Dispersion relations of the powers of complex reflection coefficient in testing the validity of THz spectra

Kramers-Kronig type dispersion relations for integer powers of complex reflection coefficient are introduced for testing the consistency of terahertz reflection spectra. By using numerical simulations we show that such dispersion relations can be applied for distillation from data with some experimental artifacts without data extrapolations beyond the measured spectral range. These dispersion relations, due to causality, provide a powerful and yet uncommon tool to examine the consistency of the spectroscopic data obtained in reflection spectroscopy at terahertz range. In particular we show that real and imaginary parts of the complex reflection coefficient obtained from raw data with systematic phase error caused by sample misplacement, not necessarily obey dispersion relations, while the ones corrected with maximum entropy method obey these relations.