Tailoring on-axis spectral density with circularly coherent light beams

TL;DR

This paper derives a closed-form expression for the on-axis cross-spectral density of circularly coherent Gaussian beams, revealing how to efficiently tailor spectral density using mathematical transforms, supported by numerical examples.

Contribution

It provides a novel analytical framework linking on-axis spectral density to the source's coherence properties through Laplace and Hilbert transforms.

Findings

Closed-form expression for on-axis CSD derived.

Efficient spectral density tailoring demonstrated.

Numerical examples validate the theoretical approach.

Abstract

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.