Radiation force and torque of structured Gaussian and Airy light-sheets on a PEMC cylinder in a lossy medium

Unlike plane-wave excitation, the interaction of structured light-sheets with a particle exhibiting TM⇌TE mode conversion requires beam-shape coefficients that break the symmetry preserved under plane-wave illumination, giving rise to transverse force and axial torque components that are otherwise absent. The purpose of this work is therefore to extend the near-field optomechanical formalism for a perfect electromagnetic conductor (PEMC) cylinder in a lossy medium to nonparaxial Gaussian and Airy light-sheet illumination. Exact expressions for the radiation force vector and axial torque are derived from angular-spectrum decomposition together with near-field Maxwell stress tensor integration. The weakly truncated Airy beam is found to generate a monotonically expanding cross-polarized high-efficiency force region that is absent for the Gaussian beam. Furthermore, the radiation torque under Airy illumination reveals an antagonistic competition mechanism, in which the cross-polarized channel systematically opposes the co-polarized geometric torque, leading to near-complete torque suppression for larger size parameters. The spatial evolution of the cross-polarized null-force line is also examined: Gaussian focusing strongly suppresses its non-monotonic interference root, whereas Airy truncation preserves its structural stability, while the admittance independence of this null line is maintained throughout. Importantly, the radiation torque is shown to be driven by the extrinsic dissipation of the host medium rather than by intrinsic absorption: it vanishes identically once the host loss is removed. The present formalism provides a quantitative framework for predicting wavefront-mediated optomechanical control of polarization-converting scatterers in realistic dissipative environments.