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MS 1 MINISYMPOSIUM: ADVANCED IMAGING FOR INDUSTRIAL APPLICATION Read chapter Read first chapter

2016 | Supplement | Chapter

Maxwell’s Fish-Eye in (2+1)D Spacetime Acoustics

Authors : M. M. Tung, J. M. Gambi, M. L. García del Pino

Published in: Progress in Industrial Mathematics at ECMI 2014

Publisher: Springer International Publishing

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Abstract

In the past few years Maxwell’s fish-eye lens has been subject to intense investigation in the context of transformation optics, mainly spurred by the possibility to create perfect imaging without the need to resort to negative refraction, one of the outstanding—but difficult to implement—properties of metamaterials. Here we extend this discussion to an acoustical fish-eye constructed in (2+1)D spacetime. The underlying acoustic wave is governed by a homogeneous spherical Helmholtz equation, which is shown to emerge from a variational principle in inherently covariant manner. The formal analytical solutions of the acoustic potential are derived.

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Footnotes
1
It is customary to denote by Greek indices the usage of the full range of spacetime values for tensors, whereas Latin indices only run over the spatial values. Comma and semicolon are standard notation for partial and covariant derivatives, respectively.
 
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Metadata
Title
Maxwell’s Fish-Eye in (2+1)D Spacetime Acoustics
Authors
M. M. Tung
J. M. Gambi
M. L. García del Pino
Copyright Year
2016
Book
Progress in Industrial Mathematics at ECMI 2014

Print ISBN: 978-3-319-23412-0

Electronic ISBN: 978-3-319-23413-7

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-23413-7_126

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