doc. Ing. Lukáš Jelínek, Ph.D.

Physics is built upon fundamental limitations or bounds, well know examples being the first law of thermodynamics or the energy mass relation E = m c^2. These limitations present important theoretical concepts, but equally important are in judging the performance of processes made by nature or stimulated by humans. Electromagnetic interaction is a guiding principle of the world we live in and knowledge of fundamental limitations on electromagnetic metrics is of great importance. The thesis will focus on mathematical formulation of single objective and multi objective bounds to metrics relevant to electromagnetic scattering such as space-time field concentration, absorption or stimulated fluorescence. Understanding these limits will have significant consequences in optical spectroscopy or in the design of high-speed switches.

The topic concerns fundamental limitations on field-matter interactions in linear wave phenomena such as electromagnetism and acoustics. Tweezing and trapping will be among the core interests. The primary goal is to quantify physical limits on these processes, which can serve as natural benchmarks for designing devices that directly employ these interactions. Among them are optical tweezers, electrophoresis benches, or Raman spectroscopes, indispensable tools in chemistry and biology. Field-integral equations discretized using Galerkin’s procedure and optimal source densities will be the primary tool. This doctoral topic presents multidisciplinary research connecting physical understanding with mathematical modeling and optimization.