Second-harmonic generation from the quadrupole response inC60films

By applying the numerically computed energy levels and wave functions of the π electrons of the ${\mathrm{C}}_{60}$ molecule following the Su-Schrieffer-Heeger model, we calculated the second-order quadrupole nonlinear susceptibility ${\mathrm{\chi }}_{\mathit{z}\mathit{z}\mathit{z}\mathit{z}}^{\mathit{Q}}$ for the ${\mathrm{C}}_{60}$ medium and the calculated value is 1.7×${10}^{\mathrm{-}20}$ ${\mathrm{m}}^2$/V for the fundamental wave λ=1.064 μm. For the fundamental wave λ=1.064 μm, the second-order susceptibility ${\mathrm{\chi }}_{\mathit{z}\mathit{z}\mathit{z}}^{\mathrm{}\left(2\right)\mathrm{}}$ caused by the second-order nonlinear quadrupole polarization has the magnitude 1.1×${10}^{\mathrm{-}13}$ m/V (i.e., 2.5×${10}^{\mathrm{-}9}$ esu). This result is in excellent agreement with the recent experimental measurements. In addition, we also calculated the quadrupole-induced reflection and transmission second-order harmonic generation by further considering the effect of finite film thickness.