Large Optical Nonlinearity of Semiconducting Single-Walled Carbon Nanotubes under Resonant Excitations

We measured third-order nonlinear susceptibility (${\chi }^{(3)}$) spectra in semiconducting single-walled carbon nanotubes (SWNTs) by the $Z$-scan method. $|\mathrm{I}\mathrm{m}{\chi }^{(3)}|$ is remarkably enhanced under resonant excitation to the lowest interband transition, reaching $4.2\times {10}^{-6}\mathrm{e}\mathrm{s}\mathrm{u}$ and $1.5\times {10}^{-7}\mathrm{e}\mathrm{s}\mathrm{u}$ in SWNTs grown by the laser ablation and HiPco methods, respectively. A comparison of the transient absorption changes evaluated by degenerate and nondegenerate pump-probe measurements suggests that the resonant enhancement of $|\mathrm{I}\mathrm{m}{\chi }^{(3)}|$ is dominated by a coherent process rather than by saturation of absorption.

Figure 1

Absorption spectra of L-SWNTs and H-SWNTs.

Figure 2

(a) Typical $Z$-scan profile of the L-SWNT film in the open-aperture configuration at 0.704 eV. (b) Incident-power dependences of $-f^{-1}\mathbf{(}T(0)\mathbf{)}$ in L-SWNTs at 0.704 eV and in H-SWNTs at 0.970 eV. The solid lines show a linear relation between $-f^{-1}\mathbf{(}T(0)\mathbf{)}$ and the incident power.

Figure 3

$-\mathrm{I}\mathrm{m}{\chi }^{(3)}$ spectra (solid circles) of L-SWNTs (a) and H-SWNTs (b). $n_0$ and ${\kappa }_0$ are also shown by the solid and dashed lines, respectively. The gray lines show the normalized ${ϵ}_2$ spectra, in which the background [the straight line from 0.50 eV (0.60 eV) to 0.83 eV (1.31 eV) for L- (H-)SWNTs] is excluded. The solid and open arrows indicate the energy positions of the pump light used in the degenerate and nondegenerate PP measurements shown in Fig. 4, respectively.

Figure 4

Time characteristics of $-\Delta {\alpha }_0$ (solid circles) in L- and H-SWNTs with the degenerate [(a),(b)] and the nondegenerate [(c),(d)] condition [(a) $E_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}=E_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{e}}=0.688\mathrm{e}\mathrm{V}$; (b) $E_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}=E_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{e}}=0.953\mathrm{e}\mathrm{V}$; (c) $E_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}=0.739\mathrm{e}\mathrm{V}$, $E_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{e}}=0.688\mathrm{e}\mathrm{V}$; and (d) $E_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}=1.022\mathrm{e}\mathrm{V}$, $E_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{e}}=0.953\mathrm{e}\mathrm{V}$]. Solid lines show the fitting curves by Eq. (3). The shaded area and the broken line in (a) and (b) show the ultrafast and slow components, respectively.