Sculpting microscopic magnetic flux landscapes in a BSCCO2212 vortex lens

We demonstrate experimentally that the micromagnetic profile of the out-of-plane component of magnetic induction, B_z, in the crossing lattices regime of layered superconductors can be manipulated by varying the in-plane magnetic field, H_{||}. Moving Josephson vortices drag/push pancake vortex stacks, and the magnetic profile, B_z(x), can be controllably sculpted across the entire single crystal sample. Depending on the H-history and temperature we can increase or decrease the flux density at the center and near the edges of the crystal by as much as 40%, realising both 'convex' and 'concave' magnetic flux lenses. Our experimental results are well described by molecular dynamics simulations.