Universal framework for anisotropic particles with resonance laws and splitting

Nanophotonics enables precise control over light-matter interactions, though most established design frameworks for subwavelength nanoparticles rely on isotropic materials. Uniaxial and biaxial particles -- common in natural and engineered systems -- introduce new degrees of freedom coupling geometry and material properties, unlocking multispectral and directional response in previously unexplored spectral regions. We present a universal full-wave framework for eigenmodes and resonances in such nanoparticles. Closed-form solutions reveal axial-permittivity sum rules and anisotropy-induced symmetry breaking, producing resonance splitting and novel radiation patterns. Generalizing to ellipsoids enables geometric tuning of multispectral response, while analytic quality factors elucidate mode localization and loss. Full-wave simulations of h-BN and $\alpha$-MoO3 particles confirm the theory. This framework unifies the understanding of anisotropic nanostructures across optics, magnetism, and thermal transport, opening pathways to a new generation of photonic devices with tunable multispectral response and controlled emission with direct applications in sensing and imaging