| Issue |
J. Eur. Opt. Soc.-Rapid Publ.
Volume 12, Number 1, 2016
|
|
|---|---|---|
| Article Number | 7 | |
| Number of page(s) | 8 | |
| DOI | https://doi.org/10.1186/s41476-016-0008-6 | |
| Published online | 28 June 2016 | |
Research
Propagation algorithms for Wigner functions
1
Friedrich-Schiller-University Jena, Institute of Applied Physics, 07743, Jena, Germany
2
Fraunhofer Institute for Applied Optics and Precision Engineering IOF, 07745, Jena, Germany
Received:
3
April
2016
Accepted:
25
May
2016
We propose an algorithm to remove a parabolic wavefront from a convergent or divergent beam in the Wigner function. Using this approach we numerically collimate the beam. This avoids a dense sampling in phase space to describe a convergent wavefront. Thereby we reduce the required computer memory, but maintain computational accuracy and physical effects. Furthermore, we compare two algorithms, shearing and Radon transform, to propagate the Wigner function in free space. We use the fast Fourier transform to accurately perform shearing. However, zero-padding is necessary to circumvent aliasing. We prove that the Radon transform is a more efficient approach for a long propagated distance.
Key words: Phase space / Parabolic wavefront / Sampling / Shearing / Radon transform
© The Author(s) 2016
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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