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Transformation Optics

  • Chapter
Analogue Gravity Phenomenology

Part of the book series: Lecture Notes in Physics ((LNP,volume 870))

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Abstract

Transformation optics applies ideas from Einstein’s general theory of relativity in optical and electrical engineering for designing devices that can do the (almost) impossible: invisibility cloaking, perfect imaging, levitation, and the creation of analogues of the event horizon. This chapter gives an introduction to this field requiring minimal prerequisites.

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Notes

  1. 1.

    We consider purely spatial geometries first and then, in Sect. 10.5, we generalise our theory to spacetime geometries.

  2. 2.

    In gravitational lensing, gravity alters primarily the measure of time, but due to the conformal invariance of electromagnetism (see Sect. 10.5.2) this is equivalent to altering the measure of space.

  3. 3.

    It might be reassuring to know that perfect deception is impossible; the truth will always appear in the end.

  4. 4.

    A repulsive Casimir force was observed [31] between three materials with ε 1<ε 2<ε 3 over a sufficiently broad frequency range [32], i.e. in materials but not in empty space yet.

  5. 5.

    Of course, in a more realistic theory the charged particle should not be regarded as being a classical object interacting with the quantum vacuum, as in Casimir’s case [44], but rather as a self-consistent quantum structure.

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Acknowledgements

I am most grateful for the discussions I had with many distinguished scientists about geometry, light and a wee bit of magic. In particular, I thank my group at St Andrews and wish them well, Simon Horsley, Susanne Kehr, Thomas Philbin, Sahar Sahebdivan, and William Simpson. My work has been supported by the University of St Andrews, the Engineering and Physical Sciences Research Council and the Royal Society.

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Authors and Affiliations

  1. School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews, KY16 9SS, UK

    Ulf Leonhardt

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  1. Ulf Leonhardt
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Correspondence to Ulf Leonhardt .

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Editors and Affiliations

  1. School of Engineering and Physical Science, Heriot-Watt University, Edinburgh, United Kingdom

    Daniele Faccio

  2. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Francesco Belgiorno

  3. Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Como, Italy

    Sergio Cacciatori

  4. Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Como, Italy

    Vittorio Gorini

  5. Int. School for Adv. Studies (SISSA), Trieste, Italy

    Stefano Liberati

  6. Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Como, Italy

    Ugo Moschella

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Leonhardt, U. (2013). Transformation Optics. In: Faccio, D., Belgiorno, F., Cacciatori, S., Gorini, V., Liberati, S., Moschella, U. (eds) Analogue Gravity Phenomenology. Lecture Notes in Physics, vol 870. Springer, Cham. https://doi.org/10.1007/978-3-319-00266-8_10

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