Determine the principal polarizations for a wave traveling in the direction (x̂ + ŷ)/√2 in a crystal with dielectric tensor (3.5.23). A program like Mathematica can easily diagonalize a 3 × 3 matrix. Convert the Christoffel equation (3.5.22) to an equation for D(vector) = ϵ̃E(vector).

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€ = €1 0 0 0 €2 0 0 0 €3 (3.5.23)