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$${\bigg|\frac{E_{r0}^ \parallel}{E_{i0}^\parallel} \bigg| \exp(i\delta^\parallel )=-\frac{ \tilde n_2^2 \cos \alpha - \sqrt{\tilde n_2^2 - \sin^2 \alpha}}{\tilde n_2^2 \cos \alpha + \sqrt{\tilde n_2^2 - \sin^2 \alpha}} \\ \bigg|\frac{E_{r0}^ \perp}{E_{i0}^\perp} \bigg| \exp(i\delta^\perp) = \frac{\cos \alpha - \sqrt{\tilde n_2^2 - \sin^2 \alpha}}{\cos \alpha + \sqrt{\tilde n_2^2 - \sin^2 \alpha}}}$$