/sci/ - Science & Math

Question about plasmon dispersion relation. Why does the attached plot implies that:
"for [math]\omega<\omega_p[/math] the propagation of transverse electromagnetic waves is forbidden inside the metal plasma. For [math]\omega>\omega_p[/math] however, the plasma supports transverse waves propagating"
?
I understand that the straight line is the dispersion relation of light in a dielectric and that the hyperbola branch is the dispersion relation of volume plasmons, but I don't get their interplay.