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According to this paper (https://doi.org/10.1063/1.5128679), the dispersion relation of hyperbolic materials is as follows:

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then it is said, that he first term in brackets in the equation describes a TE polarized wave while the second brackets represents TE modes. I'm having a really hard time understanding this. Is there anyway to deduce polarization modes from dispersion relation? Any help would be highly appreciated.

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