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We investigate exemplary the longitudinal optical (LO) mode order incompounds with a plasmon or plasmon-like phonon mode and additional phononmodes. When the oscillator strength of the plasmon or plasmon-like mode isgradually increased, a reordering of the modes takes place. Since it is notpossible in crystals with orthorhombic or higher symmetry that a LO modecrosses a transverse optical (TO) mode's position, this reordering takes placevia mode hybridization. During this mode hybridization, the plasmon orplasmon-like LO mode gradually becomes the originally higher situated LO modewhile the latter morphs into the former. As a consequence, an inner (LO-TO) andan outer (TO-LO) mode pair is formed. This process continues until the LOoscillator strength is so high that all other phonons are inverted and formLO-TO pairs within the outer TO-LO mode pair of the plasmon or plasmon-likemode. These insights can be readily transferred to other semiconductors or manymode materials with reststrahlen bands and allow simple mode assignments. Thesemode assignments will help to understand the nature of surface modes ofstructured layers of these materials for application of surface plasmonpolariton and surface phonon polaritons based metamaterials.

Revisiting longitudinal optical modes in materials with plasmon and plasmon-like absorptions -- SrTiO$_3$ and $\beta$-Ga$_2$O$_3$