Energy and Dispersion in Electromagnetic Systems

Abstract

The total average electromagnetic energy of a loss-free system is expressed in terms of the frequency dependence of the fields on an arbitrary mathematical surface enclosing the system. By introducing scattering, admittance, and impedance matrices the surface integral is reduced and the energy written as quadratic forms involving the frequency derivatives of these matrices. The arguments are of sufficient generality to apply in the presence of inhomogeneous, dispersive, and anisotropic or gyrotropic media. The requirement that the total energy be positive leads to important restrictions on the frequency dependence of the parameter matrices. The application to extensions of Foster's reactance theorem is discussed.