Abstract

The optical nonlocality near the Dirac point in infinite periodic metal-dielectric multilayer metamaterials is investigated through the dispersion relation analysis according to the transfer-matrix method. It is revealed that both the symmetric and asymmetric surface plasmon polariton modes present the zero nonlocal effective permittivity, and the degeneracy of these two modes results in the emergence of the Dirac point. Furthermore, the Zitterbewegung effect near the Dirac point induced by the optical nonlocality is demonstrated due to the coherent coupling between the symmetric and asymmetric modes.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Giant optical nonlocality near the Dirac point in metal-dielectric multilayer metamaterials

Lei Sun, Jie Gao, and Xiaodong Yang
Opt. Express 21(18) 21542-21555 (2013)

Experimental characterization of optical nonlocality in metal-dielectric multilayer metamaterials

Lei Sun, Fei Cheng, Cherian J. Mathai, Shubhra Gangopadhyay, Jie Gao, and Xiaodong Yang
Opt. Express 22(19) 22974-22980 (2014)

Experimental demonstration of near-infrared epsilon-near-zero multilayer metamaterial slabs

Xiaodong Yang, Changyu Hu, Huixu Deng, Daniel Rosenmann, David A. Czaplewski, and Jie Gao
Opt. Express 21(20) 23631-23639 (2013)

References

  • View by:
  • |
  • |
  • |

  1. H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
    [Crossref]
  2. X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
    [Crossref] [PubMed]
  3. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
    [Crossref] [PubMed]
  4. G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B 79, 201103 (2009).
    [Crossref]
  5. L. Sun, S. Feng, and X. Yang, “Loss enhanced transmission and collimation in anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 101, 241101 (2012).
    [Crossref]
  6. Y. He, L. Sun, S. He, and X. Yang, “Deep subwavelength beam propagation in extremely loss-anisotropic metamaterials,” J. Opt. 15, 055105 (2013).
    [Crossref]
  7. L. Sun, X. Yang, W. Wang, and J. Gao, “Diffraction-free optical beam propagation with near-zero phase variation in extremely anisotropic metamaterials,” J. Opt. 17, 035101 (2015).
    [Crossref]
  8. X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6, 450–454 (2012).
    [Crossref]
  9. J. Zhao, H. Zhang, X. Zhang, D. Li, H. Lu, and M. Xu, “Abnormal behaviors of Goos-Hänchen shift in hyperbolic metamaterials made of aluminum zinc oxide materials,” Photon. Res. 1, 160–163 (2013).
    [Crossref]
  10. J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
    [Crossref]
  11. A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
    [Crossref]
  12. S. Feng, J. M. Elson, and P. L. Overfelt, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express 13, 4113–4124 (2005).
    [Crossref] [PubMed]
  13. K. Sakoda, “Universality of mode symmetries in creating photonic Dirac cones,” J. Opt. Soc. Am. B 29, 2770–2778 (2012).
    [Crossref]
  14. X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
    [Crossref] [PubMed]
  15. L. Sun, J. Gao, and X. Yang, “Giant optical nonlocality near the Dirac point in metal-dielectric multilayer metamaterials,” Opt. Express 21, 21542–21555 (2013).
    [Crossref] [PubMed]
  16. A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84, 115438 (2011).
    [Crossref]
  17. A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
    [Crossref]
  18. L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91, 195147 (2015).
    [Crossref]
  19. X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100, 113903 (2008).
    [Crossref] [PubMed]
  20. L.-G. Wang, Z.-G. Wang, and S.-Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positivie index metamaterial,” Europhys. Lett. 86, 47008 (2009).
    [Crossref]
  21. W. Cai and V. Shalaev, Optical Metamaterials (Springer, 2010).
    [Crossref]
  22. I. H. Malitson and M. J. Dodge, “Refractive index and birefringence of synthetic sapphire,” J. Opt. Soc. Am. 62, 1405 (1972).
  23. S. H. Nam, A. J. Taylor, and A. Efimov, “Diabolical point and conical-like diffraction in periodic plasmonic nanostructures,” Opt. Express 18, 10120–10126 (2010).
    [Crossref] [PubMed]
  24. K. E. Ballantine, J. F. Donegan, and P. R. Eastham, “Conical diffraction and the dispersion surface of hyperbolic metamaterials,” Phys. Rev. A 90, 013803 (2014).
    [Crossref]
  25. S. H. Nam, J. Zhou, A. J. Taylor, and A. Efimov, “Dirac dynamics in one-dimensional graphene-like plasmonic crystals: pseudo-spin, chirality, and diffraction anomaly,” Opt. Express 18, 25329–25338 (2010).
    [Crossref] [PubMed]

2015 (2)

L. Sun, X. Yang, W. Wang, and J. Gao, “Diffraction-free optical beam propagation with near-zero phase variation in extremely anisotropic metamaterials,” J. Opt. 17, 035101 (2015).
[Crossref]

L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91, 195147 (2015).
[Crossref]

2014 (1)

K. E. Ballantine, J. F. Donegan, and P. R. Eastham, “Conical diffraction and the dispersion surface of hyperbolic metamaterials,” Phys. Rev. A 90, 013803 (2014).
[Crossref]

2013 (3)

2012 (4)

K. Sakoda, “Universality of mode symmetries in creating photonic Dirac cones,” J. Opt. Soc. Am. B 29, 2770–2778 (2012).
[Crossref]

L. Sun, S. Feng, and X. Yang, “Loss enhanced transmission and collimation in anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 101, 241101 (2012).
[Crossref]

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6, 450–454 (2012).
[Crossref]

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

2011 (3)

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref] [PubMed]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84, 115438 (2011).
[Crossref]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[Crossref]

2010 (2)

2009 (3)

L.-G. Wang, Z.-G. Wang, and S.-Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positivie index metamaterial,” Europhys. Lett. 86, 47008 (2009).
[Crossref]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[Crossref] [PubMed]

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B 79, 201103 (2009).
[Crossref]

2008 (1)

X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100, 113903 (2008).
[Crossref] [PubMed]

2007 (1)

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

2006 (2)

H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
[Crossref]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[Crossref] [PubMed]

2005 (1)

1972 (1)

I. H. Malitson and M. J. Dodge, “Refractive index and birefringence of synthetic sapphire,” J. Opt. Soc. Am. 62, 1405 (1972).

Avrutsky, I.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Ballantine, K. E.

K. E. Ballantine, J. F. Donegan, and P. R. Eastham, “Conical diffraction and the dispersion surface of hyperbolic metamaterials,” Phys. Rev. A 90, 013803 (2014).
[Crossref]

Bartal, G.

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B 79, 201103 (2009).
[Crossref]

Belov, P. A.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84, 115438 (2011).
[Crossref]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[Crossref]

Cai, W.

W. Cai and V. Shalaev, Optical Metamaterials (Springer, 2010).
[Crossref]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[Crossref] [PubMed]

Chan, C. T.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref] [PubMed]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[Crossref] [PubMed]

Chebykin, A. V.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84, 115438 (2011).
[Crossref]

Dodge, M. J.

I. H. Malitson and M. J. Dodge, “Refractive index and birefringence of synthetic sapphire,” J. Opt. Soc. Am. 62, 1405 (1972).

Donegan, J. F.

K. E. Ballantine, J. F. Donegan, and P. R. Eastham, “Conical diffraction and the dispersion surface of hyperbolic metamaterials,” Phys. Rev. A 90, 013803 (2014).
[Crossref]

Eastham, P. R.

K. E. Ballantine, J. F. Donegan, and P. R. Eastham, “Conical diffraction and the dispersion surface of hyperbolic metamaterials,” Phys. Rev. A 90, 013803 (2014).
[Crossref]

Efimov, A.

Elser, J.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Elson, J. M.

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[Crossref] [PubMed]

H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
[Crossref]

Fan, X.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[Crossref] [PubMed]

Feng, S.

L. Sun, S. Feng, and X. Yang, “Loss enhanced transmission and collimation in anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 101, 241101 (2012).
[Crossref]

S. Feng, J. M. Elson, and P. L. Overfelt, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express 13, 4113–4124 (2005).
[Crossref] [PubMed]

Gao, J.

L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91, 195147 (2015).
[Crossref]

L. Sun, X. Yang, W. Wang, and J. Gao, “Diffraction-free optical beam propagation with near-zero phase variation in extremely anisotropic metamaterials,” J. Opt. 17, 035101 (2015).
[Crossref]

L. Sun, J. Gao, and X. Yang, “Giant optical nonlocality near the Dirac point in metal-dielectric multilayer metamaterials,” Opt. Express 21, 21542–21555 (2013).
[Crossref] [PubMed]

Hang, Z. H.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref] [PubMed]

He, S.

Y. He, L. Sun, S. He, and X. Yang, “Deep subwavelength beam propagation in extremely loss-anisotropic metamaterials,” J. Opt. 15, 055105 (2013).
[Crossref]

He, Y.

Y. He, L. Sun, S. He, and X. Yang, “Deep subwavelength beam propagation in extremely loss-anisotropic metamaterials,” J. Opt. 15, 055105 (2013).
[Crossref]

Huang, X.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref] [PubMed]

Kivshar, Y. S.

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[Crossref]

Kivshar, Yu. S.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84, 115438 (2011).
[Crossref]

Lai, Y.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref] [PubMed]

Lee, J. C. W.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[Crossref] [PubMed]

Lerosey, G.

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B 79, 201103 (2009).
[Crossref]

Li, D.

Li, Z.

L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91, 195147 (2015).
[Crossref]

Lu, H.

Luk, T. S.

L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91, 195147 (2015).
[Crossref]

Malitson, I. H.

I. H. Malitson and M. J. Dodge, “Refractive index and birefringence of synthetic sapphire,” J. Opt. Soc. Am. 62, 1405 (1972).

Maslovski, S. I.

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84, 115438 (2011).
[Crossref]

Nam, S. H.

Orlov, A. A.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84, 115438 (2011).
[Crossref]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[Crossref]

Overfelt, P. L.

Podolskiy, V. A.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Rho, J.

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6, 450–454 (2012).
[Crossref]

Sakoda, K.

Salakhutdinov, I.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Shalaev, V.

W. Cai and V. Shalaev, Optical Metamaterials (Springer, 2010).
[Crossref]

Shin, H.

H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
[Crossref]

Simovski, C. R.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

Sun, L.

L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91, 195147 (2015).
[Crossref]

L. Sun, X. Yang, W. Wang, and J. Gao, “Diffraction-free optical beam propagation with near-zero phase variation in extremely anisotropic metamaterials,” J. Opt. 17, 035101 (2015).
[Crossref]

Y. He, L. Sun, S. He, and X. Yang, “Deep subwavelength beam propagation in extremely loss-anisotropic metamaterials,” J. Opt. 15, 055105 (2013).
[Crossref]

L. Sun, J. Gao, and X. Yang, “Giant optical nonlocality near the Dirac point in metal-dielectric multilayer metamaterials,” Opt. Express 21, 21542–21555 (2013).
[Crossref] [PubMed]

L. Sun, S. Feng, and X. Yang, “Loss enhanced transmission and collimation in anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 101, 241101 (2012).
[Crossref]

Taylor, A. J.

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[Crossref] [PubMed]

Voroshilov, P. M.

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[Crossref]

Vozianova, A. V.

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84, 115438 (2011).
[Crossref]

Wang, G. P.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[Crossref] [PubMed]

Wang, L.-G.

L.-G. Wang, Z.-G. Wang, and S.-Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positivie index metamaterial,” Europhys. Lett. 86, 47008 (2009).
[Crossref]

Wang, W.

L. Sun, X. Yang, W. Wang, and J. Gao, “Diffraction-free optical beam propagation with near-zero phase variation in extremely anisotropic metamaterials,” J. Opt. 17, 035101 (2015).
[Crossref]

Wang, Z.-G.

L.-G. Wang, Z.-G. Wang, and S.-Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positivie index metamaterial,” Europhys. Lett. 86, 47008 (2009).
[Crossref]

Xu, M.

Yang, X.

L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91, 195147 (2015).
[Crossref]

L. Sun, X. Yang, W. Wang, and J. Gao, “Diffraction-free optical beam propagation with near-zero phase variation in extremely anisotropic metamaterials,” J. Opt. 17, 035101 (2015).
[Crossref]

Y. He, L. Sun, S. He, and X. Yang, “Deep subwavelength beam propagation in extremely loss-anisotropic metamaterials,” J. Opt. 15, 055105 (2013).
[Crossref]

L. Sun, J. Gao, and X. Yang, “Giant optical nonlocality near the Dirac point in metal-dielectric multilayer metamaterials,” Opt. Express 21, 21542–21555 (2013).
[Crossref] [PubMed]

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6, 450–454 (2012).
[Crossref]

L. Sun, S. Feng, and X. Yang, “Loss enhanced transmission and collimation in anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 101, 241101 (2012).
[Crossref]

Yao, J.

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6, 450–454 (2012).
[Crossref]

Yin, X.

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6, 450–454 (2012).
[Crossref]

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[Crossref] [PubMed]

Zhang, H.

Zhang, X.

J. Zhao, H. Zhang, X. Zhang, D. Li, H. Lu, and M. Xu, “Abnormal behaviors of Goos-Hänchen shift in hyperbolic metamaterials made of aluminum zinc oxide materials,” Photon. Res. 1, 160–163 (2013).
[Crossref]

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6, 450–454 (2012).
[Crossref]

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B 79, 201103 (2009).
[Crossref]

X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100, 113903 (2008).
[Crossref] [PubMed]

Zhao, J.

Zheng, H.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref] [PubMed]

Zhou, J.

Zhu, S.-Y.

L.-G. Wang, Z.-G. Wang, and S.-Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positivie index metamaterial,” Europhys. Lett. 86, 47008 (2009).
[Crossref]

Appl. Phys. Lett. (3)

L. Sun, S. Feng, and X. Yang, “Loss enhanced transmission and collimation in anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 101, 241101 (2012).
[Crossref]

H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
[Crossref]

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Europhys. Lett. (1)

L.-G. Wang, Z.-G. Wang, and S.-Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positivie index metamaterial,” Europhys. Lett. 86, 47008 (2009).
[Crossref]

J. Opt. (2)

Y. He, L. Sun, S. He, and X. Yang, “Deep subwavelength beam propagation in extremely loss-anisotropic metamaterials,” J. Opt. 15, 055105 (2013).
[Crossref]

L. Sun, X. Yang, W. Wang, and J. Gao, “Diffraction-free optical beam propagation with near-zero phase variation in extremely anisotropic metamaterials,” J. Opt. 17, 035101 (2015).
[Crossref]

J. Opt. Soc. Am. (1)

I. H. Malitson and M. J. Dodge, “Refractive index and birefringence of synthetic sapphire,” J. Opt. Soc. Am. 62, 1405 (1972).

J. Opt. Soc. Am. B (1)

Nat. Mater. (1)

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref] [PubMed]

Nat. Photonics (1)

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6, 450–454 (2012).
[Crossref]

Opt. Express (4)

Photon. Res. (1)

Phys. Rev. A (1)

K. E. Ballantine, J. F. Donegan, and P. R. Eastham, “Conical diffraction and the dispersion surface of hyperbolic metamaterials,” Phys. Rev. A 90, 013803 (2014).
[Crossref]

Phys. Rev. B (5)

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[Crossref]

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B 79, 201103 (2009).
[Crossref]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84, 115438 (2011).
[Crossref]

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91, 195147 (2015).
[Crossref]

Phys. Rev. Lett. (3)

X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100, 113903 (2008).
[Crossref] [PubMed]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[Crossref] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[Crossref] [PubMed]

Other (1)

W. Cai and V. Shalaev, Optical Metamaterials (Springer, 2010).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

(a) Schematic of the infinite periodic Au-Al2O3 multilayer stack with respect to the TM polarized light. (b) The dispersion relation of frequency ω/ωp versus wave vector ky/kp (red-solid curves) of the Au-Al2O3 multilayer stack, compared with the typical SPP dispersion based on k y / k p = ω / ω p ε m ε d / ( ε m + ε d ) (black-dashed curve). The light lines in Air (green-solid line) and in Au-Al2O3 (green-dashed line) are also displayed. The distributions of the magnetic field Hz for the symmetric and asymmetric modes at the point S and the point A are presented. (c) The corresponding band structure of frequency ω/ωp versus wave vector kx/kp with the Dirac point at the Brillouin zone center.

Fig. 2
Fig. 2

The IFCs based on the dispersion relation of Eq. (1) (red-solid curves), the nonlocal effective permittivities of Eq. (6) (black-dashed curves), and the local effective permittivities (blue-solid curves) with respect to the frequency (a) 0.085ωp as 186.689THz (below the Dirac point), (b) 0.092ωp as 202.692THz (at the Dirac point), and (c) 0.1ωp as 219.634THz (above the Dirac point). The IFCs of air are plotted in green circles for reference.

Fig. 3
Fig. 3

The beam propagation patterns in the Au-Al2O3 multilayer stack for a TM polarized Gaussian beam incident from air with respect to the frequency at (a) 0.085ωp (below the Dirac point), (b) 0.092ωp (at the Dirac point), and (c) 0.1ωp (above the Dirac point) in terms of the distributions of the normalized magnetic field intensity |Hz|. (d) The oscillation of the beam center in the Au-Al2O3 multilayer stack calculated from the beam propagation patterns at the frequency of 0.085ωp (blue-solid curve) and 0.1ωp (red-solid curve) indicates the Zitterbewegung effect around the Dirac point.

Fig. 4
Fig. 4

The beam propagation patterns of the Zitterbewegung in the Au-Al2O3 multilayer stack for a TM polarized Gaussian beam at the frequency of 0.085ωp (below the Dirac point) with respect to different Au damping factors of (a) 0.1γ, (b) 0.5γ, and (c) 1.0γ in terms of the distributions of the normalized magnetic field intensity |Hz|. (d) The oscillation of the beam center in the Au-Al2O3 multilayer stack calculated from the beam propagation patterns with respect to different Au damping factors of 0.1γ (red-solid curve), 0.5γ (blue-solid curve), and 1.0γ (black-solid curve).

Fig. 5
Fig. 5

The beam propagation patterns of the Zitterbewegung in the Au-Al2O3 multilayer stack for a TM polarized Gaussian beam at the frequency of 0.1ωp (above the Dirac point) with respect to different Au damping factors of (a) 0.1γ, (b) 0.5γ, and (c) 1.0γ in terms of the distributions of the normalized magnetic field intensity |Hz|. (d) The oscillation of the beam center in the Au-Al2O3 multilayer stack calculated from the beam propagation patterns with respect to different Au damping factors of 0.1γ (red-solid curve), 0.5γ (blue-solid curve), and 1.0γ (black-solid curve).

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

cos ( k x ( a m + a d ) ) = cos ( k m x a m ) cos ( k d x a d ) 1 2 ( ε m k d x ε d k m x + ε d k m x ε m k d x ) sin ( k m x a m ) sin ( k d x a d )
cos ( k m x a m ) cos ( k d x a d ) 1 2 ( ε m k d x ε d k m x + ε d k m x ε m k d x ) sin ( k m x a m ) sin ( k d x a d ) = 1
{ k x / k p = 0 k y / k p = ε d a m a d / ( ( a d a m ) ( ε a m + ε d a d ) ) ω / ω p = a m / ( ε a m + ε d a d )
k x ( ω , k y ) = arccos [ cos ( k m x a m ) cos ( k d x a d ) 1 2 ( ε m k d x ε d k m x + ε d k m x ε m k d x ) sin ( k m x a m ) sin ( k d x a d ) ] a m + a d .
k x 2 / ε y nloc + k y 2 ε x nloc = k 0 2
{ ε x nloc ( ω , k y ) = ε x loc = ε m ε d ( a m + a d ) / ( ε m a d + ε d a m ) ε y nloc ( ω , k y ) = k x ( ω , k y ) 2 / [ k 0 2 k y 2 / ε x nloc ( ω , k y ) ]

Metrics