  We investigate exemplary the longitudinal optical (LO) mode order in
compounds with a plasmon or plasmon-like phonon mode and additional phonon
modes. When the oscillator strength of the plasmon or plasmon-like mode is
gradually increased, a reordering of the modes takes place. Since it is not
possible in crystals with orthorhombic or higher symmetry that a LO mode
crosses a transverse optical (TO) mode's position, this reordering takes place
via mode hybridization. During this mode hybridization, the plasmon or
plasmon-like LO mode gradually becomes the originally higher situated LO mode
while the latter morphs into the former. As a consequence, an inner (LO-TO) and
an outer (TO-LO) mode pair is formed. This process continues until the LO
oscillator strength is so high that all other phonons are inverted and form
LO-TO pairs within the outer TO-LO mode pair of the plasmon or plasmon-like
mode. These insights can be readily transferred to other semiconductors or many
mode materials with reststrahlen bands and allow simple mode assignments. These
mode assignments will help to understand the nature of surface modes of
structured layers of these materials for application of surface plasmon
polariton and surface phonon polaritons based metamaterials.
