Spin-polarized neutron-reflectivity measurements have been performed on superconducting Pb films. For fields applied in the plane of the film we are able to determine the magnetic field profile across the thickness of the film in the superconducting state. This allows the direct observation of distinct mesoscopic ground states in this geometry, from Meissner expulsion to a double row of vortices, which occur as a function of film thickness and external magnetic field. The data can be compared directly with solutions of the time-dependent Ginzburg-Landau equations, where we demonstrate good agreement between data and simulation. This provides a powerful demonstration of this widely applicable experimental technique to study mesoscopic ground states and a useful validation of this theoretical approach.

• Received 3 September 2009

DOI:https://doi.org/10.1103/PhysRevB.80.134510