FDTD simulation of enhanced Faraday effect in plasmonic composite structures with rectangularly arranged Au particles.
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2018 IEEE International Magnetic Conference (INTERMAG), Seite 1-2. (April 2018)

Summary form only given. Magneto-optical (MO) effects enable non-reciprocal optical components like optical circulators and isolators as well as a magneto-optical spatial light modulator with switching speeds superior to a digital micromirror and a liquid crystal device. To develop a magneto-optical device with high performance, it is desirable to use materials with large rotation angles and small extinction coefficients. In other approaches introduction of nanostructures, magnetophotonic crystals 1 and localized surface plasmon resonance (LSPR) 2 has been shown to provide enhancement of the Faraday effect for distinct wavelengths. This work shows how rectangular arrays of gold (Au) particles embedded into thin films of bismuth-substituted yttrium iron garnet (Bi:YIG) offer different phenomena in comparison with the square arrays previously studied 3 4 5. This enhancement of Faraday rotation was first observed in samples fabricated and characterized experimentally 6. 2. Simulation approach Our finite-difference time-domain (FDTD) simulations focus on a periodic array of spherical Au particles embedded into a fi lm of Bi:YIG on a fused quartz substrate, as shown in fi gure 1. The structure uses a rectangular unit cell with a width of 200 nm and a depth of 200 to 300 nm. A diameter of 120 nm was chosen for the Au particles. The dimensions are chosen this way to observe the enhancement of the Faraday effect, as similar to previous experimental samples 6. The magnetic fi eld is oriented perpendicular to the surface. Large rotation of several tens of degrees of linearly polarized light incident at au angle of 45° between the x and Y axes of the unit cell is mainly caused by the structure effect of the rectangular array of Au particles. To determine the Faraday rotation (FR), it is necessary to remove this structure effect from the results through simulations for both positive and negative magnetic fi elds, which is the same procedure as the conventional measurement method of Faraday rotation angle. 3. Results and Discussion From components of the electrical field of the transmitted light, it was observed that this large rotation cau be attributed to different transmission minima for the x- and y- polarized components of the fi eld. Figure 2 shows FR and transmission of a 200 by 250 nm array after removal of the effects mentioned above. While enhanced FRs were observed for distinct structure geometries for incident polarizations of 0'' and 90'', transmissivity minima coincident with the Faraday rotation maxima were caused by the excitation of surface plasmon resonance for the polarized incident light waves in x- and y -directions. However, for diagonally polarized incident light at 45'', the FR maximum does not coincide with auy minima, which is not observed in the square arranged particles. At 45'' the peak in FR occurs at the wavelength where the structure -induced polarization rotation becomes zero. FDTD simulations with varied Bi:YIG layer thickness and particle spacing in y -direction were performed in search of the optimum geometry. Taking into account the transmission as well through computing a fi gure of merit as the product of the absolute value of the FR and the square root of the transmission is a well -established method to gauge the utility of magneto -optical materials and devices. There appears to be a specific Bi:YIG layer thickness for each y -direction array spacing where significant Faraday rotation enhancement happens, which can be attributed to coupling of the plasmon and waveguide modes of the structure. The wavelength where this maximum enhancement occurs was found to increase linearly with the y -direction particle spacing when the Bi:YIG layer thickness is chosen optimally. A Bi:YIG layer thickness of 160 nm and a particle spacing of 260 nm in y -direction appeared to provide the highest fi gure of merit, and thus seem favorable for experiments. 4. Conclusion The extraordinary enhancement of the Faraday effect in thin garnet fi lms through rectangular Au particle arrays, as previously observed experimentally, has been thoroughly examined and visualized by simulation. The non -square geometry can help overcoming the spectral coincidence of high magneto -optical response and low transmissivity, known as a major problem in the efforts to achieve high-performance, thin MO devices through utilization of LSPR. Experimental analysis based the ideal geometric parameters determined by simulation is ongoing in order to corroborate the simulation results as well as prior experiments.
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