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I need to determine the TE and TM reflections at the interface between a uniaxial crystal and air, using a matrix-based method, such as the TMM.

I can do so using the Fresnel equation with ease, but I'm not sure how to incorporate the indices in the matrices.

I know nothing about the fields, just the refractive indices. Is the TMM the right method for this job? If so, how do I convert the field matrix to one incorporating the refractive index?

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