Graphene hyperlens for terahertz radiation

We propose a graphene hyperlens for the terahertz (THz) range. We employ and numerically examine a structured graphene-dielectric multilayered stack that is an analog of a metallic wire medium. As an example of the graphene hyperlens in action, we demonstrate an imaging of two point sources separated by a distance ${\lambda }_0/5$. An advantage of such a hyperlens as compared to a metallic one is the tunability of its properties by changing the chemical potential of graphene. We also propose a method to retrieve the hyperbolic dispersion, check the effective medium approximation, and retrieve the effective permittivity tensor.

Figure 1

(a) The unit cell of the graphene wire medium consists of a graphene stripe of width $w$ embedded into a dielectric. (b) To characterize the hyperbolic medium we calculated the complex reflection $R$ and transmission $T$ coefficients for various angles of incidence $\varphi$. A block of the hyperbolic medium is placed between high-index $n_s$ dielectric layers.

Figure 2

Contour plots of restored (a) $\mathrm{Re}\left[q\right(\omega ,\kappa \left)\right]$ and (b) $\mathrm{Im}\left[q\right(\omega ,\kappa \left)\right]$ for a graphene stripe of $w=80$ nm show the absence of resonances at low frequencies, but a resonance at $f=17$ THz. Looking at the $q\left(\kappa \right)$ for certain frequencies (5, 10, and 15 THz) we observe a flat $\mathrm{Re}\left[q\right(\kappa \left)\right]$ dependence (c) and smaller losses (d) for the frequency 5 THz. Effective radial permittivity ${\varepsilon }_r$(e) shows Drude-like behavior, while azimuthal permittivity ${\varepsilon }_{\theta }$ (f) is positive with small losses.

Figure 3

Comparison of the properties of the graphene wire medium for various stripe widths (0, 80, 160, and 200 nm). The radial wave vector shows larger values of (a) $\mathrm{Re}\left(q\right)$ (that means worse coupling to the surrounding medium) and (b) $\mathrm{Im}\left(q\right)$ (larger losses) for $w=160$ nm compared to the width $w=80$ nm. Also, a “more metallic” Drude behavior of ${\varepsilon }_r$ (c) and higher azimuthal permittivity ${\varepsilon }_{\theta }$ (d) is observed for $w=160$ nm. The absence of graphene ($w=0$) and full coverage ($w=200$ nm) show fully dielectric and Drude-like behaviors, respectively.

Figure 4

(a) A single structured graphene layer that constitutes the hyperlens. (b) An artistic 3D view of the hyperlens in action: The image of two line sources is magnified with the hyperlens. Full-size 3D cst simulation of the hyperlens (c) in action and no hyperlens (d), when two magnetic line sources separated by ${\lambda }_0/5=10\mu$m are emitting TM polarized waves (magnetic field perpendicular to the plane of image). The cst results are in a good agreement with equivalent 2D comsol simulations of the hyperlens (e) and no hyperlens (f). Comparison of the intensity distribution at the output interface of the hyperlens (g) confirms that the images are well resolved.

Figure 5

(a) A thicker hyperlens with $R_2=10R_1$ magnifies two subwavelength sources until the images can be captured with a conventional THz imaging system. (b) Tracing the maximum of the broadband THz transient pulse shows that the hyperlens works in the range of frequencies around 6 THz.