Surface magnetoplasmons (SMPs) is a kind of near-field electromagnetic wave, which propagates at the interface of dielectricand magneto-optical material under the action of biased magnetic field. Because SMPs have excellent anti-interference and backscattering-immune properties, it has attracted wide attention of researchers in recent years, but there are still many problems in the design of waveguide structures. When electromagnetic waves propagate in magneto-optical materials, the faraday rotation effect makes the bias magnetic field and the magnetic field vector (or electrical displacement vector) not in the same direction, so the anti-angle elements of the second-order matrix of magnetic permeability (or dielectric constant) are asymmetric. This asymmetrymakes electromagnetic waves non-reciprocal when propagating in specific directions in magneto-optical materials, and can even achieve one-way propagation in a certain frequency range. In this paper, a structure of three-layerplanar waveguide with silver, silicon, and magneto-optical material is studied. SMPs propagate at the interface between silicon and magneto-optical materials. This work numerically calculates the dispersion relation of the waveguide and the band gap of the magneto-optical material. It is found that both the fundamental mode and the higher-order mode of SMPs have one-way propagation characteristics in forward or backward directionwithin a specific frequency range. The dispersion relation of the planar waveguides with gyromagnetic material andgyroelectricmaterial are calculated respectively. As a result, the thickness of silicon layer and the external magnetic field have significant influence on bulk mode and the one-way propagation region of SMPs. By increasing the thickness of the silicon layer or increasing the intensity of the magnetic field, the higher-order mode can appear at the lower frequency region, thus compressing the one-way propagation region or even losing the one-way propagation mode. The one-way propagation bandwidth of planar waveguideswith gyromagnetic material YIG and gyroelectric material InSbare calculated. Bycalculating the dispersion relation of the waveguide SMPs and the band gap of the magneto-optical material for each group of magnetic field and the thickness of Si, the colormap of YIG waveguideand InSbwaveguide under 400–2000Oe magnetic field and 0.1–1 T magnetic field are obtained. As a result, the one-way mode of YIG waveguide appears in GHz band, and the maximum bandwidth for both forward and backward one-way propagation is 2.45 GHz. While, the one-way mode of InSbwaveguide appears in THz band, the maximum one-way propagation bandwidth in forward and backward directions are 3.9 THz and 3.12 THz. The research results in this paper are of great significance for the design and fabrication of non-reciprocal waveguides with one-waypropagation characteristics.
A C-band rectangular waveguide with gyroelectric semiconductor is designed to study the non-reciprocal propagation characteristics of surface magnetoplasmons (SMPs), which are generated by an external magnetic field. The effective refractive index method is used to obtain the effective refractive index and transverse electric field distribution of the waveguide, and a two-dimensional rectangular waveguide is approximately regarded as a combination of two one-dimensional planar waveguides. The dispersion equation of planar waveguide with <inline-formula><tex-math id="M2">\begin{document}$ {\rm{E}}_{mn}^x$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20190109_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20190109_M2.png"/></alternatives></inline-formula> mode in rectangular waveguide is derived. The influences of the structural parameters of rectangular waveguide and the refractive index of material on the non-reciprocal dispersion relation and time-delay characteristics are analyzed by numerical method. Due to the effect of external magnetic field, the off-diagonal elements of dielectric tensor in magnetic photonic crystal are changed. The generation of electrical anisotropy leads the time reversal symmetry to be broken. As a result, the dispersion curves of the rectangular waveguide are asymmetric with respect to propagation constant, and the complete one-way transmission of SMPs can be realized in the asymmetric frequency region. The dispersion curve tends to be a dispersion curve of planar waveguide as the width of rectangular waveguide increases, but the non-reciprocal frequency range is approximately unchanged. The width of the core region and the refractive index of the side material have a significant influence on the non-reciprocal dispersion characteristics: the group velocity of SMPs decreases with <i>ω</i> and propagation constant decreasing. The group velocity is related to the waveguide width, propagation constant and the operating wavelength. The relationship between the normalized group velocity and the width of the waveguide separately operating at 1530, 1550 and 1565 nm are studied. The group velocity is relatively slow when the width of waveguide’s core region is between 140 nm and 233.5 nm, and the minimum group velocity reaches 5.43 × 10<sup>-2</sup><i>c</i>. As for the slow light effect, the rectangular waveguide is better than planar waveguide. The rectangular waveguide has a large engineering tolerance in the width of core region, which is 93.5 nm. In addition, the dispersion curves of the rectangular waveguide with SiO<sub>2</sub>, Air, Au and Ag as the left and right cladding layers are calculated. As a result, the group velocity is proportional to the refractive index of the side material in the <i>y</i> direction of the rectangular waveguide. The slow light effect is the most obvious when the material is silver, and the minimum transmission speed can reach 2.8 × 10<sup>-3</sup><i>c</i>.
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