Abstract

A metal-dielectric subwavelength grating structure was investigated for making single-peak narrow linewidth optical reflection filters in the near-infrared region. The subwavelength grating filter structure consists of a one-dimensional periodic array of metal (gold) and dielectric (Al2O3) elements on a dielectric substrate. Optimized reflection filters have a single reflection peak with ~10 nm linewidth in the infrared region over a wide spectral band. Finite-difference time-domain (FDTD) simulations and multipole analysis show that the narrow linewidth reflection is due to the coupling of the Rayleigh anomaly wave to the quadrupole plasmon resonance mode of the subwavelength metal-dielectric grating. Additionally, it was found that the contrast of the indices of refraction of two dielectric materials in the subwavelength structure is critical for realizing optical filter effect.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2016 (2)

G. Chen, K. J. Lee, and R. Magnusson, “Periodic photonic filters: theory and experiment,” Opt. Eng. 55(3), 037108 (2016).
[Crossref]

X. Liu, G. Liu, G. Fu, M. Liu, and Z. Liu, “Monochromatic filter with multiple manipulation approaches by the layered all-dielectric patch array,” Nanotechnology 27(12), 125202 (2016).
[Crossref] [PubMed]

2015 (2)

L. Duempelmann, A. Luu-Dinh, B. Gallinet, and L. Novotny, “Four-fold color filter based on plasmonic phase retarder,” ACS Photonics 3(2), 190–196 (2015).
[Crossref]

T. Kondo, S. Ura, and R. Magnusson, “Design of guided-mode resonance mirrors for short laser cavities,” J. Opt. Soc. Am. A 32(8), 1454–1458 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (3)

A. B. Evlyukhin, C. Reinhardt, E. Evlyukhin, and B. N. Chichkov, “Multipole analysis of light scattering by arbitrary-shaped nanoparticles on a plane surface,” J. Opt. Soc. Am. B 30(10), 2589–2598 (2013).
[Crossref]

B. Zeng, Y. Gao, and F. J. Bartoli, “Ultrathin nanostructured metals for highly transmissive plasmonic subtractive color filters,” Sci. Rep. 3(1), 2840 (2013).
[Crossref] [PubMed]

B. Yun, G. Hu, and Y. Cui, “Resonant mode analysis of the nanoscale surface plasmon polariton waveguide filter with rectangle cavity,” Plasmonics 8(2), 267–275 (2013).
[Crossref]

2012 (4)

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

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(23), 235147 (2012).
[Crossref]

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85(24), 245411 (2012).
[Crossref]

X. Buet, E. Daran, D. Belharet, F. Lozes-Dupuy, A. Monmayrant, and O. Gauthier-Lafaye, “High angular tolerance and reflectivity with narrow bandwidth cavity-resonator-integrated guided-mode resonance filter,” Opt. Express 20(8), 9322–9327 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (2)

2009 (4)

2008 (2)

B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for periodic targets: theory and tests,” J. Opt. Soc. Am. A 25(11), 2693–2703 (2008).
[Crossref] [PubMed]

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[Crossref] [PubMed]

2004 (1)

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

1997 (1)

1993 (1)

1907 (1)

L. Rayleigh, “III. Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14(79), 60–65 (1907).
[Crossref]

Auguié, B.

B. Auguié and W. L. Barnes, “Diffractive coupling in gold nanoparticle arrays and the effect of disorder,” Opt. Lett. 34(4), 401–403 (2009).
[Crossref] [PubMed]

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[Crossref] [PubMed]

Awatsuji, Y.

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

Barnes, W. L.

B. Auguié and W. L. Barnes, “Diffractive coupling in gold nanoparticle arrays and the effect of disorder,” Opt. Lett. 34(4), 401–403 (2009).
[Crossref] [PubMed]

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[Crossref] [PubMed]

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Bartoli, F. J.

B. Zeng, Y. Gao, and F. J. Bartoli, “Ultrathin nanostructured metals for highly transmissive plasmonic subtractive color filters,” Sci. Rep. 3(1), 2840 (2013).
[Crossref] [PubMed]

Belharet, D.

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(23), 235147 (2012).
[Crossref]

Borges, B.-H. V.

Boye, R. R.

Buet, X.

Carter, T. R.

Chan, C. T.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Chen, G.

G. Chen, K. J. Lee, and R. Magnusson, “Periodic photonic filters: theory and experiment,” Opt. Eng. 55(3), 037108 (2016).
[Crossref]

Chen, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Chichkov, B. N.

A. B. Evlyukhin, C. Reinhardt, E. Evlyukhin, and B. N. Chichkov, “Multipole analysis of light scattering by arbitrary-shaped nanoparticles on a plane surface,” J. Opt. Soc. Am. B 30(10), 2589–2598 (2013).
[Crossref]

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85(24), 245411 (2012).
[Crossref]

Clarkson, J.

Cui, Y.

B. Yun, G. Hu, and Y. Cui, “Resonant mode analysis of the nanoscale surface plasmon polariton waveguide filter with rectangle cavity,” Plasmonics 8(2), 267–275 (2013).
[Crossref]

Daran, E.

Devaux, E.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Dintinger, J.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Draine, B. T.

Duempelmann, L.

L. Duempelmann, A. Luu-Dinh, B. Gallinet, and L. Novotny, “Four-fold color filter based on plasmonic phase retarder,” ACS Photonics 3(2), 190–196 (2015).
[Crossref]

Ebbesen, T. W.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Evlyukhin, A. B.

A. B. Evlyukhin, C. Reinhardt, E. Evlyukhin, and B. N. Chichkov, “Multipole analysis of light scattering by arbitrary-shaped nanoparticles on a plane surface,” J. Opt. Soc. Am. B 30(10), 2589–2598 (2013).
[Crossref]

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85(24), 245411 (2012).
[Crossref]

Evlyukhin, E.

Fan, Z.

Fauchet, P.

Flatau, P. J.

Fu, G.

X. Liu, G. Liu, G. Fu, M. Liu, and Z. Liu, “Monochromatic filter with multiple manipulation approaches by the layered all-dielectric patch array,” Nanotechnology 27(12), 125202 (2016).
[Crossref] [PubMed]

Fu, X.

Gallinet, B.

L. Duempelmann, A. Luu-Dinh, B. Gallinet, and L. Novotny, “Four-fold color filter based on plasmonic phase retarder,” ACS Photonics 3(2), 190–196 (2015).
[Crossref]

Gao, H.

Gao, Y.

B. Zeng, Y. Gao, and F. J. Bartoli, “Ultrathin nanostructured metals for highly transmissive plasmonic subtractive color filters,” Sci. Rep. 3(1), 2840 (2013).
[Crossref] [PubMed]

Gauthier-Lafaye, O.

Giannini, V.

G. Vecchi, V. Giannini, and J. G. Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[Crossref]

Gray, S. K.

Guo, H.

Hatanaka, K.

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

Henzie, J.

Hu, G.

B. Yun, G. Hu, and Y. Cui, “Resonant mode analysis of the nanoscale surface plasmon polariton waveguide filter with rectangle cavity,” Plasmonics 8(2), 267–275 (2013).
[Crossref]

Inoue, J.

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

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(23), 235147 (2012).
[Crossref]

Kellogg, R. A.

Kemme, S. A.

Kintaka, K.

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

Kondo, T.

Lai, Z.

Lee, K. J.

Lee, M. H.

Lin, Z.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Liu, G.

X. Liu, G. Liu, G. Fu, M. Liu, and Z. Liu, “Monochromatic filter with multiple manipulation approaches by the layered all-dielectric patch array,” Nanotechnology 27(12), 125202 (2016).
[Crossref] [PubMed]

Liu, M.

X. Liu, G. Liu, G. Fu, M. Liu, and Z. Liu, “Monochromatic filter with multiple manipulation approaches by the layered all-dielectric patch array,” Nanotechnology 27(12), 125202 (2016).
[Crossref] [PubMed]

Liu, W.

Liu, X.

X. Liu, G. Liu, G. Fu, M. Liu, and Z. Liu, “Monochromatic filter with multiple manipulation approaches by the layered all-dielectric patch array,” Nanotechnology 27(12), 125202 (2016).
[Crossref] [PubMed]

Liu, Y.

Liu, Z.

X. Liu, G. Liu, G. Fu, M. Liu, and Z. Liu, “Monochromatic filter with multiple manipulation approaches by the layered all-dielectric patch array,” Nanotechnology 27(12), 125202 (2016).
[Crossref] [PubMed]

Lozes-Dupuy, F.

Luu-Dinh, A.

L. Duempelmann, A. Luu-Dinh, B. Gallinet, and L. Novotny, “Four-fold color filter based on plasmonic phase retarder,” ACS Photonics 3(2), 190–196 (2015).
[Crossref]

Magnusson, R.

Majima, T.

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

Mazulquim, D. B.

McMahon, J. M.

Monmayrant, A.

Muniz, L. V.

Murray, W. A.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Neto, L. G.

Ng, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Nishio, K.

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

Novotny, L.

L. Duempelmann, A. Luu-Dinh, B. Gallinet, and L. Novotny, “Four-fold color filter based on plasmonic phase retarder,” ACS Photonics 3(2), 190–196 (2015).
[Crossref]

Odom, T. W.

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(23), 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(23), 235147 (2012).
[Crossref]

Peters, D. W.

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(23), 235147 (2012).
[Crossref]

Rayleigh, L.

L. Rayleigh, “III. Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14(79), 60–65 (1907).
[Crossref]

Reinhardt, C.

A. B. Evlyukhin, C. Reinhardt, E. Evlyukhin, and B. N. Chichkov, “Multipole analysis of light scattering by arbitrary-shaped nanoparticles on a plane surface,” J. Opt. Soc. Am. B 30(10), 2589–2598 (2013).
[Crossref]

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85(24), 245411 (2012).
[Crossref]

Rivas, J. G.

G. Vecchi, V. Giannini, and J. G. Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[Crossref]

Samora, S.

Schatz, G. C.

Shao, J.

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(23), 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(23), 235147 (2012).
[Crossref]

Tibuleac, S.

Ura, S.

T. Kondo, S. Ura, and R. Magnusson, “Design of guided-mode resonance mirrors for short laser cavities,” J. Opt. Soc. Am. A 32(8), 1454–1458 (2015).
[Crossref] [PubMed]

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

Vecchi, G.

G. Vecchi, V. Giannini, and J. G. Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[Crossref]

Wang, S. S.

Wendt, J. R.

Winans, J.

Yi, K.

Yoon, J. W.

Yun, B.

B. Yun, G. Hu, and Y. Cui, “Resonant mode analysis of the nanoscale surface plasmon polariton waveguide filter with rectangle cavity,” Plasmonics 8(2), 267–275 (2013).
[Crossref]

Zeng, B.

B. Zeng, Y. Gao, and F. J. Bartoli, “Ultrathin nanostructured metals for highly transmissive plasmonic subtractive color filters,” Sci. Rep. 3(1), 2840 (2013).
[Crossref] [PubMed]

Zywietz, U.

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85(24), 245411 (2012).
[Crossref]

ACS Photonics (1)

L. Duempelmann, A. Luu-Dinh, B. Gallinet, and L. Novotny, “Four-fold color filter based on plasmonic phase retarder,” ACS Photonics 3(2), 190–196 (2015).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Express (1)

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

J. Opt. Soc. Am. A (3)

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

Nanotechnology (1)

X. Liu, G. Liu, G. Fu, M. Liu, and Z. Liu, “Monochromatic filter with multiple manipulation approaches by the layered all-dielectric patch array,” Nanotechnology 27(12), 125202 (2016).
[Crossref] [PubMed]

Nat. Photonics (1)

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Opt. Eng. (1)

G. Chen, K. J. Lee, and R. Magnusson, “Periodic photonic filters: theory and experiment,” Opt. Eng. 55(3), 037108 (2016).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Opt. Mater. Express (1)

Philos. Mag. (1)

L. Rayleigh, “III. Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14(79), 60–65 (1907).
[Crossref]

Phys. Rev. B (3)

G. Vecchi, V. Giannini, and J. G. Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[Crossref]

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85(24), 245411 (2012).
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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(23), 235147 (2012).
[Crossref]

Phys. Rev. Lett. (2)

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[Crossref] [PubMed]

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Plasmonics (1)

B. Yun, G. Hu, and Y. Cui, “Resonant mode analysis of the nanoscale surface plasmon polariton waveguide filter with rectangle cavity,” Plasmonics 8(2), 267–275 (2013).
[Crossref]

Sci. Rep. (1)

B. Zeng, Y. Gao, and F. J. Bartoli, “Ultrathin nanostructured metals for highly transmissive plasmonic subtractive color filters,” Sci. Rep. 3(1), 2840 (2013).
[Crossref] [PubMed]

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D. L. Forti, Transverse Stratified Structure for Tunable Beaming and Filtering at Terahertz Frequencies (The University of Alabama in Huntsville, 2016).

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic of the subwavelength metal-dielectric grating filter structure. (b) Reflection and transmission spectra of an optimized filter with grating period Λ = 1100 nm, w1 = 450 nm, w2 = 450 nm, and h = 270 nm. The inset shows the narrow band filter has a full-width at the half-maximum (FWHM) linewidth of 10 nm.
Fig. 2
Fig. 2 (a) Optical reflectance versus the wavelength and the index of refraction of the dielectric-1 when the dielectric-2 is air. (b) Optical reflectance versus the wavelength and the refractive index of dielectric-2 material, the white dash line indicates the refractive index of Al2O3 at 1915 nm (n = 1.74). The other structure parameters are Λ = 1100 nm, w1 = 450 nm, w2 = 450 nm and h = 270 nm.
Fig. 3
Fig. 3 Reflectance spectra of optical filters with different geometric parameters. (a) and (b) Reflectance spectrum versus grating height h with a fixed grating period Λ = 1100 nm, (c) and (d) Reflectance spectrum versus period Λ with a fixed grating height of h = 270 nm.
Fig. 4
Fig. 4 Reflection spectra of filters with different height and dielectric width ratio γ. (a) h = 270 nm, (b) h = 300 nm, (c) h = 350 nm, (d) h = 400 nm. (e) Designed narrow linewidth filters by varying the period Λ and the ratio γ of the widths of two dielectric materials with a fixed height. The peak wavelength ranges from 1800 nm to 2300 nm with FWHM linewidths less than 15 nm.
Fig. 5
Fig. 5 Calculated reflection spectra at different angles of incidence at: (a) h = 270 nm, (b) h = 300 nm, (c) h = 350 nm, (d) h = 400 nm. The subwavelength grating period is Λ = 1100 nm. The width of dielectric one (w1) and with of dielectric two (w2) are 450 nm.
Fig. 6
Fig. 6 (a) Electric field distribution in the filter structure at 1915 nm wavelength. (b) Magnetic field distribution at 1915 nm wavelength. (c) Electric field distribution at a non-resonance wavelength of 1850 nm. (d) Magnetic field distribution at the non-resonance wavelength of 1850 nm. The figures (a-d) show the field distributions in a unit cell of the structure. The scale bar is 200 nm for figures (a-d). (e) Calculated magnetic dipole moment my and the electric quadrupole moment Qxz versus wavelength. (f) Calculated electric dipole moment px versus wavelength plotted together with the reflectance spectrum.

Equations (4)

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Λ= w 1 + w 2 +2 w Au
p= ε 0 (ε( r j )1)E( r j ) ,
m= ω ε 0 (ε( r j )1) 2i ( r j r 0 )×E( r j ) = ω 2i ( r j r 0 )× p j ,
Q ^ = [( r j r 0 ) p j + p j ( r j r 0 )] ,

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