## 1 Introduction  
Terahertz (THz) waves, located between millimeter radio waves and far infrared waves, have been widely investigated in the fields of spectroscopy, imaging, and communications [1; 2; 3; 4]. In particular, the THz waveguide has become a hot research topic, and semiconductor based plasmonic waveguides [5], pure dielectric waveguides [6; 7; 8], and noble metal plasmon waveguides [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20] have been proposed to guide THz waves. However, in the THz range, surface plasmon effects are very weak, which leads to relatively poor confinement, thus hindering the applications in the subwavelength scale. Although the strong mode confinement could be achieved, it usually results in a limited propagation length [21; 22].  
Recent reports show that graphene [23] can also support plasmons [24; 25], which provides an alternative approach to transmitting THz waves [26]. Compared with the metal plasmon waveguides, GP waveguides show very strong modal field confinement, and the chemical potential of graphenecould be tuned to improve the waveguiding performance [25]. So far, graphene sheet [27], graphene gap waveguide [28], V-shaped graphene waveguide [29], graphene-based parallel-plate waveguide [30], dielectric loaded graphene waveguide [31], graphene hybrid waveguides [32; 33; 34; 35; 36], and graphene-coated dielectric nanowires [37; 38; 39; 40; 41; 42; 43; 44] have been proposed and investigated. Among them, graphene hybrid waveguides have shown very good waveguiding performances in the THz band. [PERSON] et al. [32] proposed a graphene hybrid plasmonic waveguide with a propagation distance of approximately 127 \(\upmu\)m, and a normalized mode area of approximately \(10^{-2}\) at 3 THz. Later, a symmetric hybrid plasmonic waveguide [33] was proposed to achieve a propagation length of 26.7 mm at 10 THz, while the normalized mode area is still around \(10^{-2}\). To further downscale the mode area, [PERSON] et al. [34; 35] proposed two graphene-based hybrid plasmonic waveguides, which could simultaneously achieve a very small normalized modal area of approximately \(10^{-4}\)-\(10^{-3}\) and a propagation length of approximately several hundreds of micrometers at 3 THz. Recently, graphene-coated nanowires have attracted lots of research interest and been investigated mainly in the mid-infrared band [37; 38; 39; 40; 41; 42; 43; 44]. In the THz band, a graphene-coated nanowire with a drop-shaped cross section was suggested for low loss waveguiding with ultra-strong mode confinement [44]. Although the propagation distance has been enhanced to millimeter range, these structures are relatively complicated for practical implementations.  
Here, we present that a simple graphene-coated elliptical nanowire (GCENW) could simultaneously achieve a very small normalized modal area of approximately \(10^{-4}\)-\(10^{-3}\) and a propagation length of several hundreds of micrometers. Meanwhile, in addition to the simple structure, the GCENW could provide two focal spots with the same size. Results show that the ratio of _b/a_ has significant influence on mode properties, increasing _b/a_ could simultaneously achieve both a long propagation length and a very small full width at half maximum (FWHM) of the focal spots. By adjusting the chemical potential of graphene, the waveguiding properties could also be tuned to achieve better performance.