Third-order nonlinear optical response in double-walled carbon nanotubes

Resonant behavior and magnitudes of third-order nonlinear optical susceptibilities in double-walled carbon nanotubes (DWNTs) have been investigated by means of femtosecond pump-probe spectroscopy with different pump-photon energies. With the selective excitation of the E₂₂ exciton transition of the inner tubes labeled by the chiral vector indices (7,5) and (7,6), the imaginary part of nonlinear susceptibility Imχ⁽³⁾ has shown the resonant enhancement compared with the case of the nonresonant excitation of the specific tube. The nonlinear response signal at the E₂₂ transition energy of the (8,7) tube has been also enhanced for the excitation of the G-band phonon sideband of its E₂₂ transition. This result is consistent with the phonon-mediated nonlinear optical process observed for the E₂₂ transitions in single-walled carbon nanotubes (SWNTs). It has been also found that the values of the figure of merit Im χ⁽³⁾/α (α: absorption coefficient) of the inner tubes in DWNTs are smaller than those of the corresponding SWNTs, which is interpreted in terms of decay time shortening due to the energy relaxation between the inner and outer tubes.