Kramers-Kronig relations and the barrier interaction time problem

It is shown that the two characteristic interaction times \(\) and \(\) for classical electromagnetic waves with an arbitrarily shaped barrier are not independent quantities, but are connected by Kramers-Kronig relations for the real and imaginary components of a causal magnitude. The corresponding macroscopic sum rule for the complex time is also derived. An analogy between the interaction time problem and an electrical circuit with capacitive and conducting frequency dependent components is established.