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Scattering of electromagnetic fields by a defect layer embedded in aslow-light periodically layered ambient medium exhibits phenomena markedlydifferent from typical scattering problems. In a slow-light periodic medium,constructed by Figotin and Vitebskiy, the energy velocity of a propagating modein one direction slows to zero, creating a "frozen mode" at a single frequencywithin a pass band, where the dispersion relation possesses a flat inflectionpoint. The slow-light regime is characterized by a $3\!\times\!3$ Jordan blockof the log of the $4\!\times\!4$ monodromy matrix for EM fields in a periodicmedium at special frequency and parallel wavevector. The scattering problembreaks down as the 2D rightward and leftward mode spaces intersect in thefrozen mode and therefore span only a 3D subspace $\mathring{V}$ of the 4Dspace of EM fields.  Analysis of pathological scattering near the slow-light frequency andwavevector is based on the interaction between the flux-unitary transfer matrix$T$ across the defect layer and the projections to the rightward and leftwardspaces, which blow up as Laurent-Puiseux series. Two distinct cases emerge: thegeneric, non-resonant case when $T$ does not map $\mathring{V}$ to itself andthe quadratically growing mode is excited; and the resonant case, when$\mathring{V}$ is invariant under $T$ and a guided frozen mode is resonantlyexcited.

Pathological scattering by a defect in a slow-light periodic layered medium