Optical-phonon tunneling

LO phonons in polar material can tunnel resonantly through a rigid barrier provided that they can excite an interface polariton. A theory of phonon tunneling based on a macroscopic continuum model is presented. The ability of LO phonons to be transmitted is shown to be dependent upon there being sufficient dispersion for the LO frequency band to overlap significantly the ‘‘classical’’ dispersion of interface modes. The interaction with electrons in the barrier is discussed. It is also shown that interface modes appear in their own right only in the frequency range below the LO band but above ${\mathrm{\omega }}_{\mathrm{TO}}$.