Surface plasmon is a new technology that can break the diffraction limit and manipulate light on a sub-wavelength scale. It is considered one of the most promising means to shrink traditional optoelectronic devices to the micro-nano level. Surface plasmonic waveguides are fundamental components for miniaturized and compact optoelectronic devices and integrated optical circuits. Terahertz (THz) plasmonic waveguides are fundamental components for transmitting THz signals and constructing various THz functional devices, such as optical switches, optical modulation, filtering, and near-field imaging. This is of significance for realizing high-density integration of terahertz functional devices and high-speed ultra-wideband terahertz communication. Graphene features excellent optoelectronic properties and tunability. In the terahertz to the mid-infrared band, graphene plasmons (GPs) with low loss, strong confinement, and tunability provide a platform for the realization of miniaturized, highly integrated, and dynamically tunable terahertz waveguides and devices. Although various graphene-based hybrid plasmonic waveguides (GHPWs) have been proposed, the optical confinement properties of these structures still need to be improved. Additionally, it is necessary to systematically evaluate the waveguide performance because of the mutual restriction between confinement and loss. We propose a graphene V-groove hybrid plasmonic waveguide and study the influence of geometric structure parameters on the characteristics and transmission characteristics of hybrid plasmonic modes. In addition, the behavior of hybrid modes caused by changes in the chemical potential of graphene is analyzed, and the crosstalk between two adjacent hybrid structures is discussed in detail. This study provides theoretical references for the design and research of dynamically tunable terahertz sub-wavelength photonic devices.

Finite element analysis method is adopted to calculate the eigenmode of the graphene-based V-groove hybrid waveguide system. In the convergence analysis, the calculation regions in x- and y-direction are assumed to be large enough to ensure an accurate eigenvalue. The mode effective index and propagation length are determined by the real and imaginary parts of the eigenvalue, respectively.

The proposed graphene V-groove hybrid plasmonic waveguide features excellent mode confinement by optimizing the groove geometry and adjusting the chemical potential of graphene. First, the effect of GaAs height on the mode properties of fundamental hybrid plasmons guided by the graphene V-groove hybrid plasmonic waveguide is discussed. In Fig. 4, when the groove height hw=4.9μm and the GaAs height is reduced from 30 μm to 6 μm, the normalized mode area Aeff/A0 is as small as 2.0×10^-3; the corresponding propagation length is 63.4 μm; the figure of merit is 50.4. Second, the effect o f the groove size on the mode properties of fundamental hybrid plasmons is studied. In Fig. 5, when the groove height hw=4.9μm and the groove angle is increased from 30° to θmax, the normalized mode area Aeff/A0 is as small as 1.7×10^-3; the corresponding propagation length is 81.2 μm; the figure of merit is 69.5. Third, we discuss the effect of the chemical potential of graphene on the mode properties of fundamental hybrid plasmons. In Fig. 6, when the groove height hw=4.9μm and chemical potential of graphene is reduced from 1 eV to 0.2 eV, the normalized mode area Aeff/A0 is as small as 8.6×10^-5; the corresponding propagation length is 24.5 μm; the figure of merit is 93.5. Finally, the crosstalk between two graphene V-groove hybrid plasmonic waveguides is discussed by changing the groove size and chemical potential of graphene. In Fig. 8, when the angle of the groove is 90° and the chemical potential of graphene is 0.3 eV, the minimum distance without crosstalk between the two graphene V-groove hybrid plasmonic waveguides could be reduced to 22 μm. This can be attributed to the decreasing chemical potential, which leads to the decrease in the mode field area of hybrid plasmons (consistent with results in Fig. 6). Finally, the overlapping area of the optical field is decreased and the coupling effect between the two hybrid waveguides is weakened, thus resulting in crosstalk decrease.

In this paper, a graphene V-groove hybrid plasmonic waveguide is studied, and the influence of geometric parameters and graphene chemical potential on the fundamental hybrid plasmon mode supported by the hybrid structure is analyzed. The effective area of the hybrid mode can be effectively compressed by increasing the groove and reducing the chemical potential of graphene, and the effective mode area is reduced by two orders of magnitude compared with the structure without grooves. Although the transmission length is reduced, the figure of merit is increased by 34.5%-88.5%. In addition, the crosstalk between two graphene-V-groove hybrid plasmonic waveguides placed side by side is analyzed, and the minimum distance without crosstalk between the two waveguides could be reduced to 22 μm by optimizing the groove geometry and adjusting the chemical potential of graphene. This paper provides a theoretical reference for the development and performance optimization of dynamically tunable terahertz subwavelength waveguides.