Ultrabroadband electromagnetically indefinite medium formed by aligned carbon nanotubes

Anisotropic materials with different signs of components of the permittivity tensor are called indefinite materials. The known realizations of indefinite media at ir and optical frequencies suffer from high absorption losses and narrow bandwidth. Here we show that periodic arrays of parallel carbon nanotubes (CNTs) can behave as low-loss indefinite media in the infrared range. We demonstrate that a finite-thickness slab of CNTs supports propagation of backward waves with small attenuation in an ultrabroad frequency band.

Figure 1

Isofrequencies in the plane of the normalized wave vector components $k_{x}d$ and $k_{z}d$, calculated at 1 (magenta line), 10 (black line), 30 (blue line), and 50 THz (red line). The lattice constant $d=15$ nm.

Figure 2

Frequency as a function of the normalized wave numbers in the transverse plane $k_{x}d/\pi$, $k_{y}d/\pi$. $d=15$ nm and $h=1.5\mu$m.

Figure 3

Comparison between the results of the effective medium model (black solid curve) and the electrodynamic model (red dashed curve), calculated for the square lattice. The period of the CNT lattice is $d=15$ nm.