Abstract

We show that the value of the total angular momentum (AM) carried by a surface mode can be interpreted as representing the transverse position of the center or balance point of the power flow through the mode. Especially in the lossless cases, the value of the Abraham AM per unit power (multiplied by the square of the speed of light in vacuum) is exactly the same as the transverse position of this power-flow center. However, the Minkowski counterpart becomes proportional to that position with a coefficient in the form of 1 + η, where η is determined mainly by the constitutive parameters of media.

© 2014 Optical Society of America

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References

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  1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [Crossref] [PubMed]
  3. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [Crossref] [PubMed]
  4. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
    [Crossref] [PubMed]
  5. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photon. 2, 351–354 (2008).
    [Crossref]
  6. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1, 41–48 (2007).
    [Crossref]
  7. 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).
  8. K.-Y. Kim, J. Kim, I.-M. Lee, and B. Lee, “Analysis of transverse power flow via surface modes in metamaterial waveguides,” Phys. Rev. A 85, 023840 (2012).
    [Crossref]
  9. K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85, 061801(R) (2012).
    [Crossref]
  10. K.-Y. Kim, I.-M. Lee, J. Kim, J. Jung, and B. Lee, “Time reversal and the spin angular momentum of transverse-electric and transverse-magnetic surface modes,” Phys. Rev. A 86, 063805 (2012).
    [Crossref]
  11. A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88, 033831 (2013).
    [Crossref]
  12. X. Xiao, M. Faryad, and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part V: Spin and orbital angular momentums,” J. Nanophoton. 7, 073081 (2013).
    [Crossref]
  13. K.-Y. Kim, “Origin of the Abraham spin angular momentum of surface modes,” Opt. Lett. 39, 682–684 (2014).
    [Crossref] [PubMed]
  14. K.-Y. Kim, “Transverse spin angular momentum of Airy beams,” IEEE Photon. J. 4, 2333–2339 (2012).
    [Crossref]
  15. S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
    [Crossref]
  16. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011).
    [Crossref]
  17. K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21, 1502–1504 (2009).
    [Crossref]
  18. K.-Y. Kim, C.-Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19, 2286–2293 (2011).
    [Crossref] [PubMed]
  19. R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Constraining validity of the Minkowski energy-momentum tensor,” Phys. Rev. A 79, 023813 (2009).
    [Crossref]
  20. S. M. Barnett, “Resolution of the Abraham–Minkowski dilemma,” Phys. Rev. Lett. 104, 070401 (2010).
    [Crossref]
  21. B. A. Kemp, “Resolution of the Abraham–Minkowski debate: implications for the electromagnetic wave theory of light in matter,” J. Appl. Phys. 109, 111101 (2011).
    [Crossref]
  22. W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
    [Crossref]

2014 (1)

2013 (2)

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88, 033831 (2013).
[Crossref]

X. Xiao, M. Faryad, and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part V: Spin and orbital angular momentums,” J. Nanophoton. 7, 073081 (2013).
[Crossref]

2012 (4)

K.-Y. Kim, “Transverse spin angular momentum of Airy beams,” IEEE Photon. J. 4, 2333–2339 (2012).
[Crossref]

K.-Y. Kim, J. Kim, I.-M. Lee, and B. Lee, “Analysis of transverse power flow via surface modes in metamaterial waveguides,” Phys. Rev. A 85, 023840 (2012).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85, 061801(R) (2012).
[Crossref]

K.-Y. Kim, I.-M. Lee, J. Kim, J. Jung, and B. Lee, “Time reversal and the spin angular momentum of transverse-electric and transverse-magnetic surface modes,” Phys. Rev. A 86, 063805 (2012).
[Crossref]

2011 (4)

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).

B. A. Kemp, “Resolution of the Abraham–Minkowski debate: implications for the electromagnetic wave theory of light in matter,” J. Appl. Phys. 109, 111101 (2011).
[Crossref]

K.-Y. Kim, C.-Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19, 2286–2293 (2011).
[Crossref] [PubMed]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011).
[Crossref]

2010 (1)

S. M. Barnett, “Resolution of the Abraham–Minkowski dilemma,” Phys. Rev. Lett. 104, 070401 (2010).
[Crossref]

2009 (2)

K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21, 1502–1504 (2009).
[Crossref]

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Constraining validity of the Minkowski energy-momentum tensor,” Phys. Rev. A 79, 023813 (2009).
[Crossref]

2008 (2)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[Crossref]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photon. 2, 351–354 (2008).
[Crossref]

2007 (3)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1, 41–48 (2007).
[Crossref]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[Crossref] [PubMed]

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

2006 (2)

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

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

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[Crossref]

Barnett, S. M.

S. M. Barnett, “Resolution of the Abraham–Minkowski dilemma,” Phys. Rev. Lett. 104, 070401 (2010).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85, 061801(R) (2012).
[Crossref]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[Crossref] [PubMed]

Bratkovsky, A. M.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Canaguier-Durand, A.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88, 033831 (2013).
[Crossref]

Cuche, A.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88, 033831 (2013).
[Crossref]

Ebbesen, T. W.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88, 033831 (2013).
[Crossref]

Fang, N.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Faryad, M.

X. Xiao, M. Faryad, and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part V: Spin and orbital angular momentums,” J. Nanophoton. 7, 073081 (2013).
[Crossref]

Fedotov, V. A.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photon. 2, 351–354 (2008).
[Crossref]

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[Crossref]

Genet, C.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88, 033831 (2013).
[Crossref]

Heckenberg, N. R.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Constraining validity of the Minkowski energy-momentum tensor,” Phys. Rev. A 79, 023813 (2009).
[Crossref]

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[Crossref] [PubMed]

Hwang, C.-Y.

Jung, J.

K.-Y. Kim, I.-M. Lee, J. Kim, J. Jung, and B. Lee, “Time reversal and the spin angular momentum of transverse-electric and transverse-magnetic surface modes,” Phys. Rev. A 86, 063805 (2012).
[Crossref]

Kemp, B. A.

B. A. Kemp, “Resolution of the Abraham–Minkowski debate: implications for the electromagnetic wave theory of light in matter,” J. Appl. Phys. 109, 111101 (2011).
[Crossref]

Kim, E.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Kim, J.

K.-Y. Kim, I.-M. Lee, J. Kim, J. Jung, and B. Lee, “Time reversal and the spin angular momentum of transverse-electric and transverse-magnetic surface modes,” Phys. Rev. A 86, 063805 (2012).
[Crossref]

K.-Y. Kim, J. Kim, I.-M. Lee, and B. Lee, “Analysis of transverse power flow via surface modes in metamaterial waveguides,” Phys. Rev. A 85, 023840 (2012).
[Crossref]

Kim, K.-Y.

K.-Y. Kim, “Origin of the Abraham spin angular momentum of surface modes,” Opt. Lett. 39, 682–684 (2014).
[Crossref] [PubMed]

K.-Y. Kim, “Transverse spin angular momentum of Airy beams,” IEEE Photon. J. 4, 2333–2339 (2012).
[Crossref]

K.-Y. Kim, J. Kim, I.-M. Lee, and B. Lee, “Analysis of transverse power flow via surface modes in metamaterial waveguides,” Phys. Rev. A 85, 023840 (2012).
[Crossref]

K.-Y. Kim, I.-M. Lee, J. Kim, J. Jung, and B. Lee, “Time reversal and the spin angular momentum of transverse-electric and transverse-magnetic surface modes,” Phys. Rev. A 86, 063805 (2012).
[Crossref]

K.-Y. Kim, C.-Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19, 2286–2293 (2011).
[Crossref] [PubMed]

K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21, 1502–1504 (2009).
[Crossref]

Lakhtakia, A.

X. Xiao, M. Faryad, and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part V: Spin and orbital angular momentums,” J. Nanophoton. 7, 073081 (2013).
[Crossref]

Lee, B.

K.-Y. Kim, J. Kim, I.-M. Lee, and B. Lee, “Analysis of transverse power flow via surface modes in metamaterial waveguides,” Phys. Rev. A 85, 023840 (2012).
[Crossref]

K.-Y. Kim, I.-M. Lee, J. Kim, J. Jung, and B. Lee, “Time reversal and the spin angular momentum of transverse-electric and transverse-magnetic surface modes,” Phys. Rev. A 86, 063805 (2012).
[Crossref]

K.-Y. Kim, C.-Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19, 2286–2293 (2011).
[Crossref] [PubMed]

K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21, 1502–1504 (2009).
[Crossref]

Lee, I.-M.

K.-Y. Kim, I.-M. Lee, J. Kim, J. Jung, and B. Lee, “Time reversal and the spin angular momentum of transverse-electric and transverse-magnetic surface modes,” Phys. Rev. A 86, 063805 (2012).
[Crossref]

K.-Y. Kim, J. Kim, I.-M. Lee, and B. Lee, “Analysis of transverse power flow via surface modes in metamaterial waveguides,” Phys. Rev. A 85, 023840 (2012).
[Crossref]

K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21, 1502–1504 (2009).
[Crossref]

Leonhardt, U.

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

Liu, Y.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Nieminen, T. A.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Constraining validity of the Minkowski energy-momentum tensor,” Phys. Rev. A 79, 023813 (2009).
[Crossref]

Nori, F.

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85, 061801(R) (2012).
[Crossref]

Padgett, M.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[Crossref]

Padgett, M. J.

Papasimakis, N.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photon. 2, 351–354 (2008).
[Crossref]

Pendry, J. B.

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

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

Pfeifer, R. N. C.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Constraining validity of the Minkowski energy-momentum tensor,” Phys. Rev. A 79, 023813 (2009).
[Crossref]

Ponizovskaya, E.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Prosvirnin, S. L.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photon. 2, 351–354 (2008).
[Crossref]

Rubinsztein-Dunlop, H.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Constraining validity of the Minkowski energy-momentum tensor,” Phys. Rev. A 79, 023813 (2009).
[Crossref]

Schurig, D.

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

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1, 41–48 (2007).
[Crossref]

Shen, Y. R.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Smith, D. R.

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

Soukoulis, C. M.

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).

Sun, C.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Tong, W.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[Crossref] [PubMed]

Wang, S.-Y.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Wegener, M.

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).

Williams, R. S.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Wu, W.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Xiao, X.

X. Xiao, M. Faryad, and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part V: Spin and orbital angular momentums,” J. Nanophoton. 7, 073081 (2013).
[Crossref]

Yao, A. M.

Yu, Z.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Zhang, X.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

Zheludev, N. I.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photon. 2, 351–354 (2008).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Phys. A (1)

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S.-Y. Wang, and R. S. Williams, “Optical metamaterials at near and mid-IR range fabricated by nanoim-print lithography,” Appl. Phys. A 87, 143–150 (2007).
[Crossref]

IEEE Photon. J. (1)

K.-Y. Kim, “Transverse spin angular momentum of Airy beams,” IEEE Photon. J. 4, 2333–2339 (2012).
[Crossref]

IEEE Photon. Technol. Lett. (1)

K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21, 1502–1504 (2009).
[Crossref]

J. Appl. Phys. (1)

B. A. Kemp, “Resolution of the Abraham–Minkowski debate: implications for the electromagnetic wave theory of light in matter,” J. Appl. Phys. 109, 111101 (2011).
[Crossref]

J. Nanophoton. (1)

X. Xiao, M. Faryad, and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part V: Spin and orbital angular momentums,” J. Nanophoton. 7, 073081 (2013).
[Crossref]

Laser Photon. Rev. (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[Crossref]

Nat. Photon. (2)

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Figures (3)

Fig. 1
Fig. 1 (a) An interface with a surface mode along the +x direction. (b) and (c) Schematics showing the instantaneous power flow via the surface mode at t = 0 and t = π/2ω, respectively. The arrows represent power flows integrated over z = (−∞, 0], z = [0, ∞), x = [0, π/2β], and x = [π/2β, π/β]. Their width is proportional to the relative amount of each power flow. In figures, we assumed negative-index metamaterial (left) and dielectric (right) layers. + and − in each quadrant indicate that the internal electromagnetic energy increases and decreases, respectively. Refer to [8] for details.
Fig. 2
Fig. 2 (a) Geometrical interpretation of Eq. (7). It is notable that the direction of S(x), i.e, Φ remains constant even though its magnitude is dependent on x in lossy waveguides. Please note that Φ < 0 in this figure. (b) Abraham AMs of surface modes per unit power at the wavelength λ = 1550 nm. Lp denotes the propagation length of the surface mode. Solid and dotted lines correspond, respectively, to the mode at the NIM (εr = −2.2 + 0.5i and μr = −0.8)-silica interface and the mode at the ENG (εr = −2 + 0.5i and μr = 1)-MNG (εr = 1.2 and μr = −0.5 + 0.1i) interface. We took r0 = (0, 0) where x = 0 denotes the launching position of light to the waveguide (see the inset).
Fig. 3
Fig. 3 Abraham and Minkowski AMs of surface modes per unit power. The same interfaces as those in Fig. 2(b) were adopted neglecting material losses. Solid lines denote the Minkowski AMs while dotted lines show the Abraham counterparts. We also took r0 = (0, 0).

Equations (11)

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g = e 2 β i x 2 ω { x ^ ( β r ξ r + β i ξ i ) | ϕ | 2 + z ^ [ ξ r ( ϕ r ϕ i ϕ r ϕ i ) ξ i ( ϕ r ϕ r + ϕ i ϕ i ) ] } ,
j = e 2 β i x 2 ω y ^ { ( z z 0 ) ( β r ξ r + β i ξ i ) | ϕ | 2 ( x x 0 ) [ ξ r ( ϕ r ϕ i ϕ r ϕ i ) ξ i ( ϕ r ϕ r + ϕ i ϕ i ) ] } .
J ( x ) = j d z = e 2 β i x 2 ω y ^ [ Λ ( x x 0 ) Γ ] ,
Λ = 1 2 [ ( β r ξ 1 r + β i ξ 1 i ) ( 1 2 ( κ 1 r ) 2 + z 0 κ 1 r ) + ( β r ξ 2 r + β i ξ 2 i ) ( 1 2 ( κ 2 r ) 2 z 0 κ 2 r ) ] ,
Γ = 1 2 ( ξ 1 r κ 1 i κ 1 r ξ 1 i ξ 2 r κ 2 i κ 2 r + ξ 2 i ) .
c 2 J A ( x ) = y ^ [ ( z z 0 ) s x d z ( x x 0 ) s z d z ] .
c 2 J 0 A ( x ) = y ^ [ ( z z 0 ) s x d z s x d z ( x x 0 ) tan Φ ] ,
tan Φ = Γ ( β r ξ r + β i ξ i ) | ϕ | 2 d z .
c 2 J 0 M ( x ) = y ^ ( z z 0 ) ε r μ r s x d z s x d z .
c 2 J 0 M ( x ) = y ^ [ z z 0 + ε r μ r 1 ( z z 0 ) s ˜ x d z s ˜ x d z ] = y ^ [ z z 0 + ( ε r μ r 1 ) z z 0 s ˜ x ] ,
c 2 J 0 M ( x ) = y ^ ( 1 + η ) z z 0 ,

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