Finite-difference time-domain method is used to investigate the optical properties of vertical arrays of multi-walled carbon nanotubes. Individual carbon nanotubes are treated as solid circular cylinders with an effective dielectric tensor. Our results confirm that carbon nanotube arrays have extremely low reflectivity as observed in experiments. Compared with the commonly used Maxwell-Garnett theory, our calculations generally give larger reflectance and absorptance and smaller transmittance, which are attributed to the diffraction and scattering within the cylinder array structure. The effects of volume fraction, tube length, and incidence angle on radiative properties are investigated respectively. Low volume fraction and long tubes are more favorable to achieve low reflectance and high absorptance. The angular dependence study shows that there exists an optimum incidence angle at which the reflectance can be minimized, indicating that a small misalignment in carbon nanotube arrays can slightly enhance the absorptance. Our results also indicate that an even darker material could be achieved by using carbon nanotubes with good alignment on the top surface.

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