Designing arrays of Josephson junctions for specific static responses

We consider the inverse problem of designing an array of superconducting Josephson junctions that has a given maximum static current pattern as a function of the applied magnetic field. Such devices are used for magnetometry and as terahertz oscillators. The model is a 2D semilinear elliptic operator with Neuman boundary conditions so the direct problem is difficult to solve because of the nonlinearity and the multiplicity of solutions. For an array of small junctions in a passive region, the model can be reduced to a 1D linear partial differential equation with Dirac distribution sine nonlinearities. For small junctions and a symmetric device, the maximum current is the absolute value of a cosine Fourier series whose coefficients (respectively wave numbers) are proportional to the areas (respectively the positions) of the junctions. The inverse problem is solved by inverse cosine Fourier transform after choosing the area of the central junction. We present several examples and show that the reconstruction is robust and that its accuracy can be controlled. These new devices could then be tailored to meet specific applications.