Tailoring on-axis spectral density with circularly coherent light beams

O. Korotkova; J. C. G. de Sande; M. Santarsiero; R. Martínez-Herrero; G. Piquero; F. Gori

doi:10.1364/OL.458262

Optics Letters
Vol. 47,
Issue 10,
pp. 2394-2397
(2022)
•https://doi.org/10.1364/OL.458262

Tailoring on-axis spectral density with circularly coherent light beams

O. Korotkova, J. C. G. de Sande, M. Santarsiero, R. Martínez-Herrero, G. Piquero, and F. Gori

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O. Korotkova, J. C. G. de Sande, M. Santarsiero, R. Martínez-Herrero, G. Piquero, and F. Gori, "Tailoring on-axis spectral density with circularly coherent light beams," Opt. Lett. 47, 2394-2397 (2022)

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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.

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No data were generated or analyzed in the presented research.

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Equations (34)

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$μ (q τ_{d})$	$p (v)$	$S (ζ)$
$1$	$δ (v)$	$\frac{1}{1 + ζ^{2}}$
$\exp (- q^{2} τ_{d}^{2})$	$\frac{\exp (- v^{2} / 4 q^{2})}{2 q \sqrt{π}}$	$\frac{\sqrt{π}}{2 q ζ^{2}} ℜ {\exp [\frac{(ζ - i)^{2}}{4 q^{2} ζ^{2}}]$
		$\times erfc (\frac{ζ - i}{2 q ζ})}$
$\cos (q τ_{d})$	$\frac{1}{2} [δ (v - q) + δ (v + q)]$	$\frac{1 + (1 + q^{2}) ζ^{2}}{1 - 2 (q^{2} - 1) ζ^{2} + (1 + q^{2})^{2} ζ^{4}}$
$\frac{\sin (q τ_{d})}{q τ_{d}}$	$\frac{1}{2 q} rect (v / 2 q)$	$\frac{1}{q ζ^{2}} ℜ {\arctan (\frac{q ζ}{ζ - i})}$
$J_{0} (q τ_{d})$	$\frac{rect (v / 2 q)}{π \sqrt{q^{2} - v^{2}}}$	$\frac{1}{ζ^{2}} ℜ {\frac{1}{\sqrt{q^{2} + (1 - i / ζ)^{2}}}}$
$\frac{2 J_{1} (q τ_{d})}{q τ_{d}}$	$\frac{2 step (q^{2} - v^{2})}{π q^{2} (q^{2} - v^{2})^{- 1 / 2}}$	$\frac{2 ℜ {\sqrt{q^{2} + (1 - i / ζ)^{2}}} - 2}{q^{2} ζ^{2}}$

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