The quasistatic response of anisotropic particles

Anisotropic particles are prevalent in a wide range of systems, ranging from ice and snow particles, to liquid crystal droplets, biological structures, magnetized plasmas, and ferromagnetic and anisotropic-phonon bulk particles. In particular, nanostructures synthesized from anisotropic phonon-supporting bulk hold promise for a new generation of high-Q tunable and directional resonators which cover unexplored midinfrared regions. However, only the dipole mode of anisotropic spherical and ellipsoidal particles has been analytically derived and experiments on the modes and resonances of such particles remain to be performed. Here, we develop an analytic theory of the complete response of subwavelength anisotropic particles, which exhibit axial-permittivity resonance sum rules. We then confirm our theoretical predictions by synthesizing biaxial particles and performing near-field measurements, with excellent agreement. Our research may find applications in devices for vibrational spectroscopy, thermal imaging, and detection of dark matter. Our theoretical analysis applies to other fields of physics such as quasi-magnetostatics and heat conduction.