Korotkova, O.de Sande, J. C. G.Santarsiero, MassimoMartínez Herrero, RosarioPiquero Sanz, Gemma MaríaGori, Franco2023-06-222023-06-222022-05-150146-959210.1364/OL.458262https://hdl.handle.net/20.500.14352/71586© 2022 Optica Publishing Group. Funding. Ministerio de Economía y Competitividad (PID2019-104268 GB-C21).The on-axis cross-spectral density (CSD) of a beam radiated by a stationary source with a circular coherence state and a Gaussian spectral density is obtained in the closed form. It is revealed that the on-axis CSD is expressed via the Laplace transform of the source's degree of coherence or the Hilbert transform of the corresponding pseudo-mode weighting function. Such relations enable efficient tailoring of the on-axis spectral density, as we show with a slew of numerical examples.engjournal articlehttp://dx.doi.org/10.1364/OL.458262https://opg.optica.orgopen access535OpticsÓptica (Física)2209.19 Óptica Física