Bridge in micron-sized Bi$_2$ Sr$_2$ CaCu$_2$ O$_{8 + y}$ sample act as converging lens for vortices

We report on direct imaging of vortex matter nucleated in micron-sized Bi$_2$ Sr$_2$ CaCu$_2$ O$_{8 + y}$ superconducting samples that incidentally present a bridge structure. We find that when nucleating vortices in a field-cooling condition the deck of the bridge acts as a converging lens for vortices. By means of Bitter decoration images allowing us to quantify the enhancement of vortex-vortex interaction energy per unit length in the deck of the bridge, we are able to estimate that the deck is thinner than ∼ 0.6 μm. We show that the structural properties of vortex matter nucleated in micron-sized thin samples are not significantly affected by sample-thickness variations of the order of half a micron, an important information for type-II superconductors-based mesoscopic technological devices.