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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Notes
- 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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Tung, M.M., Gambi, J.M., del Pino, M.L.G. (2016). Maxwell’s Fish-Eye in (2+1)D Spacetime Acoustics. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds) Progress in Industrial Mathematics at ECMI 2014. ECMI 2014. Mathematics in Industry(), vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-23413-7_126
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DOI: https://doi.org/10.1007/978-3-319-23413-7_126
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