Analytical solution for the field lines of dipole radiation energy flow in a dissipating host medium

We have studied the power flow out of a linear dipole embedded in an absorbing host medium. An analytical solution for the flow lines of energy has been obtained. It appears that field lines come in two types. Field lines of the first kind run from the dipole to infinity. Near the dipole, the field lines are curved, and in the far field, they approach asymptotically straight lines. These field lines are similar to the free-space field lines, with the exception that there is curving in the near field due to dissipation in the material. Field lines of the second kind curve out of the dipole and end on the dipole axis, which is a singular line of the flow field. There exists a transition field line, separating the field lines of the first and the second kind. We have shown that all field lines emanate from the dipole in a direction perpendicular to the dipole axis, and we have shown that field lines of the second kind hit the dipole axis under 90 ∘ . A simplified expression has been derived for the practical case of small damping in the material.