Abstract

Explicit partial wave coefficients are derived for nondiffractive vector Bessel beam of arbitrary order and polarization. Calculations based on the analytical partial wave expansion yield results that agree well with recent numerical calculations and experiments on optical binding. We have also investigated how one can tailor the interparticle interaction by overlaying different coatings. It is found that the Ag and low dielectric coating can increase the number of equilibrium positions, whereas the antireflection coating reduces it.

© 2010 Optical Society of America

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Corrections

Jun Chen, Jack Ng, Pei Wang, and Zhifang Lin, "Analytical partial wave expansion of vector Bessel beam and its application to optical binding: erratum," Opt. Lett. 36, 1243-1243 (2011)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-36-7-1243

References

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  18. The data of in Fig. are retrieved by a computer software and are replotted here, together with our own independent results.
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    [CrossRef]
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2009 (4)

G. Gouesbet, J. Quant. Spectrosc. Radiat. Transf. 110, 1223 (2009).
[CrossRef]

J. M. Taylor and G. D. Love, J. Opt. Soc. Am. A 26, 278 (2009).
[CrossRef]

J. Chen, J. Ng, S. Y. Liu, and Z. F. Lin, Phys. Rev. E 80, 026607 (2009).
[CrossRef]

V. Karasek, O. Brzobohaty, and P. Zemanek, J. Opt. A 11, 034009 (2009).
[CrossRef]

2008 (3)

Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Appl. Phys. 103, 093119 (2008).
[CrossRef]

V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schaffer, Opt. Express 16, 13831 (2008).
[CrossRef] [PubMed]

V. Karasek, T. Cizmar, O. Brzobohaty, and P. Zemanek, Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef] [PubMed]

2006 (2)

2005 (2)

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Phys. Rev. B 72, 085130 (2005).
[CrossRef]

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

2002 (2)

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

J. Tervo, P. Vahimaa, and J. Turunen, J. Mod. Opt. 49, 1537 (2002).
[CrossRef]

2001 (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

2000 (1)

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

1995 (1)

Z. Bouchal and M. Olivik, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

1993 (1)

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
[CrossRef] [PubMed]

1987 (1)

Ander, M.

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

Barbosa, L. C.

Bohren, C. F.

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

Bormuth, V.

Bouchal, Z.

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, New J. Phys. 8, 43 (2006).
[CrossRef]

Z. Bouchal and M. Olivik, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

Brzobohaty, O.

V. Karasek, O. Brzobohaty, and P. Zemanek, J. Opt. A 11, 034009 (2009).
[CrossRef]

V. Karasek, T. Cizmar, O. Brzobohaty, and P. Zemanek, Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef] [PubMed]

Cesar, C. L.

Chan, C. T.

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Phys. Rev. B 72, 085130 (2005).
[CrossRef]

Chen, J.

J. Chen, J. Ng, S. Y. Liu, and Z. F. Lin, Phys. Rev. E 80, 026607 (2009).
[CrossRef]

Cizmar, T.

V. Karasek, T. Cizmar, O. Brzobohaty, and P. Zemanek, Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef] [PubMed]

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, New J. Phys. 8, 43 (2006).
[CrossRef]

Cruz, C. H. B.

Dholakia, K.

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

Durnin, J.

Fontes, A.

Garces-Chavez, V.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

Gouesbet, G.

G. Gouesbet, J. Quant. Spectrosc. Radiat. Transf. 110, 1223 (2009).
[CrossRef]

Hecht, B.

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

Heckenberg, N. R.

Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Appl. Phys. 103, 093119 (2008).
[CrossRef]

Herminghaus, S.

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
[CrossRef] [PubMed]

Hitomi, T.

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

Howard, J.

Hu, Y.

Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Appl. Phys. 103, 093119 (2008).
[CrossRef]

Huffman, D. R.

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

Jannasch, A.

Karasek, V.

V. Karasek, O. Brzobohaty, and P. Zemanek, J. Opt. A 11, 034009 (2009).
[CrossRef]

V. Karasek, T. Cizmar, O. Brzobohaty, and P. Zemanek, Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef] [PubMed]

Kollarova, V.

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, New J. Phys. 8, 43 (2006).
[CrossRef]

Lin, Z. F.

J. Chen, J. Ng, S. Y. Liu, and Z. F. Lin, Phys. Rev. E 80, 026607 (2009).
[CrossRef]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Phys. Rev. B 72, 085130 (2005).
[CrossRef]

Liu, S. Y.

J. Chen, J. Ng, S. Y. Liu, and Z. F. Lin, Phys. Rev. E 80, 026607 (2009).
[CrossRef]

Love, G. D.

McGloin, D.

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

Melville, H.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

Neves, A. A. R.

Ng, J.

J. Chen, J. Ng, S. Y. Liu, and Z. F. Lin, Phys. Rev. E 80, 026607 (2009).
[CrossRef]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Phys. Rev. B 72, 085130 (2005).
[CrossRef]

Nieminen, T. A.

Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Appl. Phys. 103, 093119 (2008).
[CrossRef]

Novotny, L.

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

Olivik, M.

Z. Bouchal and M. Olivik, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

Padilha, L. A.

Rodriguez, E.

Rubinsztein-Dunlop, H.

Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Appl. Phys. 103, 093119 (2008).
[CrossRef]

Schaffer, E.

Sheng, P.

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Phys. Rev. B 72, 085130 (2005).
[CrossRef]

Sibbett, W.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

Taylor, J. M.

Tervo, J.

J. Tervo, P. Vahimaa, and J. Turunen, J. Mod. Opt. 49, 1537 (2002).
[CrossRef]

Turunen, J.

J. Tervo, P. Vahimaa, and J. Turunen, J. Mod. Opt. 49, 1537 (2002).
[CrossRef]

Vahimaa, P.

J. Tervo, P. Vahimaa, and J. Turunen, J. Mod. Opt. 49, 1537 (2002).
[CrossRef]

van Blaaderen, A.

van Kats, C. M.

Wulle, T.

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
[CrossRef] [PubMed]

Zemanek, P.

V. Karasek, O. Brzobohaty, and P. Zemanek, J. Opt. A 11, 034009 (2009).
[CrossRef]

V. Karasek, T. Cizmar, O. Brzobohaty, and P. Zemanek, Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef] [PubMed]

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, New J. Phys. 8, 43 (2006).
[CrossRef]

Appl. Phys. B (1)

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

J. Appl. Phys. (1)

Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Appl. Phys. 103, 093119 (2008).
[CrossRef]

J. Mod. Opt. (2)

Z. Bouchal and M. Olivik, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

J. Tervo, P. Vahimaa, and J. Turunen, J. Mod. Opt. 49, 1537 (2002).
[CrossRef]

J. Opt. A (1)

V. Karasek, O. Brzobohaty, and P. Zemanek, J. Opt. A 11, 034009 (2009).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transf. (1)

G. Gouesbet, J. Quant. Spectrosc. Radiat. Transf. 110, 1223 (2009).
[CrossRef]

Nature (1)

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

New J. Phys. (1)

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, New J. Phys. 8, 43 (2006).
[CrossRef]

Opt. Commun. (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Phys. Rev. B 72, 085130 (2005).
[CrossRef]

Phys. Rev. E (1)

J. Chen, J. Ng, S. Y. Liu, and Z. F. Lin, Phys. Rev. E 80, 026607 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

V. Karasek, T. Cizmar, O. Brzobohaty, and P. Zemanek, Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef] [PubMed]

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
[CrossRef] [PubMed]

Other (3)

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

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

The data of in Fig. are retrieved by a computer software and are replotted here, together with our own independent results.

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Figures (2)

Fig. 1
Fig. 1

Comparing our optical force with [12]. (a) The long-range multistability and (b) an enlarged view of (a) showing the short-range multistability. The crosses denote the stable interparticle separations by Karasek et al. [12]. Parameters for our calculations are the same as those in Fig. 1 of [12].

Fig. 2
Fig. 2

Force acting on two coated spheres. The wavelength of BBs in vacuum is 1064 nm, and the core radii ρ 0 = 1.8 μ m . The radius of the spheres in water ( ε m = 1.77 ) is 500 nm (size parameter = 3.9 ), and refractive index, n s = 1.8 . r s is the total radius of one coated sphere. (a) Without coating, (b) low dielectric coating ( thickness = 100   nm , n low = 1.18 ), (c) Ag coating ( thickness = 5   nm , n Ag = 0.226 + 6.99 i ), and (d) antireflection coating ( thickness = 172   nm , n anti = 1.55 ). The insets show apparent short-range multistability (marked by vertical dotted lines).

Equations (11)

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E ( r , θ , ϕ ) = | E 0 | 2 π α = 0 α max β = 0 2 π Q P ( α , β ) exp { i k r [ S   α   S   θ   C ( β ϕ ) + C   α   C   θ ] } S   α d α d β ,
Q = [ p x ( C   α C 2 β + S 2 β ) p y ( 1 C   α ) S   β   C   β p x ( 1 C   α ) S   β   C   β + p y ( C   α S 2 β + C 2 β ) p x   S   α   C   β p y   S   α   S   β ] ,
E = n = 1 m = n n i E m n [ p m n N m n ( s ) + q m n M m n ( s ) ] ,
[ p m n q m n ] = [ i i m 2 ] γ m n 1 / 2 2 π α = 0 α max β = 0 2 π d α d β   S   α exp ( i m β ) P ( α , β ) exp ( i k z 0   C   α ) exp [ i k ϱ 0   S   α   C ( β ϕ 0 ) ] [ ( p y   C   β p x   S   β ) π m n ( C   α ) + i ( p y   S   β + p x   C   β ) τ m n ( C   α ) ] ,
0 2 π exp [ i x   C ( β ϕ ) ] [ C   n ϕ S   n ϕ ] exp ( i m ϕ ) d ϕ = [ π i n m J n m ( x ) exp [ i ( n m ) β ] + π i n + m J n + m ( x ) exp [ i ( n + m ) β ] i π i n m J n m ( x ) exp [ i ( n m ) β ] i π i n + m J n + m ( x ) exp [ i ( n + m ) β ] ] ,
0 π P n m ( C   θ ) J m ( k r   S   α   S   θ ) exp ( i k r   C   α   C   θ ) S   θ d θ = 2 i n m P n m ( C   α ) j n ( k r ) ,
[ p m n i q m n ] = i l m + 1 exp [ i ( l m ) ϕ 0 ] γ m n 1 / 2 exp ( i b z 0 ) ϑ ,
ϑ = [ ( m l ) J m l ( a ϱ 0 ) π m n ( C   α 0 ) / a ϱ 0 + J m l ( a ϱ 0 ) τ m n ( C   α 0 ) ] [ p x   C   ϕ 0 + p y   S   ϕ 0 p y   C   ϕ 0 p x   S   ϕ 0 ] + i [ ( m l ) J m l ( a ϱ 0 ) τ m n ( C   α 0 ) / a ϱ 0 + J m l ( a ϱ 0 ) π m n ( C   α 0 ) ] [ p x   S   ϕ 0 p y   C   ϕ 0 p y   S   ϕ 0 + p x   C   ϕ 0 ] ,
[ p m n q m n ] = i l m exp [ i ( l m ) ϕ 0 ] γ m n 1 / 2 J m l ( a ϱ 0 ) exp ( i b z 0 ) ζ ,
ζ = [ τ m n ( C   α 0 ) π m n ( C   α 0 ) ]
ζ = [ i π m n ( C   α 0 ) i τ m n ( C   α 0 ) ]

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