Propagation of terahertz pulses in photoexcited media: Analytical theory for layered systems

Optical pump-terahertz probe spectroscopy has become a widely used experimental tool for the investigation of the ultrafast far-infrared response of polar systems. In this paper the authors present an analytical method of calculating the propagation of ultrashort terahertz pulses in photoexcited media. The transient terahertz wave form transmitted through the sample is equal to a product of the incident terahertz field (at a mixed frequency), transient susceptibility, and a so called transfer function which depends on the properties of the sample in equilibrium. The form of the transfer function is derived for general layered systems and for specific cases including one-dimensional photonic crystals, thin films, and bulk samples. Simplified expressions directly applicable to the analysis of the experimental results related to the most common sample geometries are shown and discussed.