The Pseudo-Maxwell Equations Revisited

Orestes N. Stavroudis

doi:10.1117/12.932352

26 February 1982 The Pseudo-Maxwell Equations Revisited

Orestes N. Stavroudis

Proceedings Volume 0294, New Methods for Optical, Quasi-Optical, Acoustic, and Electromagnetic Synthesis; (1982) https://doi.org/10.1117/12.932352
Event: 25th Annual Technical Symposium, 1981, San Diego, United States

Abstract

The so-called pseudo-Maxwell are a set of partial differential eauations that strongly resemble the Maxwell equations, yet are based only on Fermat's principle, the idea of an orthotomic system of rays, and certain theorems from differential gecmetry. From Fermat's principle, applying the Euler equation from the variational calculus, one obtains the ray equation whose solutions describe ray paths in an inhomogeneous medium. We define an aggregate of such rays as an orthotomic system if it is possible to find a sur-face orthogonal to all rays in the aggregate. Making use of the Frenet equations from differential geometry, one may derive relationships between certain geometrical vectors and their derivatives. These are the pseudo-Maxwell equations. Their existence is' paradoxical. Are they merely a mathematical artifact, an accidental quirk of the notation we are accustomed to use? Or do they indicate that there is more geometry lurking in the physics of electricity and magnetism than we ever dreamed of in our philosophies?

Citation Download Citation

Orestes N. Stavroudis "The Pseudo-Maxwell Equations Revisited", Proc. SPIE 0294, New Methods for Optical, Quasi-Optical, Acoustic, and Electromagnetic Synthesis, (26 February 1982); https://doi.org/10.1117/12.932352

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