Indirect Coupling and Antiresonance of Two Optic Phonons

Using Green's function techniques we calculate the spectrum for two optic phonons interacting via anharmonic coupling to two acoustic phonons. The single-phonon density of states, which is related to the first-order Raman spectrum, exhibits a zero (antiresonance) between the individual phonon peaks and yields a line shape in excellent agreement with Scott's recent experimental results for AlP${\mathrm{O}}_4$.