Abstract
Understanding the intricate properties of spatiotemporal optical vortices (STOVs) is crucial for their growing number of applications, particularly where they drive light-matter interactions that can create up-converted STOV-like structures at attosecond and nanometer scales. We derive closed-form expressions for the propagation of STOVs, and spatiotemporal (ST) tilted Hermite-lobed (THL) pulses forming STOVs, through cascaded optical systems represented by ABCD matrices such as free space propagation, lenses, mirrors, similar in simplicity as those in Gaussian beam optics. STOVs and ST THL pulses are found to be spatial and temporal Fourier transform pairs at the same time, so that a STOV is a spatiospectral (SS) THL pulse in SS domain and a ST THL pulse is a SS vortex. This duality allow us to find expressions for the transformation of their spatiospectra through arbitrary optics, which is particularly important at the attosecond and nanometer scales, where ST characterization techniques are limited.