Magnetic field of an in-plane vortex inside and outside a layered superconducting film

In the present work we study an anisotropic layered superconducting film of finite thickness. The film surfaces are considered parallel to the bc face of the crystal. The vortex lines are oriented perpendicular to the film surfaces and parallel to the superconducting planes. We calculate the local field and the London free energy for this geometry. Our calculation is a generalization of previous works where the sample is taken as a semi-infinite superconductor. As an application of this theory we investigate the flux spreading at the super-conducting surface.