Media for ultrafast THz photonics

Designing of the ultrafast terahertz photonics devices requires materials with the biggest nonlinear refractive index coefficient $n_2$ and the lowest nonlinear response settling time $\tau$ in the terahertz spectral range. In the present study, we show that the ratio $n_2/\tau$ for media with the vibrational nonlinearity in the terahertz range is determined by the square of the medium thermal expansion coefficient and the fifth power of its dominative stretching vibrational mode frequency. These findings are based on the theory of the media vibrational nature nonlinear polarization response to incident THz radiation. We provide estimated values of the $n_2/\tau$ ratio for a group of liquids and crystal materials. According to our evaluations, $n_2/\tau$ value for alpha-pinene in the terahertz spectral range is about 10$^6$ cm$^2$/J and is almost the biggest one compared to materials with different nonlinearity types in various spectral ranges.