Abstract
In contrast to plane waves, twisted or vortex beams have a complex spatial structure. Both their intensity and energy flow vary within the wave front. Beyond that, polychromatic vortex beams, such as $X$ waves, have a spatially dependent energy distribution. We propose a method to measure this (local) energy spectrum. The method is based on the measurement of the energy distribution of photoelectrons from alkali-metal atoms. On the basis of our fully relativistic calculations, we argue that even ensembles of atoms can be used to probe the local energy spectrum of short twisted pulses.
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