Abstract

We show that engineered photonic metamaterials composed of alternating layers of suitable dielectrics and metals can support different kinds of surface waves (SWs) under robust and readily achievable experimental conditions. The supported SWs include Dyakonov SWs, hybrid plasmons, and Dyakonov plasmons. In particular, in contrast to conventional physical settings, we show that the high form birefringence exhibited by the metamaterials allows Dyakonov SWs, or dyakonons, to exist within large angular existence domains and levels of localization similar to plasmons, thus making dyakonons available for practical applications.

© 2012 Optical Society of America

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  1. J. A. Polo and A. Lakhtakia, Laser Photon. Rev. 5, 234 (2011).
    [CrossRef]
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature (London) 424, 824 (2003).
    [CrossRef]
  3. H. Raether, Surface Plasmons (Springer-Verlag, 1988).
  4. S. A. Maier and H. A. Atwater, J. Appl. Phys. 98, 011101 (2005).
    [CrossRef]
  5. M. I. D’yakonov, Sov. Phys. JETP 67, 714 (1988).
  6. O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, Electromagnetics 28, 126 (2008).
    [CrossRef]
  7. O. Takayama, L. Crasovan, D. Artigas, and L. Torner, Phys. Rev. Lett. 102, 043903 (2009).
    [CrossRef]
  8. O. Takayama, D. Artigas, and L. Torner, Opt. Lett. 37, 1983 (2012).
    [CrossRef]
  9. L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, J. Lightwave Technol. 13, 2027 (1995).
    [CrossRef]
  10. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, Appl. Opt. 22, 1099 (1983).
    [CrossRef]
  11. D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
    [CrossRef]
  12. R. Li, C. Cheng, F.-F. Ren, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, Appl. Phys. Lett. 92, 141115 (2008).
    [CrossRef]
  13. J. Jacob and E. E. Narimonov, Appl. Phys. Lett. 93, 221109 (2008).
    [CrossRef]
  14. H. Krishnamoorthy, Z. Jacob, E. Narimonov, I. Kretzschmar, and V. M. Menon, Science 336, 205 (2012).
    [CrossRef]

2012

H. Krishnamoorthy, Z. Jacob, E. Narimonov, I. Kretzschmar, and V. M. Menon, Science 336, 205 (2012).
[CrossRef]

O. Takayama, D. Artigas, and L. Torner, Opt. Lett. 37, 1983 (2012).
[CrossRef]

2011

J. A. Polo and A. Lakhtakia, Laser Photon. Rev. 5, 234 (2011).
[CrossRef]

2009

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, Phys. Rev. Lett. 102, 043903 (2009).
[CrossRef]

2008

R. Li, C. Cheng, F.-F. Ren, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, Appl. Phys. Lett. 92, 141115 (2008).
[CrossRef]

J. Jacob and E. E. Narimonov, Appl. Phys. Lett. 93, 221109 (2008).
[CrossRef]

O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, Electromagnetics 28, 126 (2008).
[CrossRef]

2005

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef]

S. A. Maier and H. A. Atwater, J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature (London) 424, 824 (2003).
[CrossRef]

1995

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, J. Lightwave Technol. 13, 2027 (1995).
[CrossRef]

1988

M. I. D’yakonov, Sov. Phys. JETP 67, 714 (1988).

1983

Alexander, R. W.

Artigas, D.

O. Takayama, D. Artigas, and L. Torner, Opt. Lett. 37, 1983 (2012).
[CrossRef]

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, Phys. Rev. Lett. 102, 043903 (2009).
[CrossRef]

O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, Electromagnetics 28, 126 (2008).
[CrossRef]

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef]

Atwater, H. A.

S. A. Maier and H. A. Atwater, J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature (London) 424, 824 (2003).
[CrossRef]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Chen, J.

R. Li, C. Cheng, F.-F. Ren, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, Appl. Phys. Lett. 92, 141115 (2008).
[CrossRef]

Cheng, C.

R. Li, C. Cheng, F.-F. Ren, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, Appl. Phys. Lett. 92, 141115 (2008).
[CrossRef]

Crasovan, L.

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, Phys. Rev. Lett. 102, 043903 (2009).
[CrossRef]

O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, Electromagnetics 28, 126 (2008).
[CrossRef]

D’yakonov, M. I.

M. I. D’yakonov, Sov. Phys. JETP 67, 714 (1988).

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature (London) 424, 824 (2003).
[CrossRef]

Ding, J.

R. Li, C. Cheng, F.-F. Ren, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, Appl. Phys. Lett. 92, 141115 (2008).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature (London) 424, 824 (2003).
[CrossRef]

Fan, Y.-X.

R. Li, C. Cheng, F.-F. Ren, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, Appl. Phys. Lett. 92, 141115 (2008).
[CrossRef]

Jacob, J.

J. Jacob and E. E. Narimonov, Appl. Phys. Lett. 93, 221109 (2008).
[CrossRef]

Jacob, Z.

H. Krishnamoorthy, Z. Jacob, E. Narimonov, I. Kretzschmar, and V. M. Menon, Science 336, 205 (2012).
[CrossRef]

Johansen, S. K.

O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, Electromagnetics 28, 126 (2008).
[CrossRef]

Kretzschmar, I.

H. Krishnamoorthy, Z. Jacob, E. Narimonov, I. Kretzschmar, and V. M. Menon, Science 336, 205 (2012).
[CrossRef]

Krishnamoorthy, H.

H. Krishnamoorthy, Z. Jacob, E. Narimonov, I. Kretzschmar, and V. M. Menon, Science 336, 205 (2012).
[CrossRef]

Lakhtakia, A.

J. A. Polo and A. Lakhtakia, Laser Photon. Rev. 5, 234 (2011).
[CrossRef]

Li, R.

R. Li, C. Cheng, F.-F. Ren, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, Appl. Phys. Lett. 92, 141115 (2008).
[CrossRef]

Long, L. L.

Maier, S. A.

S. A. Maier and H. A. Atwater, J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Menon, V. M.

H. Krishnamoorthy, Z. Jacob, E. Narimonov, I. Kretzschmar, and V. M. Menon, Science 336, 205 (2012).
[CrossRef]

Mihalache, D.

O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, Electromagnetics 28, 126 (2008).
[CrossRef]

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, J. Lightwave Technol. 13, 2027 (1995).
[CrossRef]

Narimonov, E.

H. Krishnamoorthy, Z. Jacob, E. Narimonov, I. Kretzschmar, and V. M. Menon, Science 336, 205 (2012).
[CrossRef]

Narimonov, E. E.

J. Jacob and E. E. Narimonov, Appl. Phys. Lett. 93, 221109 (2008).
[CrossRef]

Ojeda, C.

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, J. Lightwave Technol. 13, 2027 (1995).
[CrossRef]

Ordal, M. A.

Polo, J. A.

J. A. Polo and A. Lakhtakia, Laser Photon. Rev. 5, 234 (2011).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons (Springer-Verlag, 1988).

Ren, F.-F.

R. Li, C. Cheng, F.-F. Ren, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, Appl. Phys. Lett. 92, 141115 (2008).
[CrossRef]

Takayama, O.

O. Takayama, D. Artigas, and L. Torner, Opt. Lett. 37, 1983 (2012).
[CrossRef]

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, Phys. Rev. Lett. 102, 043903 (2009).
[CrossRef]

O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, Electromagnetics 28, 126 (2008).
[CrossRef]

Torner, L.

O. Takayama, D. Artigas, and L. Torner, Opt. Lett. 37, 1983 (2012).
[CrossRef]

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, Phys. Rev. Lett. 102, 043903 (2009).
[CrossRef]

O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, Electromagnetics 28, 126 (2008).
[CrossRef]

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef]

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, J. Lightwave Technol. 13, 2027 (1995).
[CrossRef]

Torres, J. P.

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, J. Lightwave Technol. 13, 2027 (1995).
[CrossRef]

Wang, H.-T.

R. Li, C. Cheng, F.-F. Ren, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, Appl. Phys. Lett. 92, 141115 (2008).
[CrossRef]

Ward, C. A.

Appl. Opt.

Appl. Phys. Lett.

R. Li, C. Cheng, F.-F. Ren, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, Appl. Phys. Lett. 92, 141115 (2008).
[CrossRef]

J. Jacob and E. E. Narimonov, Appl. Phys. Lett. 93, 221109 (2008).
[CrossRef]

Electromagnetics

O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, Electromagnetics 28, 126 (2008).
[CrossRef]

J. Appl. Phys.

S. A. Maier and H. A. Atwater, J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

J. Lightwave Technol.

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, J. Lightwave Technol. 13, 2027 (1995).
[CrossRef]

Laser Photon. Rev.

J. A. Polo and A. Lakhtakia, Laser Photon. Rev. 5, 234 (2011).
[CrossRef]

Nature (London)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature (London) 424, 824 (2003).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, Phys. Rev. Lett. 102, 043903 (2009).
[CrossRef]

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef]

Science

H. Krishnamoorthy, Z. Jacob, E. Narimonov, I. Kretzschmar, and V. M. Menon, Science 336, 205 (2012).
[CrossRef]

Sov. Phys. JETP

M. I. D’yakonov, Sov. Phys. JETP 67, 714 (1988).

Other

H. Raether, Surface Plasmons (Springer-Verlag, 1988).

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Figures (4)

Fig. 1.
Fig. 1.

Structure under consideration, composed of alternating layers of a metal and a dielectric, with permittivity εm and εd, respectively. The thickness of metal and dielectric layers are dm and dd, respectively, and form the lattice constant a=dm+dd. The homogenized material is uniaxial birefringent with effective ordinary and extraordinary permittivities εo and εe. An isotropic medium with its permittivity, εc, is placed on top of the metamaterial. The corresponding OA is perpendicular to the alternating layers. Light propagates along the z direction forming an angle θ with the OA.

Fig. 2.
Fig. 2.

Real parts of the relative permittivities εo (red line) and εe (blue line) of the metamaterial as a function of frequency. The white regions indicate conditions of permittivity εc that do not support SWs. The color-labeled regions indicate conditions for the permittivity εc and frequency that support SWs. Three different SWs exist in the metamaterial: (I) dyakonon, (II) the four types of hybrid plasmons described in [12], and (III) dyakonon plasmons, where two type of SWs are identified.

Fig. 3.
Fig. 3.

Existence angular domain of dyakonons for different frequencies as a function of the cover relative permittivity. The blue area corresponds to εc>1 for conventional dielectric media and the yellow region indicates the permittivity range of 0<εc<1 that can be achieved by using metamaterials. The inset shows the selected frequencies within the existence range of dyakonons (region I in Fig. 2).

Fig. 4.
Fig. 4.

Penetration depth in the cover (blue solid line) and in the metamaterial (red dashed line) in terms of the propagation direction (angle with respect to the OA). (a) ν=450THz, εc=1.0, εo=0.1891, and εe=2.5345. The lower and upper cutoff angles are 62.8° and 75.9°, respectively, with Δθ=13.1°. Arrows indicate points at which the pointing vector is calculated in (c)–(h). (b) ν=500THz, εc=1.0 εo=0.6329, and εe=2.5457. The lower and upper cutoff angles are 39.3° and 52.9°, respectively, with Δθ=13.6°. (c) Calculated Poynting vector and (d) walk off angle at θ=63° for ν=450THz. (e) and (g) Poynting vector, and (f) and (h) walk off angle at θ=69° and θ=75°, respectively. Axes of (c)–(h) are in wavelength units and the walk off angle, θP, is measured from the wave propagation direction, z.

Equations (3)

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εo<εc<εe,
εo=fmεm+εd(1fm),
1/εe=fm/εm+(1fm)/εd.

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