Numerical Stability Analysis of an Acoustically Levitated Thin Reflective Plate for Contactless Optical Beam Steering

Acoustically levitated thin reflective plates provide a promising approach for contactless optical beam steering by eliminating mechanical hinges, sliding interfaces, and the associated wear and friction losses. However, unlike conventional spherical particles or droplets, thin planar reflectors exhibit highly geometry-dependent acoustic force distributions and are highly susceptible to lateral drift and angular destabilization when the acoustic field is dynamically reconfigured for beam steering. Here, we present a theoretical and simulation-based stability analysis of an acoustically levitated thin reflective plate driven by a phase-controlled dual-array acoustic field. A reduced-order model based on the Gor'kov potential is developed to characterize the acoustic potential landscape, escape-barrier depth, and local restoring stiffness during phase-gradient-induced mirror tilting. The simulations reveal that increasing the phase gradient progressively distorts the trapping potential and reduces the available trapping stability margin. Among the translational degrees of freedom, the lateral restoring stiffness deteriorates much more rapidly than the axial stiffness, indicating that lateral slippage is the primary instability pathway during continuous steering. Parametric analysis further shows that thinner mirrors with larger radii can improve trapping stability by increasing the effective acoustic interaction area while reducing gravitational and inertial penalties. The influence of non-ideal acoustic driving conditions is also evaluated to determine practical operating limits for stable operation. These results clarify the stability mechanisms governing acoustically suspended planar reflectors and provide theoretical design guidelines for robust contactless optical beam-steering systems.