= Solution
In <Raman scattering>, the <photon> transfers $\hbar\omega=\hbar(\omega_i-\omega_s)$ and $\mathbf q=\mathbf k_i-\mathbf k_s$ to a collective excitation. Changing scattering geometry selects different $q$ and probes its dispersion.
The open circles rise and then flatten near $45\,\mathrm{meV}$: they trace the lower transverse <phonon polariton> branch. It is strongly dispersive on its <photon>-like side, then becomes predominantly TO-<phonon>-like and approaches the TO <energy> at larger <wavevector>. The open triangles stay near $50\,\mathrm{meV}$ and are the nearly nondispersive longitudinal <optical phonon>. Longitudinal motion creates its own polarization field and is shifted above the transverse resonance. It does not hybridize with a propagating transverse <photon> in the same way, and it should not be misidentified as the upper transverse <polariton> branch, which rises with <wavevector>. Raman tensor and polarization selection rules determine which excitation is visible.
\b[Scale qualification:] the source horizontal label appears to print $10^{-4}\,\mathrm{cm^{-1}}$. Taken literally, one plotted unit would have vacuum <photon> <energy> only $\hbar c\times0.01\,\mathrm{m^{-1}}\simeq2\times10^{-6}\,\mathrm{meV}$, inconsistent with the observed tens of meV and the dispersive <polariton>. The physically compatible scale is of order $10^4\,\mathrm{cm^{-1}}$; the qualitative branch identification does not require silently treating the printed negative exponent as correct. The original model figure in <past-exam-of-the-condensed-matter-physics-major-option-course-of-the-university-of-oxford/2018/4/b/solution> explicitly labels its calculated <wavevector> scale.
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