Nonlinear optical properties of one-dimensional semiconductors and conjugated polymers

We present a detailed study of the nonlinear optical properties of one-dimensional conjugated polymers and semiconductors. The Bloch wave functions and energies and the dipole transition-matrix elements previously obtained within the tight-binding approximation by linear combination of atomic orbitals (Hückel approximation) were used to calculate the nonlinear optical susceptibilities; the expressions of the lattice were obtained by the Genkin-Mednis approach. The effects of bond alternation and superalternation as well as chain pairing are explicitly considered. It is found, as for the linear optical properties, that the behavior of the nonlinear susceptibilities can be simply expressed in terms of the optical delocalization parameter $N_d$ previously defined; in particular it is shown that the third-order susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ in the transparency region of these compounds shows a sixth-power dependence on this parameter. It is further shown that chain pairing has striking effects on the second-order susceptibility and the two-photon absorption spectrum. The case of the polydiacetylene polymer crystals is explicitly discussed.