Phase Retrieval in Terahertz Time-Domain Measurements: a "how to" Tutorial

Terahertz time-domain spectroscopy (THz-TDS) is in many ways a well-established, proven, and versatile spectroscopic technique that is frequently and routinely used in many laboratories. The basis of high-quality optical data on materials using THz-TDS is the correct extraction of the complex-valued dielectric properties (index of refraction, permittivity, or conductivity) from the recorded amplitude and phase of the involved THz signals. The focus of this paper is to discuss stable methods for finding the physically meaningful frequency-dependent optical phase from time-domain signals, thereby avoiding some of the unphysical solutions to the inversion problem that is the central part of THz-TDS analysis. The paper discusses problems associated with the positioning of the THz signal in the recorded time window, phase offsets due to noise in the experimental data, and phase correction in the case of strongly dispersive media such as transparent semiconductors in the frequency range below but close to the transverse optical phonons.