Liquid crystal control of the plasmon resonances at terahertz frequencies in graphene microribbon gratings

We theoretically study the influence of the liquid crystal (LC) orientational state on the absorption, reflection, and transmission spectra of a graphene microribbon grating placed between a nematic LC and an isotropic dielectric substrate. We calculate the absorption, reflection, and transmission coefficients at normal incidence of a far-infrared transverse magnetic wave (THz) and show that control of the orientational state of the LC layer enables the manipulation of the magnitude of the absorption and reflection maxima. The influence the LC orientational state on the plasmonic resonance increases with increasing the isotropic substrate dielectric constant and the graphene microribbon width to grating spacing ratio.

Figure 1

Schematic of the graphene microribbon grating structure. $d$ is the ribbon width, $\mathrm{\Lambda }$ is the grating spacing, $\psi$ is the director angle with the $z$ axis, ${\widehat{\varepsilon }}_1$ is the LC dielectric tensor, ${\varepsilon }_2$ is the isotropic substrate dielectric permittivity, $\sigma$ is the graphene conductivity, ${\mathbf{e}}_{\mathbf{n}}$ is a unit normal to the graphene plane in the positive $z$ direction, and ${\mathit{k}}_{\mathit{i}}$ is the wave vector of an incident TM plane monochromatic wave.

Figure 2

Absorption (a), reflection, and transmission (b) spectra of the graphene microribbon grating at different angles of the nematic director and for different substrate dielectric permittivity values. $\psi =0^{\circ }$, solid line; $\psi ={90}^{\circ }$, dash-dot line. Substrate dielectric constant: ${\varepsilon }_2=3$, curves 1; ${\varepsilon }_2=11.7$, curves 2. Grating spacing, $\mathrm{\Lambda }=1\mu \mathrm{m}$; ribbon width, $d=0.5\mu \mathrm{m}$.

Figure 3

Absorption (a), reflection, and transmission (b) spectra of the graphene microribbon grating at different angles of the nematic director and for different ribbon aspect ratios at fixed grating spacing. $\psi =0^{\circ }$, solid line; $\psi ={90}^{\circ }$, dash-dot line. Ratio $d/\mathrm{\Lambda }=0.3$, curves 1; $d/\mathrm{\Lambda }=0.7$, curves 2. Substrate dielectric constant, ${\varepsilon }_2=11.7$; grating spacing, $\mathrm{\Lambda }=1\mu \mathrm{m}$.

Figure 4

Absorption (a), reflection, and transmission (b) spectra of the graphene microribbon grating at different angles of the nematic director and for different ribbon aspect ratios at fixed ribbon width. $\psi =0^{\circ }$, solid line; $\psi ={90}^{\circ }$, dash-dot line. Ratio $d/\mathrm{\Lambda }=0.7$, curves 1; $d/\mathrm{\Lambda }=0.5$, curves 2. Substrate dielectric constant, ${\varepsilon }_2=11.7$; ribbon width, $d=0.7\mu \mathrm{m}$.

Figure 5

Absorption spectra of the graphene microribbon grating at different angles of the nematic director and for different ribbon aspect ratios at fixed ribbon width. In this figure, the ribbon width $d$ is 14 times smaller than in Fig. 4. $\psi =0^{\circ }$, solid line; $\psi ={90}^{\circ }$, dash-dot line; $d/\mathrm{\Lambda }=0.357$, curves 1; $d/\mathrm{\Lambda }=0.5$, curves 2; $d/\mathrm{\Lambda }=0.641$, curves 3. Substrate dielectric constant, ${\varepsilon }_2=11.7$; ribbon width, $d=0.05\mu \mathrm{m}$.