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Analysis of the Bloch mode spectra of surface polaritonic crystals in the weak and strong coupling regimes: grating-enhanced transmission at oblique incidence and suppression of SPP radiative losses

D. Gérard, L. Salomon, F. de Fornel, and A. V. Zayats

Open Access Open Access

Abstract

The Bloch mode spectrum of surface plasmon polaritons (SPPs) on a finite thickness metal film has been analyzed in the regimes of weak and strong coupling between SPP modes on the opposite film interfaces. The SPP mode dispersion and associated field distributions have been studied. The results have been applied to the description of the light transmission through thick and thin periodically structured metal films at oblique incidence. In contrast to normal incidence, all SPP Bloch modes on a grating structure participate in the resonant photon tunnelling leading to the transmission enhancement. However, at the angle of incidence corresponding to the crossing of different symmetry film SPP Bloch modes, the far-field transmission is suppressed despite the enhanced near-field transmission. The combined SPP mode consisting of the two film SPPs having different symmetries that is achieved at the crossing frequency exhibits no radiative losses on a structured surface.

©2004 Optical Society of America

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Figures (10)
Fig. 1.
Fig. 1. Schematic of a nanostructured film.

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Fig. 2.
Fig. 2. Schematics of the band-gap structure near the second SPP band-gap in the case of weak (a) and strong (b) coupling regimes: (f +, f -) film SPP Bloch modes, (g +,g -) SPP modes in the different Brillouin zones.

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Fig. 3.
Fig. 3. (Colour) Reflection (a), absorption (b), and transmission (c) spectra of the nanostructured silver film (H=100 nm) at different angles of incidence: (black) θ=0°, (blue) θ=2°, (red) θ=4°. The structure consists of the silver ridges (h=20 nm, d=250 nm and D=500 nm) on both film interfaces.

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Fig. 4.
Fig. 4. Dispersion of the SPP Bloch modes in the vicinity of the second band-gap on a periodic structure in a weak coupling regime. The parametres of the structure are the same as in Fig. 3

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Fig. 5.
Fig. 5. (Colour) The magnetic field Hz distribution in the near-field region of the metallic structure at the wavelengths corresponding to (a) lower (λ=564 nm) and (b) upper (λ=506 nm) branches of the SPP Bloch modes around the second band-gap in a weak-coupling regime. Angle of incidence is θ=4°. The parametres of the film are the same as in Fig. 3. Geometry of the film is also shown.

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Fig. 6.
Fig. 6. (Colour) Reflection (a), absorption (b), and transmission (c) spectra of the nanostructured silver film (H=40 nm) at different angles of incidence: (black) θ=0°, (blue) θ=1°, (green) θ=2°, (red) θ=4°. The structure consists of the silver ridges (h=20 nm, d=250 nm and D=500 nm) on both film interfaces.

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Fig. 7.
Fig. 7. Dispersion of the SPP Bloch modes in the vicinity of the second band-gap on a periodic structure in a strong coupling regime. The parametres of the structure are the same as in Fig. 6.

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Fig. 8.
Fig. 8. (Colour) (a) The magnetic field Hz distribution in the near-field region of the metallic structure and (b) the intensity distribution of the transmitted field over the structure at the wavelength corresponding to the crossing of the SPP modes of different symmetries in a strong-coupling regime (λ=539 nm, θ=2°). The parametres of the structure are the same as in Fig. 6.

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Fig. 9.
Fig. 9. (Colour) The magnetic field Hz (a,b) and electric field Ex (c,d) distributions in the near-field of the metallic structure at the wavelengths corresponding to (a,c) f - g + (λ=527 nm) and (b,d) f + g + (λ=552 nm) SPP Bloch modes at around the second-band gap in a strong-coupling regime. Angle of incidence is θ=0°. The parametres of the structure are the same as in Fig. 6. Geometry of the film is also shown.

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Fig. 10.
Fig. 10. (Colour) The magnetic field Hz distribution in the near-field region of the metallic structure at the wavelengths corresponding to (a) f - g - (λ=493 nm), (b) f - g + (λ=555 nm), (c) f + g - (λ=527 nm), and (d) f + g + (λ=579 nm) film SPP Bloch modes around the respective second-band gaps in a strong-coupling regime. Angle of incidence is θ=4°. The parametres of the structure are the same as in Fig. 6. Geometry of the film is also shown.

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