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

The magnitude and spectral response of second-harmonic generation (SHG) from $0.4\mathrm{nm}$ single-walled carbon nanotubes (CNTs) in the channels of $\mathrm{Al}\mathrm{P}{\mathrm{O}}_4\text{−}5$ 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° to the tube axis. A SH resonance peak at $2\mathrm{eV}$ was observed, which corresponds to the lowest-energy excitonic state in chiral (4,2) CNTs. The second-order optical susceptibility ${\chi }^{\left(2\right)}$ of the system was determined to be ${10}^{-6}\mathrm{esu}$, which agrees with the large ${\chi }^{\left(2\right)}$ predicted for small diameter CNTs. These experimental results suggest that SHG can be used to characterize the symmetry and chirality of CNTs.

Figure 1

(Color online) The SHG signal excited by $150\mathrm{fs}$ light psulses at $800\mathrm{nm}$. Inset (a): diagram of the geometry and the polarization arrangement in the experimental setup. Inset (b): the integrated SHG intensity as a function of the pump laser power and the quadratic fit.

Figure 2

(Color online) (a) The integrated SHG intensity from SWCNT and from AFI zeolite as a function of the excitation polarization angle $\varphi$. The curve pointed by an arrow was calculated using Eqs. (3). (b) The integrated SHG intensity from SWCNT as a function of the emission light polarization angle $\theta$ with the excitation angle $\varphi =45°$ together with a ${\cos }^2\theta$ fit.

Figure 3

(Color online) SHG intensity as a function of the excitation laser wavelength and the theoretical curve for chiral (4,2) tubes. The absorption of fundamentals and second harmonics through the sample used in the calculation was taken from Ref. 7.