We introduce a novel class of planar, scalar sources whose cross-spectral density is a function of a single complex variable. For a typical pair of source points, the modulus and argument of such a variable equal the product of their radial coordinates and the difference of their angular coordinates, respectively. As functions of a single complex variable, the corresponding cross-spectral densities (CSD) are expandable in power series in their convergence domain, and a virtually infinite number of source models can be devised. All such sources are shown to have vortex fields as modes. The closed analytical form of these uni-variable CSDs makes it possible to evaluate in a simple way the significant quantities characterizing the sources and the ones of the fields they radiate. The basic tool leading to the definition of the uni-variable CSDs are the reproducing-kernel Hilbert spaces. As an example, the CSD derived from the so called Szeg & ouml; kernel is studied in some detail, and its features are derived, together with of those of the radiated field in the far zone.

Gori, F., Santarsiero, M., Martínez-Herrero, R. (2025). Uni-variable cross-spectral densities. OPTICS AND LASER TECHNOLOGY, 180, 111511 [10.1016/j.optlastec.2024.111511].

Uni-variable cross-spectral densities

Santarsiero, M.
;
2025-01-01

Abstract

We introduce a novel class of planar, scalar sources whose cross-spectral density is a function of a single complex variable. For a typical pair of source points, the modulus and argument of such a variable equal the product of their radial coordinates and the difference of their angular coordinates, respectively. As functions of a single complex variable, the corresponding cross-spectral densities (CSD) are expandable in power series in their convergence domain, and a virtually infinite number of source models can be devised. All such sources are shown to have vortex fields as modes. The closed analytical form of these uni-variable CSDs makes it possible to evaluate in a simple way the significant quantities characterizing the sources and the ones of the fields they radiate. The basic tool leading to the definition of the uni-variable CSDs are the reproducing-kernel Hilbert spaces. As an example, the CSD derived from the so called Szeg & ouml; kernel is studied in some detail, and its features are derived, together with of those of the radiated field in the far zone.
2025
Gori, F., Santarsiero, M., Martínez-Herrero, R. (2025). Uni-variable cross-spectral densities. OPTICS AND LASER TECHNOLOGY, 180, 111511 [10.1016/j.optlastec.2024.111511].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/490424
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