Abstract

The magnetic field component of light in dielectric materials generally plays a negligible role at optical frequency values. However, it is a key component of metal based metamaterials. Here we report on the dominant role of the magnetic interaction in a dielectric spherical silicon nanocavity coupled to a silicon waveguide. The analytical method, as well as the finite difference time domain (FDTD) simulation, show a three dimensional (3D) magnetic trap effect when the magnetic like Mie resonances of the nanocavity are excited.

© 2012 OSA

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2012

2011

D. Erickson, X. Serey, Y. F. Chen, and S. Mandal, “Nanomanipulation using near field photonics,” Lab Chip 11(6), 995–1009 (2011).
[CrossRef] [PubMed]

M. Nieto-Vesperinas, R. Gomez-Medina, and J. J. Saenz, “Angle-suppressed scattering and optical forces on submicronmeter dielectric particles,” J. Opt. Soc. Am. A 28(1), 54–60 (2011).
[CrossRef]

E. Xifré-Pérez, R. Fenollosa, and F. Meseguer, “Low order modes in microcavities based on silicon colloids,” Opt. Express 19(4), 3455–3463 (2011).
[CrossRef] [PubMed]

E. Xifré-Pérez, J. D. Domenech, R. Fenollosa, P. Muñoz, J. Capmany, and F. Meseguer, “All silicon waveguide spherical microcavity coupler device,” Opt. Express 19(4), 3185–3192 (2011).
[CrossRef] [PubMed]

M. Lapine, I. V. Shadrivov, D. A. Powell, and Y. S. Kivshar, “Magnetoelastic metamaterials,” Nat. Mater. 11(1), 30–33 (2011).
[CrossRef] [PubMed]

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[CrossRef] [PubMed]

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
[CrossRef]

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
[CrossRef] [PubMed]

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

R. Gómez-Medina, M. Nieto-Vesperinas, and J. J. Saenz, “Nonconservative electric and magnetic optical forces on submicron dielectric particles,” Phys. Rev. A 83(3), 033825 (2011).
[CrossRef]

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11(2), 321–328 (2011).
[CrossRef] [PubMed]

2010

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18(11), 11428–11443 (2010).
[CrossRef] [PubMed]

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105(12), 123902 (2010).
[CrossRef] [PubMed]

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105(12), 123901 (2010).
[CrossRef] [PubMed]

R. Zhao, P. Tassin, T. Koschny, and C. M. Soukoulis, “Optical forces in nanowire pairs and metamaterials,” Opt. Express 18(25), 25665–25676 (2010).
[CrossRef] [PubMed]

J. T. Harris, J. L. Hueso, and B. A. Korgel, “Hydrogenated Amorphous Silicon (a-Si:H) Colloids,” Chem. Mater. 22(23), 6378–6383 (2010).
[CrossRef]

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
[CrossRef] [PubMed]

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010).
[CrossRef] [PubMed]

2009

P. C. Chaumet and A. Rahmani, “Electromagnetic force and torque on magnetic and negative-index scatterers,” Opt. Express 17(4), 2224–2234 (2009).
[CrossRef] [PubMed]

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106(6), 1693–1698 (2009).
[CrossRef] [PubMed]

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326(5952), 550–553 (2009).
[CrossRef] [PubMed]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[CrossRef] [PubMed]

2008

M. Greiner and S. Fölling, “Condensed-matter physics: optical lattices,” Nature 453(7196), 736–738 (2008).
[CrossRef] [PubMed]

R. Fenollosa, F. Meseguer, and M. Tymczenko, “Silicon colloids: from microcavities to photonic sponges,” Adv. Mater. (Deerfield Beach Fla.) 20(1), 95–98 (2008).
[CrossRef]

B. I. Popa and S. A. Cummer, “Compact dielectric particles as a building block for low-loss magnetic metamaterials,” Phys. Rev. Lett. 100(20), 207401 (2008).
[CrossRef] [PubMed]

2007

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(10), 107401 (2007).
[CrossRef] [PubMed]

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Photonics 3, 477–480 (2007).

2006

V. Garcés-Chávez, R. Quidant, P. J. Reece, G. Badenes, L. Torner, and K. Dholakia, “Extended organization of colloidal microparticles by surface plasmon polariton excitation,” Phys. Rev. B 73(8), 085417 (2006).
[CrossRef]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 21–27 (2006).
[CrossRef] [PubMed]

2005

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1(1), 23–30 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

2004

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

2003

T. Iida and H. Ishihara, “Theoretical study of the optical manipulation of semiconductor nanoparticles under an excitonic resonance condition,” Phys. Rev. Lett. 90(5), 057403 (2003).
[CrossRef] [PubMed]

2002

S. O'Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14(15), 4035–4044 (2002).
[CrossRef]

W. Ketterle, “Nobel lecture: when atoms behave as waves: Bose-Einstein condensation and the atom laser,” Rev. Mod. Phys. 74(4), 1131–1151 (2002).
[CrossRef]

1998

S. Chu, “Noble lecture: the manipulation of neutral particles,” Rev. Mod. Phys. 70(3), 685–706 (1998).
[CrossRef]

1997

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 4853–4860 (1997).
[CrossRef] [PubMed]

1991

S. Chu, “Laser manipulation of atoms and particles,” Science 253(5022), 861–866 (1991).
[CrossRef] [PubMed]

1977

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38(23), 1351–1354 (1977).
[CrossRef]

1970

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[CrossRef]

Albaladejo, S.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 4853–4860 (1997).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38(23), 1351–1354 (1977).
[CrossRef]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[CrossRef]

Badenes, G.

V. Garcés-Chávez, R. Quidant, P. J. Reece, G. Badenes, L. Torner, and K. Dholakia, “Extended organization of colloidal microparticles by surface plasmon polariton excitation,” Phys. Rev. B 73(8), 085417 (2006).
[CrossRef]

Balet, L.

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105(12), 123902 (2010).
[CrossRef] [PubMed]

Bloch, I.

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1(1), 23–30 (2005).
[CrossRef]

Block, S. M.

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
[CrossRef] [PubMed]

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(10), 107401 (2007).
[CrossRef] [PubMed]

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

Burresi, M.

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105(12), 123901 (2010).
[CrossRef] [PubMed]

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Capmany, J.

Chantada, L.

Chaumet, P. C.

Chen, Y. F.

D. Erickson, X. Serey, Y. F. Chen, and S. Mandal, “Nanomanipulation using near field photonics,” Lab Chip 11(6), 995–1009 (2011).
[CrossRef] [PubMed]

Chu, S.

S. Chu, “Noble lecture: the manipulation of neutral particles,” Rev. Mod. Phys. 70(3), 685–706 (1998).
[CrossRef]

S. Chu, “Laser manipulation of atoms and particles,” Science 253(5022), 861–866 (1991).
[CrossRef] [PubMed]

Crozier, K.

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
[CrossRef] [PubMed]

Cummer, S. A.

B. I. Popa and S. A. Cummer, “Compact dielectric particles as a building block for low-loss magnetic metamaterials,” Phys. Rev. Lett. 100(20), 207401 (2008).
[CrossRef] [PubMed]

Dholakia, K.

V. Garcés-Chávez, R. Quidant, P. J. Reece, G. Badenes, L. Torner, and K. Dholakia, “Extended organization of colloidal microparticles by surface plasmon polariton excitation,” Phys. Rev. B 73(8), 085417 (2006).
[CrossRef]

Domenech, J. D.

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38(23), 1351–1354 (1977).
[CrossRef]

Enkrich, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

Erickson, D.

D. Erickson, X. Serey, Y. F. Chen, and S. Mandal, “Nanomanipulation using near field photonics,” Lab Chip 11(6), 995–1009 (2011).
[CrossRef] [PubMed]

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010).
[CrossRef] [PubMed]

Fazal, F. M.

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
[CrossRef] [PubMed]

Fenollosa, R.

Fiore, A.

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105(12), 123902 (2010).
[CrossRef] [PubMed]

Firsov, A. A.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Fölling, S.

M. Greiner and S. Fölling, “Condensed-matter physics: optical lattices,” Nature 453(7196), 736–738 (2008).
[CrossRef] [PubMed]

Francardi, M.

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105(12), 123902 (2010).
[CrossRef] [PubMed]

Garcés-Chávez, V.

V. Garcés-Chávez, R. Quidant, P. J. Reece, G. Badenes, L. Torner, and K. Dholakia, “Extended organization of colloidal microparticles by surface plasmon polariton excitation,” Phys. Rev. B 73(8), 085417 (2006).
[CrossRef]

García de Abajo, F. J.

Geim, A. K.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Gerardino, A.

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105(12), 123902 (2010).
[CrossRef] [PubMed]

Girard, C.

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A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
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R. Gómez-Medina, M. Nieto-Vesperinas, and J. J. Saenz, “Nonconservative electric and magnetic optical forces on submicron dielectric particles,” Phys. Rev. A 83(3), 033825 (2011).
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M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18(11), 11428–11443 (2010).
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M. Greiner and S. Fölling, “Condensed-matter physics: optical lattices,” Nature 453(7196), 736–738 (2008).
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A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
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S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105(12), 123902 (2010).
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M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326(5952), 550–553 (2009).
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J. T. Harris, J. L. Hueso, and B. A. Korgel, “Hydrogenated Amorphous Silicon (a-Si:H) Colloids,” Chem. Mater. 22(23), 6378–6383 (2010).
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M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
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M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326(5952), 550–553 (2009).
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M. Lapine, I. V. Shadrivov, D. A. Powell, and Y. S. Kivshar, “Magnetoelastic metamaterials,” Nat. Mater. 11(1), 30–33 (2011).
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J. T. Harris, J. L. Hueso, and B. A. Korgel, “Hydrogenated Amorphous Silicon (a-Si:H) Colloids,” Chem. Mater. 22(23), 6378–6383 (2010).
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Koschny, Th.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
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Kuipers, L.

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105(12), 123901 (2010).
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M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326(5952), 550–553 (2009).
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M. Lapine, I. V. Shadrivov, D. A. Powell, and Y. S. Kivshar, “Magnetoelastic metamaterials,” Nat. Mater. 11(1), 30–33 (2011).
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S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009).
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M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326(5952), 550–553 (2009).
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S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105(12), 123902 (2010).
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S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
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C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
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X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11(2), 321–328 (2011).
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Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
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D. Erickson, X. Serey, Y. F. Chen, and S. Mandal, “Nanomanipulation using near field photonics,” Lab Chip 11(6), 995–1009 (2011).
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S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010).
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S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009).
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Muñoz, P.

Nieto-Vesperinas, M.

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M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105(12), 123901 (2010).
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S. O'Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14(15), 4035–4044 (2002).
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X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11(2), 321–328 (2011).
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D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
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S. O'Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14(15), 4035–4044 (2002).
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A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
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M. Lapine, I. V. Shadrivov, D. A. Powell, and Y. S. Kivshar, “Magnetoelastic metamaterials,” Nat. Mater. 11(1), 30–33 (2011).
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Prangsma, J. C.

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105(12), 123901 (2010).
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Quidant, R.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
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M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Photonics 3, 477–480 (2007).

V. Garcés-Chávez, R. Quidant, P. J. Reece, G. Badenes, L. Torner, and K. Dholakia, “Extended organization of colloidal microparticles by surface plasmon polariton excitation,” Phys. Rev. B 73(8), 085417 (2006).
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Reece, P. J.

V. Garcés-Chávez, R. Quidant, P. J. Reece, G. Badenes, L. Torner, and K. Dholakia, “Extended organization of colloidal microparticles by surface plasmon polariton excitation,” Phys. Rev. B 73(8), 085417 (2006).
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S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105(12), 123902 (2010).
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Righini, M.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
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M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Photonics 3, 477–480 (2007).

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R. Gómez-Medina, M. Nieto-Vesperinas, and J. J. Saenz, “Nonconservative electric and magnetic optical forces on submicron dielectric particles,” Phys. Rev. A 83(3), 033825 (2011).
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M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18(11), 11428–11443 (2010).
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S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[CrossRef] [PubMed]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

Schoenmaker, H.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326(5952), 550–553 (2009).
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S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
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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(10), 107401 (2007).
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D. Erickson, X. Serey, Y. F. Chen, and S. Mandal, “Nanomanipulation using near field photonics,” Lab Chip 11(6), 995–1009 (2011).
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S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010).
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M. Lapine, I. V. Shadrivov, D. A. Powell, and Y. S. Kivshar, “Magnetoelastic metamaterials,” Nat. Mater. 11(1), 30–33 (2011).
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Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Song, B. S.

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105(12), 123901 (2010).
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C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

R. Zhao, P. Tassin, T. Koschny, and C. M. Soukoulis, “Optical forces in nanowire pairs and metamaterials,” Opt. Express 18(25), 25665–25676 (2010).
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C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
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Taubner, T.

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(10), 107401 (2007).
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V. Garcés-Chávez, R. Quidant, P. J. Reece, G. Badenes, L. Torner, and K. Dholakia, “Extended organization of colloidal microparticles by surface plasmon polariton excitation,” Phys. Rev. B 73(8), 085417 (2006).
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R. Fenollosa, F. Meseguer, and M. Tymczenko, “Silicon colloids: from microcavities to photonic sponges,” Adv. Mater. (Deerfield Beach Fla.) 20(1), 95–98 (2008).
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M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105(12), 123901 (2010).
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M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326(5952), 550–553 (2009).
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S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105(12), 123902 (2010).
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C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
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Wiersma, D. S.

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105(12), 123902 (2010).
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D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Xifré-Pérez, E.

Yang, X.

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11(2), 321–328 (2011).
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X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11(2), 321–328 (2011).
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Zelenina, A. S.

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Photonics 3, 477–480 (2007).

Zhang, X.

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11(2), 321–328 (2011).
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Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
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Zhang, Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Zhao, R.

Zhou, J. F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

Zia, R.

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(10), 107401 (2007).
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C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
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Adv. Mater. (Deerfield Beach Fla.)

R. Fenollosa, F. Meseguer, and M. Tymczenko, “Silicon colloids: from microcavities to photonic sponges,” Adv. Mater. (Deerfield Beach Fla.) 20(1), 95–98 (2008).
[CrossRef]

Chem. Mater.

J. T. Harris, J. L. Hueso, and B. A. Korgel, “Hydrogenated Amorphous Silicon (a-Si:H) Colloids,” Chem. Mater. 22(23), 6378–6383 (2010).
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Chem. Soc. Rev.

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
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J. Opt. Soc. Am. A

J. Phys. Condens. Matter

S. O'Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14(15), 4035–4044 (2002).
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Lab Chip

D. Erickson, X. Serey, Y. F. Chen, and S. Mandal, “Nanomanipulation using near field photonics,” Lab Chip 11(6), 995–1009 (2011).
[CrossRef] [PubMed]

Nano Lett.

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
[CrossRef] [PubMed]

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010).
[CrossRef] [PubMed]

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11(2), 321–328 (2011).
[CrossRef] [PubMed]

Nat. Mater.

M. Lapine, I. V. Shadrivov, D. A. Powell, and Y. S. Kivshar, “Magnetoelastic metamaterials,” Nat. Mater. 11(1), 30–33 (2011).
[CrossRef] [PubMed]

Nat. Photonics

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Photonics 3, 477–480 (2007).

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
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F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
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C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

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I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1(1), 23–30 (2005).
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Nature

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 21–27 (2006).
[CrossRef] [PubMed]

M. Greiner and S. Fölling, “Condensed-matter physics: optical lattices,” Nature 453(7196), 736–738 (2008).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. A

R. Gómez-Medina, M. Nieto-Vesperinas, and J. J. Saenz, “Nonconservative electric and magnetic optical forces on submicron dielectric particles,” Phys. Rev. A 83(3), 033825 (2011).
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Figures (6)

Fig. 1
Fig. 1

Schematic view of a spherical silicon nanocavity located above the top side of a silicon waveguide (dark red). The gap between silicon nanocavity and waveguide is 20 nm. Two counter-propagative guided light beams (yellow arrows) interfere themselves forming a standing wave. The waveguide cross section and the field distribution of Ex in the waveguide is shown in the inset of the Fig. 1. The diameter of the silicon sphere is 430 nm. The height and the width of waveguide are 220 nm and 500 nm respectively. The lowest order guided mode is used. The white dotted line is along the symmetry line of the top surface of waveguide in y direction.

Fig. 2
Fig. 2

(a) Light scattering efficiency of a single silicon spherical nanocavity, 430 nm large, immersed in air as a function of the wavelength. The results of the Mie analytical method (solid line) and the FDTD method (dash line) are shown. The black line corresponds to the total scattering efficiency. The red and blue lines correspond to the magnetic and electric contributions to the total scattering efficiency. (b) The same as (a) for the same size PS sphere. (c) The magnetic (red) and electric (blue) polarizabilities as a function of wavelength of light. The solid and dash lines correspond to the real and the imaginary parts of polarizabilities. (d) The same as (c) but for a PS nanocavity.

Fig. 3
Fig. 3

The upper panel shows the analytical results of the evanescent electric (blue line) and magnetic (red line) fields along the y direction. The middle panel shows the optical force on a silicon 430 nm large nanocavity located above the top surface of the planar waveguide. The gap between the nanocavity and the waveguide is 20 nm. The black line corresponds to the total optical force acting on the silicon sphere, and the red, blue and yellow dashed lines correspond to the magnetic, electric, and the interaction between the electric and the magnetic dipoles optical forces appearing in the expression shown in Eq. (5). The lower panel shows the optical potential along the y direction. Left and right panels correspond to light wavelength values of 1.6 ��m (a), and 1.5 ��m (b), respectively.

Fig. 4
Fig. 4

The upper panel of (a, b) shows the FDTD results of the evanescent electric (blue line) and magnetic (red line) fields along the y direction above the top surface of the waveguide. The bottom panel of (a, b) shows the optical force (black line) and the optical potential (purple line) acting on the silicon sphere 430 nm large separated 20 nm from the top surface of the waveguide in y direction (see white dashed line shown in Fig. 1). The wavelength of guided light is 1.6 ��m (a), and 1.5 ��m (b). The electric (c), and the magnetic (d) fields distributions on the equatorial xy plane of the nanocavity are shown. The field plot at (e) shows the magnetic field distribution in the xz plane cross section of the system. In all (c), (d) and (e) field plot cases, the nanocavity is located at the high magnetic field region along y direction, the wavelength of guided light being 1.6 ��m.

Fig. 5
Fig. 5

The upper panel shows the FDTD results of the evanescent electric (blue line) and the magnetic (red line) field distribution at the highest magnetic field region along x direction. The lower panel shows the optical force (black line) and the optical potential (purple line) on a silicon sphere 430 nm large 20 nm above the top surface of waveguide along x direction. The sphere is located at the high magnetic field region along y direction, and the wavelength of the guided light is 1.6 ��m.

Fig. 6
Fig. 6

The potential difference between the high magnetic field region and high electric field region at the waveguide as a function of wavelength for both the analytical model (blue line) and FDTD simulation (red line). For comparison purposes, we have also plotted the PS sphere as a blue dash line. The diameter of silicon and PS spheres are 430 nm, and the intensity of guided light in waveguide is 0.9 mW.

Equations (15)

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σ= 6π k 0 2 ( | a n | 2 + | b n | 2 ),
P= α e E, M= α m H.
α e =i( 6π k 0 3 ) ε 0 a 1 , α m =i( 6π k 0 3 ) b 1 .
F = S T n dS=( 1 2 )Re( S ε 0 ( E n ) E * + 1 μ 0 ( B n ) B * ( 1 2 ){ ε 0 E 2 +[ 1 μ 0 ] B 2 } n ),
F = F e + F m + F em .
F e =(1/4)Re( α e ) | E | 2 +(1/2) σ ext e Re((1/c) S )+c σ ext e × L spe .
F m =( μ 0 /4)Re( α m ) | H | 2 +(1/2) σ ext m Re((1/c) S )+c σ ext m × L spm ,
F em =[ k 0 4 /(12π)] μ 0 / ε 0 Re(P× M * ).
U= F dr .
E x =A e rz [ e iβy + e iβy ]=2A e rz cos(βy),
H y =2i/(ω μ 0 )Ar e rz cos(βy),
H z =2β/(iω μ 0 )A e rz sin(βy).
F e =Re( α e )β A 2 e 2rz sin(2βy),
F m =Re( α m )β A 2 e 2rz sin(2βy) k 0 2 /( ω 2 μ 0 ),
F em =[ k 0 3 /(6π)][Im( α m )Re( α e )Im( α e )Re( α m )][ A 2 e 2rz βsin(2βy)].

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