Negative frequencies in pulse propagation equations and the double analytic signal
In recent years, the topic of negative frequencies has resurfaced in optics motivated by the optical analogue of Hawking radiation. We discuss the physical meaning of negative frequencies and the conditions under which they are relevant. We review how negative frequencies are treated in current puls...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ad0322 |
| _version_ | 1827783788847955968 |
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| author | Raul Aguero-Santacruz David Bermudez |
| author_facet | Raul Aguero-Santacruz David Bermudez |
| author_sort | Raul Aguero-Santacruz |
| collection | DOAJ |
| description | In recent years, the topic of negative frequencies has resurfaced in optics motivated by the optical analogue of Hawking radiation. We discuss the physical meaning of negative frequencies and the conditions under which they are relevant. We review how negative frequencies are treated in current pulse propagation models based on the electric field (EF) and the analytic signal (AS). We focus on experimentally measured signals predicted by the conservation of negative comoving frequency in the nonlinear polarization terms to advance these concepts. We propose a new formalism called the double analytic signal (DAS) which clearly separates negative frequencies from positive ones. Additionally, we reduce this new formalism to the AS to prove their equivalence. Throughout the paper, we present numerical solutions of the unidirectional pulse propagation equation to illustrate the EF, AS, and DAS formalisms and to highlight their differences. |
| first_indexed | 2024-03-11T15:53:21Z |
| format | Article |
| id | doaj.art-bfecda462d3241aabb1fe2acd6788f86 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-11T15:53:21Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-bfecda462d3241aabb1fe2acd6788f862023-10-25T13:36:23ZengIOP PublishingNew Journal of Physics1367-26302023-01-01251010304510.1088/1367-2630/ad0322Negative frequencies in pulse propagation equations and the double analytic signalRaul Aguero-Santacruz0https://orcid.org/0000-0001-6897-7633David Bermudez1https://orcid.org/0000-0002-2977-0303Department of Physics, Cinvestav , A.P. 14-740, 07000 Ciudad de México, MexicoDepartment of Physics, Cinvestav , A.P. 14-740, 07000 Ciudad de México, MexicoIn recent years, the topic of negative frequencies has resurfaced in optics motivated by the optical analogue of Hawking radiation. We discuss the physical meaning of negative frequencies and the conditions under which they are relevant. We review how negative frequencies are treated in current pulse propagation models based on the electric field (EF) and the analytic signal (AS). We focus on experimentally measured signals predicted by the conservation of negative comoving frequency in the nonlinear polarization terms to advance these concepts. We propose a new formalism called the double analytic signal (DAS) which clearly separates negative frequencies from positive ones. Additionally, we reduce this new formalism to the AS to prove their equivalence. Throughout the paper, we present numerical solutions of the unidirectional pulse propagation equation to illustrate the EF, AS, and DAS formalisms and to highlight their differences.https://doi.org/10.1088/1367-2630/ad0322opticsanalogue gravitynegative frequenciespulse propagationoptical fibers |
| spellingShingle | Raul Aguero-Santacruz David Bermudez Negative frequencies in pulse propagation equations and the double analytic signal New Journal of Physics optics analogue gravity negative frequencies pulse propagation optical fibers |
| title | Negative frequencies in pulse propagation equations and the double analytic signal |
| title_full | Negative frequencies in pulse propagation equations and the double analytic signal |
| title_fullStr | Negative frequencies in pulse propagation equations and the double analytic signal |
| title_full_unstemmed | Negative frequencies in pulse propagation equations and the double analytic signal |
| title_short | Negative frequencies in pulse propagation equations and the double analytic signal |
| title_sort | negative frequencies in pulse propagation equations and the double analytic signal |
| topic | optics analogue gravity negative frequencies pulse propagation optical fibers |
| url | https://doi.org/10.1088/1367-2630/ad0322 |
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