Abstract

Layered medium comprised of metal-dielectrics constituents is of much interest in the field of metamaterials. Here we introduce a novel analysis approach based on competing coupled structures of plasmonic gaps (MIM) and slabs (IMI) for the detailed comprehension of the band structure of periodic metal-dielectric stacks. This approach enables the rigorous identification of many interesting features including the intersections between plasmonic bands, flat or negative band formation, and the field symmetry of the propagating modes. Furthermore – the “gap-slab competition” concept allows us to develop design tools for incorporating desired dispersion properties of both gap and slab modes into the stack’s band structure, as well as effects of finite stack termination.

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  1. H. A. Macleod, Thin-Film Optical Filters, Institute of Physics Publishing (2001).
  2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism From Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
    [CrossRef]
  3. S. A. Ramakrishna, “Physics of Negative Refractive Index Materials,” Rep. Prog. Phys. 68, 3966–3969 (2000).
  4. S. Feng and J. M. Elson, “Diffraction-suppressed high-resolution imaging through metallodielectric nanofilms,” Opt. Express 14(1), 216–221 (2006).
    [CrossRef] [PubMed]
  5. F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).
    [CrossRef]
  6. V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B Condens. Matter 50(23), 16835–16844 (1994).
    [CrossRef] [PubMed]
  7. M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B Condens. Matter 52(16), 11744–11751 (1995).
    [CrossRef] [PubMed]
  8. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B Condens. Matter 54(16), 11245–11251 (1996).
    [CrossRef] [PubMed]
  9. M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, Metallo-Dielectric, One-Dimensional, Photonic Band-Gap Structures,” J. Appl. Phys. 83(5), 2377–2383 (1998).
    [CrossRef]
  10. S. Feng, J. M. Elson, and P. Overfelt, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express 13(11), 4113–4124 (2005).
    [CrossRef] [PubMed]
  11. S. Feng, J. M. Elson, and P. Overfelt, “Transparent Photonic Band in Metallodielectric Nanostructures,” Phys. Rev. B 72(8), 085117 (2005).
    [CrossRef]
  12. M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83(5), 2377 (1998).
    [CrossRef]
  13. M. Sarajlic, Z. Jaksic, O. Jaksic, M Maksimovic, and D. Jovanovic, “Dispersion of Propagating and Evanescent Modes in 1D Metallodielectric Photonic Crystal,” 14th Telecommunications Forum TELFOR (2006).
  14. J. Zhang, H. Jiang, S. Enoch, G. Tayeb, B. Gralak, and M. Lequime, “Two-Dimensional Complete Band Gaps in One-Dimensional Metlo-Dielectric Periodic Structures,” Appl. Phys. Lett. 92(5), 053104 (2008).
    [CrossRef]
  15. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
    [CrossRef] [PubMed]
  16. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
    [CrossRef] [PubMed]
  17. G. Rosenblatt, E. Feigenbaum, and M. Orenstein, “Circular motion of electromagnetic power shaping the dispersion of Surface Plasmon Polaritons,” Opt. Express 18(25), 25861–25872 (2010).
    [CrossRef] [PubMed]
  18. E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reflection pole method and wavevector density method,” J Lightwave Technol. 17(5), 929-941 (1999).

2010 (1)

2008 (1)

J. Zhang, H. Jiang, S. Enoch, G. Tayeb, B. Gralak, and M. Lequime, “Two-Dimensional Complete Band Gaps in One-Dimensional Metlo-Dielectric Periodic Structures,” Appl. Phys. Lett. 92(5), 053104 (2008).
[CrossRef]

2006 (1)

2005 (2)

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

S. Feng, J. M. Elson, and P. Overfelt, “Transparent Photonic Band in Metallodielectric Nanostructures,” Phys. Rev. B 72(8), 085117 (2005).
[CrossRef]

2002 (1)

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[CrossRef] [PubMed]

2000 (2)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[CrossRef] [PubMed]

S. A. Ramakrishna, “Physics of Negative Refractive Index Materials,” Rep. Prog. Phys. 68, 3966–3969 (2000).

1999 (2)

E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reflection pole method and wavevector density method,” J Lightwave Technol. 17(5), 929-941 (1999).

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism From Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

1998 (2)

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83(5), 2377 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, Metallo-Dielectric, One-Dimensional, Photonic Band-Gap Structures,” J. Appl. Phys. 83(5), 2377–2383 (1998).
[CrossRef]

1996 (1)

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B Condens. Matter 54(16), 11245–11251 (1996).
[CrossRef] [PubMed]

1995 (1)

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B Condens. Matter 52(16), 11744–11751 (1995).
[CrossRef] [PubMed]

1994 (1)

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B Condens. Matter 50(23), 16835–16844 (1994).
[CrossRef] [PubMed]

1991 (1)

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).
[CrossRef]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[CrossRef] [PubMed]

Anemogiannis, E.

E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reflection pole method and wavevector density method,” J Lightwave Technol. 17(5), 929-941 (1999).

Bloemer, M. J.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, Metallo-Dielectric, One-Dimensional, Photonic Band-Gap Structures,” J. Appl. Phys. 83(5), 2377–2383 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83(5), 2377 (1998).
[CrossRef]

Bowden, C. M.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83(5), 2377 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, Metallo-Dielectric, One-Dimensional, Photonic Band-Gap Structures,” J. Appl. Phys. 83(5), 2377–2383 (1998).
[CrossRef]

Bradberry, G. W.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).
[CrossRef]

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[CrossRef] [PubMed]

Chan, C. T.

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B Condens. Matter 52(16), 11744–11751 (1995).
[CrossRef] [PubMed]

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, Metallo-Dielectric, One-Dimensional, Photonic Band-Gap Structures,” J. Appl. Phys. 83(5), 2377–2383 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83(5), 2377 (1998).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[CrossRef] [PubMed]

Elson, J. M.

Enoch, S.

J. Zhang, H. Jiang, S. Enoch, G. Tayeb, B. Gralak, and M. Lequime, “Two-Dimensional Complete Band Gaps in One-Dimensional Metlo-Dielectric Periodic Structures,” Appl. Phys. Lett. 92(5), 053104 (2008).
[CrossRef]

Fan, S.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B Condens. Matter 54(16), 11245–11251 (1996).
[CrossRef] [PubMed]

Feigenbaum, E.

Feng, S.

Gaylord, T. K.

E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reflection pole method and wavevector density method,” J Lightwave Technol. 17(5), 929-941 (1999).

Glytsis, E. N.

E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reflection pole method and wavevector density method,” J Lightwave Technol. 17(5), 929-941 (1999).

Gralak, B.

J. Zhang, H. Jiang, S. Enoch, G. Tayeb, B. Gralak, and M. Lequime, “Two-Dimensional Complete Band Gaps in One-Dimensional Metlo-Dielectric Periodic Structures,” Appl. Phys. Lett. 92(5), 053104 (2008).
[CrossRef]

Ho, K. M.

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B Condens. Matter 52(16), 11744–11751 (1995).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism From Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Jiang, H.

J. Zhang, H. Jiang, S. Enoch, G. Tayeb, B. Gralak, and M. Lequime, “Two-Dimensional Complete Band Gaps in One-Dimensional Metlo-Dielectric Periodic Structures,” Appl. Phys. Lett. 92(5), 053104 (2008).
[CrossRef]

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B Condens. Matter 54(16), 11245–11251 (1996).
[CrossRef] [PubMed]

Kuzmiak, V.

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B Condens. Matter 50(23), 16835–16844 (1994).
[CrossRef] [PubMed]

Lederer, F.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[CrossRef] [PubMed]

Lequime, M.

J. Zhang, H. Jiang, S. Enoch, G. Tayeb, B. Gralak, and M. Lequime, “Two-Dimensional Complete Band Gaps in One-Dimensional Metlo-Dielectric Periodic Structures,” Appl. Phys. Lett. 92(5), 053104 (2008).
[CrossRef]

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83(5), 2377 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, Metallo-Dielectric, One-Dimensional, Photonic Band-Gap Structures,” J. Appl. Phys. 83(5), 2377–2383 (1998).
[CrossRef]

Maradudin, A. A.

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B Condens. Matter 50(23), 16835–16844 (1994).
[CrossRef] [PubMed]

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[CrossRef] [PubMed]

Orenstein, M.

Overfelt, P.

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

S. Feng, J. M. Elson, and P. Overfelt, “Transparent Photonic Band in Metallodielectric Nanostructures,” Phys. Rev. B 72(8), 085117 (2005).
[CrossRef]

Pendry, J. B.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism From Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[CrossRef] [PubMed]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[CrossRef] [PubMed]

Pethel, A. S.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, Metallo-Dielectric, One-Dimensional, Photonic Band-Gap Structures,” J. Appl. Phys. 83(5), 2377–2383 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83(5), 2377 (1998).
[CrossRef]

Pincemin, F.

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B Condens. Matter 50(23), 16835–16844 (1994).
[CrossRef] [PubMed]

Ramakrishna, S. A.

S. A. Ramakrishna, “Physics of Negative Refractive Index Materials,” Rep. Prog. Phys. 68, 3966–3969 (2000).

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism From Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Rosenblatt, G.

Sambles, J. R.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).
[CrossRef]

Scalora, M.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, Metallo-Dielectric, One-Dimensional, Photonic Band-Gap Structures,” J. Appl. Phys. 83(5), 2377–2383 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83(5), 2377 (1998).
[CrossRef]

Sigalas, M. M.

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B Condens. Matter 52(16), 11744–11751 (1995).
[CrossRef] [PubMed]

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B Condens. Matter 52(16), 11744–11751 (1995).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism From Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Tayeb, G.

J. Zhang, H. Jiang, S. Enoch, G. Tayeb, B. Gralak, and M. Lequime, “Two-Dimensional Complete Band Gaps in One-Dimensional Metlo-Dielectric Periodic Structures,” Appl. Phys. Lett. 92(5), 053104 (2008).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B Condens. Matter 54(16), 11245–11251 (1996).
[CrossRef] [PubMed]

Yang, F.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).
[CrossRef]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[CrossRef] [PubMed]

Zhang, J.

J. Zhang, H. Jiang, S. Enoch, G. Tayeb, B. Gralak, and M. Lequime, “Two-Dimensional Complete Band Gaps in One-Dimensional Metlo-Dielectric Periodic Structures,” Appl. Phys. Lett. 92(5), 053104 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

J. Zhang, H. Jiang, S. Enoch, G. Tayeb, B. Gralak, and M. Lequime, “Two-Dimensional Complete Band Gaps in One-Dimensional Metlo-Dielectric Periodic Structures,” Appl. Phys. Lett. 92(5), 053104 (2008).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism From Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J Lightwave Technol. (1)

E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reflection pole method and wavevector density method,” J Lightwave Technol. 17(5), 929-941 (1999).

J. Appl. Phys. (2)

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallo-dielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83(5), 2377 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, Metallo-Dielectric, One-Dimensional, Photonic Band-Gap Structures,” J. Appl. Phys. 83(5), 2377–2383 (1998).
[CrossRef]

Opt. Express (3)

Phys. Rev. B (2)

S. Feng, J. M. Elson, and P. Overfelt, “Transparent Photonic Band in Metallodielectric Nanostructures,” Phys. Rev. B 72(8), 085117 (2005).
[CrossRef]

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).
[CrossRef]

Phys. Rev. B Condens. Matter (3)

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B Condens. Matter 50(23), 16835–16844 (1994).
[CrossRef] [PubMed]

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B Condens. Matter 52(16), 11744–11751 (1995).
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B Condens. Matter 54(16), 11245–11251 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

S. A. Ramakrishna, “Physics of Negative Refractive Index Materials,” Rep. Prog. Phys. 68, 3966–3969 (2000).

Other (2)

M. Sarajlic, Z. Jaksic, O. Jaksic, M Maksimovic, and D. Jovanovic, “Dispersion of Propagating and Evanescent Modes in 1D Metallodielectric Photonic Crystal,” 14th Telecommunications Forum TELFOR (2006).

H. A. Macleod, Thin-Film Optical Filters, Institute of Physics Publishing (2001).

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Figures (10)

Fig. 1
Fig. 1

A periodic stack of alternating metal and dielectric layers of thicknesses dD,M and permittivity εD,M respectively. Wave propagation through the structure via vertical evanescent coupling (x-direction) of competing propagating plasmonic gap (blue) and slab (orange) modes (z-direction) is illustrated.

Fig. 2
Fig. 2

The two plasmonic bands (yellow filling) of a periodic metal-dielectric stack of layer thicknesses (a) dD = 30nm, dM = 40nm, and (b) dD = 40nm, dM = 20nm. The kB = 0 curves – the S-curve (red) and AS-curve (green) – intersect in (b), additional kB-curves (blue) include kB = 0.25,0.5,0.75·π/L (order of increasing kB is noted by blue arrows in each band) and kB = π/L (thick black). The light-line and SPP frequency – dashed black lines. The gray shaded area is a mirror image of the negative branch of the AS-band into the positive β range – it is there for visual convenience alone while the actual band is located in the negative β range, since its kB-curves have a negative index.

Fig. 3
Fig. 3

The coupling strengths cD (orange) and cM (purple) for (a) the AS-curve (green) and (c) S-curve (red) and (b) the curves themselves, for a metal dielectric stack of layer thicknesses dM = 30nm and dD = 100nm (solid), dD = 50nm (dashed), dD = 20nm (dotted). Intersections of the S-curve and AS-curve are noted by magenta lines.

Fig. 4
Fig. 4

The two plasmonic bands (‘gap-like’ region – yellow, ‘slab-like’ region – purple) of a periodic metal-dielectric stack of layer thicknesses (a) dD = 30nm, dM = 40nm and (a) dD = 40nm, dM = 20nm. The dispersion curves of the symmetric (solid) and anti-symmetric (dashed) gap (orange) and slab (purple) modes ‘lead’ the bands in their corresponding regions, as seen by the magenta markings, as well as by inspecting Δe (lower subplots). Only the boundary curves in (b) are centered on the gap modes (Δe≈0 in teal) throughout all values of β – also indicated by teal markings. The intersection of the S-curve (red) and AS-curve (green) – vertical solid black line; intersections of the gap and slab modes – vertical dashed black lines.

Fig. 5
Fig. 5

The plasmonic bands (ω as a function of β – upper subplot) and the normalized relative symmetry coefficients in dielectric (RD – oragne) and metal (RM – purple) layers plotted for kB = 0.1·π/L (as a function of β – lower subplot) of the S-band (solid lines) and AS-band (dashed lines), for a stack of (a) dD = 30nm, dM = 40nm and (b) dD = 40nm, dM = 20nm. RD,M = 0,1 denote a completely anti-symmetric and symmetric H-field distribution respectively (in the corresponding D or M layer type). ‘Gap-like’ and ‘slab-like’ regions are marked by yellow and purple fillings respectively. The kB-curves for kB = 0.01,0.25,0.5,0.75,1·π/L (thin black lines) are added (direction of increasing kB is indicated by blue arrows) – the kB = 0.1·π/L curves are emphasized in thick black. Also, α-curves in (b) are added for α·dM = −0.9,-0.5,0,0.5,1·kp (dahsed red lines, kp = ωp/c) – the α·dM = −1·kp (light-line) is in dahsed black. The β-values corresponding to the intersection of the kB = 0.1·π/L curves with the transition curve (α = 0) are marked by thick vertical dashed lines, while the intersection with the light-line by a thin vertical black line.

Fig. 6
Fig. 6

The real vs imaginary parts of the H-field symmetry coefficients in dielectric (rD – orange) and metal (rM – purple) layers for the S-band (solid lines) and AS-band (dashed lines), plotted along (a) α-curves (constant α) for α·dM = −0.9,-0.5,0,0.5,1·kp, and (b) kB-curves (constant kB) for kB = 0.01,0.25,0.5,0.75,1·π/L. Since |rD,M| ≡1, different plots of rD,M are joined one alongside another by plotting them at diffAerent radii, providing a convenient comparision tool – each radius corresponding to a different α or kB value (marked in red). Re{rD,M} = −1 and 1 correspond to a completely anti-symmetric and symmetric H-field distribution respectively (in the corresponding D or M layer type). The direction of change in β (from 0 to ∞) for the rD,M plots of both bands in (b), is indicated by a corresponding arrow (color coded). The stack’s layer thicknesses are dD = 40nm, dM = 20nm. The α-curves and kB-curves for which rD,M is plotted are shown in Fig. 5b.

Fig. 7
Fig. 7

The normalized relative symmetry coefficient in dielectric (RD – orange) and metal (RM – purple) layers for the (a) AS-band (dashed lines) and (b) S-band (solid lines) as a function of kB, plotted along different α-curves (constant α) fitting α·dM = −0.2,-0.05,-0.01,0,0.01,0.05,0.2·kp (red arrows indicate direction of increasing α). The α·dM = −0.2·kp curves are thicker for better visual convinience. RD,M = 0,1 denote a completely anti-symmetric and symmetric H-field distribution respectively (in the corresponding D or M layer type), while RD,M = 0.5 is the exact middle where dominant symmetry is not defined. The α = 0 curves are in solid black – where the field symmetry in both bands swithces. The stack’s layer thicknesses are dD = 40nm and dM = 20nm.

Fig. 8
Fig. 8

The two plasmonic bands (‘gap-like’ region – yellow, ‘slab-like’ region – purple) for a metal-dielectric stack of (a) dD = 26nm, dM = 20nm and (b) dD = 55nm, dM = 60nm, where the AS-band has kB-curves of mostly negative slope (negative index) or relatively flat respectively. The leading modes are added (TM1G - orange, TM1S – purple), as well as kB-curves for kB = 0.2,0.3,0.4,0.5,0.6·π/L (thin black lines) with the direction of increasing kB marked by blue arrows, and the band boundaries (thick black lines). The local maximum of TM1S in (a) coincides with the transition curve intersection (marked by a red circle). Light-line and SPP frequency – dashed black lines.

Fig. 9
Fig. 9

An illustration of (a) a metal coated and (b) a dielectric coated finite metal (εM) dielectric (εD) stack of N periods and layer thicknesses dM,D respectively.

Fig. 10
Fig. 10

The two plasmonic bands (‘gap-like’ region – yellow, ‘slab-like’ region – purple) of a periodic metal-dielectric stack of layer thicknesses dD = 40nm, dM = 20nm and the modes (dotted blue) of the analogue finite stack of N = 10 periods for (a) a metal coated stack, and (b) a dielectric coated stack. The S-mode and AS-mode are colored magenta – their cut-off at their intersection is noted by a red circle. For (b) the intersection is magnified inset. The S-curve (red) and AS-curve (red) are added for comparison. Light line – dashed black line.

Equations (18)

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H y ( x,z )= e jβz { A D e κ D x + B D e κ D x 0<x< d D A M e κ M x + B M e κ M x d D <x<L ,
( κ D ε M + κ M ε D ) 2  4 κ D κ M ε D ε M cosh( κ D d D + κ M d M ) ( κ D ε M κ M ε D ) 2  4 κ D κ M ε D ε M cosh( κ D d D κ M d M )=cos( k B L ),
[ κ D ε D tanh( κ D d D 2 )+ κ M ε M tanh( κ M d M 2 ) ][ κ D ε D coth( κ D d D 2 )+ κ M ε M coth( κ M d M 2 ) ]=0.
H y S,AS ( x,z )= e jβz { (1) l h S,AS ( κ D ( x d D /2 ) )/ h S,AS ( κ D d D /2 ) 0<x< d D h S,AS ( κ M ( xL+ d M /2 ) )/ h S,AS ( κ M d M /2 ) d D <x<L ,
c D =( 1/ d D ) 0 d D f SPP ( x ) f SPP ( x+ d D )dx = e κ D d D ,
c M =( 1/ d M ) d M 0 f SPP ( x ) f SPP ( x d M )dx = e κ M d M ,
( κ D d D κ M d M ) | ω i , k B =0.
( κ D ε M + κ M ε D ) | ω i , k B =0 =0.
ω i = ω p / 1+ ε D ( d D / d M ) ,
β i =( ω i /c ) ε D /( 1 d M / d D ) ,
( a + / a ) 2 =( cos( k B L )cosh( φ ) )/( cos( k B L )cosh( φ + ) ).
κ D ε M + κ M ε D =0 { κ D d D + κ M d M =0 , k B =0 } .
κ D ε D tanh( κ D d D 2 )+ κ M ε M =0,
κ D ε D + κ M ε M coth( κ M d M 2 )=0,
H y ( x,z )= e jβz { D + cosh( κ D ( x d D /2 ) )+ D sinh( κ D ( x d D /2 ) ) 0<x< d D M + cosh( κ M ( xL+ d M /2 ) )+ M sinh( κ M ( xL+ d M /2 ) ) d D <x<L
R D,M D, M D, M + = 1+ r D,M 1 r D,M ,
r D = κ D ε M + κ M ε D κ D ε M κ M ε D cosh( κ M d M )cosh( κ D d D )cos( k B L )+jsinh( κ D d D )sin( k B L ) cosh( κ D d D κ M d M )cos( k B L ) ,
κ M 2 / κ D 2 1= κ M d M /sinh( κ M d M ).

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