Analysis of the behavior of highly focused, radially coherent Dirichlet sources

We introduce a novel class of electromagnetic light sources that exhibit radial coherence, a degree of coherence characterized by a Dirichlet kernel, and with radial or azimuthal polarization. We provide a mathematical description of the spectral irradiance, 3D degree of polarization, and electromagnetic degree of coherence for such sources when they are focused using a high numerical aperture microscope lens. Since the incident beam can be described as a modal expansion, we also consider how the number of terms affects the behavior of the field in the focal area. The formal analysis is complemented with numerical simulations. The study reveals interesting properties in the focal area, despite the focused beam is no longer radially coherent. •We introduce a novel class of electromagnetic light sources with radial coherence.•The degree of coherence is described by a Dirichlet kernel.•The polarization of the focused field on axis is independent of incident coherence.•Focused fields remain unpolarized on-axis with azimuthally polarized input beams.•The focused field is no longer radially coherent.