Optical forces and torques on rotating dielectric spheres: symmetry-breaking mechanisms for rotation-rate sensing

The extreme rotation of optically levitated dielectric spheres has opened new frontiers in inertial metrology and fundamental light-matter interactions. However, standard scattering theories relying on static assumptions fail to reveal how particle rotation actively modulates the electromagnetic response. Here, we present a rigorous analytical theory for the optical forces and torques on a uniformly rotating dielectric sphere. By incorporating the dimensionless rotation parameter γ = Ωa/c into the Generalized Lorenz-Mie Theory (GLMT) framework, we derive analytical expressions that explicitly relate the rotation rate to mechanical observables. Our analysis reveals that rotation breaks the azimuthal degeneracy (m ↔ -m) of Mie modes, unlocking asymmetric inter-mode interference channels strictly forbidden in static systems. This mechanism induces rotation-dependent resonances in the transverse-force response and in the Cartesian components of the optical torque. Furthermore, we identify specific "rotation-sensitive windows" within the parameter space, where these observables exhibit strong, monotonic rotation dependence. These findings establish a theoretical benchmark for extreme-rotation levitodynamics and provide an analytical framework for understanding rotation-dependent mechanical responses in high-quality-factor (high-Q) micro-rotors.