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Timestamp: 2019-04-20 05:20:13+00:00

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We show that the enhancement of the transverse magneto-optical Kerr effect of a smooth magnetic dielectric film covered by a noble metal grating, is strongly dependent on the precise geometry of this grating. Up till now this magnetoplasmonic enhancement was solely attributed to a nonreciprocal shift of the dispersion of the surface plasmon polariton resonances at the interface with the magnetized substrate. It is demonstrated that by hybridization of surface and cavity resonances in this 1D plasmonic grating, the transverse Kerr effect can be further enhanced, extinguished or even switched in sign and that without inverting or modifying the film’s magnetization. This strong geometrical dispersion and the accompanying anomalous sign change of the magneto-plasmonic effects in such systems has never been considered before, and might find interesting applications in sensing and nanophotonics.
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Fig. 1 Coordinate system and schematic representation of studied structure: gold grating with a period Λ and a thickness h1 on a magneto-optic garnet substrate in transversal configuration with incident plane wave in y −z plane at the incident angle φ0 and with s- or p-polarization.
Fig. 2 Specular reflectivity (bottom line) and associated TMOKE spectrum (top line) of p-polarized light incident on the grating structure in Fig. 1 with Λ = 500 nm, h1 = 150 nm and r =20 nm.
Fig. 3 Distribution of square of the magnitude of the magnetic field component Hx at 0.901 eV (A), at 1.014 eV (B), at 1.318 eV (C), at 1.589 eV (D), at 2.035 eV (E). Field distribution is plotted for grating with the period Λ =500 nm, the thickness h1 = 150 nm, the air-slit width r =20 nm and the incidence of p-polarization at φ0 =10°.
Fig. 4 Left: gold/air/gold waveguide and its extension into resonant cavity by introducing of the garnet and air media is shown schematically. Right: field profile of guided mode for thickness of the air gap r = 20 nm, the photon energy 1.318 eV, and the effective index of guided mode neff =1.966 + 0.0367i.
Fig. 5 Left: Simulated dispersion of reflection for the grating with various thickness h1 from 30 nm to 600 nm and the fixed period Λ = 500 nm. Right: spectral position and geometrical dispersion of resonant modes calculated with analytical dispersion models Eqs. (8,7) and Eqs. (9,10).
Fig. 6 Left: Simulated dispersion of reflection for the grating with various period Λ from 200 nm to 900 nm and fixed thickness h1 = 200 nm,. Right: spectral position and geometrical dispersion of resonant modes calculated with analytical dispersion models Eq. (8,7) and Eq. (9,10).
Fig. 7 Distribution of square of the magnitude of the magnetic field component Hx. Left subplot: coupled resonant mode of +1st plasmon and cavity mode for the photon energy 0.89 eV and the grating thickness 200 nm. Right subplot: coupled resonant mode of −1st plasmon and cavity mode for the photon energy 0.98 eV and the grating thickness 200 nm.
Fig. 8 Shift of SPP by TMOKE: comparison between the exact solution from the Eq. (12) (circle dots) and the linear approximation model Eq. (13) (dashed line) calculated at the photon energy 1eV. The green line represents pure SPP mode.
Fig. 9 Magnetooptical shift and dispersion of SPP modes described by Eqs. (12,8) and dispersion curves of cavity modes Eqs. (9,10).
Fig. 10 Top left: detail of TMOKE spectral dependence ΔRp for the grating thickness h1 from 30 nm to 600 nm (left) and period Λ = 500 nm. Top right: variance of the TMOKE spectral position and amplitude for chosen grating thicknesses h1 = 140, 170 and 200 nm. Bottom left: switching of the TMOKE sign at fixed photon energy 0.98 eV and 1.01 eV by variation of the thickness of the grating. Bottom right: dependence of the TMOKE amplitude on the grating thickness.
Fig. 11 Left: detail of TMOKE spectral dependence ΔRp for the grating period Λ from 300 nm to 700 nm (left) and thickness h1 = 200 nm. Right: TMOKE response for chosen grating period Λ = 500, 550, 600 and 650 nm.

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