Abstract

Symmetric metal-dielectric guided-mode resonators (GMR) can operate as infrared band-pass filters, thanks to high-transmission resonant peaks and good rejection ratio. Starting from matrix formalism, we show that the behavior of the system can be described by a two-mode model. This model reduces to a scalar formula and the GMR is described as the combination of two independent Fabry-Perot resonators. The formalism has then been applied to the case of asymmetric GMR, in order to restore the properties of the symmetric system. This result allows designing GMR-on-substrate as efficient as free-standing systems, the same high transmission maximum value and high quality factor being conserved.

© 2015 Optical Society of America

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References

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  1. T. W. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
    [Crossref]
  2. H. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).
    [Crossref]
  3. T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24, 256–258 (1999).
    [Crossref]
  4. S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
    [Crossref]
  5. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
    [Crossref] [PubMed]
  6. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
    [Crossref] [PubMed]
  7. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
    [Crossref] [PubMed]
  8. J. Porto, F. García-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).
    [Crossref]
  9. R. Haïdar, G. Vincent, S. Collin, N. Bardou, N. Guérineau, J. Deschamps, and J.-L. Pelouard, “Free-standing subwavelength metallic gratings for snapshot multispectral imaging,” Appl. Phys. Lett. 96, 221104 (2010).
    [Crossref]
  10. E. Sakat, G. Vincent, P. Ghenuche, N. Bardou, S. Collin, F. Pardo, J.-L. Pelouard, and R. Haïdar, “Guided mode resonance in subwavelength metallodielectric free-standing grating for bandpass filtering,” Opt. Lett. 36, 3054–3056 (2011).
    [Crossref] [PubMed]
  11. E. Sakat, G. Vincent, P. Ghenuche, N. Bardou, C. Dupuis, S. Collin, F. Pardo, R. Haïdar, and J.-L. Pelouard, “Free-standing guided-mode resonance band-pass filters: from 1d to 2d structures,” Opt. Express 20, 13082–13090 (2012).
    [Crossref] [PubMed]
  12. C.-H. Park, Y.-T. Yoon, and S.-S. Lee, “Polarization-independent visible wavelength filter incorporating a symmetric metal-dielectric resonant structure,” Opt. Express 20, 23769–23777 (2012).
    [Crossref] [PubMed]
  13. E. Sakat, S. Héron, P. Bouchon, G. Vincent, F. Pardo, S. Collin, J.-L. Pelouard, and R. Haïdar, “Metal-dielectric bi-atomic structure for angular-tolerant spectral filtering,” Opt. Lett. 38, 425–427 (2013).
    [Crossref] [PubMed]
  14. J. Le Perchec, R. E. de Lamaestre, M. Brun, N. Rochat, O. Gravrand, G. Badano, J. Hazart, and S. Nicoletti, “High rejection bandpass optical filters based on sub-wavelength metal patch arrays,” Opt. Express 19, 15720–15731 (2011).
    [Crossref] [PubMed]
  15. S. S. Wang, M. G. Moharam, R. Magnusson, and J. S. Bagby, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990).
    [Crossref]
  16. R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
    [Crossref]
  17. P. Lalanne, J.-P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48 (2000).
    [Crossref]
  18. S. Collin, F. Pardo, and J.-L. Pelouard, “Waveguiding in nanoscale metallic apertures,” Opt. Express 15, 4310–4320 (2007).
    [Crossref] [PubMed]
  19. B. Portier, F. Pardo, P. Bouchon, R. Haïdar, and J.-L. Pelouard, “Fast modal method for crossed grating computation, combining finite formulation of maxwell equations with polynomial approximated constitutive relations,” J. Opt. Soc. Am. A 30, 573–581 (2013).
    [Crossref]
  20. C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haïdar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett. 99, 241104 (2011).
    [Crossref]
  21. R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
    [Crossref]
  22. P. T. Leung, S. Y. Liu, and K. Young, “Completeness and orthogonality of quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3057–3067 (1994).
    [Crossref] [PubMed]
  23. R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, 1996).
  24. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, Inc., 2001).
  25. T. Estruch, J. Jaeck, F. Pardo, S. Derelle, J. Primot, J.-L. Pelouard, and R. Haïdar, “Perfect extinction in subwave-length dual metallic transmitting gratings,” Opt. Lett. 36, 3160–3162 (2011).
    [Crossref] [PubMed]
  26. V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Matrix fabry-perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36, 1704–1706 (2011).
    [Crossref] [PubMed]
  27. C.J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4, 379–440 (2012).
    [Crossref]

2013 (2)

2012 (4)

2011 (5)

2010 (3)

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[Crossref] [PubMed]

R. Haïdar, G. Vincent, S. Collin, N. Bardou, N. Guérineau, J. Deschamps, and J.-L. Pelouard, “Free-standing subwavelength metallic gratings for snapshot multispectral imaging,” Appl. Phys. Lett. 96, 221104 (2010).
[Crossref]

2008 (1)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref] [PubMed]

2007 (2)

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[Crossref]

S. Collin, F. Pardo, and J.-L. Pelouard, “Waveguiding in nanoscale metallic apertures,” Opt. Express 15, 4310–4320 (2007).
[Crossref] [PubMed]

2000 (1)

P. Lalanne, J.-P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48 (2000).
[Crossref]

1999 (2)

T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24, 256–258 (1999).
[Crossref]

J. Porto, F. García-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).
[Crossref]

1998 (2)

T. W. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

H. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).
[Crossref]

1994 (1)

P. T. Leung, S. Y. Liu, and K. Young, “Completeness and orthogonality of quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3057–3067 (1994).
[Crossref] [PubMed]

1992 (1)

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[Crossref]

1990 (1)

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref] [PubMed]

Astilean, S.

P. Lalanne, J.-P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48 (2000).
[Crossref]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[Crossref] [PubMed]

Badano, G.

Bagby, J. S.

Bardou, N.

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Boreman, G. D.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Bouchon, P.

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Brun, M.

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Campillo, A. J.

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, 1996).

Chang, R. K.

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, 1996).

Chang-Hasnain, C. J.

Chang-Hasnain, C.J.

C.J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4, 379–440 (2012).
[Crossref]

Chase, C.

Collin, S.

de Lamaestre, R. E.

Derelle, S.

Deschamps, J.

R. Haïdar, G. Vincent, S. Collin, N. Bardou, N. Guérineau, J. Deschamps, and J.-L. Pelouard, “Free-standing subwavelength metallic gratings for snapshot multispectral imaging,” Appl. Phys. Lett. 96, 221104 (2010).
[Crossref]

Dupuis, C.

Ebbesen, T. W.

T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24, 256–258 (1999).
[Crossref]

T. W. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

H. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).
[Crossref]

Estruch, T.

García-Vidal, F.

J. Porto, F. García-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).
[Crossref]

Ghaemi, H.

H. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).
[Crossref]

T. W. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Ghenuche, P.

Gravrand, O.

Grupp, D. E.

T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24, 256–258 (1999).
[Crossref]

H. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).
[Crossref]

Guérineau, N.

R. Haïdar, G. Vincent, S. Collin, N. Bardou, N. Guérineau, J. Deschamps, and J.-L. Pelouard, “Free-standing subwavelength metallic gratings for snapshot multispectral imaging,” Appl. Phys. Lett. 96, 221104 (2010).
[Crossref]

Haïdar, R.

E. Sakat, S. Héron, P. Bouchon, G. Vincent, F. Pardo, S. Collin, J.-L. Pelouard, and R. Haïdar, “Metal-dielectric bi-atomic structure for angular-tolerant spectral filtering,” Opt. Lett. 38, 425–427 (2013).
[Crossref] [PubMed]

B. Portier, F. Pardo, P. Bouchon, R. Haïdar, and J.-L. Pelouard, “Fast modal method for crossed grating computation, combining finite formulation of maxwell equations with polynomial approximated constitutive relations,” J. Opt. Soc. Am. A 30, 573–581 (2013).
[Crossref]

E. Sakat, G. Vincent, P. Ghenuche, N. Bardou, C. Dupuis, S. Collin, F. Pardo, R. Haïdar, and J.-L. Pelouard, “Free-standing guided-mode resonance band-pass filters: from 1d to 2d structures,” Opt. Express 20, 13082–13090 (2012).
[Crossref] [PubMed]

E. Sakat, G. Vincent, P. Ghenuche, N. Bardou, S. Collin, F. Pardo, J.-L. Pelouard, and R. Haïdar, “Guided mode resonance in subwavelength metallodielectric free-standing grating for bandpass filtering,” Opt. Lett. 36, 3054–3056 (2011).
[Crossref] [PubMed]

C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haïdar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett. 99, 241104 (2011).
[Crossref]

T. Estruch, J. Jaeck, F. Pardo, S. Derelle, J. Primot, J.-L. Pelouard, and R. Haïdar, “Perfect extinction in subwave-length dual metallic transmitting gratings,” Opt. Lett. 36, 3160–3162 (2011).
[Crossref] [PubMed]

R. Haïdar, G. Vincent, S. Collin, N. Bardou, N. Guérineau, J. Deschamps, and J.-L. Pelouard, “Free-standing subwavelength metallic gratings for snapshot multispectral imaging,” Appl. Phys. Lett. 96, 221104 (2010).
[Crossref]

Halas, N. J.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[Crossref]

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref] [PubMed]

Hazart, J.

Héron, S.

Hugonin, J.-P.

P. Lalanne, J.-P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48 (2000).
[Crossref]

Jaeck, J.

C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haïdar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett. 99, 241104 (2011).
[Crossref]

T. Estruch, J. Jaeck, F. Pardo, S. Derelle, J. Primot, J.-L. Pelouard, and R. Haïdar, “Perfect extinction in subwave-length dual metallic transmitting gratings,” Opt. Lett. 36, 3160–3162 (2011).
[Crossref] [PubMed]

Johnson, T. W.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Karagodsky, V.

Kim, T. J.

Koechlin, C.

C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haïdar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett. 99, 241104 (2011).
[Crossref]

Lafosse, X.

C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haïdar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett. 99, 241104 (2011).
[Crossref]

Lal, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[Crossref]

Lalanne, P.

P. Lalanne, J.-P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48 (2000).
[Crossref]

Le Perchec, J.

Lee, S.-S.

Leung, P. T.

P. T. Leung, S. Y. Liu, and K. Young, “Completeness and orthogonality of quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3057–3067 (1994).
[Crossref] [PubMed]

Lezec, H.

T. W. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

H. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).
[Crossref]

Lezec, H. J.

Link, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[Crossref]

Liu, S. Y.

P. T. Leung, S. Y. Liu, and K. Young, “Completeness and orthogonality of quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3057–3067 (1994).
[Crossref] [PubMed]

Lyandres, O.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref] [PubMed]

Magnusson, R.

Moharam, M. G.

Möller, K. D.

P. Lalanne, J.-P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48 (2000).
[Crossref]

Nicoletti, S.

Oh, S.-H.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Olmon, R. L.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Palamaru, M.

P. Lalanne, J.-P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48 (2000).
[Crossref]

Pardo, F.

B. Portier, F. Pardo, P. Bouchon, R. Haïdar, and J.-L. Pelouard, “Fast modal method for crossed grating computation, combining finite formulation of maxwell equations with polynomial approximated constitutive relations,” J. Opt. Soc. Am. A 30, 573–581 (2013).
[Crossref]

E. Sakat, S. Héron, P. Bouchon, G. Vincent, F. Pardo, S. Collin, J.-L. Pelouard, and R. Haïdar, “Metal-dielectric bi-atomic structure for angular-tolerant spectral filtering,” Opt. Lett. 38, 425–427 (2013).
[Crossref] [PubMed]

E. Sakat, G. Vincent, P. Ghenuche, N. Bardou, C. Dupuis, S. Collin, F. Pardo, R. Haïdar, and J.-L. Pelouard, “Free-standing guided-mode resonance band-pass filters: from 1d to 2d structures,” Opt. Express 20, 13082–13090 (2012).
[Crossref] [PubMed]

E. Sakat, G. Vincent, P. Ghenuche, N. Bardou, S. Collin, F. Pardo, J.-L. Pelouard, and R. Haïdar, “Guided mode resonance in subwavelength metallodielectric free-standing grating for bandpass filtering,” Opt. Lett. 36, 3054–3056 (2011).
[Crossref] [PubMed]

C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haïdar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett. 99, 241104 (2011).
[Crossref]

T. Estruch, J. Jaeck, F. Pardo, S. Derelle, J. Primot, J.-L. Pelouard, and R. Haïdar, “Perfect extinction in subwave-length dual metallic transmitting gratings,” Opt. Lett. 36, 3160–3162 (2011).
[Crossref] [PubMed]

S. Collin, F. Pardo, and J.-L. Pelouard, “Waveguiding in nanoscale metallic apertures,” Opt. Express 15, 4310–4320 (2007).
[Crossref] [PubMed]

Park, C.-H.

Pelouard, J.-L.

E. Sakat, S. Héron, P. Bouchon, G. Vincent, F. Pardo, S. Collin, J.-L. Pelouard, and R. Haïdar, “Metal-dielectric bi-atomic structure for angular-tolerant spectral filtering,” Opt. Lett. 38, 425–427 (2013).
[Crossref] [PubMed]

B. Portier, F. Pardo, P. Bouchon, R. Haïdar, and J.-L. Pelouard, “Fast modal method for crossed grating computation, combining finite formulation of maxwell equations with polynomial approximated constitutive relations,” J. Opt. Soc. Am. A 30, 573–581 (2013).
[Crossref]

E. Sakat, G. Vincent, P. Ghenuche, N. Bardou, C. Dupuis, S. Collin, F. Pardo, R. Haïdar, and J.-L. Pelouard, “Free-standing guided-mode resonance band-pass filters: from 1d to 2d structures,” Opt. Express 20, 13082–13090 (2012).
[Crossref] [PubMed]

E. Sakat, G. Vincent, P. Ghenuche, N. Bardou, S. Collin, F. Pardo, J.-L. Pelouard, and R. Haïdar, “Guided mode resonance in subwavelength metallodielectric free-standing grating for bandpass filtering,” Opt. Lett. 36, 3054–3056 (2011).
[Crossref] [PubMed]

C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haïdar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett. 99, 241104 (2011).
[Crossref]

T. Estruch, J. Jaeck, F. Pardo, S. Derelle, J. Primot, J.-L. Pelouard, and R. Haïdar, “Perfect extinction in subwave-length dual metallic transmitting gratings,” Opt. Lett. 36, 3160–3162 (2011).
[Crossref] [PubMed]

R. Haïdar, G. Vincent, S. Collin, N. Bardou, N. Guérineau, J. Deschamps, and J.-L. Pelouard, “Free-standing subwavelength metallic gratings for snapshot multispectral imaging,” Appl. Phys. Lett. 96, 221104 (2010).
[Crossref]

S. Collin, F. Pardo, and J.-L. Pelouard, “Waveguiding in nanoscale metallic apertures,” Opt. Express 15, 4310–4320 (2007).
[Crossref] [PubMed]

Pendry, J.

J. Porto, F. García-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).
[Crossref]

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[Crossref] [PubMed]

Portier, B.

Porto, J.

J. Porto, F. García-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).
[Crossref]

Primot, J.

Raschke, M. B.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Rochat, N.

Sakat, E.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, Inc., 2001).

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Shah, N. C.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref] [PubMed]

Shelton, D.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Slovick, B.

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, Inc., 2001).

Thio, T.

T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24, 256–258 (1999).
[Crossref]

H. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).
[Crossref]

T. W. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Van Duyne, R. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref] [PubMed]

Vincent, G.

Wang, S. S.

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Wolff, P.

T. W. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Yang, W.

C.J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4, 379–440 (2012).
[Crossref]

Yoon, Y.-T.

Young, K.

P. T. Leung, S. Y. Liu, and K. Young, “Completeness and orthogonality of quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3057–3067 (1994).
[Crossref] [PubMed]

Zhao, J.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

C.J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4, 379–440 (2012).
[Crossref]

Appl. Phys. Lett. (3)

C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haïdar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett. 99, 241104 (2011).
[Crossref]

R. Haïdar, G. Vincent, S. Collin, N. Bardou, N. Guérineau, J. Deschamps, and J.-L. Pelouard, “Free-standing subwavelength metallic gratings for snapshot multispectral imaging,” Appl. Phys. Lett. 96, 221104 (2010).
[Crossref]

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

P. Lalanne, J.-P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48 (2000).
[Crossref]

J. Opt. Soc. Am. A (2)

Nat. Mater. (3)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref] [PubMed]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[Crossref] [PubMed]

Nat. Photonics (1)

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[Crossref]

Nature (1)

T. W. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. A (1)

P. T. Leung, S. Y. Liu, and K. Young, “Completeness and orthogonality of quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3057–3067 (1994).
[Crossref] [PubMed]

Phys. Rev. B (2)

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86, 235147 (2012).
[Crossref]

H. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).
[Crossref]

Phys. Rev. Lett. (1)

J. Porto, F. García-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).
[Crossref]

Other (2)

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, 1996).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, Inc., 2001).

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Figures (5)

Fig. 1
Fig. 1 Optical response of a metal-dielectric GMR filter. (a) Schematic of the freestanding GMR filter (surrounded by air). The geometrical parameters are: grating period d = 2 μm, SiC layer thickness td = 700 nm, metal thickness tm = 100 nm and slit width a = 250 nm. (b) Transmission spectra at normal incidence of the metal-dielectric structure considering all the diffracted orders (solid line) and considering only the three first diffracted orders (dashed line). (c) Definition of the S-matrices used for the transmission spectrum calculations. Contour plots of the magnetic field distributions of the overall field H y sum and the field contributions H y 0, H y ± 1, H y 0 , ± 1 and H y evan .: (d) at λa = 4.65 μm and (e) at λb = 4.04 μm.
Fig. 2
Fig. 2 Scalar expression for the transmitted intensity. (a) Plot of the scalar expression using Eq. (4) (black dashed line) separated in two terms: term proportional to 1/1 − da (light blue line) and term proportional to 1/1 − db (red line). (b) Plot of the two complex eigenvalues da and db of the loop matrix M.
Fig. 3
Fig. 3 Validation of the symmetry criterion. (a) Schematic of three freestanding GMR structures A, B and C. For the structures A and B, the gold grating period is d = 2 μm, the SiC layer thickness is td = 700 nm, the gold grating slit width is a = 250 nm and the gold grating thickness is tm = 100 nm. For the structure C, the gold grating period is d = 2 μm; the SiC layer is divided in two parts of thickness t = 350 nm and t2 = 320 nm; the gold gratings are different, the upper one having a thickness tm = 100 nm and a slit width a = 250 nm, and the lower one a thickness tm2 = 60 nm and slit width a2 = 350 nm. (b) Modules and arguments of coefficients d212 and d232 corresponding to the structures A, B and C. (c) Transmission spectra at normal incidence of the structures A, B and C calculated using Eq. (2).
Fig. 4
Fig. 4 Determinant as a function of wavelength of the 2 × 2 matrix IM compared to the numerically-calculated expression (1 − |da|eiδkaα)(1 − |db|eiδkbβ).
Fig. 5
Fig. 5 Symmetrisation of GMR filters on a sapphire substrate of refractive 1.7. (a) Schematic of three GMR structures A, B′ and C′. The structure B′ has the same geometrical parameters than the structure B. For the structure C′, the gold grating period is d = 2 μm; the SiC layer is divided in two parts of thickness t = 350 nm and t2 = 230 nm; the gold gratings are different, the upper one having a thickness tm = 100 nm and a slit width a = 250 nm, and the lower one a thickness tm2 = 50 nm and slit width a2 = 290 nm. (b) Modules and arguments of coefficients d212 and d232 corresponding to the structures A, B′ and C′. (c) Transmission spectra at normal incidence of the structures A, B′ and C′ calculated using equation (2).

Equations (9)

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S 31 = S 32 P 1 / 2 ( k = 0 P 1 / 2 S 212 P S 232 P 1 / 2 ) k ) P 1 / 2 S 21 ,
S 31 = S 32 P 1 / 2 ( I P 1 / 2 S 212 P S 232 P 1 / 2 ) 1 P 1 / 2 S 21 ,
S 31 = S 32 P 1 / 2 Π ( I D ) 1 Π 1 P 1 / 2 S 21 .
S 31 = ( Π 0 a p 0 1 / 2 s 0 β + Π 1 a p 1 1 / 2 s 1 β ) 1 1 d a ( Π a 0 p 0 1 / 2 s 0 α + Π a 1 p 1 1 / 2 s 1 α ) + ( Π 0 b p 0 1 / 2 s 0 β + Π 1 b p 1 1 / 2 s 1 β ) 1 1 d b ( Π b 0 p 0 1 / 2 s 0 α + Π b 1 p 1 1 / 2 s 1 α )
T = | S 31 | 2 T a + T b ,
Q = k 0 2 | d a | 1 / 2 1 | d a | α
δ d a = ( δ Π a 1 ) P 1 / 2 S 212 P 1 / 2 P 2 1 / 2 S 232 P 2 1 / 2 Π a + Π a 1 ( δ P 1 / 2 ) S 212 P 1 / 2 P 2 1 / 2 S 232 P 2 1 / 2 Π a + Π a 1 P 1 / 2 ( δ S 212 ) P 1 / 2 P 2 1 / 2 S 232 P 2 1 / 2 Π a + Π a 1 P 1 / 2 S 212 ( δ P 1 / 2 ) P 2 1 / 2 S 232 P 2 1 / 2 Π a + Π a 1 P 1 / 2 S 212 P 1 / 2 ( δ P 2 1 / 2 ) S 232 P 2 1 / 2 Π a + Π a 1 P 1 / 2 S 212 P 1 / 2 P 2 1 / 2 ( δ S 232 ) P 2 1 / 2 Π a + Π a 1 P 1 / 2 S 212 P 1 / 2 P 2 1 / 2 S 232 ( δ P 1 / 2 ) Π a + Π a 1 P 1 / 2 S 212 P 1 / 2 P 2 1 / 2 S 232 P 2 1 / 2 ( δ Π a ) + o ( δ d a ) .
det ( I M ) = 0 .
Q = k 0 2 | r | 1 / 2 1 | r | ( 2 n d t d ) ,

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