Quantitative 2D fitting of fluorescence-excitation maps: excitation lineshape of single-wall carbon nanotubes

Two-dimensional (2D) fluorescence-excitation (PLE) spectroscopy offers a powerful way to analyse samples of semiconducting single-wall carbon nanotubes (SWCNTs). The one-to-one correspondence between the SWCNT chiral structure and its optically excited states allows for the identification of individual species based on peaks in 2D PLE data. Changes in the position, width and other features of the lineshape associated with a given peak reveal a plethora of information about the associated SWCNT chirality and e.g. its interactions with the environment. Consistent and physically relevant quantification of that information requires accurate fitting of the 2D data, which has long been hindered by the fact that a sufficiently accurate functional form for the excitation profile of SWCNTs was not known. Here we present a highly accurate analytical empirical model for the excitation lineshape and combine it with one for the emission lineshape in a 2D fitting model that produces accurate fits of 2D PLE maps for any SWCNT sample and allows straightforward extraction of lineshape features, including peak positions, linewidths and intensities as well as other relevant physical quantities such as phonon sidebands in the emission and excitation spectra.