Direct Measurement of the Polarized Optical Absorption Cross Section of Single-Wall Carbon Nanotubes

We determine optical absorption cross sections of single-wall carbon nanotubes for visible light copolarized and cross polarized with respect to the nanotube axis. The need for perfectly aligned ensembles in absorbance measurements is eliminated by using Raman scattering to measure the nematic order parameter in magnetically aligned nanotube suspensions. The absorbance data allow the first quantitative, spectral comparisons with theories of local field depolarization, and provide benchmark spectra for simple, rapid, and quantitative measurements of alignment within nanotube dispersions.

Figure 1

(a) $G$-band Raman intensity for sample 2 with $VV$ polarizations parallel and perpendicular to the alignment axis ($\phi =0$ and $90°$, respectively). (b),(c) Raman peak intensity versus sample orientation $\phi$ for samples 1–4. Insets show polar representations of the same data.

Figure 2

(a) Raw optical transmission for light copolarized relative to the alignment field axis for all samples. (b) Copolarized and cross-polarized absorbance for sample 2.

Figure 3

(a) Polarization of absorbance, $\rho$, and (b) depolarized absorbance, $\alpha$, for all samples, as defined in the text.

Figure 4

Bare SWNT optical cross sections for copolarized and cross-polarized light (${\sigma }_{\parallel }$ and ${\sigma }_{\perp }$, respectively) for (a) all samples and (b) averaged over all samples. (c) Calculated cross sections for ${\sigma }_{\parallel }$ (solid line) and ${\sigma }_{\perp }$ with (dashed line) and without (dotted line) a depolarization correction.