Terahertz (THz) waveguides are essential functional devices for the long-distance propagation and interconnection of THz waves; thus, they play an increasingly important role in THz applications, i.e., in wireless communications, medical imaging, and security inspections. To achieve high transmission efficiency and integration, various THz waveguides using different guiding mechanisms have been developed, including dielectric, photonic crystal, anti-resonance, and surface plasmonic waveguides. Recently, graphene-based hybrid plasmonic THz waveguides have attracted significant attention because of their tunable and flexible transmission. However, the inherent optical properties of two-dimensional graphene, such as the low absorption of incident waves and weak electromagnetic response, pose challenges in the design of high-performance waveguides. Emerging three-dimensional Dirac semimetals (3D DSMs) have high carrier mobilities and tunable energy band characteristics comparable to those of graphene, while overcoming the above-mentioned inherent shortcomings of graphene. In this study, we propose a tunable broadband hybrid plasmonic THz waveguide based on a 3D DSM dielectric ridge structure. The transmission characteristics are systematically simulated using the finite element method, and the effects of the structural parameters and Fermi energy of the DSM are analyzed.

A THz waveguide structure is designed in this study based on a 3D DSM hybrid plasmonic mechanism, which comprises a DSM layer, SiO₂ layer, and Si layer from top to bottom (Fig. 1). The corresponding thicknesses are optimized to be 4, 2, and 10 μm, respectively. First, the complex permittivity of the 3D DSM at different Fermi levels in the THz regime is calculated based on the Kubo formula and two-band model (Fig. 2). Finite element method-based simulations are performed to reveal the quantitative influences of the structural geometric parameters and DSM Fermi energy on the THz transmission characteristics, including the real part of the effective mode index, normalized mode area, propagation length, figure of merit, and propagation mode.

The simulated results show that the effective mode refractive index decreases and the normalized mode area increases with increasing dielectric gap height. Owing to the enhanced low-loss dielectric mode characteristics, the propagation length and figure of merit (FOM) increase with the gap height, and the 3D DSM plasmonic properties weaken as the frequency increases (Fig. 3). It can be observed from the mode-field diagram that the loss of the waveguide gradually decreases as the gap height increases, and most of the modes in the waveguide can be restricted from propagating at the tip of the rhombic Si region (Fig. 4). As the size of the rhombic Si medium increases, more modes propagate into the high-refractive-index Si medium, and the role of the dielectric mode increases. As the mixed mode confined by the 3D DSM layer is weakened, the effective mode refractive index and mode area increase, and the dielectric mode gradually becomes dominant in the mixed mode, causing an increase in the propagation length (Fig. 5). Finally, the influence of the Fermi level on the propagation characteristics is analyzed. As the Fermi level changes from 0.01 eV to 0.1 eV, the propagation length of the waveguide can be greatly tuned from 3.33×10² μm to 1.72×10⁴ μm with the maximum modulation depth of the propagation length up to 98.06%, and a modulation depth of more than 90% in the broad frequency range of 0.5?2.0 THz can be achieved (Fig. 7).

A tunable broadband THz waveguide based on a 3D DSM is demonstrated through numerical simulations. The transmission characteristics in response to the dielectric gap height, medium size, and Fermi level of 3D DSM are investigated. The simulated results show that as the gap height increases, the real parts of the effective mode refractive index, normalized mode area, and propagation length increase. The side length of the rhombus medium also has a certain impact on the propagation characteristics. Specifically, the real parts of the effective mode refractive index, mode area, and propagation length increase with the side length of the rhombus medium. The Fermi level has a significant effect on the propagation characteristics. As the Fermi level of the 3D DSM increases, the real part of the effective mode refractive index decreases, whereas the mode area and propagation length increase. As the Fermi level increases from 0.01 eV to 0.10 eV, the propagation length of the waveguide increases from 3.33×10² μm to 1.72×10⁴ μm, and the modulation depth of the propagation length exceeds 90% in the broadband working frequency of 0.5?2.0 THz. These findings provide an important reference for understanding the propagation mechanism of 3D DSM hybrid plasmonic waveguides, hence they are good candidates for various applications in tunable and broadband THz waveguides and modulators.