A time domain energy theorem for scattering of plane electromagnetic waves
Abstract
A time domain energy theorem for the scattering of plane electromagnetic waves by an obstacle of bounded extent is derived. It is the counterpart in the time domain of the "optical theorem" or the "extinction cross section theorem" in the frequency domain. No assumptions as to the electromagnetic behavior of the obstacle need to be made; so, the obstacle may be electromagnetically nonlinear and/or time variant (a kind of behavior that is excluded in the frequency domain result). As to the wave motion, three different kinds of time behavior are distinguished: (1) transient, (2) periodic, and (3) perpetuating, but with finite mean power flow density. For all three cases the total energy (case 1) or the timeaveraged power (cases 2 and 3) that is both absorbed and scattered by the obstacle is related to a certain time interaction integral of the incident plane wave and the sphericalwave amplitude of the scattered wave in the farfield region, when observed in the direction of propagation of the incident wave. The practical implications of the energy theorem are briefly indicated.
 Publication:

Radio Science
 Pub Date:
 September 1984
 DOI:
 10.1029/RS019i005p01179
 Bibcode:
 1984RaSc...19.1179D
 Keywords:

 Absorption Cross Sections;
 Electromagnetic Absorption;
 Electromagnetic Scattering;
 Energy Absorption;
 Plane Waves;
 Time Response;
 Far Fields;
 Scatter Propagation;
 Scattering Amplitude;
 Spherical Waves;
 Communications and Radar