Abstract

We present general properties of surface modes in binary metal-dielectric metamaterials. We show mechanism for surface mode formation and analyze their existence conditions for semi-infinite metamaterials in the frame of couple mode theory.

© 2010 OSA

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  1. W. Shockley, “On the surface states associated with a periodic potential,” Phys. Rev. 56(4), 317–323 (1939).
    [CrossRef]
  2. S. G. Davison, and M. Steslicka, Basic Theory of Surface States, (Oxford Univ. Press, 1996).
  3. N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73(11), 113113 (2006).
    [CrossRef]
  4. K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
    [CrossRef] [PubMed]
  5. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
    [CrossRef] [PubMed]
  6. S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Backward surface waves at photonic crystals,” Phys. Rev. B 75(24), 245116 (2007).
    [CrossRef]
  7. P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32(2), 104 (1978).
    [CrossRef]
  8. N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Transition between Tamm-like and Shockley-like surface states in optically induced photonic superlattices,” Phys. Rev. A 80(4), 043806 (2009).
    [CrossRef]
  9. S. H. Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “Deep subwavelength surface modes in metal-dielectric metamaterials,” Opt. Lett. 35(11), 1847–1849 (2010).
    [CrossRef]
  10. Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
    [CrossRef] [PubMed]
  11. G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B 79(20), 201103 (2009).
    [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(11), 4113–4124 (2005).
    [CrossRef] [PubMed]
  13. J. Yang, X. Hu, X. Li, Z. Liu, X. Jiang, and J. Zi, “Cancellation of reflection and transmission at metamaterial surfaces,” Opt. Lett. 35(1), 16–18 (2010).
    [CrossRef] [PubMed]
  14. S. H. Nam, A. J. Taylor, and A. Efimov, “Diabolical point and conical-like diffraction in periodic plasmonic nanostructures,” Opt. Express 18(10), 10120–10126 (2010).
    [CrossRef] [PubMed]
  15. P. Yeh, Optical waves in layered media, (John Wiley & Sons, 1988).
  16. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
    [CrossRef]
  17. 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(7), 073901 (2006).
    [CrossRef] [PubMed]
  18. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
    [CrossRef]
  19. J. Kłos, “Conditions of Tamm and Shockley state existence in chains of resonant cavities in a photonic crystal,” Phys. Rev. B 76(16), 165125 (2007).
    [CrossRef]

2010 (3)

S. H. Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “Deep subwavelength surface modes in metal-dielectric metamaterials,” Opt. Lett. 35(11), 1847–1849 (2010).
[CrossRef]

J. Yang, X. Hu, X. Li, Z. Liu, X. Jiang, and J. Zi, “Cancellation of reflection and transmission at metamaterial surfaces,” Opt. Lett. 35(1), 16–18 (2010).
[CrossRef] [PubMed]

S. H. Nam, A. J. Taylor, and A. Efimov, “Diabolical point and conical-like diffraction in periodic plasmonic nanostructures,” Opt. Express 18(10), 10120–10126 (2010).
[CrossRef] [PubMed]

2009 (3)

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B 79(20), 201103 (2009).
[CrossRef]

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Transition between Tamm-like and Shockley-like surface states in optically induced photonic superlattices,” Phys. Rev. A 80(4), 043806 (2009).
[CrossRef]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
[CrossRef] [PubMed]

2008 (1)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

2007 (3)

J. Kłos, “Conditions of Tamm and Shockley state existence in chains of resonant cavities in a photonic crystal,” Phys. Rev. B 76(16), 165125 (2007).
[CrossRef]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[CrossRef] [PubMed]

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Backward surface waves at photonic crystals,” Phys. Rev. B 75(24), 245116 (2007).
[CrossRef]

2006 (2)

N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73(11), 113113 (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(7), 073901 (2006).
[CrossRef] [PubMed]

2005 (1)

S. Feng, J. M. Elson, and P. L. Overfelt, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express 13(11), 4113–4124 (2005).
[CrossRef] [PubMed]

1991 (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
[CrossRef] [PubMed]

1978 (1)

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32(2), 104 (1978).
[CrossRef]

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

1939 (1)

W. Shockley, “On the surface states associated with a periodic potential,” Phys. Rev. 56(4), 317–323 (1939).
[CrossRef]

Nam, S. H.

S. H. Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “Deep subwavelength surface modes in metal-dielectric metamaterials,” Opt. Lett. 35(11), 1847–1849 (2010).
[CrossRef]

Bartal, G.

S. H. Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “Deep subwavelength surface modes in metal-dielectric metamaterials,” Opt. Lett. 35(11), 1847–1849 (2010).
[CrossRef]

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B 79(20), 201103 (2009).
[CrossRef]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[CrossRef] [PubMed]

Brommer, K. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
[CrossRef] [PubMed]

Bryant, G.

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Transition between Tamm-like and Shockley-like surface states in optically induced photonic superlattices,” Phys. Rev. A 80(4), 043806 (2009).
[CrossRef]

Chan, C. T.

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(7), 073901 (2006).
[CrossRef] [PubMed]

Chen, Z.

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Transition between Tamm-like and Shockley-like surface states in optically induced photonic superlattices,” Phys. Rev. A 80(4), 043806 (2009).
[CrossRef]

Cho, A. Y.

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32(2), 104 (1978).
[CrossRef]

Economou, E. N.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Backward surface waves at photonic crystals,” Phys. Rev. B 75(24), 245116 (2007).
[CrossRef]

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

Efimov, A.

S. H. Nam, A. J. Taylor, and A. Efimov, “Diabolical point and conical-like diffraction in periodic plasmonic nanostructures,” Opt. Express 18(10), 10120–10126 (2010).
[CrossRef] [PubMed]

Elson, J. M.

S. Feng, J. M. Elson, and P. L. Overfelt, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express 13(11), 4113–4124 (2005).
[CrossRef] [PubMed]

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(7), 073901 (2006).
[CrossRef] [PubMed]

Feng, S.

S. Feng, J. M. Elson, and P. L. Overfelt, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express 13(11), 4113–4124 (2005).
[CrossRef] [PubMed]

Foteinopoulou, S.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Backward surface waves at photonic crystals,” Phys. Rev. B 75(24), 245116 (2007).
[CrossRef]

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[CrossRef] [PubMed]

Hromada, I.

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Transition between Tamm-like and Shockley-like surface states in optically induced photonic superlattices,” Phys. Rev. A 80(4), 043806 (2009).
[CrossRef]

Hu, X.

J. Yang, X. Hu, X. Li, Z. Liu, X. Jiang, and J. Zi, “Cancellation of reflection and transmission at metamaterial surfaces,” Opt. Lett. 35(1), 16–18 (2010).
[CrossRef] [PubMed]

Ishizaki, K.

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
[CrossRef] [PubMed]

Jiang, X.

J. Yang, X. Hu, X. Li, Z. Liu, X. Jiang, and J. Zi, “Cancellation of reflection and transmission at metamaterial surfaces,” Opt. Lett. 35(1), 16–18 (2010).
[CrossRef] [PubMed]

Joannopoulos, J. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
[CrossRef] [PubMed]

Kafesaki, M.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Backward surface waves at photonic crystals,” Phys. Rev. B 75(24), 245116 (2007).
[CrossRef]

Klos, J.

J. Kłos, “Conditions of Tamm and Shockley state existence in chains of resonant cavities in a photonic crystal,” Phys. Rev. B 76(16), 165125 (2007).
[CrossRef]

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(7), 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(20), 201103 (2009).
[CrossRef]

Li, X.

J. Yang, X. Hu, X. Li, Z. Liu, X. Jiang, and J. Zi, “Cancellation of reflection and transmission at metamaterial surfaces,” Opt. Lett. 35(1), 16–18 (2010).
[CrossRef] [PubMed]

Liu, Y.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[CrossRef] [PubMed]

Liu, Z.

J. Yang, X. Hu, X. Li, Z. Liu, X. Jiang, and J. Zi, “Cancellation of reflection and transmission at metamaterial surfaces,” Opt. Lett. 35(1), 16–18 (2010).
[CrossRef] [PubMed]

Malkova, N.

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Transition between Tamm-like and Shockley-like surface states in optically induced photonic superlattices,” Phys. Rev. A 80(4), 043806 (2009).
[CrossRef]

N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73(11), 113113 (2006).
[CrossRef]

Meade, R. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
[CrossRef] [PubMed]

Nam, S. H.

S. H. Nam, A. J. Taylor, and A. Efimov, “Diabolical point and conical-like diffraction in periodic plasmonic nanostructures,” Opt. Express 18(10), 10120–10126 (2010).
[CrossRef] [PubMed]

Ning, C. Z.

N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73(11), 113113 (2006).
[CrossRef]

Noda, S.

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
[CrossRef] [PubMed]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Overfelt, P. L.

S. Feng, J. M. Elson, and P. L. Overfelt, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express 13(11), 4113–4124 (2005).
[CrossRef] [PubMed]

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Rappe, A. M.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
[CrossRef] [PubMed]

Shockley, W.

W. Shockley, “On the surface states associated with a periodic potential,” Phys. Rev. 56(4), 317–323 (1939).
[CrossRef]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Soukoulis, C. M.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Backward surface waves at photonic crystals,” Phys. Rev. B 75(24), 245116 (2007).
[CrossRef]

Taylor, A. J.

S. H. Nam, A. J. Taylor, and A. Efimov, “Diabolical point and conical-like diffraction in periodic plasmonic nanostructures,” Opt. Express 18(10), 10120–10126 (2010).
[CrossRef] [PubMed]

Ulin-Avila, E.

S. H. Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “Deep subwavelength surface modes in metal-dielectric metamaterials,” Opt. Lett. 35(11), 1847–1849 (2010).
[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(7), 073901 (2006).
[CrossRef] [PubMed]

Wang, X.

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Transition between Tamm-like and Shockley-like surface states in optically induced photonic superlattices,” Phys. Rev. A 80(4), 043806 (2009).
[CrossRef]

Yang, J.

J. Yang, X. Hu, X. Li, Z. Liu, X. Jiang, and J. Zi, “Cancellation of reflection and transmission at metamaterial surfaces,” Opt. Lett. 35(1), 16–18 (2010).
[CrossRef] [PubMed]

Yariv, A.

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32(2), 104 (1978).
[CrossRef]

Yeh, P.

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32(2), 104 (1978).
[CrossRef]

Zhang, X.

S. H. Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “Deep subwavelength surface modes in metal-dielectric metamaterials,” Opt. Lett. 35(11), 1847–1849 (2010).
[CrossRef]

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B 79(20), 201103 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[CrossRef] [PubMed]

Zi, J.

J. Yang, X. Hu, X. Li, Z. Liu, X. Jiang, and J. Zi, “Cancellation of reflection and transmission at metamaterial surfaces,” Opt. Lett. 35(1), 16–18 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32(2), 104 (1978).
[CrossRef]

Nat. Photonics (1)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Nature (1)

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
[CrossRef] [PubMed]

Opt. Express (2)

S. Feng, J. M. Elson, and P. L. Overfelt, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express 13(11), 4113–4124 (2005).
[CrossRef] [PubMed]

S. H. Nam, A. J. Taylor, and A. Efimov, “Diabolical point and conical-like diffraction in periodic plasmonic nanostructures,” Opt. Express 18(10), 10120–10126 (2010).
[CrossRef] [PubMed]

Opt. Lett. (2)

J. Yang, X. Hu, X. Li, Z. Liu, X. Jiang, and J. Zi, “Cancellation of reflection and transmission at metamaterial surfaces,” Opt. Lett. 35(1), 16–18 (2010).
[CrossRef] [PubMed]

S. H. Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “Deep subwavelength surface modes in metal-dielectric metamaterials,” Opt. Lett. 35(11), 1847–1849 (2010).
[CrossRef]

Phys. Rev. (2)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

W. Shockley, “On the surface states associated with a periodic potential,” Phys. Rev. 56(4), 317–323 (1939).
[CrossRef]

Phys. Rev. A (1)

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Transition between Tamm-like and Shockley-like surface states in optically induced photonic superlattices,” Phys. Rev. A 80(4), 043806 (2009).
[CrossRef]

Phys. Rev. B (4)

N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73(11), 113113 (2006).
[CrossRef]

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Backward surface waves at photonic crystals,” Phys. Rev. B 75(24), 245116 (2007).
[CrossRef]

J. Kłos, “Conditions of Tamm and Shockley state existence in chains of resonant cavities in a photonic crystal,” Phys. Rev. B 76(16), 165125 (2007).
[CrossRef]

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B 79(20), 201103 (2009).
[CrossRef]

Phys. Rev. B Condens. Matter (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett. (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(7), 073901 (2006).
[CrossRef] [PubMed]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[CrossRef] [PubMed]

Other (2)

P. Yeh, Optical waves in layered media, (John Wiley & Sons, 1988).

S. G. Davison, and M. Steslicka, Basic Theory of Surface States, (Oxford Univ. Press, 1996).

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Figures (3)

Fig. 1
Fig. 1

(a)-(c) Three types of metal-dielectric metamaterials and the corresponding dispersion curves for the unit cell parameters (a) metal (Au, 20nm, dark grey) and dielectric (n = 1.5, 100nm, light orange), (b) metal 1 (Au, 20nm), metal 2 (Au, 40nm), and dielectric (n = 1.5, 100nm), (c) metal (Au, 20nm), dielectric 1 (n = 1.34, 50nm, yellow), dielectric 2 (n = 3.48, 200nm, light grey), and dielectric 3 (n = 1.34, 50nm). L: low index, H: high index dielectric. κis the transverse wave vector multiplied by the lattice periodΛ. The excitation wavelength is 1550nm. (d)-(e) Normal and anomalous coupling between two coupled SPP modes in metal-dielectric multilayers. Blue curves indicate transverse electric fields (Ex ). (d) single SPP mode in a metal-dielectric-metal layer, (e) symmetric and antisymmetric mode by anomalous coupling of two gap SPP modes through a thin metal layer, (f) single hybrid SPP mode in a metal-three dielectric layer (low index/high index/low index), (g-h) symmetric and antisymmetric hybrid SPP modes by normal coupling through a high index dielectric layer and by anomalous coupling through a thin metal layer, respectively. The diagrams in the right display schematic mode splitting in the propagation constant.

Fig. 2
Fig. 2

Bandgap closing & band crossing. (a), (b), (c) Band diagrams for the metal (Au) layer thickness dAu = 15nm (a), for dAu = 8.4nm (b), and for dAu = 5nm (c). The thickness of the other layers is kept as dMgF2 = 50nm and dSi = 200nm. B, B’: band edges of the upper bands, T, T’: band edges of the lower bands in (a) and (c). The arrow in (b) indicates the singular point. (d) Band evolution calculated by coupled mode theory as a function ofη. The bands are marked in blue, the direct bandgap (D) in yellow, and the inverted bandgap (I) is in grey. The arrow in (d) marks the bandgap closing point C at η = 1 . (e-h) Eigenmodes at the bandedges B (e), T (f), B’ (g), and T’ (h), respectively.

Fig. 3
Fig. 3

(a) Existence conditions for surface modes in η Z plane corresponding to the plus solution in Eq. (3). The contours with constant r indicate degree of localization. (b) Existence conditions corresponding to the minus solution in Eq. (3). (c) Top: A schematic for semi-infinite binary metamaterials with termination of C- coupling at the left end. The an and bn indicate amplitudes of SPP modes at nth even-numbered and odd-numbered SPP modes from the surface, not the physical layers. The arrow and Z indicate the location of surface and the surface perturbation, respectively. Bottom: Band diagram for positive (red dotted) and negative (solid) η, and shift of the surface mode locations in the band diagram with increasing surface perturbation Z. (d) The corresponding eigenvectors for the surface modes in the regions a-f marked in (a) and (b).

Equations (3)

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( i z + β 0 ) a n + C b n 1 + C + b n = 0 , ​ ​ ​ ​ ​       ( i z + β 0 ) b n + C + a n + C a n + 1 = 0 ,
q 0 = ( K + Z ) ​   p 0 K p 0 + ( η r + 1 ) q 0 = 0 , K q 0 + ( η r + 1 ) p 0 = 0 ,
r = 1 2 ( ( η 3 Z 2 η ) ± ( η 3 Z 2 η ) 2 + 4 ( η Z ) 2 ) .

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