A phase-space approach for propagating field–field correlation functions
We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation functions and the Wigner function and admits in its simplest approx...
| Main Authors: | , , , , |
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| Format: | Article |
| Published: |
IOP Publishing
2015
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| Online Access: | https://eprints.nottingham.ac.uk/45680/ |
| _version_ | 1848797173159821312 |
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| author | Gradoni, Gabriele Creagh, Stephen C. Tanner, Gregor Smartt, Chris Thomas, David W.P. |
| author_facet | Gradoni, Gabriele Creagh, Stephen C. Tanner, Gregor Smartt, Chris Thomas, David W.P. |
| author_sort | Gradoni, Gabriele |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation functions and the Wigner function and admits in its simplest approximation a direct representation in terms of the evolution of ray densities in phase space. We show that next leading order corrections to the ray-tracing approximation lead to Airy-function type phase space propagators. By exploiting the exact Wigner function propagator, inherently wave-like effects such as evanescent decay or radiation from more heterogeneous sources as well as diffraction and reflection can be included and analysed. We discuss in particular the role of evanescent waves in the near-field of non-paraxial sources and give explicit expressions for the growth rate of the correlation length as a function of the distance from the source. The approximations are validated using full-wave simulations of model sources. In particular, results for the reflection of partially coherent sources from flat mirrors are given where the influence of Airy function corrections can be demonstrated. We focus here on electromagnetic sources at microwave frequencies and modelling efforts in the context of electromagnetic compatibility. |
| first_indexed | 2025-11-14T19:59:40Z |
| format | Article |
| id | nottingham-45680 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:59:40Z |
| publishDate | 2015 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-456802020-05-04T17:16:55Z https://eprints.nottingham.ac.uk/45680/ A phase-space approach for propagating field–field correlation functions Gradoni, Gabriele Creagh, Stephen C. Tanner, Gregor Smartt, Chris Thomas, David W.P. We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation functions and the Wigner function and admits in its simplest approximation a direct representation in terms of the evolution of ray densities in phase space. We show that next leading order corrections to the ray-tracing approximation lead to Airy-function type phase space propagators. By exploiting the exact Wigner function propagator, inherently wave-like effects such as evanescent decay or radiation from more heterogeneous sources as well as diffraction and reflection can be included and analysed. We discuss in particular the role of evanescent waves in the near-field of non-paraxial sources and give explicit expressions for the growth rate of the correlation length as a function of the distance from the source. The approximations are validated using full-wave simulations of model sources. In particular, results for the reflection of partially coherent sources from flat mirrors are given where the influence of Airy function corrections can be demonstrated. We focus here on electromagnetic sources at microwave frequencies and modelling efforts in the context of electromagnetic compatibility. IOP Publishing 2015-09-16 Article PeerReviewed Gradoni, Gabriele, Creagh, Stephen C., Tanner, Gregor, Smartt, Chris and Thomas, David W.P. (2015) A phase-space approach for propagating field–field correlation functions. New Journal of Physics, 17 . 093027/1-093027/16. ISSN 1367-2630 http://iopscience.iop.org/article/10.1088/1367-2630/17/9/093027/meta doi:10.1088/1367-2630/17/9/093027 doi:10.1088/1367-2630/17/9/093027 |
| spellingShingle | Gradoni, Gabriele Creagh, Stephen C. Tanner, Gregor Smartt, Chris Thomas, David W.P. A phase-space approach for propagating field–field correlation functions |
| title | A phase-space approach for propagating field–field correlation functions |
| title_full | A phase-space approach for propagating field–field correlation functions |
| title_fullStr | A phase-space approach for propagating field–field correlation functions |
| title_full_unstemmed | A phase-space approach for propagating field–field correlation functions |
| title_short | A phase-space approach for propagating field–field correlation functions |
| title_sort | phase-space approach for propagating field–field correlation functions |
| url | https://eprints.nottingham.ac.uk/45680/ https://eprints.nottingham.ac.uk/45680/ https://eprints.nottingham.ac.uk/45680/ |