The wave equation: from eikonal to anti-eikonal approximation
https://doi.org/10.17073/1609-3577-2016-2-103-107
Abstract
When the refractive index changes very slowly compared to the wave-length we may use the eikonal approximation to the wave equation. In the opposite case, when the refractive index highly variates over the distance of one wave-length, we have what can be termed as the anti-eikonal limit. This situation is addressed in this work. The anti- eikonal limit seems to be a relevant tool in the modelling and design of new optical media. Besides, it describes a basic universal behaviour, independent of the actual values of the refractive index and, thus, of the media, for the components of a wave with wave-length much greater than the characteristic scale of the refractive index.
Supporting agencies: Instituto de Investigaciones Económicas y Sociales Francisco de Vitoria
About the Authors
L. Vázquez
Universidad Complutense de Madrid
Spain
Spain
Luis Vázquez — Dept. Matemática Aplicada, Facultad de Informática
Madrid
S. Jiménez
Universidad Politécnica de Madrid
Spain
Spain
Salvador Jiménez — Dept. Matemática Aplicada a las TIC, ETSI Telecomunicación
30 Complutense Ave., 28040, Madrid
A. B. Shvartsburg
Joint Institute for High Temperatures Russian Academy of Sciences;
Institute for Space Researches Russian Academy of Sciences
Russian Federation
Russian Federation
Alexander B. Shvartsburg
13/2 Izhorskaya Str., Moscow 125412
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Review
For citations:
Vázquez L., Jiménez S., Shvartsburg A.B. The wave equation: from eikonal to anti-eikonal approximation. Izvestiya Vysshikh Uchebnykh Zavedenii. Materialy Elektronnoi Tekhniki = Materials of Electronics Engineering. 2016;19(2):103-107. (In Russ.) https://doi.org/10.17073/1609-3577-2016-2-103-107
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