Error analysis of complex refractive index obtained from reflection-type THz time-domain spectroscopy with phase mismatching condition

Reflection-type terahertz (THz) time-domain spectroscopy (THz-TDS) allows us to obtain optical properties of opaque samples in the THz frequency range, e.g., carrier density and mobility. In this study, we theoretically investigate the influence of phase inaccuracy on the extracted complex refractive index from reflection-type THz-TDS. Phase inaccuracy often arises from the placement mismatch between the perfect reflector, serving as the reference, and the target samples in reflection-type THz-TDS. By considering two representative systems, where free and bound carriers dominate the optical properties, and introducing arbitrarily translated placement mismatch, we confirm that significant errors in the extracted complex refractive index occur when the mismatch position exceeds a certain distance, i.e., 3 mu m. Interestingly, the general profile of the reflectivity spectrum is not sensitive to variations in D, whereas oscillatory behavior emerges when D deviates from the ideal case, i.e., there is no translational mismatch between the sample and the reference. This suggests that the best alignment condition can be achieved by adjusting D to find the minimum oscillatory behavior in the reflectivity spectrum.