On the use of transmission eigenvalues to estimate the index of refraction from far field data

@article{Cakoni2007OnTU,
  title={On the use of transmission eigenvalues to estimate the index of refraction from far field data},
  author={Fioralba Cakoni and David Colton and Peter B. Monk},
  journal={Inverse Problems},
  year={2007},
  volume={23},
  pages={507-522}
}
We consider the scattering of time harmonic electromagnetic plane waves by a bounded inhomogeneous medium and show that under certain assumptions a lower bound on the index of refraction can be obtained from a knowledge of the smallest transmission eigenvalue corresponding to the medium. It is then shown by numerical examples that this eigenvalue can be determined from a knowledge of the far field pattern of the scattered wave, thus providing a practical method for estimating the index of… 

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