Empirical formulation of broadband complex refractive index spectra of single-chirality carbon nanotube assembly

Assemblies of single-walled carbon nanotubes with a specific chiral structure are promising future optofunctional materials because of their strong light-matter coupling arising from sharp optical resonances of quasi-one-dimensional excitons. Their strong optical resonances, which lie in the infrared-to-visible wavelength region, can be selected by their chiralities, and this selectivity promises a wide range of applications including photonic and thermo-optic devices. However, the broadband complex optical spectra of single-chirality carbon nanotube assemblies are scarce in the literature, which has prevented researchers and engineers from designing devices using them. Here, we experimentally determine broadband complex refractive index spectra of single-chirality carbon nanotube assemblies. Free-standing carbon nanotube membranes and those placed on sapphire substrates were fabricated via filtration of the nanotube solution prepared by the separation method using gel chromatography. Transmission and reflection spectra were measured in the mid-infrared to visible wavelength region, and the complex refractive indices of nanotube assemblies were determined as a function of photon energy. The real and imaginary parts of the refractive indices of the nanotube membrane with a bulk density of 1 g cm^-3 at the first subband exciton resonance were determined to be approximately 2.7-3.6 and 1.3i-2.4i, respectively. We propose an empirical formula that phenomenologically describes the complex refractive index spectra of various single-chirality nanotube membranes, which can facilitate the design of photonic devices using carbon nanotubes as the material.