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A detailed analysis of the optical response of a system accommodating severalcoupled modes is needed for the complete understanding of the strong couplingeffect. In this paper, we report on the analysis of scattering cross sectionspectra 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 resonantenergies, damping rates and coupling strengths of four phonon polariton modesin the SiO$_{2}$ layer coupled to a localized surface plasmon mode in a Auantenna. The calculated Hopfield mixing coefficients then show the contributionof the individual uncoupled modes to the hybrid modes of the coupled system.

Strong coupling in a Au plasmonic antenna-SiO$_{2}$ layer system: a hybrid mode analysis