Coupled modes withA1symmetry in tetragonal BaTiO3

The infrared properties of a system of first-order-coupled phonons are analyzed. The dielectric function and the Raman line shape of the polariton modes are derived. The parameters involved in the theory can be obtained from the Raman spectra of the TO and LO modes or from the Raman spectrum of the TO modes plus infrared-reflectivity measurements. It is shown that we can objectively distinguish real coupling from imaginary, contrary to the current belief. Numerical calculations are performed for the $A_1$-symmetry modes of tetragonal BaTi${\mathrm{O}}_3$, with good agreement for the polariton shapes and complete disagreement for the infrared reflectivity; damage at the crystal surface is pointed out as the probable cause of the discrepancy. In addition to the coupling between the lowest and the middle mode, previously known, a much larger coupling between the middle mode and the highest is shown to exist. Both couplings are shown to be real or nearly so. The discrepancy between the dielectric constant created by the resonant modes (electronic plus phonons) and the value obtained by electrical measurements is interpreted as a new indication that the crystal has a dynamical disorder; this disorder could also be cause of an anomalous broadening observed in the lowest polariton.