Third-harmonic generation of polyacetylene

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Abstract
We present an exact calculation of third-harmonic generation (THG) for a one-dimensional electron-lattice system. The result shows that once the conjugated length of a polyene is finite, the transitions between inside-band electronic states will be important. A random distribution of conjugated lengths is used to simulate the polymer chains of polyacetylene. The average spectrum of THG distinctly demonstrates two peaks: one is the three-photon resonance exactly at one-third of the energy gap; the other sits near half of the energy gap, which is induced by the transitions between the inside-band states. This spectrum agrees quite well with that of THG experiments for trans-polyacetylene.