Abstract

A full-vectorial finite element method is developed to analyze the surface waves propagating at the interface between two media which could be dissipative particularly. The dissipative wave possessing a complex-valued propagation constant can be determined precisely for any given propagation direction and thus the property of losses could be thoroughly analyzed. Besides, by applying a special characteristic of the implicit circular block matrix, we reduce the computational consumptions in the analysis. By utilizing this method, the Dyakonov surface wave (DSW) at the interface between a dielectric and a metal-dielectric multilayered (MDM) structure which serves as a hyperbolic medium is discussed. Its propagation loss is smaller for larger period of the MDM structure but its field becomes less confined to the interface.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2016 (2)

A. G. Ardakani, M. Naserpour, and C. J. Zapata-Rodríguez, “Dyakonov-like surface waves in the THz regime,” Photon Nanostruct: Fundam. Appl. 20, 1–6 (2016).
[Crossref]

J. J. Miret, J. A. Sorní, M. Naserpour, A. G. Ardakani, and C. J. Zapata-Rodríguez, “Nonlocal dispersion anomalies of Dyakonov-like surface waves at hyperbolic media interfaces,” Photon Nanostruct: Fundam. Appl. 18, 16–22 (2016).
[Crossref]

2015 (2)

J. A. Sorní, M. Naserpour, C. J. Zapata-Rodríguez, and J. J. Miret, “Dyakonov surface waves in lossy metamaterials,” Opt. Commun. 355, 251–255 (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, 195174 (2015).
[Crossref]

2014 (2)

O. Takayama, D. Artigas, and L. Torner, “Lossless directional guiding of light in dielectric nanosheets using Dyakonov surface waves,” Nature Nanotech. 9, 419–424 (2014).
[Crossref]

Y. Xiang, J. Guo, X. Dai, S. Wen, and D. Tang, “Engineered surface bloch waves in graphene-based hyperbolic metamaterials,” Opt. Express 22, 3054–3062 (2014).
[Crossref] [PubMed]

2013 (3)

H. H. Liu and H. C. Chang, “Leaky surface plasmon polariton modes at an interface between metal and uniaxially anisotropic materials,” IEEE Photonics J. 5, 4800806 (2013).
[Crossref]

C. J. Zapata-Rodríguez, J. J. Miret, S. Vuković, and M. R. Belić, “Engineered surface waves in hyperbolic metamaterials,” Opt. Express 21, 19113–19127 (2013).
[Crossref] [PubMed]

C. J. Zapata-Rodríguez, J. J. Miret, J. A. Sorni, and S. Vuković, “Propagation of dyakonon wave-packets at the boundary of metallodielectric lattices,” IEEE J. Sel. Top. Quant. Electron. 19, 4601408 (2013).
[Crossref]

2012 (2)

J. J. Miret, C. J. Zapata-Rodríguez, Z. Jaksić, S. Vuković, and M. R. Belić, “Substantial enlargement of angular existence range for dyakonov-like surface waves at semi-infinite metal-dielectric superlattice,” J. Nanophoton. 6, 063525 (2012).
[Crossref]

O. Takayama, D. Artigas, and L. Torner, “Practical dyakonons,” Opt. Lett. 37, 4311–4313 (2012).
[Crossref] [PubMed]

2011 (3)

X. B. Kang, W. Tan, and Z. G. Wang, “Validity of effective medium theory for metal-dielectric lamellar gratings,” Opt. Commun. 284, 4237–4242 (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]

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. B 84, 115438 (2011).
[Crossref]

2009 (1)

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of dyakonov surface waves,” Phys. Rev. Lett. 102, 043903 (2009).
[Crossref] [PubMed]

2008 (1)

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

2007 (3)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1 (2007).
[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]

S. M. Hsu and H. C. Chang, “Full-vectorial finite element method based eigenvalue algorithm for the analysis of 2d photonic crystals with arbitrary 3d anisotropy,” Opt. Express 15, 15797–15811 (2007).
[Crossref] [PubMed]

2006 (1)

M. Hofer, N. Finger, G. Kovacs, J. Schoberl, S. Zaglmayr, U. Langer, and R. Lerch, “Finite-element simulation of wave propagation in periodic piezoelectric saw structures,” IEEE Trans. Ultrason. Ferroelectr. Freq. Cont 53, 1192–1201 (2006).
[Crossref]

2005 (1)

D. Artigas and L. Torner, “Dyakonov surface waves in photonic metamaterials,” Phys. Rev. Lett. 94, 013901 (2005).
[Crossref] [PubMed]

2001 (2)

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101 (2001).
[Crossref]

F. Tisseur and K. Meerbergen, “The quadratic eigenvalue problem,” SIAM Rev. 43, 235–286 (2001).
[Crossref]

2000 (1)

1993 (1)

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[Crossref]

1988 (1)

M. I. Dyakonov, “New type of electromagnetic wave propagating at an interface,” Sov. Phys. JETP 67, 714–716 (1988).

1983 (1)

T. D. Mazancourt and D. Gerlic, “The inverse of a block-circulant matrix,” IEEE Trans. Antennas Propagat. 31, 808–810 (1983).
[Crossref]

1977 (1)

Ardakani, A. G.

A. G. Ardakani, M. Naserpour, and C. J. Zapata-Rodríguez, “Dyakonov-like surface waves in the THz regime,” Photon Nanostruct: Fundam. Appl. 20, 1–6 (2016).
[Crossref]

J. J. Miret, J. A. Sorní, M. Naserpour, A. G. Ardakani, and C. J. Zapata-Rodríguez, “Nonlocal dispersion anomalies of Dyakonov-like surface waves at hyperbolic media interfaces,” Photon Nanostruct: Fundam. Appl. 18, 16–22 (2016).
[Crossref]

Artigas, D.

O. Takayama, D. Artigas, and L. Torner, “Lossless directional guiding of light in dielectric nanosheets using Dyakonov surface waves,” Nature Nanotech. 9, 419–424 (2014).
[Crossref]

O. Takayama, D. Artigas, and L. Torner, “Practical dyakonons,” Opt. Lett. 37, 4311–4313 (2012).
[Crossref] [PubMed]

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of dyakonov surface waves,” Phys. Rev. Lett. 102, 043903 (2009).
[Crossref] [PubMed]

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

D. Artigas and L. Torner, “Dyakonov surface waves in photonic metamaterials,” Phys. Rev. Lett. 94, 013901 (2005).
[Crossref] [PubMed]

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]

Belic, M. R.

C. J. Zapata-Rodríguez, J. J. Miret, S. Vuković, and M. R. Belić, “Engineered surface waves in hyperbolic metamaterials,” Opt. Express 21, 19113–19127 (2013).
[Crossref] [PubMed]

J. J. Miret, C. J. Zapata-Rodríguez, Z. Jaksić, S. Vuković, and M. R. Belić, “Substantial enlargement of angular existence range for dyakonov-like surface waves at semi-infinite metal-dielectric superlattice,” J. Nanophoton. 6, 063525 (2012).
[Crossref]

Belov, P. A.

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]

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. B 84, 115438 (2011).
[Crossref]

Birner, A.

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101 (2001).
[Crossref]

Chan, C. T.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[Crossref]

Chang, H. C.

H. H. Liu and H. C. Chang, “Leaky surface plasmon polariton modes at an interface between metal and uniaxially anisotropic materials,” IEEE Photonics J. 5, 4800806 (2013).
[Crossref]

S. M. Hsu and H. C. Chang, “Full-vectorial finite element method based eigenvalue algorithm for the analysis of 2d photonic crystals with arbitrary 3d anisotropy,” Opt. Express 15, 15797–15811 (2007).
[Crossref] [PubMed]

Chebykin, 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. B 84, 115438 (2011).
[Crossref]

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1 (2007).
[Crossref]

Crasovan, L.

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of dyakonov surface waves,” Phys. Rev. Lett. 102, 043903 (2009).
[Crossref] [PubMed]

Crasovan, L. C.

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

Dai, X.

Datta, S.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[Crossref]

Duff, I.

I. Duff, A. Erisman, and J. Reid, Direct methods for sparse matrices (Clarendon, 1986).

Dyakonov, M. I.

M. I. Dyakonov, “New type of electromagnetic wave propagating at an interface,” Sov. Phys. JETP 67, 714–716 (1988).

Echenique, P. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1 (2007).
[Crossref]

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]

Erisman, A.

I. Duff, A. Erisman, and J. Reid, Direct methods for sparse matrices (Clarendon, 1986).

Finger, N.

M. Hofer, N. Finger, G. Kovacs, J. Schoberl, S. Zaglmayr, U. Langer, and R. Lerch, “Finite-element simulation of wave propagation in periodic piezoelectric saw structures,” IEEE Trans. Ultrason. Ferroelectr. Freq. Cont 53, 1192–1201 (2006).
[Crossref]

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, 195174 (2015).
[Crossref]

Genereux, F.

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101 (2001).
[Crossref]

Gerlic, D.

T. D. Mazancourt and D. Gerlic, “The inverse of a block-circulant matrix,” IEEE Trans. Antennas Propagat. 31, 808–810 (1983).
[Crossref]

Geuzaine, C.

A. Nicolet and C. Geuzaine, “Waveguide propagation modes and quadratic eigenvalue problems,” in “6th International Conference on Computational Electromagnetics,” (2006), pp. 1–3.

Ghosh, G.

E. D. Palik, G. Ghosh, and A. Press, The electronic handbook of optical constants of solids (Academic, 1999).

Gösele, U.

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101 (2001).
[Crossref]

Guo, J.

Ho, K. M.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[Crossref]

Hofer, M.

M. Hofer, N. Finger, G. Kovacs, J. Schoberl, S. Zaglmayr, U. Langer, and R. Lerch, “Finite-element simulation of wave propagation in periodic piezoelectric saw structures,” IEEE Trans. Ultrason. Ferroelectr. Freq. Cont 53, 1192–1201 (2006).
[Crossref]

Hsu, S. M.

Jaksic, Z.

J. J. Miret, C. J. Zapata-Rodríguez, Z. Jaksić, S. Vuković, and M. R. Belić, “Substantial enlargement of angular existence range for dyakonov-like surface waves at semi-infinite metal-dielectric superlattice,” J. Nanophoton. 6, 063525 (2012).
[Crossref]

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics (Wiley-IEEE, 2014).

Johansen, S. K.

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

Kang, X. B.

X. B. Kang, W. Tan, and Z. G. Wang, “Validity of effective medium theory for metal-dielectric lamellar gratings,” Opt. Commun. 284, 4237–4242 (2011).
[Crossref]

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]

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. B 84, 115438 (2011).
[Crossref]

Koshiba, M.

Kovacs, G.

M. Hofer, N. Finger, G. Kovacs, J. Schoberl, S. Zaglmayr, U. Langer, and R. Lerch, “Finite-element simulation of wave propagation in periodic piezoelectric saw structures,” IEEE Trans. Ultrason. Ferroelectr. Freq. Cont 53, 1192–1201 (2006).
[Crossref]

Langer, U.

M. Hofer, N. Finger, G. Kovacs, J. Schoberl, S. Zaglmayr, U. Langer, and R. Lerch, “Finite-element simulation of wave propagation in periodic piezoelectric saw structures,” IEEE Trans. Ultrason. Ferroelectr. Freq. Cont 53, 1192–1201 (2006).
[Crossref]

Leonard, S. W.

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101 (2001).
[Crossref]

Lerch, R.

M. Hofer, N. Finger, G. Kovacs, J. Schoberl, S. Zaglmayr, U. Langer, and R. Lerch, “Finite-element simulation of wave propagation in periodic piezoelectric saw structures,” IEEE Trans. Ultrason. Ferroelectr. Freq. Cont 53, 1192–1201 (2006).
[Crossref]

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, 195174 (2015).
[Crossref]

Liu, H. H.

H. H. Liu and H. C. Chang, “Leaky surface plasmon polariton modes at an interface between metal and uniaxially anisotropic materials,” IEEE Photonics J. 5, 4800806 (2013).
[Crossref]

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, 195174 (2015).
[Crossref]

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

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. B 84, 115438 (2011).
[Crossref]

Mazancourt, T. D.

T. D. Mazancourt and D. Gerlic, “The inverse of a block-circulant matrix,” IEEE Trans. Antennas Propagat. 31, 808–810 (1983).
[Crossref]

Meerbergen, K.

F. Tisseur and K. Meerbergen, “The quadratic eigenvalue problem,” SIAM Rev. 43, 235–286 (2001).
[Crossref]

Mihalache, D.

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

Miret, J. J.

J. J. Miret, J. A. Sorní, M. Naserpour, A. G. Ardakani, and C. J. Zapata-Rodríguez, “Nonlocal dispersion anomalies of Dyakonov-like surface waves at hyperbolic media interfaces,” Photon Nanostruct: Fundam. Appl. 18, 16–22 (2016).
[Crossref]

J. A. Sorní, M. Naserpour, C. J. Zapata-Rodríguez, and J. J. Miret, “Dyakonov surface waves in lossy metamaterials,” Opt. Commun. 355, 251–255 (2015).
[Crossref]

C. J. Zapata-Rodríguez, J. J. Miret, J. A. Sorni, and S. Vuković, “Propagation of dyakonon wave-packets at the boundary of metallodielectric lattices,” IEEE J. Sel. Top. Quant. Electron. 19, 4601408 (2013).
[Crossref]

C. J. Zapata-Rodríguez, J. J. Miret, S. Vuković, and M. R. Belić, “Engineered surface waves in hyperbolic metamaterials,” Opt. Express 21, 19113–19127 (2013).
[Crossref] [PubMed]

J. J. Miret, C. J. Zapata-Rodríguez, Z. Jaksić, S. Vuković, and M. R. Belić, “Substantial enlargement of angular existence range for dyakonov-like surface waves at semi-infinite metal-dielectric superlattice,” J. Nanophoton. 6, 063525 (2012).
[Crossref]

Naserpour, M.

A. G. Ardakani, M. Naserpour, and C. J. Zapata-Rodríguez, “Dyakonov-like surface waves in the THz regime,” Photon Nanostruct: Fundam. Appl. 20, 1–6 (2016).
[Crossref]

J. J. Miret, J. A. Sorní, M. Naserpour, A. G. Ardakani, and C. J. Zapata-Rodríguez, “Nonlocal dispersion anomalies of Dyakonov-like surface waves at hyperbolic media interfaces,” Photon Nanostruct: Fundam. Appl. 18, 16–22 (2016).
[Crossref]

J. A. Sorní, M. Naserpour, C. J. Zapata-Rodríguez, and J. J. Miret, “Dyakonov surface waves in lossy metamaterials,” Opt. Commun. 355, 251–255 (2015).
[Crossref]

Nicolet, A.

A. Nicolet and C. Geuzaine, “Waveguide propagation modes and quadratic eigenvalue problems,” in “6th International Conference on Computational Electromagnetics,” (2006), pp. 1–3.

Orlov, A. A.

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. 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]

Palik, E. D.

E. D. Palik, G. Ghosh, and A. Press, The electronic handbook of optical constants of solids (Academic, 1999).

Pitarke, J. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1 (2007).
[Crossref]

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]

Press, A.

E. D. Palik, G. Ghosh, and A. Press, The electronic handbook of optical constants of solids (Academic, 1999).

Reid, J.

I. Duff, A. Erisman, and J. Reid, Direct methods for sparse matrices (Clarendon, 1986).

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]

Schoberl, J.

M. Hofer, N. Finger, G. Kovacs, J. Schoberl, S. Zaglmayr, U. Langer, and R. Lerch, “Finite-element simulation of wave propagation in periodic piezoelectric saw structures,” IEEE Trans. Ultrason. Ferroelectr. Freq. Cont 53, 1192–1201 (2006).
[Crossref]

Silkin, V. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1 (2007).
[Crossref]

Sorensen, D. C.

R. B. L. Yang and D. C. Sorensen, and C., ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods (SIAM1997).

Sorni, J. A.

C. J. Zapata-Rodríguez, J. J. Miret, J. A. Sorni, and S. Vuković, “Propagation of dyakonon wave-packets at the boundary of metallodielectric lattices,” IEEE J. Sel. Top. Quant. Electron. 19, 4601408 (2013).
[Crossref]

Sorní, J. A.

J. J. Miret, J. A. Sorní, M. Naserpour, A. G. Ardakani, and C. J. Zapata-Rodríguez, “Nonlocal dispersion anomalies of Dyakonov-like surface waves at hyperbolic media interfaces,” Photon Nanostruct: Fundam. Appl. 18, 16–22 (2016).
[Crossref]

J. A. Sorní, M. Naserpour, C. J. Zapata-Rodríguez, and J. J. Miret, “Dyakonov surface waves in lossy metamaterials,” Opt. Commun. 355, 251–255 (2015).
[Crossref]

Soukoulis, C. M.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[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, 195174 (2015).
[Crossref]

Takayama, O.

O. Takayama, D. Artigas, and L. Torner, “Lossless directional guiding of light in dielectric nanosheets using Dyakonov surface waves,” Nature Nanotech. 9, 419–424 (2014).
[Crossref]

O. Takayama, D. Artigas, and L. Torner, “Practical dyakonons,” Opt. Lett. 37, 4311–4313 (2012).
[Crossref] [PubMed]

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of dyakonov surface waves,” Phys. Rev. Lett. 102, 043903 (2009).
[Crossref] [PubMed]

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

Tan, W.

X. B. Kang, W. Tan, and Z. G. Wang, “Validity of effective medium theory for metal-dielectric lamellar gratings,” Opt. Commun. 284, 4237–4242 (2011).
[Crossref]

Tang, D.

Tisseur, F.

F. Tisseur and K. Meerbergen, “The quadratic eigenvalue problem,” SIAM Rev. 43, 235–286 (2001).
[Crossref]

Torner, L.

O. Takayama, D. Artigas, and L. Torner, “Lossless directional guiding of light in dielectric nanosheets using Dyakonov surface waves,” Nature Nanotech. 9, 419–424 (2014).
[Crossref]

O. Takayama, D. Artigas, and L. Torner, “Practical dyakonons,” Opt. Lett. 37, 4311–4313 (2012).
[Crossref] [PubMed]

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of dyakonov surface waves,” Phys. Rev. Lett. 102, 043903 (2009).
[Crossref] [PubMed]

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

D. Artigas and L. Torner, “Dyakonov surface waves in photonic metamaterials,” Phys. Rev. Lett. 94, 013901 (2005).
[Crossref] [PubMed]

Tsuji, Y.

van Driel, H. M.

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101 (2001).
[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. B 84, 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. B 84, 115438 (2011).
[Crossref]

Vukovic, S.

C. J. Zapata-Rodríguez, J. J. Miret, J. A. Sorni, and S. Vuković, “Propagation of dyakonon wave-packets at the boundary of metallodielectric lattices,” IEEE J. Sel. Top. Quant. Electron. 19, 4601408 (2013).
[Crossref]

C. J. Zapata-Rodríguez, J. J. Miret, S. Vuković, and M. R. Belić, “Engineered surface waves in hyperbolic metamaterials,” Opt. Express 21, 19113–19127 (2013).
[Crossref] [PubMed]

J. J. Miret, C. J. Zapata-Rodríguez, Z. Jaksić, S. Vuković, and M. R. Belić, “Substantial enlargement of angular existence range for dyakonov-like surface waves at semi-infinite metal-dielectric superlattice,” J. Nanophoton. 6, 063525 (2012).
[Crossref]

Wang, Z. G.

X. B. Kang, W. Tan, and Z. G. Wang, “Validity of effective medium theory for metal-dielectric lamellar gratings,” Opt. Commun. 284, 4237–4242 (2011).
[Crossref]

Wen, S.

Xiang, Y.

Yang, R. B. L.

R. B. L. Yang and D. C. Sorensen, and C., ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods (SIAM1997).

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, 195174 (2015).
[Crossref]

Yariv, A.

Yeh, P.

Zaglmayr, S.

M. Hofer, N. Finger, G. Kovacs, J. Schoberl, S. Zaglmayr, U. Langer, and R. Lerch, “Finite-element simulation of wave propagation in periodic piezoelectric saw structures,” IEEE Trans. Ultrason. Ferroelectr. Freq. Cont 53, 1192–1201 (2006).
[Crossref]

Zapata-Rodríguez, C. J.

J. J. Miret, J. A. Sorní, M. Naserpour, A. G. Ardakani, and C. J. Zapata-Rodríguez, “Nonlocal dispersion anomalies of Dyakonov-like surface waves at hyperbolic media interfaces,” Photon Nanostruct: Fundam. Appl. 18, 16–22 (2016).
[Crossref]

A. G. Ardakani, M. Naserpour, and C. J. Zapata-Rodríguez, “Dyakonov-like surface waves in the THz regime,” Photon Nanostruct: Fundam. Appl. 20, 1–6 (2016).
[Crossref]

J. A. Sorní, M. Naserpour, C. J. Zapata-Rodríguez, and J. J. Miret, “Dyakonov surface waves in lossy metamaterials,” Opt. Commun. 355, 251–255 (2015).
[Crossref]

C. J. Zapata-Rodríguez, J. J. Miret, J. A. Sorni, and S. Vuković, “Propagation of dyakonon wave-packets at the boundary of metallodielectric lattices,” IEEE J. Sel. Top. Quant. Electron. 19, 4601408 (2013).
[Crossref]

C. J. Zapata-Rodríguez, J. J. Miret, S. Vuković, and M. R. Belić, “Engineered surface waves in hyperbolic metamaterials,” Opt. Express 21, 19113–19127 (2013).
[Crossref] [PubMed]

J. J. Miret, C. J. Zapata-Rodríguez, Z. Jaksić, S. Vuković, and M. R. Belić, “Substantial enlargement of angular existence range for dyakonov-like surface waves at semi-infinite metal-dielectric superlattice,” J. Nanophoton. 6, 063525 (2012).
[Crossref]

Appl. Phys. Lett. (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]

Electromagnetics (1)

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

IEEE J. Sel. Top. Quant. Electron. (1)

C. J. Zapata-Rodríguez, J. J. Miret, J. A. Sorni, and S. Vuković, “Propagation of dyakonon wave-packets at the boundary of metallodielectric lattices,” IEEE J. Sel. Top. Quant. Electron. 19, 4601408 (2013).
[Crossref]

IEEE Photonics J. (1)

H. H. Liu and H. C. Chang, “Leaky surface plasmon polariton modes at an interface between metal and uniaxially anisotropic materials,” IEEE Photonics J. 5, 4800806 (2013).
[Crossref]

IEEE Trans. Antennas Propagat. (1)

T. D. Mazancourt and D. Gerlic, “The inverse of a block-circulant matrix,” IEEE Trans. Antennas Propagat. 31, 808–810 (1983).
[Crossref]

IEEE Trans. Ultrason. Ferroelectr. Freq. Cont (1)

M. Hofer, N. Finger, G. Kovacs, J. Schoberl, S. Zaglmayr, U. Langer, and R. Lerch, “Finite-element simulation of wave propagation in periodic piezoelectric saw structures,” IEEE Trans. Ultrason. Ferroelectr. Freq. Cont 53, 1192–1201 (2006).
[Crossref]

J. Lightwave Technol. (1)

J. Nanophoton. (1)

J. J. Miret, C. J. Zapata-Rodríguez, Z. Jaksić, S. Vuković, and M. R. Belić, “Substantial enlargement of angular existence range for dyakonov-like surface waves at semi-infinite metal-dielectric superlattice,” J. Nanophoton. 6, 063525 (2012).
[Crossref]

J. Opt. Soc. Am. (1)

Nature Nanotech. (1)

O. Takayama, D. Artigas, and L. Torner, “Lossless directional guiding of light in dielectric nanosheets using Dyakonov surface waves,” Nature Nanotech. 9, 419–424 (2014).
[Crossref]

Opt. Commun. (2)

J. A. Sorní, M. Naserpour, C. J. Zapata-Rodríguez, and J. J. Miret, “Dyakonov surface waves in lossy metamaterials,” Opt. Commun. 355, 251–255 (2015).
[Crossref]

X. B. Kang, W. Tan, and Z. G. Wang, “Validity of effective medium theory for metal-dielectric lamellar gratings,” Opt. Commun. 284, 4237–4242 (2011).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Photon Nanostruct: Fundam. Appl. (2)

J. J. Miret, J. A. Sorní, M. Naserpour, A. G. Ardakani, and C. J. Zapata-Rodríguez, “Nonlocal dispersion anomalies of Dyakonov-like surface waves at hyperbolic media interfaces,” Photon Nanostruct: Fundam. Appl. 18, 16–22 (2016).
[Crossref]

A. G. Ardakani, M. Naserpour, and C. J. Zapata-Rodríguez, “Dyakonov-like surface waves in the THz regime,” Photon Nanostruct: Fundam. Appl. 20, 1–6 (2016).
[Crossref]

Phys. Rev. B (5)

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[Crossref]

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101 (2001).
[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]

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. B 84, 115438 (2011).
[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, 195174 (2015).
[Crossref]

Phys. Rev. Lett. (2)

D. Artigas and L. Torner, “Dyakonov surface waves in photonic metamaterials,” Phys. Rev. Lett. 94, 013901 (2005).
[Crossref] [PubMed]

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of dyakonov surface waves,” Phys. Rev. Lett. 102, 043903 (2009).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1 (2007).
[Crossref]

SIAM Rev. (1)

F. Tisseur and K. Meerbergen, “The quadratic eigenvalue problem,” SIAM Rev. 43, 235–286 (2001).
[Crossref]

Sov. Phys. JETP (1)

M. I. Dyakonov, “New type of electromagnetic wave propagating at an interface,” Sov. Phys. JETP 67, 714–716 (1988).

Other (6)

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

A. Nicolet and C. Geuzaine, “Waveguide propagation modes and quadratic eigenvalue problems,” in “6th International Conference on Computational Electromagnetics,” (2006), pp. 1–3.

I. Duff, A. Erisman, and J. Reid, Direct methods for sparse matrices (Clarendon, 1986).

E. D. Palik, G. Ghosh, and A. Press, The electronic handbook of optical constants of solids (Academic, 1999).

J. Jin, The Finite Element Method in Electromagnetics (Wiley-IEEE, 2014).

R. B. L. Yang and D. C. Sorensen, and C., ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods (SIAM1997).

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Figures (10)

Fig. 1
Fig. 1 (a) Schematic of a planar interface between an anisotropic material and a metal. (b) Computational domain with properly placed PBCs and PMLs.
Fig. 2
Fig. 2 (a) Bases on the prism element. (b) Cubic Hermite spline functions.
Fig. 3
Fig. 3 Divisions of the computational domain as combination of identical layers.
Fig. 4
Fig. 4 Calculated Results from the 2D- and 3D-FEM for the structure displayed in Fig. 1(a). with no = 1.5, ne = 3, m = −20 − 1.2632j, and λ = 694 nm. (a) Re[Neff] versus θ. (b) Loss in dB/μm versus θ.
Fig. 5
Fig. 5 Ex and η0Hy versus y profiles for the wave at θ = 20° obtained from the 3D-FEM without the metallic loss.
Fig. 6
Fig. 6 (a) Schematic of the semi-infinite MDM surface. (b) Schematic of the MDM structure.
Fig. 7
Fig. 7 Characteristics of the e-waves in the MDM structure. (a),(b) show the spatial dispersion contours in the xz-plane without and with the metallic loss, respectively. In particular, their differences, ΔNeff, are given relative to θ in the inset for p = 12, 20, and 36 nm. The point A represents the turning point of the curve for p = 4 nm. (c) Losses versus θ curves. (d) Mode-field profiles of |Hy| along the x-axis for the e-wave propagating at θ = 20° without considering the metallic loss.
Fig. 8
Fig. 8 Spatial dispersion contours of the DSWs (solid curves) in the xz-plane, where the dotted and dashed curves represent the dispersions in the air and in the MDM structure, respectively. (a) The EMA result and p = 4 nm. (b) p = 12, 28, and 72 nm.
Fig. 9
Fig. 9 Magnetic-field profiles of the DSWs of the structure in Fig. 6(a) for the direction θ = 20°. (a) p = 12 nm. (b) p = 36 nm.
Fig. 10
Fig. 10 (a) The losses of DSWs relative to θ. (b) Comparison between the spatial dispersions of DSWs with and without the metallic loss represented by the dashed and solid curves, respectively.

Equations (27)

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

× E = j ω μ 0 [ μ r ] H
× H = j ω 0 [ r ] E
[ r ] = [ x x x y x z y x y y y z z x z y z z ] , [ μ r ] = [ μ x x μ x y μ x z μ y x μ y y μ y z μ z x μ z y μ z z ] .
× ( [ p ] × Φ ) k 0 2 [ q ] Φ = 0
[ p ] = [ p x x p x y p x z p y x p y y p y z p z x p z y p z z ] = [ μ r ] 1 , [ q ] = [ q x x q x y q x z q y x q y y q y z q z x q z y q z z ] = [ r ]
[ p ] = [ p x x p x y p x z p y x p y y p y z p z x p z y p z z ] = [ r ] 1 , [ q ] = [ q x x q x y q x z q y x q y y q y z q z x q z y q z z ] = [ μ r ]
F ( Φ ) = 1 2 v { [ p ] ( × Φ ) ( × Φ ) k 0 2 [ q ] Φ Φ } d v
= t + z .
Φ e = { ϕ t e } T ( { U } x ^ + { V } y ^ ) + { ϕ z e } T { N } z ^
[ K ] { ϕ } = { ψ }
{ ϕ } = [ { ϕ t } { ϕ z } ]
{ ψ } = [ { ψ t } { ψ z } ]
[ K ] = [ [ K t t ] [ K t z ] [ K z t ] [ K z z ] ]
[ K t t ] = e v [ p z z { { V } x { U } y } { { V } T x { U } T y } p x z { { V } z } { { V } T x { U } T y } + p y z { { U } z { { V } T x { U } T y } p z x { { V } x { U } y } { V } T z } + p z y { { V } x { U } y } { U } T z + p x x { V } z { V } T z p x y { V } z { U } T z p y x { U } z { V } T z p y y { U } z { U } T z k 0 2 q x x { U } { U } T k 0 2 q x y { V } { U } T k 0 2 q y x { U } { V } T k 0 2 q y y { V } { V } T ] d x d y d z
[ K t z ] = e v [ p z x { { V } x { U } y } { N } T y p z y { { V } x { U } y } { N } T x p x x { V } z { N } T y + p x y { V } z { N } T x + p y x { U } z { N } T y p y y { U } z { N } T x k 0 2 q z x { U } { N } T k 0 2 q z y { V } { N } T ] d x d y d z
[ K z t ] = e v [ p x z { N } y { { V } T x { U } T y } p y z { N } x { { V } T x { U } T y } p x x { N } y { V } T z + p x y { N } x { V } T z + p y x { N } y { U } T y p y y { N } z { U } T z k 0 2 q x z { N } { U } T k 0 2 q y z { N } { V } T ] d x d y d z
[ K z z ] = e v [ p x x { N } y { N } T y p x y { N } y { N } T x p y x { N } x { N } T y p y y { N } x { N } T x k 0 2 q z z { N } { N } T ] d x d y d z .
Φ | R = e j k x d x Φ | L , Φ | U = e j k y d y Φ | D , Φ | F = e j k z d z Φ | B Φ x | R = e j k x d x Φ x | L , Φ y | U = e j k y d y Φ y | D , Φ z | F = e j k z d z Φ z | B
( [ K 1 ] + φ x [ K z ] + φ y [ K 3 ] + φ z [ K 4 ] + φ x φ y [ K 5 ] + φ y φ z [ K 6 ] + φ z φ x [ K 7 ] + φ x φ y φ z [ K 8 ] ) { ϕ } = { 0 } .
( [ A ] + φ x [ B ] + φ x 2 [ C ] ) { ϕ } = { 0 } .
G i , j ( x , y , z ) = W i ( x , y ) O j ( z )
[ O 1 = 2 t 3 3 t 2 + 1 O 2 = t 3 2 t 2 + t O 3 = t 3 t 2 O 4 = 2 t 3 + 3 t 2 0 t 1
λ 2 [ C ] { v } + λ [ B ] { v } + [ A ] { v } = { 0 }
λ [ [ C ] 0 0 [ I ] ] [ λ { v } { v } ] + [ [ B ] [ A ] [ I ] 0 ] [ λ { v } { v } ] = { 0 }
[ λ 0 [ C ] + [ B ] [ A ] [ I ] λ 0 [ I ] ] [ { r 1 } { r 2 } ] = [ { s 1 } { s 2 } ]
[ { r 1 } { r 2 } ] = [ [ D ] 1 ( λ 0 { s 1 } [ A ] { s 2 } ) ( { r 1 } + { s 2 } ) / λ 0 ]
[ [ A 0 ] [ A 1 ] 0 0 [ A 2 ] / λ 0 [ A 2 ] [ A 0 ] [ A 1 ] 0 0 [ A 2 ] [ A 0 ] [ A 1 ] [ A 2 ] [ A 0 ] [ A 1 ] 0 0 [ A 2 ] [ A 0 ] [ A 1 ] λ 0 [ A 1 ] 0 0 [ A 2 ] [ A 0 ] ] [ { h 1 } { h 2 } { h 3 } { h n 2 } { h n 1 } { h n } ] = [ { g 1 } / λ 0 { g 2 } { g 3 } { g n 2 } { g n 1 } { g n } ] .

Metrics