Abstract

We report the study of a resonant bandpass filter made of a very thin subwavelength metal patch array coupled to a high index dielectric waveguide. The spectral properties of those filters can easily be tuned by playing on the lateral dimensions of the grating. They exhibit high and narrow transmission peaks together with very good rejection of light out of the pass-band and low angular dependance. An experimental demonstration using standard large scale silicon microelectronics processes is presented in the mid infrared spectral range. This concept of filters can easily be scaled throughout the optical spectrum, and can be integrated within focal plane arrays of various imaging technologies, down to visible wavelengths.

© 2011 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
  22. R. Luebbers and B. Munk, “Some effects of dielectric loading on periodic slot arrays,” IEEE Trans. Antennas Propag. 26, 536–542(1978).
    [CrossRef]
  23. V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of sub-wavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71, 235117 (2005).
    [CrossRef]
  24. S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (4)

W.-D. Li and S. Y. Chou, “Solar-blind deep-UV band-pass filter (250–350 nm) consisting of a metal nano-grid fabricated by nanoimprint lithography,” Opt. Express 18, 931–937 (2010).
[CrossRef] [PubMed]

Q. Chen and D. R. S. Cumming, “High transmission and low color cross-talk plasmonic color filters using triangular-lattice hole arrays in aluminum films,” Opt. Express 18, 14056–14062 (2010).
[CrossRef] [PubMed]

T. Xu, Y.-K. Wu, X. Luo, and L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).
[CrossRef] [PubMed]

R. Rodríguez-Berral, F. Mesa, and F. Medina, “Circuit model for a periodic array of slits sandwiched between two dielectric slabs,” Appl. Phys. Lett. 96, 161104 (2010).
[CrossRef]

2009 (1)

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filters in both transmission and reflection with metal/dielectric thin films,” Opt. Comm. 282, 242–246 (2009).
[CrossRef]

2008 (4)

J. L. Zhang, W. D. Shen, P. Gu, Y. G. Zhang, H. T. Jiang, and X. Liu, “Omnidirectional narrow bandpass filter based on metal-dielectric thin films,” Appl. Opt. 47, 6285–6290 (2008).
[CrossRef] [PubMed]

Z. Sun and Qi Lin, “Study of a Fabry–Perot-like microcavity with sandwiched metallic gratings for tunable filter arrays,” IEEE Photon. Technol. Lett. 20, 1157–1159 (2008).
[CrossRef]

G. J. Hawkins, R. E. Sherwood, B. M. Barrett, M. Wallace, H. J. B. Orr, K. Matthews, and S. Bisht, “High-performance infrared narrow-bandpass filters for the Indian National Satellite System meteorological instrument (INSAT-3D),” Appl. Opt. 47, 2346–2356 (2008).
[CrossRef] [PubMed]

G. Vincent, S. Collin, N. Bardou, J.-L. Pelouard, and R. Haïda, “Large-area dielectric and metallic freestanding gratings for midinfrared optical filtering applications,” J. Vac. Sci. Technol. B 26, 1852–1855 (2008).
[CrossRef]

2007 (2)

D. Crouse and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427 (2007).
[CrossRef] [PubMed]

C.-Y. Chen, M.-W. Tsai, T.-H. Chuang, Y.-T. Chang, and S.-C. Lee, “Extraordinary transmission through a silver film perforated with cross shaped hole arrays in a square lattice,” Appl. Phys. Lett. 91, 063108 (2007).
[CrossRef]

2006 (1)

2005 (2)

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of sub-wavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71, 235117 (2005).
[CrossRef]

A. Barbara, J. Le Perchec, P. Quémerais, T. López-Ríos, and N. Rochat, “Experimental evidence of efficient cavity modes excitation in metallic gratings by attenuated total reflection,” J. Appl. Phys. 98, 033705 (2005).
[CrossRef]

2004 (1)

K. Jefimovs, T. Vallius, V. Kettunen, M. Kuittinen, J. Turunen, and P. Vahimaa, “Inductive grid filters for rejection of infrared radiation,” J. Mod. Opt. 51, 1651–1661 (2004).

2003 (2)

H. A. Smith, M. Rebbert, and O. Sternberg, “Designer infrared filters using stacked metal lattices,” Appl. Phys. Lett. 82, 3605–3607 (2003).
[CrossRef]

S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).
[CrossRef]

2002 (1)

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

2001 (1)

2000 (1)

B. A. Munk, Frequency Selective Surfaces (Wiley-Interscience, 2000).
[CrossRef]

1998 (1)

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[CrossRef]

1995 (1)

1993 (1)

1989 (1)

1983 (1)

1978 (1)

R. Luebbers and B. Munk, “Some effects of dielectric loading on periodic slot arrays,” IEEE Trans. Antennas Propag. 26, 536–542(1978).
[CrossRef]

1977 (1)

R. McPhedran and D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[CrossRef]

1967 (1)

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[CrossRef]

1954 (1)

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80, 195415 (2009).

Barbara, A.

A. Barbara, J. Le Perchec, P. Quémerais, T. López-Ríos, and N. Rochat, “Experimental evidence of efficient cavity modes excitation in metallic gratings by attenuated total reflection,” J. Appl. Phys. 98, 033705 (2005).
[CrossRef]

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Bardou, N.

G. Vincent, S. Collin, N. Bardou, J.-L. Pelouard, and R. Haïda, “Large-area dielectric and metallic freestanding gratings for midinfrared optical filtering applications,” J. Vac. Sci. Technol. B 26, 1852–1855 (2008).
[CrossRef]

Barrett, B. M.

Bisht, S.

Bock, J. J.

Bower, J. E.

Bustarret, E.

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Carr, D. W.

Chan, H. B.

Chang, Y.-T.

C.-Y. Chen, M.-W. Tsai, T.-H. Chuang, Y.-T. Chang, and S.-C. Lee, “Extraordinary transmission through a silver film perforated with cross shaped hole arrays in a square lattice,” Appl. Phys. Lett. 91, 063108 (2007).
[CrossRef]

Chase, S. T.

Chen, C.-Y.

C.-Y. Chen, M.-W. Tsai, T.-H. Chuang, Y.-T. Chang, and S.-C. Lee, “Extraordinary transmission through a silver film perforated with cross shaped hole arrays in a square lattice,” Appl. Phys. Lett. 91, 063108 (2007).
[CrossRef]

Chen, Q.

Chou, S. Y.

Chuang, T.-H.

C.-Y. Chen, M.-W. Tsai, T.-H. Chuang, Y.-T. Chang, and S.-C. Lee, “Extraordinary transmission through a silver film perforated with cross shaped hole arrays in a square lattice,” Appl. Phys. Lett. 91, 063108 (2007).
[CrossRef]

Cirelli, R. A.

Collin, S.

G. Vincent, S. Collin, N. Bardou, J.-L. Pelouard, and R. Haïda, “Large-area dielectric and metallic freestanding gratings for midinfrared optical filtering applications,” J. Vac. Sci. Technol. B 26, 1852–1855 (2008).
[CrossRef]

Crouse, D.

Cumming, D. R. S.

Darmanyan, S. A.

S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).
[CrossRef]

Dawes, D. H.

Depine, R.

Ebbesen, T. W.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[CrossRef]

Ferry, E.

Ghaemi, H. F.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[CrossRef]

Grupp, D. E.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[CrossRef]

Gu, P.

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filters in both transmission and reflection with metal/dielectric thin films,” Opt. Comm. 282, 242–246 (2009).
[CrossRef]

J. L. Zhang, W. D. Shen, P. Gu, Y. G. Zhang, H. T. Jiang, and X. Liu, “Omnidirectional narrow bandpass filter based on metal-dielectric thin films,” Appl. Opt. 47, 6285–6290 (2008).
[CrossRef] [PubMed]

Guo, L. J.

T. Xu, Y.-K. Wu, X. Luo, and L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).
[CrossRef] [PubMed]

Haïda, R.

G. Vincent, S. Collin, N. Bardou, J.-L. Pelouard, and R. Haïda, “Large-area dielectric and metallic freestanding gratings for midinfrared optical filtering applications,” J. Vac. Sci. Technol. B 26, 1852–1855 (2008).
[CrossRef]

Hawkins, G. J.

Jefimovs, K.

K. Jefimovs, T. Vallius, V. Kettunen, M. Kuittinen, J. Turunen, and P. Vahimaa, “Inductive grid filters for rejection of infrared radiation,” J. Mod. Opt. 51, 1651–1661 (2004).

Jiang, H. T.

Joseph, R. D.

Kawada, M.

Keshavareddy, P.

Kettunen, V.

K. Jefimovs, T. Vallius, V. Kettunen, M. Kuittinen, J. Turunen, and P. Vahimaa, “Inductive grid filters for rejection of infrared radiation,” J. Mod. Opt. 51, 1651–1661 (2004).

Klemens, F.

Kuittinen, M.

K. Jefimovs, T. Vallius, V. Kettunen, M. Kuittinen, J. Turunen, and P. Vahimaa, “Inductive grid filters for rejection of infrared radiation,” J. Mod. Opt. 51, 1651–1661 (2004).

Lange, A. E.

Le Perchec, J.

A. Barbara, J. Le Perchec, P. Quémerais, T. López-Ríos, and N. Rochat, “Experimental evidence of efficient cavity modes excitation in metallic gratings by attenuated total reflection,” J. Appl. Phys. 98, 033705 (2005).
[CrossRef]

Lee, S.-C.

C.-Y. Chen, M.-W. Tsai, T.-H. Chuang, Y.-T. Chang, and S.-C. Lee, “Extraordinary transmission through a silver film perforated with cross shaped hole arrays in a square lattice,” Appl. Phys. Lett. 91, 063108 (2007).
[CrossRef]

Lezec, H. J.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[CrossRef]

Li, W.-D.

Lin, Qi

Z. Sun and Qi Lin, “Study of a Fabry–Perot-like microcavity with sandwiched metallic gratings for tunable filter arrays,” IEEE Photon. Technol. Lett. 20, 1157–1159 (2008).
[CrossRef]

Liu, X.

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filters in both transmission and reflection with metal/dielectric thin films,” Opt. Comm. 282, 242–246 (2009).
[CrossRef]

J. L. Zhang, W. D. Shen, P. Gu, Y. G. Zhang, H. T. Jiang, and X. Liu, “Omnidirectional narrow bandpass filter based on metal-dielectric thin films,” Appl. Opt. 47, 6285–6290 (2008).
[CrossRef] [PubMed]

Lochbihler, H.

Lomakin, V.

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of sub-wavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71, 235117 (2005).
[CrossRef]

Lopez-Rios, T.

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

López-Ríos, T.

A. Barbara, J. Le Perchec, P. Quémerais, T. López-Ríos, and N. Rochat, “Experimental evidence of efficient cavity modes excitation in metallic gratings by attenuated total reflection,” J. Appl. Phys. 98, 033705 (2005).
[CrossRef]

Luebbers, R.

R. Luebbers and B. Munk, “Some effects of dielectric loading on periodic slot arrays,” IEEE Trans. Antennas Propag. 26, 536–542(1978).
[CrossRef]

Luo, X.

T. Xu, Y.-K. Wu, X. Luo, and L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).
[CrossRef] [PubMed]

Luo, Z.

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filters in both transmission and reflection with metal/dielectric thin films,” Opt. Comm. 282, 242–246 (2009).
[CrossRef]

Magnusson, R.

Marcet, Z.

Matsuhara, H.

Matthews, K.

Maystre, D.

R. McPhedran and D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[CrossRef]

McPhedran, R.

R. McPhedran and D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[CrossRef]

McPhedran, R. C.

Medina, F.

R. Rodríguez-Berral, F. Mesa, and F. Medina, “Circuit model for a periodic array of slits sandwiched between two dielectric slabs,” Appl. Phys. Lett. 96, 161104 (2010).
[CrossRef]

Mesa, F.

R. Rodríguez-Berral, F. Mesa, and F. Medina, “Circuit model for a periodic array of slits sandwiched between two dielectric slabs,” Appl. Phys. Lett. 96, 161104 (2010).
[CrossRef]

Michielssen, E.

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of sub-wavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71, 235117 (2005).
[CrossRef]

Miner, J.

Munk, B.

R. Luebbers and B. Munk, “Some effects of dielectric loading on periodic slot arrays,” IEEE Trans. Antennas Propag. 26, 536–542(1978).
[CrossRef]

Munk, B. A.

B. A. Munk, Frequency Selective Surfaces (Wiley-Interscience, 2000).
[CrossRef]

Orr, H. J. B.

Oulton, R. F.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80, 195415 (2009).

Pai, C. S.

Pelouard, J.-L.

G. Vincent, S. Collin, N. Bardou, J.-L. Pelouard, and R. Haïda, “Large-area dielectric and metallic freestanding gratings for midinfrared optical filtering applications,” J. Vac. Sci. Technol. B 26, 1852–1855 (2008).
[CrossRef]

Quémerais, P.

A. Barbara, J. Le Perchec, P. Quémerais, T. López-Ríos, and N. Rochat, “Experimental evidence of efficient cavity modes excitation in metallic gratings by attenuated total reflection,” J. Appl. Phys. 98, 033705 (2005).
[CrossRef]

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Rebbert, M.

H. A. Smith, M. Rebbert, and O. Sternberg, “Designer infrared filters using stacked metal lattices,” Appl. Phys. Lett. 82, 3605–3607 (2003).
[CrossRef]

Richards, P. L.

Rochat, N.

A. Barbara, J. Le Perchec, P. Quémerais, T. López-Ríos, and N. Rochat, “Experimental evidence of efficient cavity modes excitation in metallic gratings by attenuated total reflection,” J. Appl. Phys. 98, 033705 (2005).
[CrossRef]

Rodríguez-Berral, R.

R. Rodríguez-Berral, F. Mesa, and F. Medina, “Circuit model for a periodic array of slits sandwiched between two dielectric slabs,” Appl. Phys. Lett. 96, 161104 (2010).
[CrossRef]

Shen, W.

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filters in both transmission and reflection with metal/dielectric thin films,” Opt. Comm. 282, 242–246 (2009).
[CrossRef]

Shen, W. D.

Sherwood, R. E.

Smith, H. A.

H. A. Smith, M. Rebbert, and O. Sternberg, “Designer infrared filters using stacked metal lattices,” Appl. Phys. Lett. 82, 3605–3607 (2003).
[CrossRef]

Sternberg, O.

H. A. Smith, M. Rebbert, and O. Sternberg, “Designer infrared filters using stacked metal lattices,” Appl. Phys. Lett. 82, 3605–3607 (2003).
[CrossRef]

Sun, X.

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filters in both transmission and reflection with metal/dielectric thin films,” Opt. Comm. 282, 242–246 (2009).
[CrossRef]

Sun, Z.

Z. Sun and Qi Lin, “Study of a Fabry–Perot-like microcavity with sandwiched metallic gratings for tunable filter arrays,” IEEE Photon. Technol. Lett. 20, 1157–1159 (2008).
[CrossRef]

Tanner, D. B.

Taylor, J. A.

Thio, T.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[CrossRef]

Tibuleac, S.

Tsai, M.-W.

C.-Y. Chen, M.-W. Tsai, T.-H. Chuang, Y.-T. Chang, and S.-C. Lee, “Extraordinary transmission through a silver film perforated with cross shaped hole arrays in a square lattice,” Appl. Phys. Lett. 91, 063108 (2007).
[CrossRef]

Turunen, J.

K. Jefimovs, T. Vallius, V. Kettunen, M. Kuittinen, J. Turunen, and P. Vahimaa, “Inductive grid filters for rejection of infrared radiation,” J. Mod. Opt. 51, 1651–1661 (2004).

Ulrich, R.

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[CrossRef]

Vahimaa, P.

K. Jefimovs, T. Vallius, V. Kettunen, M. Kuittinen, J. Turunen, and P. Vahimaa, “Inductive grid filters for rejection of infrared radiation,” J. Mod. Opt. 51, 1651–1661 (2004).

Vallius, T.

K. Jefimovs, T. Vallius, V. Kettunen, M. Kuittinen, J. Turunen, and P. Vahimaa, “Inductive grid filters for rejection of infrared radiation,” J. Mod. Opt. 51, 1651–1661 (2004).

Vincent, G.

G. Vincent, S. Collin, N. Bardou, J.-L. Pelouard, and R. Haïda, “Large-area dielectric and metallic freestanding gratings for midinfrared optical filtering applications,” J. Vac. Sci. Technol. B 26, 1852–1855 (2008).
[CrossRef]

Wallace, M.

Whitbourn, L. B.

Woo, K.

Wu, Y.-K.

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T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80, 195415 (2009).

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T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80, 195415 (2009).

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[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(a) Elementary structure of the proposed band-pass optical filter, with a design suitable for the mid-infrared range. Here, aluminium thickness is h = 50nm. (b) Theoretical reflectivity and transmission spectra of the system calculated with RCWA (response independent of the incident light polarization), and (c) map of the normalized magnetic field modulus at the resonance λ 0 = 4.2μm, showing the excitation of a hybrid mode, i.e. a waveguide mode coupled to a harmonic surface wave (see text).

Fig. 2
Fig. 2

(a) Calculated dispersion diagrams of the resonance mode leading to the high transmission peak of figure 1, for TE and TM polarizations. Relatively weak sensitivity to the incidence angle θ is observed. (b) Transmission spectra for different air gap w, at fixed period P = 1.8μm. We note a trade-off between the maximum signal we can reach and the quality factor of the resonance. (c) Case of an array of rectangular (non-square) metal patches with a period P 1 = 1.8μm in one direction, and P = 1.5μm in the other, with w = 200 nm. The filter becomes sensitive to polarization, and can then exhibit a dual-band type behavior.

Fig. 3
Fig. 3

Pictures of the Si wafer on which a series of infrared filter matrix were fabricated on LETI semi-industrial platform. SEM image of the subwavelength aluminium grating (corners of the metal patches are rounded), and sketch of the multi-layer stack with experimental parameters (filters are separated from the substrate by an adaptative low index quarter-wavelength layer to make the filters like optically isolated).

Fig. 4
Fig. 4

(a) Experimental FTIR transmission spectra of filters, essentially differing by their period (see Table 1 for detailed dimensions of each one and corresponding optical properties). Period is increasing with the spectral position of the transmission maximum. (b) same experimental data, but in log scale, illustrating the large rejection experimentally achieved with those filters.

Fig. 5
Fig. 5

(a) Comparison of the experimental FTIR transmission spectrum of a filter centered at 4μm with that obtained by FDTD simulation for the actual structure (see text for details). (b) Same data in log scale illustrating the rejection performance.

Fig. 6
Fig. 6

(a) Effect of round shape of the patch corners on the transmission lineshape. (b) Effect of the slope of the patch edges on the transmission lineshape.

Fig. 7
Fig. 7

Measured transmission of the filter discussed in Figures 5 and 6, as function of the wavelength, incidence angle and polarization (TE: left, TM: right).

Tables (1)

Tables Icon

Table 1 Table summarizing the main geometrical and optical characteristics of the filters whose transmission spectra are shown in the figure 4.

Equations (15)

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λ 0 / n 1 < P < 2 λ 0 / n 1 ,
n 1 > 1.7 ,
h 1 λ 0 / 2 n 1 .
H y out ( x , z ) = m = + T m e ikn out ( γ m out x + β m out ( z h g ) ) ,
Tr = ( m n in β m out n out cos θ | T m | 2 ) ,
T m = ( w / P ) S m Γ ( β m g / n g ) q m + Z p m ,
p m = cos X m + i Y n sin ( X m ) ,
q m = Y n cos X m + i sin ( X m ) ,
Γ = [ ( 1 Z ) ( 1 D g + ) + ( 1 + Z ) ( 1 + D g ) ] V ( 1 + D in ) ( 1 + D g ) e ikh ( 1 D in + ) ( 1 D g + ) e ikh ,
D g ± = ( 1 ± Z ) w P m = + p m S m 2 q m ( β m g / n g ) + Z p m ,
D in ± = ( 1 ± Z ) w P m = + S m 2 β m in + Z ,
V = 2 S 0 cos θ cos θ + Z 2.
Γ = V cos ( kh ) ( D in + D g ) + i sin ( kh ) ( 1 + D in D g ) .
Tr = n in n out | ( w / P ) Γ cos ( k n g h g ) / n out + i sin ( k n g h g ) / n g + Z p 0 | 2 .
q m ( β m g / n g ) + Z p m 0 ,

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