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We realized a time-domain simulator based on the electrodynamics of Cooper pairs and quasiparticles in Josephson junctions. The tool, based on the charge carriers&#x0027; densities of states described by the Werthamer and Harris formalisms of Bardeen-Cooper-Schrieffer (BCS) theory, allows to analyze the behavior of current- or voltage-controlled Josephson junction-based circuits for any signal waveform, at a physical temperature comprised between the absolute temperature and the critical temperature. The simulator can account for  I-V  curve hysteresis depending on the McCumber parameter, or Shapiro and photo-assisted steps in the presence of a monochromatic microwave signal. We used the simulator to assess the behavior of MgB 2 -based Josephson junctions at THz frequencies by taking into account the presence of the two anisotropic gaps of MgB2.

Time-Domain Simulator of Josephson Junctions Based on the BCS Theory