On the Twistability of Partially Coherent, Schell-model Sources
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929659417985024 |
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| author | Borghi, Riccardo |
| author_facet | Borghi, Riccardo |
| contents | In this paper, the problem of assessing the twistability of a given bona fide cross-spectral density is tackled for the class of Schell-model sources, whose shift-invariant degree of coherence is represented by a real and symmetric function, {denoted as} $μ(-\bfr)=μ(\bfr)$. By employing an abstract operatorial language, the problem of determining the highly degenerate spectrum of a twisted operator $\hat W_u$ is addressed through a modal analysis based on {the} complete knowledge of the spectrum of the {\em sole} twist operator $\hat T_u$, as found by R. Simon and N. Mukunda. [J. Opt. Soc. Am. A \textbf{15,} 1361 (1998)]. To this end, the evaluation of the complete tensor of the matrix elements $\bra n',\ell'|\hat W_u|n,\ell\ket$ is carried out within the framework of the so-called {\em extended Wigner distribution function}, a concept recently introduced by M. {VanValkenburgh} [J. Mod. Opt. \textbf{55,} 3537 - 3549 (2008)]. As a nontrivial application of the algorithm developed here, the analytical determination of the spectrum of saturated twisted astigmatic Gaussian Schell-model sources is also presented. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_19807 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Twistability of Partially Coherent, Schell-model Sources Borghi, Riccardo Optics In this paper, the problem of assessing the twistability of a given bona fide cross-spectral density is tackled for the class of Schell-model sources, whose shift-invariant degree of coherence is represented by a real and symmetric function, {denoted as} $μ(-\bfr)=μ(\bfr)$. By employing an abstract operatorial language, the problem of determining the highly degenerate spectrum of a twisted operator $\hat W_u$ is addressed through a modal analysis based on {the} complete knowledge of the spectrum of the {\em sole} twist operator $\hat T_u$, as found by R. Simon and N. Mukunda. [J. Opt. Soc. Am. A \textbf{15,} 1361 (1998)]. To this end, the evaluation of the complete tensor of the matrix elements $\bra n',\ell'|\hat W_u|n,\ell\ket$ is carried out within the framework of the so-called {\em extended Wigner distribution function}, a concept recently introduced by M. {VanValkenburgh} [J. Mod. Opt. \textbf{55,} 3537 - 3549 (2008)]. As a nontrivial application of the algorithm developed here, the analytical determination of the spectrum of saturated twisted astigmatic Gaussian Schell-model sources is also presented. |
| title | On the Twistability of Partially Coherent, Schell-model Sources |
| topic | Optics |
| url | https://arxiv.org/abs/2412.19807 |