An accurate discrete Fourier transform to analyse the absolute phase of THz pulses

Electro-optic sampling allows the electric field of THz, mid-infrared and visible light pulses to be measured directly as a function of time, with data analysis often performed in the frequency domain after fast Fourier transform. Here we introduce a version of the discrete Fourier transform that is consistent with the analytical continuous Fourier transform, enabling the quantitative study of the amplitude and phase of light pulses without the phase ambiguity inherent in the conventional definition of the discrete Fourier transform. We then show that a phenomenological time-domain model, based on carrier and envelope waves, that can reproduce the wide variety of narrow-band and broadband multi- to single-cycle THz pulses reported in the literature, such as from spintronic emitters, photoconductive antennae, optical rectification and free electron lasers. We discuss the influence of the pulse envelope's duration, the carrier-envelope phase and the pulse arrival time on the complex spectra. The methodology and results described provide a valuable toolkit that unlocks the full potential of the phase information available in time-domain spectroscopy.