Asymptotic Theory of Cerenkov Radiation in Inhomogeneous Media

Abstract

The problem of Cerenkov radiation in infinite inhomogeneous media is considered. The mathematical description of this phenomenon is given by the integro-differential system of equations for the electromagnetic field in a dispersive medium. The leading term of the asymptotic expansion of the electromagnetic field is obtained by applying an expansion procedure called the ``ray method.'' In this method all the functions that appear in the expansion satisfy ordinary differential equations along certain space-time curves called rays. The source which gives rise to the radiation is taken to be quite general. In fact, it is shown that any multipole moving along an arbitrary trajectory is a special case of the general source considered. From the expansion of the fields an expression for the total energy of the radiation is determined. Then, as an example, the case of plane-stratified media is treated in detail.