Universal framework for anisotropic particles with resonance laws and splitting

Nanophotonics enables unprecedented control over light-matter interactions, yet conventional isotropic materials limit the spectral range and mode response in subwavelength structures. Anisotropic nanoparticles -- ubiquitous in natural and engineered systems -- offer new degrees of freedom that couple geometry and material properties, unlocking previously inaccessible spectral regions. Here, we establish a universal full-wave framework describing the eigenmodes and resonance conditions of uniaxial and biaxial nanoparticles. Closed-form solutions reveal axial-permittivity sum rules and material-anisotropy-induced symmetry breaking, manifesting as resonance splitting and novel radiation patterns. Generalizing the theory to ellipsoids provides geometric tunability of the multispectral response, while analytic predictions of quality factors elucidate how anisotropy governs mode localization and energy loss. Full-wave simulations of h-BN and $\alpha$-MoO3 nanoparticles, together with our recently reported experimental observations, confirm the theory. This framework unifies the understanding of anisotropic nanostructures across optics, thermal transport, and magnetism, enabling a new generation of photonic devices with tunable multispectral response and directional emission.