Semianalytical Treatment of Collective Vibrational Strong Coupling in Infrared Phononic and Plasmonic Nanoantennas

The interaction between nanoantenna electromagnetic modes and molecular vibrations enables key nanophotonic applications such as ultrasensitive vibrational spectroscopy and molecular sensing. Here, we develop a systematic analysis to obtain the collective coupling strength, g, between bright collective vibrational modes of an assembly of molecules and infrared modes of phononic and plasmonic nanoantennas. Our approach exploits the information in the electromagnetic fields as obtained from a single classical simulation, incorporated in semianalytical equations that enable to calculate g for any arbitrary molecular distribution, thus dramatically reducing the computational effort. These semianalytical equations are validated by comparing the results of the coupling strength with those obtained from a harmonic oscillator model by fitting the extinction cross-section spectra. Furthermore, we apply the semianalytical equations in our model to compare the values of g obtained for molecules surrounding both phononic and noble-metal plasmonic nanoantennas. Our results indicate that in the infrared, the coupling with noble-metal plasmonic nanoantennas achieves larger g than with phononic nanoantennas for any molecular distribution. However, due to the large plasmonic losses, reaching the strong coupling regime is more feasible in phononic nanoantennas. Additionally, we derive simplified analytical expressions of g valid when a nanoantenna is fully surrounded by molecules. These expressions reveal that the coupling strength is governed in this case by the ratio of the electromagnetic energy inside and outside the nanoantenna. Our results provide insights on the interaction of infrared nanoantennas with molecules at infrared frequencies, facilitating the design of optimized configurations for different applications in nanophotonics.