Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems: I. Analytical solutions under dipole-dipole correlations

Abstract

The analytical solutions for the general-four-wave-mixing hyperpolarizabilities ${\chi }^{(3)}(-(w_1+w_2+w_3);w_1,w_2,w_3)$ on infinite chains under both Su-Shrieffer-Heeger and Takayama-Lin-Liu-Maki models of trans-polyacetylene are obtained through the scheme of dipole-dipole correlation. Analytical expressions of DC Kerr effect ${\chi }^{(3)}(-w;0,0,w)$, DC-induced second harmonic generation ${\chi }^{(3)}(-2w;0,w,w)$, optical Kerr effect ${\chi }^{(3)}(-w;w,-w,w)$ and DC-electric-field-induced optical rectification ${\chi }^{(3)}(0;w,-w,0)$ are derived. By including or excluding ${\nabla }_{\mathbf{k}}$ terms in the calculations, comparisons show that the intraband contributions dominate the hyperpolarizabilities if they are included. ${\nabla }_k$ term or intraband transition leads to the break of the overall permutation symmetry in ${\chi }^{(3)}$ even for the low frequency and non-resonant regions. Hence it breaks the Kleinman symmetry that is directly based on the overall permutation symmetry. Our calculations provide a clear understanding of the Kleinman symmetry breaks that are widely observed in many experiments. We also suggest a feasible experiment on ${\chi }^{(3)}$ to test the validity of overall permutation symmetry and our theoretical prediction. Finally, our calculations show the following trends for the various third-order nonlinear optical processes in the low frequency and non-resonant region: ${\chi }^{(3)}(-3w;w,w,w)>{\chi }^{(3)}(-2w;0,w,w)>{\chi }^{(3)}(-w;w,-w,w)>{\chi }^{(3)}(-w;0,0,w)>={\chi }^{(3)}(0;w,-w,0)$, and in the resonant region: ${\chi }^{(3)}(-w;0,0,w)>{\chi }^{(3)}(-w;w,-w,w)>{\chi }^{(3)}(-2w;0,w,w)>{\chi }^{(3)}(0;w,-w,0)>{\chi }^{(3)}(-3w;w,w,w)$. (w=ω)

31 pages, 6 figures

References in corpus (5)

• Dielectric response of modified Hubbard models with neutral-ionic and Peierls transitions
• Optical Susceptibilities of Polymers: Current-Current versus Dipole-Dipole Correlation
• Zero frequency divergence and gauge phase factor in the optical response theory
• Analytical solutions to the third-harmonic generation in trans-polyacetylene: Application of dipole-dipole correlation on the single electron models
• Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems: II. Dipole-dipole versus current-current correlations

Cited by in corpus (4)

• Enhancing the Hyperpolarizability of Crystals with Quantum Geometry
• Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems: II. Dipole-dipole versus current-current correlations
• Size dependence of second-order hyperpolarizability of finite periodic chain under Su-Schrieffer-Heeger model
• Breaking of the overall permutation symmetry in nonlinear optical susceptibilities of one-dimensional periodic dimerized Huckel model