# Analytical solutions to the third-harmonic generation in trans-polyacetylene: Application of dipole-dipole correlation to single-electron models

@article{Xu1999AnalyticalST,
title={Analytical solutions to the third-harmonic generation in trans-polyacetylene: Application of dipole-dipole correlation to single-electron models},
author={Minzhong Xu and Xin Sun},
journal={Physical Review B},
year={1999},
volume={61},
pages={15766-15773}
}
• Published 1 June 1999
• Physics
• Physical Review B
The analytical solutions for the third-harmonic generation (THG) on infinite chains in both Su-Shrieffer-Heeger (SSH) and Takayama-Lin-Liu-Maki (TLM) models of trans-polyacetylene are obtained through the scheme of dipole-dipole ($DD$) correlation. They are not equivalent to the results obtained through static current-current ($J_0J_0$) correlation or under polarization operator $\hat{P}$. The van Hove singularity disappears exactly in the analytical forms, showing that the experimentally…
3 Citations

## Figures from this paper

### Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems. II. Dipole-dipole versus current-current correlations.

• Physics
The Journal of chemical physics
• 2005
The results of hyperpolarizabilities under J0J0 correlation are compared with those obtained using the dipole-dipole correlation and shows that the conventional J0j0 correlation is incorrect for studying the nonlinear optical properties of periodic systems.

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

• Physics, Chemistry
The Journal of chemical physics
• 2005
The calculations provide a clear understanding of the Kleinman symmetry breaks that are widely observed in many experiments and suggest a feasible experiment on chi(3) to test the validity of overall permutation symmetry and theoretical prediction.

### Breaking of the overall permutation symmetry in nonlinear optical susceptibilities of one-dimensional periodic dimerized Hückel model

• Physics
• 2006
Based on one-dimensional single-electron infinite periodic models of trans-polyacetylene, we show analytically that the overall permutation symmetry of nonlinear optical susceptibilities is, although

## References

SHOWING 1-10 OF 27 REFERENCES

### The Elements of Nonlinear Optics

• Physics
• 1990
Introduction 1. The constitutive relation 2. Review of quantum mechanics 3. The susceptibility tensors 4. Symmetry properties 5. Resonant nonlinearities 6. Wave propagation and processes in nonlinear

### Nonlinear optical properties of polymers

• Physics
• 1988
This book contains papers presented at a symposium on the nonlinear optical properties of polymers. Topics covered include: Implementation of neural networks; optical architecture and devices; Highly

• Met. 54, 295
• 1993

### Phys

• Rev. B 42, R9736
• 1990

### Phys

• Rev. B 41, 12845
• 1990

• Met. 17, 343
• 1987

### Phys

• Rev. Lett. 62, 1492
• 1989

### The principles of nonlinear optics

• M. Levenson
• Physics
IEEE Journal of Quantum Electronics
• 1985

### Phys

• Rev. B 24, 3701
• 1981