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

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