Dispersion relation in the third-order electric susceptibility for polysilane film

Abstract

The Kramers-Kronig (KK) dispersion relation has been proved to hold between independently measured spectra of the phase shift φ(ω) and the modulus ‖χ${\mathrm{̃}}^{\mathrm{}\left(3\right)\mathrm{}}$/(ω)‖ of third-order electric susceptibility χ${\mathrm{̃}}^{\mathrm{}\left(3\right)\mathrm{}}$ (=‖χ${\mathrm{̃}}^{\mathrm{}\left(3\right)\mathrm{}}$‖${\mathit{e}}^{\mathit{i}\mathrm{\phi }}$) for the third-order harmonic generation in silicon-based polymer, poly(dihexylsilane) (PDHS) films, providing a direct experimental substantiation of the reciprocal KK relations in the nonlinear optical solids. The reciprocal dispersion relations have been also found to hold for the real and imaginary parts of χ${\mathrm{̃}}^{\mathrm{}\left(3\right)\mathrm{}}$ in PDHS films.