Abstract
The optical transition energies E-ii of carbon nanotubes (CNTs) strongly depend on the dielectric function epsilon(q) of the nanotubes and the dielectric background constant epsilon(bg) of their surroundings. It becomes particularly evident when CNTs in solution and free-standing, vertically aligned CNTs are compared via their optical spectra. Using photoluminescence-excitation spectroscopy, we determine the first two transition energies for these two types of carbon-nanotube samples, i.e., for CNT-solution and CNT-forest samples. We observe considerable energy shifts and explain them by microscopic calculations based on the density-matrix formalism. Combining experiment and theory, we determine the dielectric background constant of the CNT-forest and CNT-solution samples to be 1.3 +/- 0.1 and 1.8 +/- 0.1, respectively.