Utilization of controllable ferroelectric and ferromagnetic layers coating a conducting object to provide an attenuation capability against electromagnetic interrogation is discussed. The problem is formulated as a differential game and/or a robust optimization. The scattered field due to interrogation can be attenuated with the assumption of an uncertainty in the interrogation wave numbers. The controllable layer composed of ferromagnetic and ferroelectric materials [9, 10] is incorporated in a mathematical formulation based on the time-harmonic Maxwell equation. Fresnel's law for the reflectance index is extended to the electromagnetic propagation in anisotropic composite layers of ferromagnetic and electronic devices and used to demonstrate feasibility of control of reflections. Our methodology is also tested for a non-planar geometry of the conducting object (an NACA airfoil) in which we report our findings in the form of reduced radar cross sections (RCS).

We consider electromagnetic evasion-interrogation games wherein the evader can use ferroelectric material coatings to attempt to avoid detection while the interrogator can manipulate the interrogating frequencies (wave numbers) and angles of incidence of the interrogating inputs to enhance detection and identification. The resulting problems are formulated as two player games in which one player wishes to minimize the reflected signal while the other wishes to maximize it. Simple deterministic strategies are easily defeated and hence the players must introduce uncertainty to disguise their intentions and confuse their opponent. Mathematically, the resulting game is carried out over spaces of probability measures which in many cases are appropriately metrized using the Prohorov metric.