Abstract

In this work, we theoretically study the cavity modes with transverse orbital angular momentum in metamaterial ring based on transformation optics. The metamaterial ring is designed to transform the straight trajectory of light into the circulating one by enlarging the azimuthal angle, effectively presenting the modes with transverse orbital angular momentum. The simulation results confirm the theoretical predictions, which state that the transverse orbital angular momentum of the mode not only depends on the frequency of the incident light, but also depends on the transformation scale of the azimuthal angle. Because energy dissipation inevitably reduces the field amplitude of the modes, the confined electromagnetic energy and the quality factor of the modes inside the ring are also studied in order to evaluate the stability of those cavity modes. The results show that the metamaterial ring can effectively confine light with a high quality factor and maintain steady modes with the orbital angular momentum, even if the dimension of the ring is much smaller than the wavelength of the incident light. This technique for exploiting the modes with optical transverse orbital angular momentum may provides a unique platform for applications related to micromanipulation.

© 2015 Optical Society of America

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References

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2014 (3)

2013 (2)

2012 (3)

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

W. Shu, D. Song, Z. Tang, H. Luo, Y. Ke, X. Lü, S. Wen, and D. Fan, “Generation of optical beams with desirable orbital angular momenta by transformation media,” Phys. Rev. A 85(6), 063840 (2012).
[Crossref]

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

2011 (5)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

J. Z. Zhao, D. L. Wang, R. W. Peng, Q. Hu, and M. Wang, “Watching outside while under a carpet cloak of invisibility,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(4), 046607 (2011).
[Crossref] [PubMed]

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation light beams,” J. Opt. 13(5), 053001 (2011).
[Crossref]

M. Mansuripur, “Spin and orbital angular momenta of electromagnetic waves in free space,” Phys. Rev. A 84(3), 033838 (2011).
[Crossref]

2010 (4)

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

V. Ginis, P. Tassin, C. M. Soukoulis, and I. Veretennicoff, “Confining light in deep subwavelength electromagnetic cavities,” Phys. Rev. B 82(11), 113102 (2010).
[Crossref]

Y. F. Yu, Y. H. Fu, X. M. Zhang, A. Q. Liu, T. Bourouina, T. Mei, Z. X. Shen, and D. P. Tsai, “Pure angular momentum generator using a ring resonator,” Opt. Express 18(21), 21651–21662 (2010).
[Crossref] [PubMed]

2009 (2)

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[Crossref] [PubMed]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

2008 (3)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
[Crossref]

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

2006 (2)

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

2005 (2)

2004 (1)

2003 (2)

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

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref] [PubMed]

2002 (1)

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quantum Semiclassical Opt. 4(2), S52–S57 (2002).
[Crossref]

1998 (1)

M. V. Berry, “Paraxial beams of spinning light,” Proc. SPIE 3487, 6–11 (1998).
[Crossref]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

1990 (1)

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52(8), 429–431 (1990).

1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
[Crossref]

1909 (1)

J. H. Poynting, “The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarized light,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 82(557), 560–567 (1909).
[Crossref]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Allison, I.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quantum Semiclassical Opt. 4(2), S52–S57 (2002).
[Crossref]

Amaral, A. M.

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Barnett, S.

Bazhenov, V. Y.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52(8), 429–431 (1990).

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Bekshaev, A.

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation light beams,” J. Opt. 13(5), 053001 (2011).
[Crossref]

Berry, M. V.

M. V. Berry, “Paraxial beams of spinning light,” Proc. SPIE 3487, 6–11 (1998).
[Crossref]

Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
[Crossref]

Bliokh, K.

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation light beams,” J. Opt. 13(5), 053001 (2011).
[Crossref]

Borselli, M.

Bourouina, T.

Cai, X.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Carrasco, S.

Castaldi, G.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Chan, C. T.

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[Crossref] [PubMed]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Chávez-Cerda, S.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quantum Semiclassical Opt. 4(2), S52–S57 (2002).
[Crossref]

Chen, H.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[Crossref] [PubMed]

Cheng, Q.

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
[Crossref]

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

Cladé, P.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

Courtial, J.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[Crossref] [PubMed]

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quantum Semiclassical Opt. 4(2), S52–S57 (2002).
[Crossref]

Cui, T. J.

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
[Crossref]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref] [PubMed]

Danckaert, J.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

de Araújo, C. B.

Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

Dickinson, M. R.

N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
[Crossref]

Falcão-Filho, E. L.

Fan, D.

W. Shu, D. Song, Z. Tang, H. Luo, Y. Ke, X. Lü, S. Wen, and D. Fan, “Generation of optical beams with desirable orbital angular momenta by transformation media,” Phys. Rev. A 85(6), 063840 (2012).
[Crossref]

Fan, R. H.

Franke-Arnold, S.

Fu, Y. H.

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Galdi, V.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Gibson, G.

Ginis, V.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

V. Ginis, P. Tassin, C. M. Soukoulis, and I. Veretennicoff, “Confining light in deep subwavelength electromagnetic cavities,” Phys. Rev. B 82(11), 113102 (2010).
[Crossref]

Grier, D. G.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref] [PubMed]

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

Grigorenko, N.

N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
[Crossref]

Gutierrez-Vega, J. C.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quantum Semiclassical Opt. 4(2), S52–S57 (2002).
[Crossref]

Han, D.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Heckenberg, N. R.

Helmerson, K.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Hu, Q.

J. Z. Zhao, D. L. Wang, R. W. Peng, Q. Hu, and M. Wang, “Watching outside while under a carpet cloak of invisibility,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(4), 046607 (2011).
[Crossref] [PubMed]

Huang, X. R.

Jiang, W. X.

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
[Crossref]

Johnson, T.

Johnson-Morris, B.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Ke, Y.

W. Shu, D. Song, Z. Tang, H. Luo, Y. Ke, X. Lü, S. Wen, and D. Fan, “Generation of optical beams with desirable orbital angular momenta by transformation media,” Phys. Rev. A 85(6), 063840 (2012).
[Crossref]

Kong, X. T.

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

Lai, Y.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[Crossref] [PubMed]

Li, J.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

Li, Z. B.

Liu, A. Q.

Lü, X.

W. Shu, D. Song, Z. Tang, H. Luo, Y. Ke, X. Lü, S. Wen, and D. Fan, “Generation of optical beams with desirable orbital angular momenta by transformation media,” Phys. Rev. A 85(6), 063840 (2012).
[Crossref]

Luo, H.

W. Shu, D. Song, Z. Tang, H. Luo, Y. Ke, X. Lü, S. Wen, and D. Fan, “Generation of optical beams with desirable orbital angular momenta by transformation media,” Phys. Rev. A 85(6), 063840 (2012).
[Crossref]

Ma, H. F.

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

MacVicar, I.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quantum Semiclassical Opt. 4(2), S52–S57 (2002).
[Crossref]

Mansuripur, M.

M. Mansuripur, “Spin and orbital angular momenta of electromagnetic waves in free space,” Phys. Rev. A 84(3), 033838 (2011).
[Crossref]

McDuff, R.

Mei, T.

Moccia, M.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Natarajan, V.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

New, G. H. C.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quantum Semiclassical Opt. 4(2), S52–S57 (2002).
[Crossref]

Ng, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

O’Brien, J. L.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

O’Neil, A. T.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quantum Semiclassical Opt. 4(2), S52–S57 (2002).
[Crossref]

Padgett, M.

Padgett, M. J.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quantum Semiclassical Opt. 4(2), S52–S57 (2002).
[Crossref]

Painter, O.

Pas’ko, V.

Pendry, J. B.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Peng, R. W.

Phillips, W. D.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Poynting, J. H.

J. H. Poynting, “The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarized light,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 82(557), 560–567 (1909).
[Crossref]

Rahm, M.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Roberts, N. W.

N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
[Crossref]

Ryu, C.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Sato, Y.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Savo, S.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Shao, M. R.

Shen, Z. X.

Shu, W.

W. Shu, D. Song, Z. Tang, H. Luo, Y. Ke, X. Lü, S. Wen, and D. Fan, “Generation of optical beams with desirable orbital angular momenta by transformation media,” Phys. Rev. A 85(6), 063840 (2012).
[Crossref]

Smith, C. P.

Smith, D. R.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Song, D.

W. Shu, D. Song, Z. Tang, H. Luo, Y. Ke, X. Lü, S. Wen, and D. Fan, “Generation of optical beams with desirable orbital angular momenta by transformation media,” Phys. Rev. A 85(6), 063840 (2012).
[Crossref]

Sorel, M.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Soskin, M.

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation light beams,” J. Opt. 13(5), 053001 (2011).
[Crossref]

Soskin, M. S.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52(8), 429–431 (1990).

Soukoulis, C. M.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

V. Ginis, P. Tassin, C. M. Soukoulis, and I. Veretennicoff, “Confining light in deep subwavelength electromagnetic cavities,” Phys. Rev. B 82(11), 113102 (2010).
[Crossref]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Strain, M. J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Tang, Z.

W. Shu, D. Song, Z. Tang, H. Luo, Y. Ke, X. Lü, S. Wen, and D. Fan, “Generation of optical beams with desirable orbital angular momenta by transformation media,” Phys. Rev. A 85(6), 063840 (2012).
[Crossref]

Tassin, P.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

V. Ginis, P. Tassin, C. M. Soukoulis, and I. Veretennicoff, “Confining light in deep subwavelength electromagnetic cavities,” Phys. Rev. B 82(11), 113102 (2010).
[Crossref]

Tetienne, J. P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Thompson, M. G.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Tian, J. G.

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

L. Torner, J. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13(3), 873–881 (2005).
[Crossref] [PubMed]

Torres, J.

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Tsai, D. P.

Vasnetsov, M.

Vasnetsov, M. V.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52(8), 429–431 (1990).

Vaziri, A.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Veretennicoff, I.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

V. Ginis, P. Tassin, C. M. Soukoulis, and I. Veretennicoff, “Confining light in deep subwavelength electromagnetic cavities,” Phys. Rev. B 82(11), 113102 (2010).
[Crossref]

Wang, D. L.

J. Z. Zhao, D. L. Wang, R. W. Peng, Q. Hu, and M. Wang, “Watching outside while under a carpet cloak of invisibility,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(4), 046607 (2011).
[Crossref] [PubMed]

Wang, J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Wang, M.

Wen, S.

W. Shu, D. Song, Z. Tang, H. Luo, Y. Ke, X. Lü, S. Wen, and D. Fan, “Generation of optical beams with desirable orbital angular momenta by transformation media,” Phys. Rev. A 85(6), 063840 (2012).
[Crossref]

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Wu, H. W.

Xiao, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Xu, D. H.

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Yu, S.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Yu, Y. F.

Zhang, K.

Zhang, X. M.

Zhang, Y.

N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
[Crossref]

Zhang, Z. Q.

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[Crossref] [PubMed]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Zhao, J. Z.

J. Z. Zhao, D. L. Wang, R. W. Peng, Q. Hu, and M. Wang, “Watching outside while under a carpet cloak of invisibility,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(4), 046607 (2011).
[Crossref] [PubMed]

Zhu, J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Zhu, L. H.

Appl. Phys. Lett. (1)

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
[Crossref]

J. Opt. (1)

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation light beams,” J. Opt. 13(5), 053001 (2011).
[Crossref]

J. Opt. B Quantum Semiclassical Opt. (1)

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quantum Semiclassical Opt. 4(2), S52–S57 (2002).
[Crossref]

JETP Lett. (1)

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52(8), 429–431 (1990).

Nat. Commun. (1)

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

Nat. Photonics (2)

N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
[Crossref]

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Nature (1)

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

New J. Phys. (1)

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

Opt. Commun. (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

Opt. Express (8)

L. H. Zhu, M. R. Shao, R. W. Peng, R. H. Fan, X. R. Huang, and M. Wang, “Broadband absorption and efficiency enhancement of an ultra-thin silicon solar cell with a plasmonic fractal,” Opt. Express 21(S3), A313–A323 (2013).
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D. H. Xu, K. Zhang, M. R. Shao, H. W. Wu, R. H. Fan, R. W. Peng, and M. Wang, “Band modulation and in-plane propagation of surface plasmons in composite nanostructures,” Opt. Express 22(21), 25700–25709 (2014).
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G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
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L. Torner, J. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13(3), 873–881 (2005).
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A. M. Amaral, E. L. Falcão-Filho, and C. B. de Araújo, “Characterization of topological charge and orbital angular momentum of shaped optical vortices,” Opt. Express 22(24), 30315–30324 (2014).
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X. T. Kong, Z. B. Li, and J. G. Tian, “Mode converter in metal-insulator-metal plasmonic waveguide designed by transformation optics,” Opt. Express 21(8), 9437–9446 (2013).
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Y. F. Yu, Y. H. Fu, X. M. Zhang, A. Q. Liu, T. Bourouina, T. Mei, Z. X. Shen, and D. P. Tsai, “Pure angular momentum generator using a ring resonator,” Opt. Express 18(21), 21651–21662 (2010).
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M. Borselli, T. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13(5), 1515–1530 (2005).
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Opt. Lett. (1)

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Figures (7)

Fig. 1
Fig. 1 (a) An infinite hollow cylinder (ii) with inner radius R1 and outer radius R2 filled with the metamaterial. The regions (i) and (iii) are free space. Transverse sections of the hollow cylinder for (b) free space and (c) transformation space. The distribution of blue dashed lines indicates that the azimuthal angle of region (ii) in (c) is n times larger than the one in (b). The green solid lines in (b) and (c) represent direction of propagation of incident plane wave.
Fig. 2
Fig. 2 (a) The permittivity distribution and (b) permeability distribution of the metamaterial ring for n = 10.
Fig. 3
Fig. 3 The normalized extinction cross-section as a function of the frequency of the incident light for the metamaterial ring with inner radius R1 = 0.5m, and outer radius R2 = 1m. The resonant peaks are marked with the angular momentum indices mνii = 1, mνii = 2, mνii = 3, mνii = 4, and mνii = 5, respectively.
Fig. 4
Fig. 4 Magnetic field distributions (a1)-(d1) and field phase profiles (a2)-(d2) of circulating light in the ring with inner radius R1 = 0.5m, and outer radius R2 = 1m correspond to the angular momentum indices mνii = 1, mνii = 2, mνii = 3, and mνii = 4 at the resonant frequencies f = 3.3 × 107 Hz, f = 4.75 × 107 Hz, f = 6.02 × 107 Hz, and f = 7.085 × 107 Hz for n = 10, respectively. The total OAM (e) of circulating light in the metamaterial ring as a function of the frequency.
Fig. 5
Fig. 5 Magnetic field distributions of the ring with inner radius R1 = 0.5m, and outer radius R2 = 1m correspond to the angular momentum indices (a) mνii = 4, (b) mνii = 6, (c) mνii = 8, (d) mνii = 10 at the resonant frequency f = 7.085 × 107 Hz for transformation scales n = 10, n = 15, n = 20, and n = 25, respectively.
Fig. 6
Fig. 6 Electromagnetic energy confined in the metamaterial ring with inner radius R1 = 0.5m, and outer radius R2 = 1m as a function of the frequency for the transformation scales (a) n = 10, (b) n = 15, (c) n = 20, respectively.
Fig. 7
Fig. 7 Quality factor of the modes in the metamaterial ring with inner radius R1 = 0.5m, and outer radius R2 = 1m as a function of angular momentum index mνii for transformation scales n = 10 (triangle symbol), n = 15 (square symbol), and n = 20 (pentagram symbol).

Equations (8)

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{ 1 H z ( r ) r r ( r H z ( r ) r ) + k 0 2 r 2 = χ 1 H z ( θ ) 2 H z ( θ ) θ 2 = χ ,
H z i ( r , θ ) = A J m ν i ( k 0 r ) e x p ( i m ν i θ ) ,
H z iii ( r , θ ) = B H m ν i i i ( 1 ) ( k 0 r ) e x p ( i m ν i i i θ ) ,
θ = f ( θ ) = n θ ,
H z ii ( r , θ ) = ( C J m ν i i ( k 0 r ) + D Y m ν i i ( k 0 r ) ) e x p ( i m ν i i f ( θ ) ) ,
{ A J m ( k 0 R 1 ) = C J m ν i i ( k 0 R 1 ) + D Y m ν i i ( k 0 R 1 ) B H m ( 1 ) ( k 0 R 2 ) = C J m ν i i ( k 0 R 2 ) + D Y m ν i i ( k 0 R 2 ) A J ' m ( k 0 R 1 ) = n ( C J ' m ν i i ( k 0 R 1 ) + D Y ' m ν i i ( k 0 R 1 ) ) B H m ( 1 ) ' ( k 0 R 2 ) = n ( C J ' m ν i i ( k 0 R 2 ) + D Y ' m ν i i ( k 0 R 2 ) ) .
P θ = n m ν ii ω r μ ' | C J m ν i i ( k 0 r ) + D Y m ν i i ( k 0 r ) | 2 ,
j z = n m ν ii ω μ ' | C J m ν i i ( k 0 r ) + D Y m ν i i ( k 0 r ) | 2 .

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