Title: Localized Resonant Phonon Polaritons in Biaxial Nanoparticles

Abstract: The discovery of localized plasmon polariton resonances has been pivotal in enabling tunability of the optical resonance. Recently, extensive research efforts have aimed to expand these achievements to other polaritonic states that exhibit less loss and in other spectral regions. However, these efforts were limited to isotropic or uniaxial structures, and an eigenmode theory was derived only for isotropic particles. Here, we present a breakthrough in synthesizing biaxial nanostructures that exhibit localized hyperbolic phonon resonances with high Q-factors in the mid-infrared. Furthermore, we develop a theory that predicts high-order resonances in anisotropic particles with coupling between the axial permittivites. Finally, we confirm the theoretical predictions through near-field measurements, which demonstrate the existence of both the first and higher-order resonant modes. Our findings provide the foundation for designing a new generation of anisotropic resonators with various applications in the mid-IR range. Our analysis applies to other fields, such as quasi-magnetostatics and heat conduction.