The Fresnel equations of classical and extended electrodynamics – a review
Corresponding Author
Elena A. Ivanova
Higher School of Theoretical Mechanics and Mathematical Physics, Peter the Great St.Petersburg Polytechnic University, Saint-Petersburg, Russia
Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, Saint-Petersburg, Russia
Correspondence
Elena A. Ivanova, Higher School of Theoretical Mechanics and Mathematical Physics, Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251, Saint-Petersburg, Russia.
Email: [email protected]
Search for more papers by this authorWolfgang H. Müller
Institut für Mechanik Fachgebiet Kontinuumsmechanik und Materialtheorie, Technische Universität Berlin, Berlin, Germany
Search for more papers by this authorWilhelm Rickert
Institut für Mechanik Fachgebiet Kontinuumsmechanik und Materialtheorie, Technische Universität Berlin, Berlin, Germany
Search for more papers by this authorElena N. Vilchevskaya
Institut für Mechanik Fachgebiet Kontinuumsmechanik und Materialtheorie, Technische Universität Berlin, Berlin, Germany
Search for more papers by this authorCorresponding Author
Elena A. Ivanova
Higher School of Theoretical Mechanics and Mathematical Physics, Peter the Great St.Petersburg Polytechnic University, Saint-Petersburg, Russia
Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, Saint-Petersburg, Russia
Correspondence
Elena A. Ivanova, Higher School of Theoretical Mechanics and Mathematical Physics, Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251, Saint-Petersburg, Russia.
Email: [email protected]
Search for more papers by this authorWolfgang H. Müller
Institut für Mechanik Fachgebiet Kontinuumsmechanik und Materialtheorie, Technische Universität Berlin, Berlin, Germany
Search for more papers by this authorWilhelm Rickert
Institut für Mechanik Fachgebiet Kontinuumsmechanik und Materialtheorie, Technische Universität Berlin, Berlin, Germany
Search for more papers by this authorElena N. Vilchevskaya
Institut für Mechanik Fachgebiet Kontinuumsmechanik und Materialtheorie, Technische Universität Berlin, Berlin, Germany
Search for more papers by this authorAbstract
We study the behavior of electromagnetic waves near the interface between two media: a dielectric medium and a conducting medium leading to the so-called Fresnel equations. We discuss analytical solutions of the problem in the framework of classical as well as extended electrodynamics. As a didactic add-on a rational derivation of the classical Fresnel equations in conducting media by using a consistent application of vector representation for the wave vectors is presented for the benefit of the reader. The Fresnel equations obtained in the framework of extended electrodynamics are novel. We also discuss three mechanical models of electrodynamic processes in conducting media. The mathematical description of two of them allows one to obtain classical Maxwell's equations. The third model combines the two first models. Its mathematical description allows one to obtain the equations of extended electrodynamics.
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