Nonlinear transformation optics and engineering of the Kerr effect

@article{Bergamin2011NonlinearTO,
  title={Nonlinear transformation optics and engineering of the Kerr effect},
  author={Luzi Bergamin and Pekka Alitalo and Sergei A. Tretyakov},
  journal={Physical Review B},
  year={2011},
  volume={84},
  pages={205103}
}
The concept of transformation optics is extended to nonlinear electrodynamics. It is shown that transformation optics favors implicit constitutive relations in terms of energy densities D.E and B.H rather than E^2 and H^2. The Kerr nonlinearity is studied in detail and the transformation optics based engineering of self-interaction effects is discussed. As a specific example we introduce transformation optics applied on a self-focusing field configuration. 
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