Resonant second-harmonic generation in monosized and aligned single-walled carbon nanotubes

Abstract

The magnitude and spectral response of second-harmonic generation (SHG) from $0.4\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ single-walled carbon nanotubes (CNTs) in the channels of $\mathrm{Al}\mathrm{P}{\mathrm{O}}_{4}\text{\ensuremath{-}}5$ zeolite is reported. The second harmonics (SH) was found to be polarized perpendicular to the tube axis and maximized by an excitation polarization at 45\ifmmode^\circ\else\textdegree\fi{} to the tube axis. A SH resonance peak at $2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ was observed, which corresponds to the lowest-energy excitonic state in chiral (4,2) CNTs. The second-order optical susceptibility ${\ensuremath{\chi}}^{(2)}$ of the system was determined to be ${10}^{\ensuremath{-}6}\phantom{\rule{0.3em}{0ex}}\mathrm{esu}$, which agrees with the large ${\ensuremath{\chi}}^{(2)}$ predicted for small diameter CNTs. These experimental results suggest that SHG can be used to characterize the symmetry and chirality of CNTs.