Magnetic field of Josephson vortices outside superconductors
  We consider the structure of Josephson vortices approaching the junction boundary with vacuum in large area Josephson junctions with the Josephson length $\lambda_J$ large relative to the London penetration depth $\lambda_L$. Using the stability argument for one-dimentional solitons with respect to 2D perturbations, it is shown that on the scale $\lambda_J$ the Josephson vortices do not spread near the boundary in the direction of the junction. %, which is in a striking difference with behavior of Abrikosov vortices exiting superconductors. The field distribution in vacuum due to the Josephson vortex is evaluated, the information needed for the Scanning SQUID Microscopy. 
V. G. Kogan and V. V. Dobrovitski