We present a maximum-likelihood method for parameter estimation in terahertz time-domain spectroscopy. We derive the likelihood function for a parameterized frequency response function, given a pair of time-domain waveforms with known time-dependent
noise amplitudes. The method provides parameter estimates that are superior to other commonly-used methods, and provides a reliable measure of the goodness of fit. We also develop a simple noise model that is parameterized by three dominant sources, and derive the likelihood function for their amplitudes in terms of a set of repeated waveform measurements. We demonstrate the method with applications to material characterization.
We study the pump-probe response of three insulating cuprates and develop a model for its recombination kinetics. The dependence on time, fluence, and both pump and probe photon energies imply many-body recombination on femtosecond timescales, charac
terized by anomalously large trapping and Auger coefficients. The fluence dependence follows a universal form that includes a characteristic volume scale, which we associate with the holon-doublon excitation efficiency. This volume varies strongly with pump photon energy and peaks near twice the charge-transfer energy, suggesting that the variation is caused by carrier multiplication through impact ionization.
