Unidirectional electromagnetic mode travels along one direction and immunes from backscattering by breaking Lorentz reciprocity. As free from backscattering, it is widely used in laser and optical communication systems. In addition, the unidirectional electromagnetic mode can be realized by introducing a magnetic field to break the time inversion symmetry. The most promising method to realize a unidirectional electromagnetic mode is to use surface magnetoplasmons (SMPs) which exist in the interface between the gyro-electric and dielectric media, and an external magnetic field can be applied to separate the dispersion curves of wave vectors in both directions. When the frequency falls into the gap of the dispersion curves, the electromagnetic wave propagates in one direction. In terahertz bands, achievements on an SMPs-based unidirectional electromagnetic mode are reported in terms of the interface of the semiconductor InSb and the dielectric medium with a normal magnetic field magnitude. While in near-infrared bands, it is difficult to produce SMPs by using magneto-optical materials since the ratio of the non-diagonal term to the diagonal term of the dielectric tensor under the normal magnetic field magnitude is only about 10^-3. In order to solve this problem, a meta-material is employed to enhance the ratio of the non-diagonal term to the diagonal term of the dielectric tensor, and SMPs in a 1.1 eV band are achieved at the interface of the proposed meta-material and the dielectric material.

A physical model of a unidirectional waveguide based on SMPs was presented in this paper. The model is an interface consisting of meta-material-based gyro-electric and dielectric materials (PMMA, with a dielectric coefficient of 2.28). According to the continuity condition, a dispersion equation was obtained. The relationship between the dielectric tensor of the gyro-dielectric material and the dielectric coefficient was theoretically analyzed when SMPs existed. Since the non-diagonal term of the dielectric tensor of normal magneto-optical materials is much smaller than the diagonal term, the diagonal term of the dielectric tensor of the meta-material-based gyro-electric materials is close to the dielectric coefficient of the dielectric materials. In order to construct meta-material-based gyro-electric materials, cerium-doped yttrium iron garnet (Ce∶YIG) and silver with a negative dielectric coefficient were employed. Due to the low absorption and large non-diagonal dielectric coefficient under the normal magnitude of magnetic field (0.2 T), Ce∶YIG was widely used in the near-infrared bands. According to the effective dielectric tensor theory, the dielectric tensor of the meta-material-based gyro-electric materials with different proportions could be obtained. With a ratio of 0.108/0.892 (Ag/Ce∶YIG), the dispersion curves of the SMPs were given, from which it is obvious that the unidirectional band exists around a frequency of 1.1 eV.

The characteristics of unidirectional propagation were simulated and analyzed in this paper. The electric field distribution along the interface is shown in Fig. 4 by placing an excitation source in the interface. The electric field rapidly decays in the opposite direction, and there is almost no backscattering. In other words, the structure is immune to backscattering. Since the electric field in the opposite direction is suppressed within a distance of less than half a wavelength, it can be used to design optical isolators in sub-wavelength size, which is of great significance for improving photonic integration. By setting protrusions and depressions on the interface, the robustness of the unidirectional waveguide to interface defects is verified. As shown in Fig. 5, although the electric field amplitude oscillates violently at the setup defect, the surface wave quickly returns to the interface after bypassing the defect and converts back into its original amplitude size with little energy loss. It shows that the unidirectional waveguide has good robustness as the interface defects do not affect the transmission of surface waves or weaken the unidirectional transmission characteristics. This property is helpful to reduce the process requirements during the manufacturing of photonic devices. SMPs-based unidirectional waveguides not only show positive robustness to defects but also have excellent unidirectional characteristics for waveguides with large-angle bending. Fig. 6 shows the transmission characteristics of a structure at four right angles, and the SMPs are still well constrained at the interface after passing through the structure at four right angles without introducing backscattering. This exclusive property is critical for designing optical devices with complex structures.

The dispersion equation of the dielectric/gyro-electric model of the SMPs was theoretically analyzed, and the relationship requirement between the dielectric tensor and the dielectric coefficient was obtained, so as to achieve unidirectional transmission of the SMPs. According to the effective tensor theory, a meta-material with the combination of Ce∶YIG/Ag was proposed to construct a gyro-electric material, so as to satisfy the requirement. The dispersion characteristics of the SMPs were analyzed, and the transmission characteristics were simulated by a finite element method. An SMPs-based unidirectional waveguide operating in the near-infrared band was constructed by two materials of Ce∶YIG/Ag with a magnetic field with normal magnitude (0.2 T). The unidirectional waveguide structure with defects was also simulated, and the results show that the SMPs-based unidirectional waveguide has good robustness.