Physical Bounds on Optical Micromanipulation: Maximal Stiffness in the Dipole Regime

Abstract

Optical trapping and micromanipulation rely on carefully shaped electromagnetic fields to exert precise forces and torques on microscopic particles. Despite their widespread application in biology and nanotechnology, the absolute physical limits of trapping performance, specifically the maximum achievable optical force and trap stiffness, have not yet been rigorously quantified. This work establishes a general theoretical framework to determine these fundamental bounds in the dipole approximation. By relating the optical force and stiffness to a local Taylor expansion of the electromagnetic field at the particle location, we formulate the performance limit as a solution to a quadratically constrained quadratic program. To evaluate these bounds, we employ two complementary approaches. First, we utilize a complete basis of vector spherical wave functions to determine the absolute theoretical limits of optical force and stiffness permitted by Maxwell's equations in free space, revealing Pareto-optimal trade-offs between stable confinement and directional force. Second, we introduce an aperture-based formulation that restricts the incident fields to those realizable by finite planar apertures. This yields device-consistent bounds directly applicable to experimental setups which rely mostly on electromagnetic beams. The finding that optimized aperture fields can outperform standard Gaussian beams by removing the severe axial bottleneck is particularly important. By comparing these two regimes, we identify the specific spatial modes that contribute to stable trapping and quantify the performance trade-offs inherent to physical beam shaping. This dual framework provides provably optimal bounds for power-normalized optical tweezers and serves as a rigorous benchmark for evaluating realistic beam designs.