant field enhancement by a finite-size periodic array of surface scatterers," J.Phys.: Condens. Matter 13,3001-3010 (2001).
    [CrossRef]
  17. I.S. Gradshteyn, I.M. Ryzhik, "Table of integrals series and products," (sixth edition, Alan Jeffrey, Academic Press, 2000).
  18. O. Moine, B. Stout, "Optical force calculations in arbitrary beams using the vector addition theorem," J. Opt. Soc. Am. B 22,1620-1631 (2005).
    [CrossRef]

2006

V. Garcés-Chávez, R. Quidant, P.J. Reece, G. Badenes, L. Torner, K. Dholakia, "Extended organization of colloidal microparticles by surface plasmon polariton excitation," Phys. Rev. B 73,085417 (2006).
[CrossRef]

2005

V.A. Markel, "Divergence of dipole sums and the nature of non-Lorentzian exponentially narrow resonances in one-dimensional periodic arrays of nanospheres," Let. Ed., J. Phys. B: At. Mol. Phys. 38,7, L115-L121 (2005).
[CrossRef]

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

C.D. Mellor, C.D. Bain, "Array formation in evanescent wave," ChemPhysChem 7,329-332 (2005).
[CrossRef] [PubMed]

O. Moine, B. Stout, "Optical force calculations in arbitrary beams using the vector addition theorem," J. Opt. Soc. Am. B 22,1620-1631 (2005).
[CrossRef]

2004

V. Garcés-Chávez, D. Roskey, M.D. Summers, H. Melville, D. McGloin, E.M. Wright, K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 85,4001-4003 (2004).
[CrossRef]

2003

2002

S.A. Tatarkova, A.E. Carruthers, K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89,283901, 1-4 (2002).
[CrossRef]

2001

P. C. Chaumet,M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64,035422, 1-7 (2001).
[CrossRef]

Mufei Xiao and Sergey I. Bozhevolnyi, "Resonant field enhancement by a finite-size periodic array of surface scatterers," J.Phys.: Condens. Matter 13,3001-3010 (2001).
[CrossRef]

1994

F. Depasse, J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D: Appl. Phys. 27,914-919 (1994).
[CrossRef]

1990

M. Burns, J.-M. Fournier, J.A. Golovchenko, "Optical matter: crystallization and binding in intense optical fields," Science 249,749-754 (Aug. 1990).
[CrossRef] [PubMed]

1989

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63,12, 1233-1236 (1989).
[CrossRef] [PubMed]

1985

D. Rogovin, R. McGraw, P. Yeh, "Harmonic phase conjugation in liquid suspensions of microparticles via higherorder gratings," Phys. Rev. Lett. 55,2864-2867 (1985).
[CrossRef] [PubMed]

1984

Ashkin, A.

Badenes, G.

V. Garcés-Chávez, R. Quidant, P.J. Reece, G. Badenes, L. Torner, K. Dholakia, "Extended organization of colloidal microparticles by surface plasmon polariton excitation," Phys. Rev. B 73,085417 (2006).
[CrossRef]

Bain, C.D.

C.D. Mellor, C.D. Bain, "Array formation in evanescent wave," ChemPhysChem 7,329-332 (2005).
[CrossRef] [PubMed]

Bernet, S.

Bjorkholm, J.E.

Burns, M.

M. Burns, J.-M. Fournier, J.A. Golovchenko, "Optical matter: crystallization and binding in intense optical fields," Science 249,749-754 (Aug. 1990).
[CrossRef] [PubMed]

Burns, M. M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63,12, 1233-1236 (1989).
[CrossRef] [PubMed]

Carruthers, A.E.

S.A. Tatarkova, A.E. Carruthers, K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89,283901, 1-4 (2002).
[CrossRef]

Chaumet, P. C.

P. C. Chaumet,M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64,035422, 1-7 (2001).
[CrossRef]

Depasse, F.

F. Depasse, J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D: Appl. Phys. 27,914-919 (1994).
[CrossRef]

Dholakia, K.

V. Garcés-Chávez, R. Quidant, P.J. Reece, G. Badenes, L. Torner, K. Dholakia, "Extended organization of colloidal microparticles by surface plasmon polariton excitation," Phys. Rev. B 73,085417 (2006).
[CrossRef]

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

V. Garcés-Chávez, D. Roskey, M.D. Summers, H. Melville, D. McGloin, E.M. Wright, K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 85,4001-4003 (2004).
[CrossRef]

S.A. Tatarkova, A.E. Carruthers, K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89,283901, 1-4 (2002).
[CrossRef]

Eilenberger, D.J.

Fournier, J.-M.

M. Burns, J.-M. Fournier, J.A. Golovchenko, "Optical matter: crystallization and binding in intense optical fields," Science 249,749-754 (Aug. 1990).
[CrossRef] [PubMed]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63,12, 1233-1236 (1989).
[CrossRef] [PubMed]

Frick, M.

Garcés-Chávez, V.

V. Garcés-Chávez, R. Quidant, P.J. Reece, G. Badenes, L. Torner, K. Dholakia, "Extended organization of colloidal microparticles by surface plasmon polariton excitation," Phys. Rev. B 73,085417 (2006).
[CrossRef]

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

V. Garcés-Chávez, D. Roskey, M.D. Summers, H. Melville, D. McGloin, E.M. Wright, K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 85,4001-4003 (2004).
[CrossRef]

Golovchenko, J. A.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63,12, 1233-1236 (1989).
[CrossRef] [PubMed]

Golovchenko, J.A.

M. Burns, J.-M. Fournier, J.A. Golovchenko, "Optical matter: crystallization and binding in intense optical fields," Science 249,749-754 (Aug. 1990).
[CrossRef] [PubMed]

Markel, V.A.

V.A. Markel, "Divergence of dipole sums and the nature of non-Lorentzian exponentially narrow resonances in one-dimensional periodic arrays of nanospheres," Let. Ed., J. Phys. B: At. Mol. Phys. 38,7, L115-L121 (2005).
[CrossRef]

McGloin, D.

V. Garcés-Chávez, D. Roskey, M.D. Summers, H. Melville, D. McGloin, E.M. Wright, K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 85,4001-4003 (2004).
[CrossRef]

McGraw, R.

D. Rogovin, R. McGraw, P. Yeh, "Harmonic phase conjugation in liquid suspensions of microparticles via higherorder gratings," Phys. Rev. Lett. 55,2864-2867 (1985).
[CrossRef] [PubMed]

Mellor, C.D.

C.D. Mellor, C.D. Bain, "Array formation in evanescent wave," ChemPhysChem 7,329-332 (2005).
[CrossRef] [PubMed]

Melville, H.

V. Garcés-Chávez, D. Roskey, M.D. Summers, H. Melville, D. McGloin, E.M. Wright, K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 85,4001-4003 (2004).
[CrossRef]

Moine, O.

Nieto-Vesperinas, M.

P. C. Chaumet,M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64,035422, 1-7 (2001).
[CrossRef]

Quidant, R.

V. Garcés-Chávez, R. Quidant, P.J. Reece, G. Badenes, L. Torner, K. Dholakia, "Extended organization of colloidal microparticles by surface plasmon polariton excitation," Phys. Rev. B 73,085417 (2006).
[CrossRef]

Reece, P.J.

V. Garcés-Chávez, R. Quidant, P.J. Reece, G. Badenes, L. Torner, K. Dholakia, "Extended organization of colloidal microparticles by surface plasmon polariton excitation," Phys. Rev. B 73,085417 (2006).
[CrossRef]

Ritsch-Marte, M

Rogovin, D.

D. Rogovin, R. McGraw, P. Yeh, "Harmonic phase conjugation in liquid suspensions of microparticles via higherorder gratings," Phys. Rev. Lett. 55,2864-2867 (1985).
[CrossRef] [PubMed]

Roskey, D.

V. Garcés-Chávez, D. Roskey, M.D. Summers, H. Melville, D. McGloin, E.M. Wright, K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 85,4001-4003 (2004).
[CrossRef]

Singer, W.

Smith, P.W.

Spalding, G.C.

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

Stout, B.

Summers, M.D.

V. Garcés-Chávez, D. Roskey, M.D. Summers, H. Melville, D. McGloin, E.M. Wright, K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 85,4001-4003 (2004).
[CrossRef]

Tatarkova, S.A.

S.A. Tatarkova, A.E. Carruthers, K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89,283901, 1-4 (2002).
[CrossRef]

Torner, L.

V. Garcés-Chávez, R. Quidant, P.J. Reece, G. Badenes, L. Torner, K. Dholakia, "Extended organization of colloidal microparticles by surface plasmon polariton excitation," Phys. Rev. B 73,085417 (2006).
[CrossRef]

Vigoureux, J.-M.

F. Depasse, J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D: Appl. Phys. 27,914-919 (1994).
[CrossRef]

Wright, E.M.

V. Garcés-Chávez, D. Roskey, M.D. Summers, H. Melville, D. McGloin, E.M. Wright, K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 85,4001-4003 (2004).
[CrossRef]

Yeh, P.

D. Rogovin, R. McGraw, P. Yeh, "Harmonic phase conjugation in liquid suspensions of microparticles via higherorder gratings," Phys. Rev. Lett. 55,2864-2867 (1985).
[CrossRef] [PubMed]

Appl. Phys. Lett.

V. Garcés-Chávez, D. Roskey, M.D. Summers, H. Melville, D. McGloin, E.M. Wright, K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 85,4001-4003 (2004).
[CrossRef]

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

ChemPhysChem

C.D. Mellor, C.D. Bain, "Array formation in evanescent wave," ChemPhysChem 7,329-332 (2005).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

J. Phys. B: At. Mol. Phys.

V.A. Markel, "Divergence of dipole sums and the nature of non-Lorentzian exponentially narrow resonances in one-dimensional periodic arrays of nanospheres," Let. Ed., J. Phys. B: At. Mol. Phys. 38,7, L115-L121 (2005).
[CrossRef]

J. Phys. D: Appl. Phys.

F. Depasse, J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D: Appl. Phys. 27,914-919 (1994).
[CrossRef]

J.Phys.: Condens. Matter

Mufei Xiao and Sergey I. Bozhevolnyi, "Resonant field enhancement by a finite-size periodic array of surface scatterers," J.Phys.: Condens. Matter 13,3001-3010 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev. B

P. C. Chaumet,M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64,035422, 1-7 (2001).
[CrossRef]

V. Garcés-Chávez, R. Quidant, P.J. Reece, G. Badenes, L. Torner, K. Dholakia, "Extended organization of colloidal microparticles by surface plasmon polariton excitation," Phys. Rev. B 73,085417 (2006).
[CrossRef]

Phys. Rev. Lett.

D. Rogovin, R. McGraw, P. Yeh, "Harmonic phase conjugation in liquid suspensions of microparticles via higherorder gratings," Phys. Rev. Lett. 55,2864-2867 (1985).
[CrossRef] [PubMed]

S.A. Tatarkova, A.E. Carruthers, K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89,283901, 1-4 (2002).
[CrossRef]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63,12, 1233-1236 (1989).
[CrossRef] [PubMed]

Science

M. Burns, J.-M. Fournier, J.A. Golovchenko, "Optical matter: crystallization and binding in intense optical fields," Science 249,749-754 (Aug. 1990).
[CrossRef] [PubMed]

Other

I.S. Gradshteyn, I.M. Ryzhik, "Table of integrals series and products," (sixth edition, Alan Jeffrey, Academic Press, 2000).

J.D. Jackson, "Classical electrodynamics," second edition, New York, John Wiley & Son, Chpt 9.

M. Guillon, "Optical trapping in rarefied media: towards laser-trapped space telescopes," in Optical Trapping and Optical Micromanipulation II, K. Dholakia and G.C. Spalding, eds., Proc. SPIE, 59301T, 1-7 (2005).

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Figures (9)

Fig. 1.
Fig. 1.

Configuration of the trapped chain made of induced scattering dipoles.

Fig. 2.
Fig. 2.

Deviation of position from lambda periodicity for a finite chain. The longer the chain, the weaker the edge effects.

Fig. 3.
Fig. 3.

Numerical calculation of field enhancement (blue curve) for the dipole in the middle of the chain, is compared to the presented simple approximation (red curve) of uniform field. The maximum enhancement does not happen exactly for the same number of dipoles. The difference between these two curves is due to edge effects. For small Ndip , the field increases logarithmically. Curves plotted for k 3 α = 0.86.

Fig. 4.
Fig. 4.

Field seen by dipoles as a function of their position in the chain (starting from the middle). The red line represents the numerical value obtained by the infinite chain model.

Fig. 5.
Fig. 5.

Inverse of squared impedance ( 1 1 e 2 ikd f 2 ( k d ) 2 ) of a pair of interacting dipoles for different values of distance: d=λ 0 (blue), 2λ 0 (green), 3λ 0 (red), 4λ 0 (yellow), 5λ 0 (cyan). Curves plotted as a function of λ 0/λ.

Fig. 6.
Fig. 6.

Interaction between two dipoles.

Fig. 7.
Fig. 7.

( E n E 0 ) 2 for an infinite chain of dipoles as a function of λ 0/λ. Curve plotted for k03 α= 0.4.

Fig. 8.
Fig. 8.

Color coded intensity as a function of the grating step k d 2 π and the phase modulation period N. Curve plotted for k 3 α = 0.86. One of the tails is enlarged in the upper right corner. Field enhancement is the strongest in this part of the curve.

Fig. 9.
Fig. 9.

Cross section of the curve on Fig. 8 for N=100 (blue curve), N=150 (green curve) and N=200 (red curve).

Equations (16)

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

E s , j = k 3 α j E j e ikr ( 1 k r 1 ( k r ) 3 + i ( k r ) 2 )
E n = E 0 , n + j n ; j = 1 N k 3 α j E j e ikd n j ( 1 k d n j 1 ( k d n j ) 3 + i ( k d n j ) 2 )
n 1 , N , E n = E 0 1 k 3 α j 0 ; j = N / 2 j = N / 2 e ikd j ( 1 k d j 1 ( k d j ) 3 + i ( k d j ) 2 )
E n , res E 0 = i 3 π 2 ( 2 π ) 2 k 0 3 α = i 12 k 0 3 α
E ˜ 1 ( ω ) = E ˜ 10 ( ω ) + e ikd f ( k d ) E ˜ 2 ( ω )
E ˜ 2 ( ω ) = E ˜ 20 ( ω ) + e ikd f ( k d ) E ˜ 1 ( ω )
E ˜ 1 ( ω ) = E ˜ 10 ( ω ) + e ikd f ( k d ) E ˜ 20 ( ω ) 1 e 2 ikd f 2 ( k d )
E ˜ 2 ( ω ) = E ˜ 20 ( ω ) + e ikd f ( k d ) E ˜ 10 ( ω ) 1 e 2 ikd f 2 ( k d )
< W 1 > t = 4 παε E ˜ 1 ( ω ) 2 d ω
< W 1 > t = 4 παε ( E ˜ 10 ( ω ) 2 + f ( k d ) E ˜ 20 ( ω ) 2 1 e 2 ikd f 2 ( k d ) 2 d ω + 2 R ( E ˜ 10 ( ω ) e ikd f ( k d ) E ˜ 20 * ( ω ) ) 1 e 2 ikd f 2 ( k d ) 2 d ω )
E ˜ 10 ( ω ) 2 1 e 2 ikd f 2 ( k d ) 2 d ω = < E ˜ 0 ( ω ) 2 > ω
+ 1 ( 2 k 0 d ) 2 E ˜ 10 ( ω ) 2 cos ( 2 k d ) d ω + o ( 1 ( k 0 d ) 2 )
f ( k d ) E ˜ 20 ( ω ) 2 1 e 2 ikd f 2 ( k d ) 2 d ω = < E ˜ 0 2 > ω ( k 0 d ) 2 + o ( 1 ( k 0 d ) 2 )
2 R ( E ˜ 10 ( ω ) e ikd f ( k d ) E ˜ 20 * ( ω ) ) 1 e 2 ikd f 2 ( k d ) 2 d ω = 2 k 0 d E ˜ 0 ( ω ) 2 cos ( k d ) d ω + o ( 1 ( k 0 d ) 2 )
E ˜ n ( ω ) = E ˜ 0 ( ω ) 1 2 j > 0 e i jkd f ( jkd )
E n = E 0 1 2 j > 0 cos ( 2 iπj / N ) e i jkd f ( jkd )

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