Static properties and waveguide modes of a wide lateral window Josephson junction

We developed an efficient hybrid mode expansion method to study the maximum tunneling current as a function of the external magnetic field for a 2D la rge area lateral window junction. We consider the inhomogeneity in the crit ical current density, which is taken a piecewise constant. The natural mode s of the expansion in y, are the linearized eigen-modes around a static sol ution which satisfies the 1D sine-Gordon equation with the critical current variation in y, and the boundary conditions determined by the overlap comp onent of the bias current, which can be inline or overlap like. The magneti c field along with the inline component of the bias current enters as a bou ndary condition on the modal amplitudes. We obtain fast convergent results and for a ratio of idle to window widths of w(0)/w = 4 (in units of lambda( J)), only two modes are needed. A simple scaling is obtained for the maximu m tunneling current as we vary the idle region width. We also present the l inear electromagnetic waveguide modes taking into account the variation nor mal to the waveguide of the critical current and the capacitance.