Abstract

We show that submicrometer silicon spheres, whose polarizabilities are completely given by their two first Mie coefficients, are an excellent laboratory to test effects of both angle-suppressed and resonant differential scattering cross sections. Specifically, outstanding scattering angular distributions, with zero forward- or backward-scattered intensity, (i.e., the so-called Kerker conditions), previously discussed for hypothetical magnetodielectric particles, are now observed for those Si objects in the near infrared. Interesting new consequences for the corresponding optical forces are derived from the interplay, both in and out of resonance, between the electric- and magnetic-induced dipoles.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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2010

2009

S. Albaladejo, M. Marques, F. Scheffold, and J. J. Sáenz, “Giant enhanced diffusion of gold nanoparticles in optical vortex fields,” Nano Lett. 9, 3527–3531 (2009).
[CrossRef] [PubMed]

P. Wu, R. Huang, C. Tischer, A. Jonas, and E. L. Florin, “Direct measurement of the nonconservative force field generated by optical tweezers,” Phys. Rev. Lett. 103, 108101 (2009).
[CrossRef] [PubMed]

I. Zapata, S. Albaladejo, J. M. R. Parrondo, J. J. Sáenz, and F. Sols, “Deterministic ratchet from stationary light fields,” Phys. Rev. Lett. 103, 130601 (2009).
[CrossRef] [PubMed]

P. C. Chaumet and A. Rahmani, “Electromagnetic force and torque on magnetic and negative-index scatterers,” Opt. Express 17, 2224–2234 (2009).
[CrossRef] [PubMed]

A. Alu and N. Engheta, “The quest for magnetic plasmons at optical frequencies,” Opt. Express 17, 5723–5730 (2009).
[CrossRef] [PubMed]

M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79, 073103 (2009).
[CrossRef]

K. Vynck, D. Felbacq, E. Centeno, A. I. Ca¢buz, D. Cassagne, and B. Guizal, “All-dielectric rod-type metamaterials at optical frequencies,” Phys. Rev. Lett. 102, 133901 (2009).
[CrossRef] [PubMed]

J. A. Schuller and Mark L. Brongersma, “General properties of dielectric optical antennas,” Opt. Express 17, 24084–24095(2009).
[CrossRef]

S. Albaladejo, M. I. Marques, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef] [PubMed]

2008

B. García-Camara, F. Moreno, F. Gonzalez, and J. M. Saiz, “Exception for the zero-forward-scattering theory,” J. Opt. Soc. Am. A 25, 2875–2878 (2008).
[CrossRef]

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[CrossRef] [PubMed]

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef] [PubMed]

2007

R. C. J. Hsu, A. Ayazi, B. Houshmand, and B. Jalali, “All-dielectric photonic-assisted radio front-end technology,” Nat. Photon. 1, 535–538 (2007).
[CrossRef]

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98, 157403 (2007).
[CrossRef] [PubMed]

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401(2007).
[CrossRef] [PubMed]

2006

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

L. Jyhlä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102–043108 (2006).
[CrossRef]

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett. 96, 238101 (2006).
[CrossRef] [PubMed]

V. Wong and M. Ratner, “Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles,” Phys. Rev. B 73, 075416 (2006).
[CrossRef]

2005

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[CrossRef]

2004

K. C. Huang, M. L. Povinelli, and J. D. Joannopoulos, “Negative effective permeability in polaritonic photonic crystals,” Appl. Phys. Lett. 85, 543–545 (2004).
[CrossRef]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, “Near-field photonic forces,” Phil. Trans. R. Soc. A 362, 719 (2004).
[CrossRef] [PubMed]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2895 (2004).
[CrossRef]

2003

2001

R. Gómez-Medina, P. San Jose, A. García-Martin, M. Lester, M. Nieto-Vesperinas, and J. J. Sáenz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275–4277 (2001).
[CrossRef] [PubMed]

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

2000

P. C. Chaumet and M. Nieto-Vesperinas, “Electromagnetic force on a metallic particle in the presence of a dielectric surface,” Phys. Rev. B 62, 11185–11191 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, “Time-averaged total force on a dipolar sphere in an electromagnetic field,” Opt. Lett. 25, 1065–1067 (2000).
[CrossRef]

1997

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. U.S.A. 94, 4853–4860 (1997).
[CrossRef] [PubMed]

1994

M. C. Simon and D. C. Farías, “Reflection and refraction in uniaxial crystals with dielectric and magnetic anisotropy,” J. Mod. Opt. 41, 413–429 (1994).
[CrossRef]

R. K. Mongia and P. Bhartia, “Dielectric resonator antennas—a review and general design relations for resonant frequency and bandwidth,” Int. J. Microw. Millim. Wave Comput. Aided Eng. 4, 230–247 (1994).
[CrossRef]

1992

G. Videen and W. S. Bickel, “Light-scattering resonances in small spheres,” Phys. Rev. A 45, 6008–6012 (1992).
[CrossRef] [PubMed]

1991

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space,” J. Mod. Opt. 38, 649–657(1991).
[CrossRef]

1990

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

1986

1983

1978

P. Chylek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

1977

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

Aitchison, J. S.

M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79, 073103 (2009).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[CrossRef]

Aizpurua, J.

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Perez, C. Lopez, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Saenz, “Strong magnetic response of silicon nanoparticles in the infrared,” Opt. Express (submitted 2010), ArXiv:1005.5446v1.

Albaladejo, S.

S. Albaladejo, R. Gómez-Medina, L. S. Froufe-Pérez, H. Marinchio, R. Carminati, J. F. Torrado, G. Armelles, A. García-Martin, and J. J. Sáenz, “Radiative corrections to the polarizability tensor of an electrically small anisotropic dielectric particle,” Opt. Express 18, 3556–3572 (2010).
[CrossRef] [PubMed]

S. Albaladejo, M. I. Marques, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef] [PubMed]

S. Albaladejo, M. Marques, F. Scheffold, and J. J. Sáenz, “Giant enhanced diffusion of gold nanoparticles in optical vortex fields,” Nano Lett. 9, 3527–3531 (2009).
[CrossRef] [PubMed]

I. Zapata, S. Albaladejo, J. M. R. Parrondo, J. J. Sáenz, and F. Sols, “Deterministic ratchet from stationary light fields,” Phys. Rev. Lett. 103, 130601 (2009).
[CrossRef] [PubMed]

Alu, A.

A. Alu and N. Engheta, “How does zero forward-scattering in magnetodielectric nanoparticles comply with optical theorem,” J. Nanophoton. 4, 041590 (2010).
[CrossRef]

A. Alu and N. Engheta, “The quest for magnetic plasmons at optical frequencies,” Opt. Express 17, 5723–5730 (2009).
[CrossRef] [PubMed]

Arias-Gonzalez, J. R.

Armelles, G.

Ashkin, A.

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. U.S.A. 94, 4853–4860 (1997).
[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, 288–291 (1986).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

Ayazi, A.

R. C. J. Hsu, A. Ayazi, B. Houshmand, and B. Jalali, “All-dielectric photonic-assisted radio front-end technology,” Nat. Photon. 1, 535–538 (2007).
[CrossRef]

Badenes, G.

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett. 96, 238101 (2006).
[CrossRef] [PubMed]

Bhartia, P.

R. K. Mongia and P. Bhartia, “Dielectric resonator antennas—a review and general design relations for resonant frequency and bandwidth,” Int. J. Microw. Millim. Wave Comput. Aided Eng. 4, 230–247 (1994).
[CrossRef]

Bickel, W. S.

G. Videen and W. S. Bickel, “Light-scattering resonances in small spheres,” Phys. Rev. A 45, 6008–6012 (1992).
[CrossRef] [PubMed]

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2895 (2004).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles ( Wiley, 1998).
[CrossRef]

Brongersma, M. L.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401(2007).
[CrossRef] [PubMed]

Brongersma, Mark L.

Burns, M. M.

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

Ca¢buz, A. I.

K. Vynck, D. Felbacq, E. Centeno, A. I. Ca¢buz, D. Cassagne, and B. Guizal, “All-dielectric rod-type metamaterials at optical frequencies,” Phys. Rev. Lett. 102, 133901 (2009).
[CrossRef] [PubMed]

Carminati, R.

Cassagne, D.

K. Vynck, D. Felbacq, E. Centeno, A. I. Ca¢buz, D. Cassagne, and B. Guizal, “All-dielectric rod-type metamaterials at optical frequencies,” Phys. Rev. Lett. 102, 133901 (2009).
[CrossRef] [PubMed]

Centeno, E.

K. Vynck, D. Felbacq, E. Centeno, A. I. Ca¢buz, D. Cassagne, and B. Guizal, “All-dielectric rod-type metamaterials at optical frequencies,” Phys. Rev. Lett. 102, 133901 (2009).
[CrossRef] [PubMed]

Chantada, L.

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18, 11428–11443 (2010).
[CrossRef] [PubMed]

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Perez, C. Lopez, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Saenz, “Strong magnetic response of silicon nanoparticles in the infrared,” Opt. Express (submitted 2010), ArXiv:1005.5446v1.

Chaumet, P. C.

P. C. Chaumet and A. Rahmani, “Electromagnetic force and torque on magnetic and negative-index scatterers,” Opt. Express 17, 2224–2234 (2009).
[CrossRef] [PubMed]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, “Near-field photonic forces,” Phil. Trans. R. Soc. A 362, 719 (2004).
[CrossRef] [PubMed]

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

P. C. Chaumet and M. Nieto-Vesperinas, “Electromagnetic force on a metallic particle in the presence of a dielectric surface,” Phys. Rev. B 62, 11185–11191 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, “Time-averaged total force on a dipolar sphere in an electromagnetic field,” Opt. Lett. 25, 1065–1067 (2000).
[CrossRef]

Chen, H.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98, 157403 (2007).
[CrossRef] [PubMed]

Chen, J. I. L.

M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79, 073103 (2009).
[CrossRef]

Chu, S.

Chylek, P.

P. Chylek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

Dholakia, K.

K. Dholakia and P. Zemánek, “Gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[CrossRef]

Dziedzic, J. M.

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, 288–291 (1986).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

Engheta, N.

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Figures (2)

Fig. 1
Fig. 1

Results for an Si sphere of radius a = 230 nm , ϵ p = 12 and μ p = 1 . The host medium has ϵ = μ = 1 . (a) Normalized real and imaginary parts of both the electric and magnetic polarizabilities. (b) Normalized differential scattering cross section in the forward and backscattering direction. The first and second Kerker conditions are marked by the right and left vertical lines, respectively.

Fig. 2
Fig. 2

Different contributions to the total radiation pressure, versus the wavelength, for the Si particle of Fig. 1. Normalization is done by either the electric force magnitude F e or F 0 = k a 3 | e ( i ) | 2 / 2 . Again, the vertical lines mark, from right to left, the first and second Kerker conditions. Notice that, when the first Kerker condition is fulfilled, i.e., α e = α m and α e = α m , F = F e = F m = F e m .

Equations (21)

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α e = α e ( 0 ) 1 i 2 3 ϵ k 3 α e ( 0 ) , α m = α m ( 0 ) 1 i 2 3 μ k 3 α m ( 0 ) .
σ ( ext ) = 4 π k { ϵ 1 α e + μ α m } ,
σ ( s ) = 8 π 3 k 4 { | ϵ 1 α e | 2 + | μ α m | 2 } .
σ ( a ) = 4 π k [ ( ϵ A ) 1 α e ( 0 ) + μ B 1 α m ( 0 ) ] , A = | 1 i 2 3 ϵ k 3 α e ( 0 ) | 2 , B = | 1 i 2 3 μ k 3 α m ( 0 ) | 2 .
d σ PED ( s ) d Ω ( θ ) = k 4 2 | ϵ 1 α e | 2 ( 1 + cos 2 θ ) ,
d σ ( s ) d Ω ( θ ) = k 4 2 ( | ϵ 1 α e | 2 + | μ α m | 2 ) ( 1 + cos 2 θ ) + 2 k 4 μ ϵ ( α e α m * ) cos θ ,
d σ ( s ) d Ω ( ± ) = k 4 | ϵ 1 α e ± μ α m | 2 .
ϵ 1 α e = μ α m d σ ( s ) d Ω ( 180 ° ) = 0 .
{ ϵ 1 α e } = { μ α m } , { ϵ 1 α e } = { μ α m } d σ ( s ) d Ω ( 0 ° ) = k 4 | 2 { ϵ 1 α e } | 2 = 16 9 k 10 | ϵ 1 α e | 4 = | 2 3 k 3 ϵ 1 α e | 2 d σ ( s ) d Ω ( 180 ° ) .
F = F e + F m + F e m = s 0 F 0 [ 1 a 3 { ϵ 1 α e + μ α m } 2 k 3 3 a 3 μ ϵ ( α e α m * ) ] ,
F = s 0 F 0 1 6 k a 3 [ d σ ( s ) d Ω ( 0 ° ) + 3 d σ ( s ) d Ω ( 180 ° ) + 3 2 π σ ( a ) ] .
F PED = F e = F 0 2 k 3 3 a 3 s 0 | ϵ 1 α e | 2 .
F = F 0 2 k 3 3 a 3 s 0 3 4 [ 3 σ ( a ) 2 π k 4 + | ϵ 1 α e | 2 ] ,
d σ d Ω = k 4 ϵ 2 | α e | 2 [ 5 8 ( 1 + cos 2 θ ) + cos θ ] .
F = F 0 2 k 3 3 a 3 s 0 ϵ 2 [ 3 4 | α e | 2 + ( α e ) 2 ] ,
d σ d Ω = k 4 ϵ 2 [ 5 8 | α e | 2 ( 1 + cos 2 θ ) [ ( α e ) 2 ( α e ) 2 ] cos θ ] .
F = F 0 2 k 3 3 a 3 s 0 | ϵ 1 α e ( 0 ) | 2 ,
d σ d Ω = k 4 ϵ 2 | α e ( 0 ) | 2 [ 5 8 ( 1 + cos 2 θ ) cos θ ] .
F SK = F 0 2 k 3 a 3 s 0 | ϵ 1 α e ( 0 ) | 2 ,
F SK = F 0 2 k 3 3 a 3 s 0 ϵ 2 [ | α e | 2 + 2 ( α e ) 2 ] ,
μ α m = ( 1 / 2 ) ( 1 ± 4 R 3 ) ϵ 1 α e , μ α m = ( 1 / 2 ) | 1 ± 4 R 3 | ϵ 1 α e .

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