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Light contains both spin and orbital angular momentum. Despite contributing equally to the total photonic angular momentum, these components derive from quite different parts of the electromagnetic field profile, namely its polarization and spatial variation, respectively, and therefore do not always share equal influence in light–matter interactions. With the growing interest in utilizing light’s orbital angular momentum to practice added control in the study of atomic systems, it becomes increasingly important for students and researchers to understand the subtlety involved in these interactions. In this article, we present a review of the fundamental concepts and recent experiments related to the interaction of beams containing orbital angular momentum with atoms. An emphasis is placed on understanding light’s angular momentum from the perspective of both classical waves and individual photons. We then review the application of these beams in recent experiments, namely single- and few-photon transitions, strong-field ionization, and high-harmonic generation, highlighting the role of light’s orbital angular momentum and the atom’s location within the beam profile within each case. 

While interferometric methods exist for classifying vortex states of light, these techniques usually require destroying the beam of interest to determine the light’s OAM. A recent two-color pump-probe experiment employed strong field ionization and beam sculpting to classify vortex beams. Here, we propose an alternative strong-field method for distinguishing OAM states of light which does not require beam sculpting and instead utilizes a noncollinear terahertz standing wave to probe ionized electrons. We then use classical trajectory Monte Carlo (CTMC) methods to simulate strong-field ionization of helium under this configuration with the terahertz field both on and off. We find that the resulting electron momenta distributions can be used to extract the OAM of the beam, as long as the vortex beam spot size does not exceed 1/4 the terahertz pulse’s wavelength.