Mgr. Martin Žlábek

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 and Bessel 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.

This work introduces a rigorous framework for systematically determining fundamental performance bounds in the context of negative dielectrophoresis. To achieve this, we apply quadratically constrained quadratic programming, a powerful optimization approach particularly well-suited for quantifying theoretical performance limits under well-defined physical constraints. We generalize these results to experimentally relevant two-dimensional electrode geometries while explicitly partitioning the design domain into controllable and uncontrollable regions consistent with experimental constraints. Furthermore, we discuss the use of topology optimization techniques to identify electrode layouts that can experimentally achieve performance close to the derived theoretical limits, thus bridging the gap between theoretical analysis and practical experimental realization.

This work proposes to construct a vector set characterizing the available degrees of freedom when forming fields to achieve optimal particle trapping or tweezing. The Galerkin’s method provides the computational means to obtain this set via the solution to a generalized eigenvalue problem.

This work investigates the performance limits of optical tweezers and trapping systems using a dipole approximation of a trapped object and a basis representing the controlling variables based on a Taylor expansion of the electromagnetic field. The study uses a convex optimization framework formulated as a quadratically constrained quadratic program to determine the maximum achievable force and/or potential curvature. The study also identifies constraints that tighten these upper limits. The analysis highlights the impact of optical system parameters, such as beam geometry, polarization, and particle losses, on trapping performance. This research provides new insights into the fundamental constraints of designs used for applications in biological manipulation, precision measurement, and microfabrication.