Two Variational Principles in Geometrical Optics-Comparisons-

Masahiro HASHIMOTO  

Publication
IEICE TRANSACTIONS on Electronics   Vol.E79-C   No.10   pp.1312-1320
Publication Date: 1996/10/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Issue on Electromagnetic Theory-Foundations and Applications)
Category: 
Keyword: 
geometrical optics,  dynamical optics,  stationary optics,  energy ray,  wave-normal ray,  variational principle,  

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Summary: 
The two variational principles, the Maupertuis' and the Hamilton's principle, are discussed in conjunction with the Fermat's principle. These two principles are shown to describe two different aspects of waves, thus resulting in the different geometry of wave propagation, the treatment of which is thus called the stationary optics or the dynamical optics, respectively. Comparisons for the results obtained from these geometrical optics are given. Another new variational principle valid for the dynamical waves reflected/refracted at the inter-faces, which has not yet been discovered so far, is also derived.