Visualization of waves in the Maxwell dynamical system (the BC-method)

The paper develops an approach to the Inverse Problems using their relations to the Boundary Control Theory (the BC-method). One of main tools of the approach is the so-called Amplitude Formula (AF) based upon the Geometrical Optics and properties of controllability of dynamical systems. The AF makes the waves propagating into a domain be visible for an external observer performing measurements at a boundary. In the paper a natural analog of the AF is obtained for a system governed by the Maxwell equations. As an auxilliary result, an approximate controllability of electric component of the system is established under some assumptions of geometrical character.