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

TL;DR

This paper investigates how the second hyperpolarizability of finite polyene chains varies with size using the SSH model, revealing nonmonotonic behavior driven by intraband transitions and discussing physical effects to align theory with experiments.

Contribution

It introduces a size-dependent analysis of second hyperpolarizability in finite chains using the SSH model, highlighting the nonmonotonic size dependence caused by intraband transitions.

Findings

$ ext{γ}_N/N$ is nonmonotonic with chain length $N$

Intraband transition dominates $ ext{γ}_N$ in polyenes

Physical effects discussed to improve quantitative agreement

Abstract

The second hyperpolarizability $\gamma_N(-3\omega\omega,\omega,\omega)$ 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 $\gamma_N$. Our study shows that $\gamma_N/N$ is {\it nonmonotonic} with $N$ and that the nonmonotonicity is caused by the dominant contribution of the intraband transition to $\gamma_N$ in polyenes. Several important physical effects are discussed to reduce quantitative discrepancies between experimental and our results