  A detailed analysis of the optical response of a system accommodating several
coupled modes is needed for the complete understanding of the strong coupling
effect. In this paper, we report on the analysis of scattering cross section
spectra of Au antennas on a SiO$_{2}$ layer on a Si substrate in the IR region.
A classical model of coupled oscillators is used for determining the resonant
energies, damping rates and coupling strengths of four phonon polariton modes
in the SiO$_{2}$ layer coupled to a localized surface plasmon mode in a Au
antenna. The calculated Hopfield mixing coefficients then show the contribution
of the individual uncoupled modes to the hybrid modes of the coupled system.
