Numerical versus analytical I_c(H) patterns in Josephson junctions with periodically alternating critical current density

An analytical expression for the magnetic-field-dependent critical current I_c(#) of Josephson junctions with periodically alternating critical current density J_c(x) is derived within the uniform field approximation. Comparison with numerically calculated I_c(H) patterns for junctions with identical, thick, periodically arranged defects with the corresponding analytical expression reveals fair agreement for a wide range of parameters, due to increased characteristic length. Based on qualitative arguments, we give the dependence of the new characteristic length on the geometrical parameters of the junction, which is in agreement with self-consistent calculations with the static sine-Gordon equation. The analytical expression captures the observed qualitative features of the I _c(H) patterns, while it is practically exact for short junctions or high fields. It also produces the shift of the major peak from the zero-field position of the standard Fraunhofer pattern to another position related to the periodicity of the critical current density in φ-junctions.