Time Domain Coupled Field Dyadic Green Function Solution for Maxwell's Equations

Abstract

The free space time domain coupled electric and magnetic field integral equation solution for Maxwell's differential equations is derived. The coupled field integral equation solution is expressed as a vector containing the electric and magnetic fields found in terms of a surface integral over the equivalent surface currents on a boundary, an integral over the electric and magnetic current sources in the region enclosed by the boundary, and a volume integral over the initial field in the bounded region. Because of the irreversibility of the vector differential equation and the lack of spatial symmetry in the corresponding free space dyadic Green function, as a starting point the Green differential equation is replaced by the reciprocal (adjoint) equation and the dyadic Green function is replaced by its transpose. These replacements plus identities that relate the components of the Green function to its transpose lead in a straightforward way to the coupled field solution. The general dyadic expression derived here provides a framework for developing source current, boundary integral, and propagator methods that are based on the interaction between the electric and magnetic vector field components in the time domain.