Abstract
Using a previously derived framework that we have called the equivalence principle for electromagnetics, we analyze both transformation and moving media through a unified approach. Special emphasis is given to the application of this new method that uses the two geometric algebras defined over the tangent and cotangent bundles of space-time and is based on a technique that we have called the vacuum form reduction: the space-time constitutive relation of a class of biani-sotropic media in a rigid metric is reduced, through this transformation, to a space-time constitutive relation which has the same form of vacuum and leads to a fictitious space-time with a flexible metric. As an example of transformation media we analyze an elliptic cloak with a drag effect. Negative refraction in moving media is the other example that we have chosen to illustrate the applicability of the general framework.
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References
Burke, W.L.: Applied Differential Geometry, p. xii. Cambridge University Press, Cambridge (1985)
Lindell, I.V.: Differential Forms in Electromagnetics, pp. 1–5. IEEE/Wiley, Piscataway, NJ (2004)
Thirring, W.: Classical Mathematical Physics — Dynamical Systems and Field Theories, 3rd ed., pp. 312–328. Springer, New York (1997)
Hestenes, D.: Oersted Medal Lecture 2002: Reforming the mathematical language of physics. Am. J. Phys. 71, 104–121 (2003)
Hehl F.W., Obukhov, Yu. N.: Foundations of Classical Electrodynamics. Birkhäuser, Boston, MA (2003)
Ribeiro, M.A., Paiva, C.R.: An equivalence principle for electromagnetics through Clifford's geometric algebras. Metamaterials (2008), doi: 10.1016/j.metmat.2008.03.002
Schurig, D., Pendry, J.B., Smith, D.R.: Calculation of material properties and ray tracing in transformation media. Opt. Express 14, 9794–9804 (2006)
Leonhardt, U., Philbin, T.G.: General relativity in electrical engineering. New J. Phys. 8, 247 (2006)
Mackay, T.G., Lakhtakia, A.: Counterposition and negative refraction due to uniform motion. Microwave Opt. Technol. Lett. 49, 874–876 (2007)
Grzegorczyk, T.M., Kong, J.A.: Electrodynamics of moving media inducing positive and negative refraction. Phys. Rev. B 74, 033102 (2006)
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© 2009 Springer-Verlag Berlin Heidelberg
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Ribeiro, M.A., Paiva, C.R. (2009). Transformation and Moving Media: A Unified Approach Using Geometric Algebra. In: Zouhdi, S., Sihvola, A., Vinogradov, A.P. (eds) Metamaterials and Plasmonics: Fundamentals, Modelling, Applications. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9407-1_5
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DOI: https://doi.org/10.1007/978-1-4020-9407-1_5
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