Mgr. Martin Žlábek

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.