Fig. 4: Analytical modeling and simulations.

a \(\frac{{{S}}_{{\mathrm{bright}}}}{{{S}}_{{\mathrm{dark}}}}\) at \({\theta } \sim {90}^\circ\) plotted along with the sapphire b-axis permittivity. b \(\frac{{{S}}_{{\mathrm{bright}}}}{{{S}}_{{\mathrm{dark}}}}\) at \({\theta } \sim {0}^\circ\) plotted along with the sapphire c-axis permittivity. The green and yellow arrows in a and b indicate the \({{\omega }}_{{\mathrm{TO}}{i}}\) and \({{\omega }}_{{\mathrm{LO}}{i}}\), respectively. c, d amplitudes and phases of \({1}/{\beta }\) calculated with b-axis permittivity and c-axis permittivity together with experimental data. e and f simulated spectra plotted with experimental data for \({E}\perp {c}\) and \({E}//{c}\), respectively.