Properties of one-way propagation inthe magneto-optical planar waveguide
Authors: Li Hang-Tian , Wang Zhi , Wang Hui-Ying , Cui Can , Li Zhi-Yong ,   Key Laboratory of Luminescence and Optical Information, Ministry of Education, Institute of Optical Information, School of Science, Beijing Jiaotong University, Beijing 100044, China,   State Key Laboratory on Integrated Optoelectronics, Beijing 100083, China
Published: December 2020

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.