Dispersion features of complex waves in a graphene-coated semiconductor nanowire

Abstract

Dispersion features of a graphene-coated semiconductor nanowire operating in the terahertz frequency band are consistently studied in the framework of a special theory of complex waves. Detailed classification of the waveguide modes was carried out based on the analysis of characteristics of the phase and attenuation constants obtained from the complex roots of characteristic equation. With such a treatment, the waves are attributed to the group of either 'proper' or 'improper' waves, wherein their type is determined as the trapped surface waves, fast and slow leaky waves, and surface plasmons. The dispersion curves of axially symmetric TM 0n and TE 0n modes, as well as nonsymmetric hybrid EH 1n and HE 1n modes were plotted and analyzed in details, and both radiative regime of leaky waves and guided regime of trapped surface waves are identified. Peculiarities of propagation of the TM modes of surface plasmons were revealed. Two subregions of existence of surface plasmons were found out where they appear as propagating and reactive waves. The cut-off conditions for higher order modes were correctly determined.

Low-loss forward and backward surface plasmons in a semiconductor nanowire coated by helical graphene strips

“…From this requirement follows the dispersion equation for the wave frequency ω(k z ). Evidently, four independent boundary conditions (4) must lead to the dispersion equation in the form of vanishing determinant of a 4 × 4 matrix [2,5]. In fact, this equation can be greatly simplified.…”

“…In numerical calculations we consider a graphene-coated semiconductor nanowire described in [5]. The nanowire parameters are as follows: µ 1 = µ 2 = 1, R = 50 nm, ε 1 = 12.25, ε 2 = 1.…”

“…The graphene conductivity σ = σ(ω) (see Fig. 1(b) of [5]) is found from the Kubo formula [37] for the temperature T = 300 K, the chemical potential µ ch = 0.5 eV, and the relaxation time τ = 1.84 × 10 13 s. First we ignore the Ohmic losses and thus set Re(σ) = 0. As was found in [5], in the case of homogeneous graphene coating (u = 1) the nanowire in hand can support several TM-like surface plasmons with different azimuth indices l. As u decreases, their frequencies f r = ω/2π generally increase.…”

“…6 follows that such gaps provide a way for several-fold increase in frequency of plasmon without reducing its propagation length. Note that for the semiconductor nanowire with uniform graphene coating [5] it is hardly feasible to attain such frequency enhancement in the THz band due to limitations on the nanowire radius, core permittivity and graphene conductivity.…”

Multiple invisibility regions induced by symmetry breaking in a trimer of subwavelength graphene-coated nanowires

“…13 In the terahertz frequency range graphene shows good conductivity and provides efficient subwavelength confinement. 21 Remarkably, the conductivity of graphene is high enough to suppress the wave scattering from a coated dielectric nanowire. The tunability of graphene conductivity can be used for an additional control over the location and magnitude of the plasmonic resonances and makes it possible to achieve the invisibility effect for different wavelengths.…”