Generation of High Order Harmonics in Vacuum for Various Configurations of Interacting Electromagnetic Field
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911367423852544 |
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| author | Sasorov, Pavel Bulanov, Sergei |
| author_facet | Sasorov, Pavel Bulanov, Sergei |
| contents | High order harmonic (HOH) generation by interacting extremely intense electromagnetic waves in the quantum vacuum is investigated within the framework of the Heisenberg-Euler formalism. We consider here the process in the lowest order of a perturbation theory relative to the electromagnetic (EM) beam intensity, giving contribution to the HOH generation. The main expressions are obtained for a general geometry, whyle polarizations of different sub-beams forming the EM beam focus are almost the same. Nevertheless, explicit expressions for the HOH generation are derived for the $4π$-dipole in-coming waves and for the two crossing Gaussian beams. The former geometry of the EM beam is optimal at a given EM wave power, whereas the latter one is more realistic from the experimental point of view. We consider also a relationship of our present general results with the results, obtained earlier for the HOH generation during of collision of two plane electromagnetic waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09214 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generation of High Order Harmonics in Vacuum for Various Configurations of Interacting Electromagnetic Field Sasorov, Pavel Bulanov, Sergei Plasma Physics High Energy Physics - Phenomenology High order harmonic (HOH) generation by interacting extremely intense electromagnetic waves in the quantum vacuum is investigated within the framework of the Heisenberg-Euler formalism. We consider here the process in the lowest order of a perturbation theory relative to the electromagnetic (EM) beam intensity, giving contribution to the HOH generation. The main expressions are obtained for a general geometry, whyle polarizations of different sub-beams forming the EM beam focus are almost the same. Nevertheless, explicit expressions for the HOH generation are derived for the $4π$-dipole in-coming waves and for the two crossing Gaussian beams. The former geometry of the EM beam is optimal at a given EM wave power, whereas the latter one is more realistic from the experimental point of view. We consider also a relationship of our present general results with the results, obtained earlier for the HOH generation during of collision of two plane electromagnetic waves. |
| title | Generation of High Order Harmonics in Vacuum for Various Configurations of Interacting Electromagnetic Field |
| topic | Plasma Physics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2508.09214 |