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

TL;DR

This paper derives analytical expressions for various third-order nonlinear optical properties of one-dimensional infinite chains using the Takayama-Lin-Liu-Maki model, comparing current-current and dipole-dipole correlations.

Contribution

It provides a detailed comparison showing the inadequacy of current-current correlation for nonlinear optical properties in periodic systems.

Findings

Current-current correlation is inaccurate for nonlinear properties.

Dipole-dipole correlation yields more reliable results.

Analytical expressions for third-harmonic generation and Kerr effects are derived.

Abstract

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($J_0J_0$) correlation for one-dimensional infinite chains. The results of hyperpolarizabilities under $J_0J_0$ correlation are then compared with those obtained using the dipole-dipole ($DD$) correlation. The comparison shows that the conventional $J_0J_0$ correlation, albeit quite successful for the linear case, is incorrect for studying the nonlinear optical properties of periodic systems.