Reconstructing critical current density in Josephson junctions with phase nonlinearity

In this Letter, we show that the standard Dynes-Fulton analysis, commonly used to reconstruct the critical current density from interference patterns, breaks down in Josephson junctions with nonlinear phase distributions, leading to non-physical artifacts. To address this, we developed a simple iterative reconstruction algorithm and validated it both numerically and experimentally using a planar Josephson junction model. Unlike conventional approaches based on the logarithmic Hilbert transform, the proposed method allows for incorporating prior knowledge about the system and addresses the fundamental issue of ambiguity in reconstructing the critical current density from interference patterns.