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4Goos-Hänchen shift spatially resolves magneto-optical Kerr effect enhancement in magnetoplasmonic crystals
A.Yu. Frolov1*, A.V. Makarova1, A.A. Nerovnaya1, D.N. Gulkin1, V.V. Popov1, A.A. Fedyanin1
1- Faculty of Physics, Lomonosov Moscow State University, Moscow 199991, Russia
Active control of the optical properties offers significant opportunities for applying optical devices in optical communications and computing. The magnetic field provides a versatile way to control light properties through well-known magneto-optical effects such as the Kerr and Faraday effects. They present a change in the intensity, polarization, and phase of light under an external magnetic field. However, the use of magneto-optical effects in light modulators is only possible with large-scale magnetooptical elements, due to the inherent small values of these effects.
The excitation of the surface plasmons (SPs), which are coupled oscillations of free electrons and light, can significantly enhance the magnitudes of magneto-optical effects and shrink the size of the magneto-optical elements to the nanoscale [2]. This is made possible by magnetoplasmonic crystals (MPCs), which are one- or two-dimensional, periodically structured surfaces or arrays of plasmonic nanoantennas, containing magnetic materials. However, in most studies on the resonant enhancement of magneto-optical effects, the spatial distribution of the reflected light intensity is not taken into account. In turn, reflected light can possess the Goos-Hänchen (GH) effect, which manifests itself as a lateral displacement of the reflected beam compared to the position determined by geometrical optics.
In this work, we have demonstrated that the application of a magnetic field in a transverse geometry results in a modulation of the spatial distribution of the light intensity of reflected beams in one-dimensional nickel magnetoplasmonic crystals (Figure 1) [3]. When the surface plasmon of the -1st order is excited, the Goos-Hänchen effect occurs, resulting in two reflected light beams that are separated by a distance d. It reaches d=15.3 ^m (18^). The application of a transverse magnetic field resulted in the modulation of the spatial distribution of reflected light intensity, as shown by the red and yellow curves. The observed change in the spatial distribution of light intensity under an external transverse magnetic field is referred to as the spatially resolved transverse magneto-optical Kerr effect [TMOKE(x)], which is defined as:
TMOKE(x) = 2
l(x,+H) - I(x,-H)
x 100% ,
i(x,+H) + i(x, —H)
where I(x,+H) and I(x,-H) are the spatial distributions of the reflected light intensity in the presence of an external transverse magnetic field in the opposite directions, respectively. We show that the observed lateral variation in intensity [TMOKE(x)] is several times greater (2.6 times) than in the case of conventional TMOKE measurements, which reveal the total change in reflected beam intensity under a magnetic field.
Fig. 1. The idea of the observation of the spatially resolved transverse magneto-optical Kerr effect [TMOKE(x)] under the Goos-Hänchen shift in a one-dimensional nickel magnetoplasmonic crystal.
The work is supported by the RSF grant 24-12-00210.
[1] A.K. Zvezdin and V.A. Kotov, Modern Magnetooptics and Magnetooptical Materials (CRC Press) (1997).
[2] J. Qin, et al, Nanophotonic devices based on magneto-optical materials: recent developments and applications, Nanophotonics, vol. 11, pp. 2639-2659 (2022).
[3] A.V. Makarova, et al, Goos-Hänchen shift spatially resolves magneto-optical Kerr effect enhancement in magnetoplasmonic crystals, vol. 11, pp. 1619-1626 (2024).
