Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems. II. Dipole-dipole versus current-current correlations

Based on Takayama-Lin-Liu-Maki model, analytical expressions for the third-harmonic generation, dc Kerr effect, dc-induced second-harmonic optical Kerr effect, optical Kerr effect or intensity-dependent index of refraction, and dc-electric-field-induced optical rectification are derived under the static current-current (J0J0) correlation for one-dimensional infinite chains. The results of hyperpolarizabilities under J0J0 correlation are then compared with those obtained using the dipole-dipole correlation. The comparison shows that the conventional J0J0 correlation, albeit quite successful for the linear case, is incorrect for studying the nonlinear optical properties of periodic systems.