Far-IR spectroscopy of the nonlinear susceptibility of GaAs with an FEL

The non-linear optical properties of solid state materials in the THz frequency region are to a large extent unexplored due to missing high-intensity coherent light sources in this frequency range. Although recent advances in table-top laser based THz systems have been enormous, free-electron lasers (FEL) are at present still the only tunable lasers which provide high peak intensities and a sufficient narrow spectral width to perform nonlinear spectroscopy at THz frequencies. Recently we investigated the dispersion of the second order nonlinear susceptibility (c(2)) in thin GaAs crystals below the optical phonon resonance via second harmonic generation (SHG) experiments with an FEL [1]. These experiments provide insight into the relative contributions of higher-order cohesive lattice forces to c(2). The nonlinear optical susceptibility in polar semiconductors in the THz frequency range is strongly influenced by the presence of optical phonons and should exhibit several peculiarities: A strong resonant enhancement of the SHG at half the frequency of the TO phonon (8.0 THz in GaAs) and at the TO phonon itself as well as a zero-crossing for frequencies between 4.0 THz and the TO phonon resonance due to the cancellation of higher order ionic and electronic contributions was predicted [2]. The experiments are performed with the THz FEL FELIX (Nieuwegein, Netherlands), which delivers picosecond pulses with µJ energy. We could observe both the resonance and the zero-crossing of c(2) below the Reststrahlen-band for the first time. From the value obtained for the zero-crossing of the nonlinear susceptibility we conclude that the contribution of the phonon interaction through the second-order lattice dipole moment has to be significantly smaller and the contribution from the third-order lattice potential anharmonicity has to be larger than determined previously [3]. Besides the relevance for the THz nonlinear susceptibility these terms are also important for two-phonon sidebands in the infrared absorption, phonon decay [3] and for a quantitative description of Raman spectra [4]. We propose that SHG below the optical phonon resonance is an elegant method to quantitatively determine the higher-order potential contributions to the nonlinear susceptibility.

[1] T. Dekorsy et al., Phys. Rev. Lett. 90, 055508 (2003).
[2] A. Mayer and F. Keilmann, Phys. Rev B 33, 6954 (1986).
[3] C. Flytzanis, Phys. Rev. B 6, 1264 (1972); Phys. Rev. Lett. 29, 772 (1972).
[4] S. Go, H. Bilz, and M. Cardona, Phys. Rev. Lett. 34, 580 (1975).