Abstract

Making use of a rigorous electromagnetic treatment, we demonstrate that the approximate results that are customarily employed for the analysis of a plasmon field at a metal/dielectric boundary are incorrect even in some situations in which they are supposed to hold. We show further that a new type of surface-plasmon solution exists that does not follow from the standard approximate analysis. Energy-flow considerations indicate that the new polariton is a backward-propagating surface wave, as encountered in manmade structures. Our results are likely to find applications in metal/semiconductor and metamaterial plasmonics.

© 2013 Optical Society of America

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References

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  1. R. H. Ritchie, Phys. Rev. 106, 874 (1957).
    [CrossRef]
  2. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).
  3. L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).
  4. M. I. Stockman, Opt. Express 19, 22029 (2011).
    [CrossRef]
  5. E. N. Economou, Phys. Rev. 182, 539 (1969).
    [CrossRef]
  6. R. Ruppin, Phys. Lett. A 277, 61 (2000).
    [CrossRef]
  7. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
    [CrossRef]
  8. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
    [CrossRef]
  9. J. Zhang, L. Zhang, and W. Xu, J. Phys. D 45, 113001 (2012).
    [CrossRef]
  10. J. Yang, G. J. Brown, M. Dutta, and M. A. Stroscio, J. Appl. Phys. 98, 043517 (2005).
    [CrossRef]
  11. S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 84, 035128 (2011).
    [CrossRef]
  12. A. Boltasseva and H. A. Atwater, Science 331, 290 (2011).
    [CrossRef]
  13. A. Norrman, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. A 28, 391 (2011).
    [CrossRef]
  14. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1998).
  15. S. Foteinopoulou, G. Kenanakis, N. Katsarakis, I. Tsiapa, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 91, 214102 (2007).
    [CrossRef]

2012 (1)

J. Zhang, L. Zhang, and W. Xu, J. Phys. D 45, 113001 (2012).
[CrossRef]

2011 (4)

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 84, 035128 (2011).
[CrossRef]

A. Boltasseva and H. A. Atwater, Science 331, 290 (2011).
[CrossRef]

A. Norrman, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. A 28, 391 (2011).
[CrossRef]

M. I. Stockman, Opt. Express 19, 22029 (2011).
[CrossRef]

2007 (1)

S. Foteinopoulou, G. Kenanakis, N. Katsarakis, I. Tsiapa, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 91, 214102 (2007).
[CrossRef]

2005 (2)

J. Yang, G. J. Brown, M. Dutta, and M. A. Stroscio, J. Appl. Phys. 98, 043517 (2005).
[CrossRef]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

2003 (1)

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

2000 (1)

R. Ruppin, Phys. Lett. A 277, 61 (2000).
[CrossRef]

1969 (1)

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

1957 (1)

R. H. Ritchie, Phys. Rev. 106, 874 (1957).
[CrossRef]

Atwater, H. A.

A. Boltasseva and H. A. Atwater, Science 331, 290 (2011).
[CrossRef]

Barnes, W. L.

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

Boltasseva, A.

A. Boltasseva and H. A. Atwater, Science 331, 290 (2011).
[CrossRef]

Brown, G. J.

J. Yang, G. J. Brown, M. Dutta, and M. A. Stroscio, J. Appl. Phys. 98, 043517 (2005).
[CrossRef]

Dereux, A.

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

Dutta, M.

J. Yang, G. J. Brown, M. Dutta, and M. A. Stroscio, J. Appl. Phys. 98, 043517 (2005).
[CrossRef]

Ebbesen, T. W.

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

Economou, E. N.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 84, 035128 (2011).
[CrossRef]

S. Foteinopoulou, G. Kenanakis, N. Katsarakis, I. Tsiapa, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 91, 214102 (2007).
[CrossRef]

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Foteinopoulou, S.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 84, 035128 (2011).
[CrossRef]

S. Foteinopoulou, G. Kenanakis, N. Katsarakis, I. Tsiapa, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 91, 214102 (2007).
[CrossRef]

Friberg, A. T.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

Kafesaki, M.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 84, 035128 (2011).
[CrossRef]

S. Foteinopoulou, G. Kenanakis, N. Katsarakis, I. Tsiapa, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 91, 214102 (2007).
[CrossRef]

Katsarakis, N.

S. Foteinopoulou, G. Kenanakis, N. Katsarakis, I. Tsiapa, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 91, 214102 (2007).
[CrossRef]

Kenanakis, G.

S. Foteinopoulou, G. Kenanakis, N. Katsarakis, I. Tsiapa, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 91, 214102 (2007).
[CrossRef]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

Norrman, A.

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

Ritchie, R. H.

R. H. Ritchie, Phys. Rev. 106, 874 (1957).
[CrossRef]

Ruppin, R.

R. Ruppin, Phys. Lett. A 277, 61 (2000).
[CrossRef]

Setälä, T.

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

Soukoulis, C. M.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 84, 035128 (2011).
[CrossRef]

S. Foteinopoulou, G. Kenanakis, N. Katsarakis, I. Tsiapa, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 91, 214102 (2007).
[CrossRef]

Stockman, M. I.

Stroscio, M. A.

J. Yang, G. J. Brown, M. Dutta, and M. A. Stroscio, J. Appl. Phys. 98, 043517 (2005).
[CrossRef]

Tsiapa, I.

S. Foteinopoulou, G. Kenanakis, N. Katsarakis, I. Tsiapa, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 91, 214102 (2007).
[CrossRef]

Xu, W.

J. Zhang, L. Zhang, and W. Xu, J. Phys. D 45, 113001 (2012).
[CrossRef]

Yang, J.

J. Yang, G. J. Brown, M. Dutta, and M. A. Stroscio, J. Appl. Phys. 98, 043517 (2005).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

Zhang, J.

J. Zhang, L. Zhang, and W. Xu, J. Phys. D 45, 113001 (2012).
[CrossRef]

Zhang, L.

J. Zhang, L. Zhang, and W. Xu, J. Phys. D 45, 113001 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

S. Foteinopoulou, G. Kenanakis, N. Katsarakis, I. Tsiapa, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 91, 214102 (2007).
[CrossRef]

J. Appl. Phys. (1)

J. Yang, G. J. Brown, M. Dutta, and M. A. Stroscio, J. Appl. Phys. 98, 043517 (2005).
[CrossRef]

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

J. Phys. D (1)

J. Zhang, L. Zhang, and W. Xu, J. Phys. D 45, 113001 (2012).
[CrossRef]

Nature (1)

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

Opt. Express (1)

Phys. Lett. A (1)

R. Ruppin, Phys. Lett. A 277, 61 (2000).
[CrossRef]

Phys. Rep. (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

Phys. Rev. (2)

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

R. H. Ritchie, Phys. Rev. 106, 874 (1957).
[CrossRef]

Phys. Rev. B (1)

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 84, 035128 (2011).
[CrossRef]

Science (1)

A. Boltasseva and H. A. Atwater, Science 331, 290 (2011).
[CrossRef]

Other (3)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1998).

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Figures (4)

Fig. 1.
Fig. 1.

Electromagnetic plane waves at an interface (z=0) between two media of relative permittivities ϵr1 (complex) and ϵr2 (real). The unit vectors k^j and p^j (j{1,2}), which lie in the xz plane, specify the wave vectors and the p-polarized electric-field directions.

Fig. 2.
Fig. 2.

Behavior of the absolute values of (a) kx/k0, (b) kx/k0, (c) k2z/k0, and (d) k2z/k0 as ϵr1 varies, when ϵr1=0.83 and ϵr2=11.7. The solid (blue) and dashed (red) lines represent Eqs. (3)–(5) and (A7)–(A9), respectively. The vertical dotted (black) lines are at ϵr1=ϵr2.

Fig. 3.
Fig. 3.

Dispersion relations (a) ω(|kx/k0|) and (b) ω(|k2z/k0|) for a Ag/GaP interface. The solid (blue) and dashed (red) lines correspond to the exact and approximate wave vectors, respectively.

Fig. 4.
Fig. 4.

Poynting vector components (a) S1z and (b) S1x, as a function of ϵr1, when ϵr1=0.83, ϵr2=11.7, and x=z=0. The solid (blue) and dashed (red) lines refer to exact and approximate methods, the vertical dotted lines are at ϵr1=ϵr2, and μ0 and c are the vacuum permeability and speed of light, respectively.

Equations (21)

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

kx=k0ϵr1ϵr2ϵr1+ϵr2,
kjz=k0ϵrjϵr1+ϵr2,j{1,2},
kx=k0{ϵr2[ϵr1(ϵr1+ϵr2)+ϵr12](ϵr1+ϵr2)2+ϵr12×[1+iϵr2ϵr1ϵr1(ϵr1+ϵr2)+ϵr12]}1/2,
k1z=k0(ϵr12(ϵr1+ϵr2)+ϵr12(ϵr1ϵr2)(ϵr1+ϵr2)2+ϵr12×{1+iϵr1[ϵr1(ϵr1+2ϵr2)+ϵr12]ϵr12(ϵr1+ϵr2)+ϵr12(ϵr1ϵr2)})1/2,
k2z=k0[ϵr22(ϵr1+ϵr2)(ϵr1+ϵr2)2+ϵr12(1iϵr1ϵr1+ϵr2)]1/2.
κ2κ2=(κ2),
2κκ=(κ2).
ϵr2<ϵr1k1z<0,
(ϵr1+ϵr2)2>ϵr22ϵr12k1z<0,
(ϵr1+ϵr2)2<ϵr22ϵr12k1z>0,
(ϵr1+ϵr2)2=ϵr22ϵr12k1z=0.
k1z<0SPPI;k1z>0SPPII.
(kx2)=k02ϵr2(ϵr12+ϵr12+ϵr1ϵr2)(ϵr1+ϵr2)2+ϵr12,
(k1z2)=k02ϵr12(ϵr1+ϵr2)+ϵr12(ϵr1ϵr2)(ϵr1+ϵr2)2+ϵr12,
(k2z2)=k02ϵr22(ϵr1+ϵr2)(ϵr1+ϵr2)2+ϵr12,
(kx2)=k02ϵr22ϵr1(ϵr1+ϵr2)2+ϵr12,
(k1z2)=k02ϵr1[(ϵr1+ϵr2)2(ϵr22ϵr12)](ϵr1+ϵr2)2+ϵr12,
(k2z2)=k02ϵr22ϵr1(ϵr1+ϵr2)2+ϵr12.
kxk0(ϵr1ϵr2ϵr1+ϵr2)1/2[1+iϵr2ϵr12ϵr1(ϵr1+ϵr2)],
k1zk0ϵr1(ϵr1+ϵr2)1/2(1+iϵr12ϵr1),
k2zk0ϵr2(ϵr1+ϵr2)1/2[1iϵr12(ϵr1+ϵr2)].

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