Abstract

We propose an optical dimer formed from two spherical lenses bound by the pressure that light exerts on matter. With the help of the method of force tracing, we find the required graded-index profiles of the lenses for the existence of the dimer. We study the dynamics of the opto-mechanical interaction of lenses under the illumination of collimated light beams and quantitatively validate the performance of proposed dimer. We also examine the stability of dimer due to the lateral misalignments and we show how restoring forces bring the dimer into lateral equilibrium. The dimer can be employed in various practical applications such as optical manipulation, sensing and imaging.

© 2016 Optical Society of America

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2015 (1)

A. Akbarzadeh, J. A. Crosse, M. Danesh, C. W. Qiu, A. J. Danner, and C. M. Soukoulis, “Interplay of optical force and ray-optic behavior between Luneburg lenses,” ACS Photonics 2(9), 1384–1390 (2015).
[Crossref]

2014 (2)

A. Akbarzadeh, M. Danesh, C. W. Qiu, and A. J. Danner, “Tracing optical force fields within graded-index media,” New J. Phys. 16(5), 053035 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

2013 (2)

O. Brzobohatý, V. Karásek, M. Šiler, L. Chvátal, T. Čižmár, and P. Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics 7(2), 123–127 (2013).
[Crossref]

V. Kajorndejnuku, W. Ding, S. Sukhov, C.-W. Qiu, and A. Dogariu, “Linear momentum increases and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
[Crossref]

2012 (2)

D. B. Ruffner and D. G. Grier, “Optical conveyors: a class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

P. C. Chaumet, A. Rahmani, F. Zolla, and A. Nicolet, “Electromagnetic forces on a discrete spherical invisibility cloak under time-harmonic illumination,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(5), 056602 (2012).
[Crossref] [PubMed]

2011 (3)

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

A. Novitsky, C. W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107(20), 203601 (2011).
[Crossref] [PubMed]

P. C. Chaumet, A. Rahmani, F. Zolla, A. Nicolet, and K. Belkebir, “Optical force on a discrete invisibility cloak in time-independent fields,” Phys. Rev. A 84(3), 033808 (2011).
[Crossref]

2010 (5)

2009 (1)

H. Chen, B. Zhang, Y. Luo, B. A. Kemp, J. Zhang, L. Ran, and B. Wu, “Lorentz force and radiation pressure on a spherical cloak,” Phys. Rev. A 80(1), 011808 (2009).
[Crossref]

2008 (2)

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[Crossref] [PubMed]

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5(6), 491–505 (2008).
[Crossref] [PubMed]

2007 (1)

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79(4), 1197–1216 (2007).
[Crossref]

2006 (1)

U. Leonhardt, “Optics: momentum in an uncertain light,” Nature 444(7121), 823–824 (2006).
[Crossref] [PubMed]

2005 (1)

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

1994 (1)

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

1986 (1)

1979 (1)

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52(3), 133–201 (1979).
[Crossref]

1970 (1)

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

1903 (2)

E. F. Nichols and G. F. Hull, “The pressure due to radiation (Second paper),” Phys. Rev. 17, 26–50 (1903).

E. F. Nichols and G. F. Hull, “The pressure due to radiation,” Astrophys. J. 57, 315–351 (1903).
[Crossref]

1901 (1)

P. N. Lebedev, “Investigations on the pressure forces of light,” Ann. Phys. 6, 433–458 (1901).

1884 (1)

A. Bartoli, “Il calorico raggiante e il secondo principio di termodinamica,” Nuovo Cim. 15(1), 193–202 (1884).
[Crossref]

Akbarzadeh, A.

A. Akbarzadeh, J. A. Crosse, M. Danesh, C. W. Qiu, A. J. Danner, and C. M. Soukoulis, “Interplay of optical force and ray-optic behavior between Luneburg lenses,” ACS Photonics 2(9), 1384–1390 (2015).
[Crossref]

A. Akbarzadeh, M. Danesh, C. W. Qiu, and A. J. Danner, “Tracing optical force fields within graded-index media,” New J. Phys. 16(5), 053035 (2014).
[Crossref]

A. Akbarzadeh and A. J. Danner, “Generalization of ray tracing in a linear inhomogeneous anisotropic medium: a coordinate-free approach,” J. Opt. Soc. Am. A 27(12), 2558–2562 (2010).
[Crossref] [PubMed]

Ashkin, A.

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

Bartal, G.

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5(8), 570–573 (2010).
[Crossref] [PubMed]

Bartoli, A.

A. Bartoli, “Il calorico raggiante e il secondo principio di termodinamica,” Nuovo Cim. 15(1), 193–202 (1884).
[Crossref]

Belkebir, K.

P. C. Chaumet, A. Rahmani, F. Zolla, A. Nicolet, and K. Belkebir, “Optical force on a discrete invisibility cloak in time-independent fields,” Phys. Rev. A 84(3), 033808 (2011).
[Crossref]

Bjorkholm, J. E.

Block, S. M.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

Brevik, I.

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52(3), 133–201 (1979).
[Crossref]

Brzobohatý, O.

O. Brzobohatý, V. Karásek, M. Šiler, L. Chvátal, T. Čižmár, and P. Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics 7(2), 123–127 (2013).
[Crossref]

Chan, C. T.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Chantada, L.

Chaumet, P. C.

P. C. Chaumet, A. Rahmani, F. Zolla, and A. Nicolet, “Electromagnetic forces on a discrete spherical invisibility cloak under time-harmonic illumination,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(5), 056602 (2012).
[Crossref] [PubMed]

P. C. Chaumet, A. Rahmani, F. Zolla, A. Nicolet, and K. Belkebir, “Optical force on a discrete invisibility cloak in time-independent fields,” Phys. Rev. A 84(3), 033808 (2011).
[Crossref]

Chen, H.

H. Chen, B. Zhang, B. A. Kemp, and B. I. Wu, “Optical force on a cylindrical cloak under arbitrary wave illumination,” Opt. Lett. 35(5), 667–669 (2010).
[Crossref] [PubMed]

H. Chen, B. Zhang, Y. Luo, B. A. Kemp, J. Zhang, L. Ran, and B. Wu, “Lorentz force and radiation pressure on a spherical cloak,” Phys. Rev. A 80(1), 011808 (2009).
[Crossref]

Chen, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Chu, S.

Chvátal, L.

O. Brzobohatý, V. Karásek, M. Šiler, L. Chvátal, T. Čižmár, and P. Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics 7(2), 123–127 (2013).
[Crossref]

Cižmár, T.

O. Brzobohatý, V. Karásek, M. Šiler, L. Chvátal, T. Čižmár, and P. Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics 7(2), 123–127 (2013).
[Crossref]

Crosse, J. A.

A. Akbarzadeh, J. A. Crosse, M. Danesh, C. W. Qiu, A. J. Danner, and C. M. Soukoulis, “Interplay of optical force and ray-optic behavior between Luneburg lenses,” ACS Photonics 2(9), 1384–1390 (2015).
[Crossref]

Danesh, M.

A. Akbarzadeh, J. A. Crosse, M. Danesh, C. W. Qiu, A. J. Danner, and C. M. Soukoulis, “Interplay of optical force and ray-optic behavior between Luneburg lenses,” ACS Photonics 2(9), 1384–1390 (2015).
[Crossref]

A. Akbarzadeh, M. Danesh, C. W. Qiu, and A. J. Danner, “Tracing optical force fields within graded-index media,” New J. Phys. 16(5), 053035 (2014).
[Crossref]

Danner, A. J.

A. Akbarzadeh, J. A. Crosse, M. Danesh, C. W. Qiu, A. J. Danner, and C. M. Soukoulis, “Interplay of optical force and ray-optic behavior between Luneburg lenses,” ACS Photonics 2(9), 1384–1390 (2015).
[Crossref]

A. Akbarzadeh, M. Danesh, C. W. Qiu, and A. J. Danner, “Tracing optical force fields within graded-index media,” New J. Phys. 16(5), 053035 (2014).
[Crossref]

A. Akbarzadeh and A. J. Danner, “Generalization of ray tracing in a linear inhomogeneous anisotropic medium: a coordinate-free approach,” J. Opt. Soc. Am. A 27(12), 2558–2562 (2010).
[Crossref] [PubMed]

A. J. Danner, “Singularity removal in optical instruments without reflections or induced birefringence,” New J. Phys. 12(11), 113008 (2010).
[Crossref]

Ding, W.

V. Kajorndejnuku, W. Ding, S. Sukhov, C.-W. Qiu, and A. Dogariu, “Linear momentum increases and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
[Crossref]

Dogariu, A.

V. Kajorndejnuku, W. Ding, S. Sukhov, C.-W. Qiu, and A. Dogariu, “Linear momentum increases and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
[Crossref]

Dziedzic, J. M.

Gómez-Medina, R.

Grier, D. G.

D. B. Ruffner and D. G. Grier, “Optical conveyors: a class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Grzegorczyk, T.

Heckenberg, N. R.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79(4), 1197–1216 (2007).
[Crossref]

Hull, G. F.

E. F. Nichols and G. F. Hull, “The pressure due to radiation,” Astrophys. J. 57, 315–351 (1903).
[Crossref]

E. F. Nichols and G. F. Hull, “The pressure due to radiation (Second paper),” Phys. Rev. 17, 26–50 (1903).

Kajorndejnuku, V.

V. Kajorndejnuku, W. Ding, S. Sukhov, C.-W. Qiu, and A. Dogariu, “Linear momentum increases and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
[Crossref]

Karásek, V.

O. Brzobohatý, V. Karásek, M. Šiler, L. Chvátal, T. Čižmár, and P. Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics 7(2), 123–127 (2013).
[Crossref]

Kemp, B.

Kemp, B. A.

H. Chen, B. Zhang, B. A. Kemp, and B. I. Wu, “Optical force on a cylindrical cloak under arbitrary wave illumination,” Opt. Lett. 35(5), 667–669 (2010).
[Crossref] [PubMed]

H. Chen, B. Zhang, Y. Luo, B. A. Kemp, J. Zhang, L. Ran, and B. Wu, “Lorentz force and radiation pressure on a spherical cloak,” Phys. Rev. A 80(1), 011808 (2009).
[Crossref]

Kippenberg, T. J.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[Crossref] [PubMed]

Kong, J.

Lebedev, P. N.

P. N. Lebedev, “Investigations on the pressure forces of light,” Ann. Phys. 6, 433–458 (1901).

Leonhardt, U.

U. Leonhardt, “Optics: momentum in an uncertain light,” Nature 444(7121), 823–824 (2006).
[Crossref] [PubMed]

Lin, Z.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Liu, M.

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5(8), 570–573 (2010).
[Crossref] [PubMed]

Liu, Y.

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5(8), 570–573 (2010).
[Crossref] [PubMed]

Luo, Y.

H. Chen, B. Zhang, Y. Luo, B. A. Kemp, J. Zhang, L. Ran, and B. Wu, “Lorentz force and radiation pressure on a spherical cloak,” Phys. Rev. A 80(1), 011808 (2009).
[Crossref]

Marquardt, F.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

Nagy, A.

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5(6), 491–505 (2008).
[Crossref] [PubMed]

Neuman, K. C.

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5(6), 491–505 (2008).
[Crossref] [PubMed]

Ng, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Nichols, E. F.

E. F. Nichols and G. F. Hull, “The pressure due to radiation (Second paper),” Phys. Rev. 17, 26–50 (1903).

E. F. Nichols and G. F. Hull, “The pressure due to radiation,” Astrophys. J. 57, 315–351 (1903).
[Crossref]

Nicolet, A.

P. C. Chaumet, A. Rahmani, F. Zolla, and A. Nicolet, “Electromagnetic forces on a discrete spherical invisibility cloak under time-harmonic illumination,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(5), 056602 (2012).
[Crossref] [PubMed]

P. C. Chaumet, A. Rahmani, F. Zolla, A. Nicolet, and K. Belkebir, “Optical force on a discrete invisibility cloak in time-independent fields,” Phys. Rev. A 84(3), 033808 (2011).
[Crossref]

Nieminen, T. A.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79(4), 1197–1216 (2007).
[Crossref]

Nieto-Vesperinas, M.

Novitsky, A.

A. Novitsky, C. W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107(20), 203601 (2011).
[Crossref] [PubMed]

Pfeifer, R. N. C.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79(4), 1197–1216 (2007).
[Crossref]

Qiu, C. W.

A. Akbarzadeh, J. A. Crosse, M. Danesh, C. W. Qiu, A. J. Danner, and C. M. Soukoulis, “Interplay of optical force and ray-optic behavior between Luneburg lenses,” ACS Photonics 2(9), 1384–1390 (2015).
[Crossref]

A. Akbarzadeh, M. Danesh, C. W. Qiu, and A. J. Danner, “Tracing optical force fields within graded-index media,” New J. Phys. 16(5), 053035 (2014).
[Crossref]

A. Novitsky, C. W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107(20), 203601 (2011).
[Crossref] [PubMed]

Qiu, C.-W.

V. Kajorndejnuku, W. Ding, S. Sukhov, C.-W. Qiu, and A. Dogariu, “Linear momentum increases and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
[Crossref]

Rahmani, A.

P. C. Chaumet, A. Rahmani, F. Zolla, and A. Nicolet, “Electromagnetic forces on a discrete spherical invisibility cloak under time-harmonic illumination,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(5), 056602 (2012).
[Crossref] [PubMed]

P. C. Chaumet, A. Rahmani, F. Zolla, A. Nicolet, and K. Belkebir, “Optical force on a discrete invisibility cloak in time-independent fields,” Phys. Rev. A 84(3), 033808 (2011).
[Crossref]

Ran, L.

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O. Brzobohatý, V. Karásek, M. Šiler, L. Chvátal, T. Čižmár, and P. Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics 7(2), 123–127 (2013).
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J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
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P. C. Chaumet, A. Rahmani, F. Zolla, A. Nicolet, and K. Belkebir, “Optical force on a discrete invisibility cloak in time-independent fields,” Phys. Rev. A 84(3), 033808 (2011).
[Crossref]

H. Chen, B. Zhang, Y. Luo, B. A. Kemp, J. Zhang, L. Ran, and B. Wu, “Lorentz force and radiation pressure on a spherical cloak,” Phys. Rev. A 80(1), 011808 (2009).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

P. C. Chaumet, A. Rahmani, F. Zolla, and A. Nicolet, “Electromagnetic forces on a discrete spherical invisibility cloak under time-harmonic illumination,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(5), 056602 (2012).
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A. Novitsky, C. W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107(20), 203601 (2011).
[Crossref] [PubMed]

D. B. Ruffner and D. G. Grier, “Optical conveyors: a class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

Rev. Mod. Phys. (2)

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79(4), 1197–1216 (2007).
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T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
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Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (1668 KB)      An animation showing the performance of the proposed dimer

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Figures (8)

Fig. 1
Fig. 1

(a) 3D schematic of the proposed dimer under the illumination by a collimated light beam. (b) The geometry of the suggested dimer (for parameter definitions see main text).

Fig. 2
Fig. 2

(a) The ray tracing of the pseudo Luneburg lens. (b) The profile index of the pseudo Luneburg lens for x p =4 R 1 compared to the profile index of conventional Luneburg lens ( R 1 = R 2 =1a.u.l. ).

Fig. 3
Fig. 3

The force fields applied on the combination of a pseudo Luneburg lens with x p =4 R 1 (the red lens) and a Luneburg lens (the green lens) induced by the light rays propagating from the left for (a) Δx=1.25R (repulsion), and (b) Δx=2.4R (attraction).

Fig. 4
Fig. 4

(a) The forces applied on the pseudo Luneburg lens ( F 1 ) and the Luneburg lens ( F 2 ), as a function of the distance between the lenses. Note that F 2 is zero at points x= x a and x= x b . (b) Temporal variation of F 1 due to the fluctuation of incident light intensity over time. (c) The density plot of F 2 versus time and the separation between the lenses.

Fig. 5
Fig. 5

(a) The separation between the lenses vs time. (b) The paths of the two lenses and the corresponding center of mass vs time for Δ x 0 =1.25R , k d =0.5 s 1 . (see Visualization 1)

Fig. 6
Fig. 6

The velocity x c ( t ) (a.u.l./s) and the acceleration x c ( t ) (a.u.l./s2) of the center of mass of dimer vs time.

Fig. 7
Fig. 7

(a) The geometry of dimer with the lateral misalignment under the illumination of collimated light rays. (b) The force fields on the lenses as a result of light rays shining from below ( Δy=0.25R ).

Fig. 8
Fig. 8

The restoring force acting on the Luneburg lens vs the lateral misalignment.

Equations (5)

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{ E ( r ,t )= E 0 exp( i k 0 k r iωt ) H ( r ,t )= H 0 exp( i k 0 k r iωt )
f normalized = 2b rn ( r ) 3 dn dr ( k × e ^ n )
n( r )=exp( 1 π R 1 ρ R 1 χ( b )db r b 2 / r 2 ρ 2 )
d 2 x 1 d t 2 + k d d x 1 dt = F 1 m g
d 2 Δx d t 2 = d 2 x 2 d t 2 d 2 x 1 d t 2 = F 2 F 1 m k d dΔx dt

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