# Faraday rotation and permittivity tensor

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1. Nov 24, 2014

### Hassan2

Dear all,

In text books about optics in magneto-optic materials, we often come across a Hermitian permittivity tensor with off-diagonal imaginary components. These components are relevant to the Faraday rotation of plane of polarization of light through the material.

Now my question is: Is the knowledge of the tensor enough to solve the wave equation and calculate the wave propagation ( including rotation)?

I ask this because they usually talk about breaking the incident linearly polarized light into left and right circularly polarized lights, where the refractive index is different for each. if the knowledge of permittivity tensor is enough for the calculations, why would we need such a non-easy-to-understand trick?

2. Nov 24, 2014

### DrDu

The point is that the wave equation with the permittivity being a tensor depending on wavenumber has two solutions (for given direction of the k vector and frequency) which turn out to correspond to left and right circularly polarized waves. Basically, you have to find a basis where the permittivity tensor is diagonal. This is a matrix eigenvalue problem which you can solve with the usual methods.

3. Nov 25, 2014

### Hassan2

Very clear.Thanks.