  We derive effective photon modes that facilitate an intuitive and convenient
picture of photon dynamics in a structured Kramers-Kronig dielectric in the
limit of weak absorption. Each mode is associated with an effective line-width
which determines the temporal decay rate of the photon. These results are then
applied to obtain an expression for the Beer-Lambert-Bouguer law absorption
coefficient for unidirectional propagation in structured media consisting of
dispersive, weakly absorptive dielectric materials.
