λ is the mean ratio of E11 * and E11 (~mean number of defects) and k is the discrete defect number. Even though the distributions of each defect state (Figure ) are diverse from one another, they are not discrete. This is to be expected as the length distribution of the SWCNTs is also heterogeneous, as well as their quantum yield . To compare the experimental with the discrete Poisson distributions, it was necessary to classify the experimental ratios to obtain discrete values. For this reason, the non-defect state had to be estimated from the ratios of SWCNTs whose E11 * intensity was equal to or lower than the background noise (Figure ). A ratio of 0.5 appeared appropriate, given the bulk of SWCNTs in this category fell below this range and SWCNTs with ratios greater than 0.5 were predicted to be either extremely short or to have a relatively poor quantum yield. Therefore, E11*/E11 ratios were summed up uniformly around each natural number with a spread of one (every ratio between 0.5 and 1.5 counts towards the discrete ratio of 1). The discrete experimental distribution was fitted very well by the Poisson distribution (Figure ). Given the length of (6,5)-SWCNTs after ATPE of similar samples from our previous work (~ 1000 nm), the mean defect densities are calculated as 1.7 to 3.5 µm -1 (1 to 3 defects per SWCNT, dlowto dhigh-SWCNTs).