Direct measurement of the absolute absorption spectrum of individual semiconducting single-wall carbon nanotubes.

The optical properties of single-wall carbon nanotubes are very promising for developing novel opto-electronic components and sensors with applications in many fields. Despite numerous studies performed using photoluminescence or Raman and Rayleigh scattering, knowledge of their optical response is still partial. Here we determine using spatial modulation spectroscopy, over a broad optical spectral range, the spectrum and amplitude of the absorption cross-section of individual semiconducting single-wall carbon nanotubes. These quantitative measurements permit determination of the oscillator strength of the different excitonic resonances and their dependencies on the excitonic transition and type of semiconducting nanotube. A non-resonant background is also identified and its cross-section comparable to the ideal graphene optical absorbance. Furthermore, investigation of the same single-wall nanotube either free standing or lying on a substrate shows large broadening of the excitonic resonances with increase of oscillator strength, as well as stark weakening of polarization-dependent antenna effects, due to nanotube-substrate interaction.