The on-axis cross-spectral density (CSD) of a beam radi- ated 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.
Korotkova, O., de Sande, J.C.G., Santarsiero, M., Martínez-Herrero, R., Piquero, G., & Gori, F. (2022). Tailoring on-axis spectral density with circularly coherent light beams. OPTICS LETTERS, 47(10), 2394 [10.1364/OL.458262].