Real-time dissipation of optical pulses in passive dielectrics

We discuss the inevitable dissipation of energy that must accompany the creation of a pulse-medium excitation state in a passive dielectric. We show that there is a minimum amount of energy that an optical pulse must deposit in the medium to create a given pulse-medium state and that energy deposited beyond this minimum value must be dissipated in the medium. We compare this notion of dissipation to a related concept found by determining the fraction of energy stored in a medium that is irrecoverable by future fields. These two notions of dissipation are model-independent and form upper and lower bounds for real-time loss. Any modeldependent notion of loss that falls outside these bounds has serious conceptual difficulties. We show that a traditional notion of real-time loss based on a multiple-Lorentz oscillator model fails to give reasonable results in classes of passive linear media near EIT, while the notions of loss we introduce give sensible results for all passive media.