Magnification device for Laplace equation by using homogeneous and isotropic media with positive values

A magnification device for the Laplace equation is proposed and verified in this work. Unlike designs based on transformation optics, which are hard to realize due to the complementary media needed and the anisotropy and inhomogeneity of the resultant materials, our design only requires isotropic and homogeneous materials with positive values. The method of separation of variables is utilized to realize the magnification device, and the first experiment demonstration for the device is given, where we utilize the resistor network to mimic the problem. The measurement results validate the exact magnifying property of our proposal. Our design is suitable for the time-varying fields under quasi-static conditions, it applies directly in thermodynamics, and other problems governed by the Laplace equation.