Summary
The Helmholtz equation for the propagation of an e.m. wave in a self-focusing fiber is reduced to a Pauli-type two-component equation in the paraxial approximation. Thefiber spinor components are then shown to be related to the ray height and reduced slope. Finally, comments on the meaning of the paraxial approximation are presented.
Riassunto
In questo lavoro si dimostra come sia possibile ridurre l’equazione di Helmholtz in approssimazione parassiale e per una fibra autofocheggiante, ad un’equazione a due componenti di tipo Pauli. Si dimostra inoltre che le componenti dellospinore di fibra sono l’altezza parassiale e la cosiddettapendenza ridotta. Infine si discute una possibile estensionerelativistica della teoria sviluppata.
Резюме
Уравхение Гельмгольца для распространения электромагнитной волны в самофокусирующей нити сводится к двух-компонентному уравнению типа Паули в параксиальном проиближении. Эатем показывается, что волоконно-спинорные компоненты связаны с амплитудой луча и приведенным наклоном. Обсуждается Физический смысл парсиального приближения.
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Dattoli, G., Di Lazzaro, P. & Torre, A. A spinor approach to the propagation in self-focusing fibers. Nuovo Cim B 105, 165–178 (1990). https://doi.org/10.1007/BF02723075
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DOI: https://doi.org/10.1007/BF02723075