Meissner-London state in superconductors of rectangular cross section in a perpendicular magnetic field

The Meissner state with finite London penetration depth is analyzed for platelet samples of rectangular cross section in a perpendicular magnetic field. The exact two-dimensional numerical solution of the London equation is extended analytically to the realistic three dimensional case. Data obtained on Nb cylinders and foils, as well as single crystals of Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O, are in a good agreement with the model. The results are particularly relevant for magnetic susceptibility, rf, and microwave resonator measurements of the magnetic penetration depth in high-$T_c$ superconductors.