Abstract

We study complex eigenmodes of layered metal-dielectric metamaterials. Varying losses from weak to realistic, we analyze band structure of the metamaterial and clarify effect of lossess on its intrinsic electromagnetic properties. The structure operates in a regime with infinite numbers of eigenmodes, whereas we analyze dominant ones.

© 2013 OSA

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  1. A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
    [CrossRef]
  2. I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, “BW media - media with negative parameters, capable of supporting backward waves,” Microw. Opt. Technol. Lett.31, 129133 (2001).
    [CrossRef]
  3. A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84, 023807 (2011).
    [CrossRef]
  4. I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metaldi-electric metamaterials,” Phys. Lett. A376, 185187 (2012).
    [CrossRef]
  5. J. Elser, V. A. Podolksiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett.90, 191109 (2007).
    [CrossRef]
  6. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Oxford, Pergamon Press, 1964).
  7. D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett.90, 077405 (2003).
    [CrossRef] [PubMed]
  8. M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett.94, 151105 (2009).
    [CrossRef]
  9. Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
    [CrossRef]
  10. A. Poddubny, P. Belov, and Y. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84, 023807 (2011).
    [CrossRef]
  11. O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation,” Opt. Lett.36, 2530–2532 (2011).
    [CrossRef] [PubMed]
  12. A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B84, 115438 (2011).
    [CrossRef]
  13. A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B86, 115420 (2012).
    [CrossRef]
  14. L. Shen, T.-J. Yang, and Y.-F. Chau, “Effect of internal period on the optical dispersion of indefinite-medium materials,” Phys. Rev. B77, 205124 (2008).
    [CrossRef]
  15. A. P. Vinogradov, A. V. Dorofeenko, and I. A. Nechpurenko, “Analysis of plasmonic bloch waves and band structures of 1d plasmonic photonic crystals,” Metamaterials4, 181–200 (2010).
    [CrossRef]
  16. A. Davoyan, W. Liu, A. Miroshnichenko, I. Shadrivov, Y. Kivshar, and S. Bozhevolnyi, “Mode transformation in waveguiding plasmonic structures,” Phot. Nano. Fund. Appl.9, 207–212 (2011).
    [CrossRef]
  17. A. A. Andreev, A. A. Mak, and N. A. Solov’ev, An Introduction to Hot Laser Plasma Physics (Huntington, NY: Nova Science Publishers, 2000).
  18. A. A. Bogdanov and R. A. Suris, “Effect of the anisotropy of a conducting layer on the dispersion law of electromagnetic waves in layered metal-dielectric structures,” JETP Lett.96, 49–55 (2012).
    [CrossRef]

2012 (3)

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metaldi-electric metamaterials,” Phys. Lett. A376, 185187 (2012).
[CrossRef]

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B86, 115420 (2012).
[CrossRef]

A. A. Bogdanov and R. A. Suris, “Effect of the anisotropy of a conducting layer on the dispersion law of electromagnetic waves in layered metal-dielectric structures,” JETP Lett.96, 49–55 (2012).
[CrossRef]

2011 (6)

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation,” Opt. Lett.36, 2530–2532 (2011).
[CrossRef] [PubMed]

A. Davoyan, W. Liu, A. Miroshnichenko, I. Shadrivov, Y. Kivshar, and S. Bozhevolnyi, “Mode transformation in waveguiding plasmonic structures,” Phot. Nano. Fund. Appl.9, 207–212 (2011).
[CrossRef]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
[CrossRef]

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84, 023807 (2011).
[CrossRef]

A. Poddubny, P. Belov, and Y. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84, 023807 (2011).
[CrossRef]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B84, 115438 (2011).
[CrossRef]

2010 (2)

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

A. P. Vinogradov, A. V. Dorofeenko, and I. A. Nechpurenko, “Analysis of plasmonic bloch waves and band structures of 1d plasmonic photonic crystals,” Metamaterials4, 181–200 (2010).
[CrossRef]

2009 (1)

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett.94, 151105 (2009).
[CrossRef]

2008 (1)

L. Shen, T.-J. Yang, and Y.-F. Chau, “Effect of internal period on the optical dispersion of indefinite-medium materials,” Phys. Rev. B77, 205124 (2008).
[CrossRef]

2007 (1)

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

2003 (1)

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett.90, 077405 (2003).
[CrossRef] [PubMed]

2001 (1)

I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, “BW media - media with negative parameters, capable of supporting backward waves,” Microw. Opt. Technol. Lett.31, 129133 (2001).
[CrossRef]

Andreev, A. A.

A. A. Andreev, A. A. Mak, and N. A. Solov’ev, An Introduction to Hot Laser Plasma Physics (Huntington, NY: Nova Science Publishers, 2000).

Avrutsky, I.

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

Barnakov, Y. A.

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett.94, 151105 (2009).
[CrossRef]

Belov, P.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metaldi-electric metamaterials,” Phys. Lett. A376, 185187 (2012).
[CrossRef]

A. Poddubny, P. Belov, and Y. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84, 023807 (2011).
[CrossRef]

Belov, P. A.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B86, 115420 (2012).
[CrossRef]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B84, 115438 (2011).
[CrossRef]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
[CrossRef]

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84, 023807 (2011).
[CrossRef]

Bogdanov, A. A.

A. A. Bogdanov and R. A. Suris, “Effect of the anisotropy of a conducting layer on the dispersion law of electromagnetic waves in layered metal-dielectric structures,” JETP Lett.96, 49–55 (2012).
[CrossRef]

Boltasseva, A.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Oxford, Pergamon Press, 1964).

Bozhevolnyi, S.

A. Davoyan, W. Liu, A. Miroshnichenko, I. Shadrivov, Y. Kivshar, and S. Bozhevolnyi, “Mode transformation in waveguiding plasmonic structures,” Phot. Nano. Fund. Appl.9, 207–212 (2011).
[CrossRef]

Chau, Y.-F.

L. Shen, T.-J. Yang, and Y.-F. Chau, “Effect of internal period on the optical dispersion of indefinite-medium materials,” Phys. Rev. B77, 205124 (2008).
[CrossRef]

Chebykin, A. V.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B86, 115420 (2012).
[CrossRef]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B84, 115438 (2011).
[CrossRef]

Davoyan, A.

A. Davoyan, W. Liu, A. Miroshnichenko, I. Shadrivov, Y. Kivshar, and S. Bozhevolnyi, “Mode transformation in waveguiding plasmonic structures,” Phot. Nano. Fund. Appl.9, 207–212 (2011).
[CrossRef]

Dorofeenko, A. V.

A. P. Vinogradov, A. V. Dorofeenko, and I. A. Nechpurenko, “Analysis of plasmonic bloch waves and band structures of 1d plasmonic photonic crystals,” Metamaterials4, 181–200 (2010).
[CrossRef]

Elser, J.

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

Ilvonen, S.

I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, “BW media - media with negative parameters, capable of supporting backward waves,” Microw. Opt. Technol. Lett.31, 129133 (2001).
[CrossRef]

Iorsh, I.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metaldi-electric metamaterials,” Phys. Lett. A376, 185187 (2012).
[CrossRef]

Jacob, Z.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

Kidwai, O.

Kim, J.-Y.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

Kivshar, Y.

A. Poddubny, P. Belov, and Y. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84, 023807 (2011).
[CrossRef]

A. Davoyan, W. Liu, A. Miroshnichenko, I. Shadrivov, Y. Kivshar, and S. Bozhevolnyi, “Mode transformation in waveguiding plasmonic structures,” Phot. Nano. Fund. Appl.9, 207–212 (2011).
[CrossRef]

Kivshar, Y. S.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B86, 115420 (2012).
[CrossRef]

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metaldi-electric metamaterials,” Phys. Lett. A376, 185187 (2012).
[CrossRef]

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84, 023807 (2011).
[CrossRef]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
[CrossRef]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B84, 115438 (2011).
[CrossRef]

Li, H.

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett.94, 151105 (2009).
[CrossRef]

Lindell, I. V.

I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, “BW media - media with negative parameters, capable of supporting backward waves,” Microw. Opt. Technol. Lett.31, 129133 (2001).
[CrossRef]

Liu, W.

A. Davoyan, W. Liu, A. Miroshnichenko, I. Shadrivov, Y. Kivshar, and S. Bozhevolnyi, “Mode transformation in waveguiding plasmonic structures,” Phot. Nano. Fund. Appl.9, 207–212 (2011).
[CrossRef]

Mak, A. A.

A. A. Andreev, A. A. Mak, and N. A. Solov’ev, An Introduction to Hot Laser Plasma Physics (Huntington, NY: Nova Science Publishers, 2000).

Maslovski, S. I.

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B84, 115438 (2011).
[CrossRef]

Miroshnichenko, A.

A. Davoyan, W. Liu, A. Miroshnichenko, I. Shadrivov, Y. Kivshar, and S. Bozhevolnyi, “Mode transformation in waveguiding plasmonic structures,” Phot. Nano. Fund. Appl.9, 207–212 (2011).
[CrossRef]

Naik, G. V.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

Narimanov, E. E.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett.94, 151105 (2009).
[CrossRef]

Nechpurenko, I. A.

A. P. Vinogradov, A. V. Dorofeenko, and I. A. Nechpurenko, “Analysis of plasmonic bloch waves and band structures of 1d plasmonic photonic crystals,” Metamaterials4, 181–200 (2010).
[CrossRef]

Nikoskinen, K. I.

I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, “BW media - media with negative parameters, capable of supporting backward waves,” Microw. Opt. Technol. Lett.31, 129133 (2001).
[CrossRef]

Noginov, M. A.

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett.94, 151105 (2009).
[CrossRef]

Orlov, A.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metaldi-electric metamaterials,” Phys. Lett. A376, 185187 (2012).
[CrossRef]

Orlov, A. A.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B86, 115420 (2012).
[CrossRef]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B84, 115438 (2011).
[CrossRef]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
[CrossRef]

Poddubny, A.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metaldi-electric metamaterials,” Phys. Lett. A376, 185187 (2012).
[CrossRef]

A. Poddubny, P. Belov, and Y. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84, 023807 (2011).
[CrossRef]

Poddubny, A. N.

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84, 023807 (2011).
[CrossRef]

Podolksiy, V. A.

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

Salakhutdinov, I.

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

Schurig, D.

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett.90, 077405 (2003).
[CrossRef] [PubMed]

Shadrivov, I.

A. Davoyan, W. Liu, A. Miroshnichenko, I. Shadrivov, Y. Kivshar, and S. Bozhevolnyi, “Mode transformation in waveguiding plasmonic structures,” Phot. Nano. Fund. Appl.9, 207–212 (2011).
[CrossRef]

Shalaev, V. M.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

Shen, L.

L. Shen, T.-J. Yang, and Y.-F. Chau, “Effect of internal period on the optical dispersion of indefinite-medium materials,” Phys. Rev. B77, 205124 (2008).
[CrossRef]

Simovski, C. R.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B86, 115420 (2012).
[CrossRef]

Sipe, J. E.

Smith, D.

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett.90, 077405 (2003).
[CrossRef] [PubMed]

Solov’ev, N. A.

A. A. Andreev, A. A. Mak, and N. A. Solov’ev, An Introduction to Hot Laser Plasma Physics (Huntington, NY: Nova Science Publishers, 2000).

Suris, R. A.

A. A. Bogdanov and R. A. Suris, “Effect of the anisotropy of a conducting layer on the dispersion law of electromagnetic waves in layered metal-dielectric structures,” JETP Lett.96, 49–55 (2012).
[CrossRef]

Tretyakov, S. A.

I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, “BW media - media with negative parameters, capable of supporting backward waves,” Microw. Opt. Technol. Lett.31, 129133 (2001).
[CrossRef]

Tumkur, T.

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett.94, 151105 (2009).
[CrossRef]

Vinogradov, A. P.

A. P. Vinogradov, A. V. Dorofeenko, and I. A. Nechpurenko, “Analysis of plasmonic bloch waves and band structures of 1d plasmonic photonic crystals,” Metamaterials4, 181–200 (2010).
[CrossRef]

Voroshilov, P. M.

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
[CrossRef]

Vozianova, A. V.

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B84, 115438 (2011).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Oxford, Pergamon Press, 1964).

Yang, T.-J.

L. Shen, T.-J. Yang, and Y.-F. Chau, “Effect of internal period on the optical dispersion of indefinite-medium materials,” Phys. Rev. B77, 205124 (2008).
[CrossRef]

Zhu, G.

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett.94, 151105 (2009).
[CrossRef]

Zhukovsky, S. V.

Appl. Phys. B (1)

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

Appl. Phys. Lett. (2)

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

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett.94, 151105 (2009).
[CrossRef]

JETP Lett. (1)

A. A. Bogdanov and R. A. Suris, “Effect of the anisotropy of a conducting layer on the dispersion law of electromagnetic waves in layered metal-dielectric structures,” JETP Lett.96, 49–55 (2012).
[CrossRef]

Metamaterials (1)

A. P. Vinogradov, A. V. Dorofeenko, and I. A. Nechpurenko, “Analysis of plasmonic bloch waves and band structures of 1d plasmonic photonic crystals,” Metamaterials4, 181–200 (2010).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, “BW media - media with negative parameters, capable of supporting backward waves,” Microw. Opt. Technol. Lett.31, 129133 (2001).
[CrossRef]

Opt. Lett. (1)

Phot. Nano. Fund. Appl. (1)

A. Davoyan, W. Liu, A. Miroshnichenko, I. Shadrivov, Y. Kivshar, and S. Bozhevolnyi, “Mode transformation in waveguiding plasmonic structures,” Phot. Nano. Fund. Appl.9, 207–212 (2011).
[CrossRef]

Phys. Lett. A (1)

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metaldi-electric metamaterials,” Phys. Lett. A376, 185187 (2012).
[CrossRef]

Phys. Rev. A (2)

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84, 023807 (2011).
[CrossRef]

A. Poddubny, P. Belov, and Y. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A84, 023807 (2011).
[CrossRef]

Phys. Rev. B (4)

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B84, 115438 (2011).
[CrossRef]

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B86, 115420 (2012).
[CrossRef]

L. Shen, T.-J. Yang, and Y.-F. Chau, “Effect of internal period on the optical dispersion of indefinite-medium materials,” Phys. Rev. B77, 205124 (2008).
[CrossRef]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
[CrossRef]

Phys. Rev. Lett. (1)

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett.90, 077405 (2003).
[CrossRef] [PubMed]

Other (2)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Oxford, Pergamon Press, 1964).

A. A. Andreev, A. A. Mak, and N. A. Solov’ev, An Introduction to Hot Laser Plasma Physics (Huntington, NY: Nova Science Publishers, 2000).

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Figures (4)

Fig. 1
Fig. 1

Band structure of the structure with d1 < d2 in the absence of losses (a) and with the losses (b). Imaginary parts of the modes are on the left, real parts are on the right. Low-loss modes are marked with colors, gray curves correspond to high-order modes.

Fig. 2
Fig. 2

Band structure of the structure with d1 > d2 in the absence of losses (a) and with the losses (b). Imaginary parts of the modes are on the left, real parts are on the right.

Fig. 3
Fig. 3

Mode transformation mechanism in MMDN: a) Γ = 1.885 · 1011s−1, b) Γ = 5.655 · 1012s−1, c) Γ = 9.425 · 1012s−1, and d) Γ = 1.508 · 1013s−1, with field profiles corresponding to curves A, B, C of (d).

Fig. 4
Fig. 4

Field profiles in the case of d1 < d2 (a–c) and d1 > d2 (d–f) for three modes at the frequency of D/λ = 0.0875. Solid curves correspond to the real part of the magnetic field, dashed curves correspond to the imaginary part of the electric field.

Equations (3)

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ε eff = ( ε 0 0 0 ε | | 0 0 0 ε | | ) , ε | | = ε 1 d 1 + ε 2 d 2 d 1 + d 2 , ε = ( ε 1 1 d 1 + ε 2 1 d 2 d 1 + d 2 ) 1
cos ( k x D ) = cos ( k x ( 1 ) d 1 ) cos ( k x ( 2 ) d 2 ) 1 2 ( ε 2 k x ( 1 ) ε 1 k x ( 2 ) + ε 1 k x ( 2 ) ε 2 k x ( 1 ) ) sin ( k x ( 1 ) d 1 ) sin ( k x ( 2 ) d 2 ) .
k x = ε i k 0 2 k y 2 = ε i k 0 2 Re ( k y ) 2 + Im ( k y ) 2 2 i Re ( k y ) Im ( k y ) .

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