Time-domain mathematical modeling of external cloak metamaterials with an unconditionally stable finite element method

Since the cloaked object of the external cloaking device is outside the device, it is not affected by the space of the device and does not need to be wrapped with special materials, so the external cloaking device is of important research value. In this paper, a time-domain mathematical model of a cylindrical external cloaking device is constructed based on optical coordinate transformation and Lorentz dispersion model, and an unconditionally stable time-domain finite element scheme is developed to simulate the electromagnetic wave propagation in the external cloak by using a combination of the Leapfrog-ADI method and the finite element method, and the unconditional stability of the method is proved. The time-domain numerical simulations validate our theoretical analysis of the time-domain external cloaking device model and the effectiveness of the FETD method. For different incident wave irradiation, the external cloak shows different operating states, and the scattering direction maps and scattering power at different moments verify the scattering of electromagnetic field during the whole process.