Self-trapping of nanoparticles by bound states in the continuum

In the first tutorial part of the paper, we show that equilibrium positions of small dielectric particles inside the Fabry-Perot resonator (FPR) are sensitive to a frequency of incident electromagnetic wave and size of particle. That elucidates basic principles of resonant trapping of nanoparticles by excitation of high-$Q$ resonances of FPR. In the second part, we consider a long dielectric cylinder with submicron radius (primary cylinder) integrated into a metallic waveguide which supports symmetry-protected bound states in the continuum (BICs). We consider the case of a slightly shifted cylinder relative to the axis of symmetry of a waveguide that controls the $Q$ factor of quasi-BIC. Then, the extra nanoparticle perturbs quasi-BIC as dependent on the size of the nanoparticle and position relative to the primary cylinder. An interplay between the resonant width of quasi-BIC and a degree of frequency perturbation defines whether a dragging nanoparticle is terminated at a surface of the primary cylinder for an ultrasmall size of nanoparticles or at the definite distances from the cylinder for the larger size of nanoparticles. Thereby, we demonstrate a paradigm of resonant self-trapping and sorting of nanoparticles by use of quasi-BICs. We also show extremal sensitivity of self-trapping to the frequency of an electromagnetic (EM) wave propagating over waveguide.