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The presence of optical polarization anisotropies, such as Faraday/Kerr effects, linear birefringence, and magnetoelectric birefringence are evidence for broken symmetry states of matter.
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For a film of thickness t t on a substrate with index of refraction n n and for the case where both the off-diagonal conductivity tensor matrix elements and the differences in diagonal elements are small, the complex transmission angle is related to the elements of the complex conductivity tensor as θ ≈ σ y ′ , x ′ t Z 0 / ( 1 + n + σ t Z 0 ) \theta\approx\sigma_{y^{\prime},x^{\prime}}tZ_{0}/(1+n+\sigma tZ_{0}) . Here σ y ′ , x ′ \sigma_{y^{\prime},x^{\prime}} is the off-diagonal conductivity in the reference frame where the incoming electric field is directed along x ′ x^{\prime} , σ \sigma is the average diagonal conductivity, and Z 0 Z_{0} the impedance of free space (377 Ω \Omega ). One can see that in the high conductivity limit, the complex angle is equal to the ratio σ y ′ , x ′ / σ \sigma_{y^{\prime},x^{\prime}}/\sigma
Cited in the paper.
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C.M. Varma, to be submitted 2013
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