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Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems: I. Analytical solutions under dipole-dipole correlations | | Shidong Jiang
; Minzhong Xu
; | | Date: |
14 May 2005 | | Journal: | J.Chem.Phys. 123 (2005) 064901 DOI: 10.1063/1.1989307 | | Subject: | Other; Materials Science; Optics; Atomic and Molecular Clusters; Atomic Physics | cond-mat.other astro-ph cond-mat.mtrl-sci physics.atm-clus physics.atom-ph physics.optics | | 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 ${f
abla_k}$ terms in the calculations, comparisons show that the intraband contributions dominate the hyperpolarizabilities if they are included. $
abla_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=omega) | | Source: | arXiv, cond-mat/0505363 | | Services: | Forum | Review | PDF | Favorites | |
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