Generalized framework for determining time origin in terahertz emission spectroscopy on the basis of causality

We develop a generalized causality-based framework for determining the time origin in terahertz emission spectroscopy. Our framework is formulated in terms of a multiply subtractive Kramers-Kronig relation and can treat all major mechanisms of terahertz emission, which include the occurrence of a delta-function-like instantaneous polarization observed typically in nonlinear optical processes. We show that a function derived within our framework properly determines the positions of t = 0 both for simulated terahertz waveforms and for a measured one obtained in biased conjugated polymers. This function will be useful for an in-depth understanding of ultrafast phenomena involving terahertz emission in various optoelectronic materials.