Size dependence of second-order hyperpolarizability of finite periodic chain under Su-Schrieffer-Heeger model

The second hyperpolarizability $γ_N(-3ωω,ω,ω)$ of $N$ double-bond finite chain of trans-polyactylene is analyzed using the Su-Schrieffer-Heeger model to explain qualitative features of the size-dependence behavior of $γ_N$. Our study shows that $γ_N/N$ is {\it nonmonotonic} with $N$ and that the nonmonotonicity is caused by the dominant contribution of the intraband transition to $γ_N$ in polyenes. Several important physical effects are discussed to reduce quantitative discrepancies between experimental and our results

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