Scattering of electromagnetic fields by a defect layer embedded in a slow-light periodically layered ambient medium exhibits phenomena markedly different from typical scattering problems. Such a medium, constructed by Figotin and Vitebskiy, possesses a “frozen mode” at a frequency within a pass band, where the dispersion relation has a flat inflection point. The slow-light regime is characterized by a 3×3 Jordan block of the monodromy matrix. This results in the breakdown of the harmonic scattering problem at a single frequency and complicated and subtle pathological scattering nearby, exhibiting delicate cancelation of large modal coefficients. Two distinct cases emerge: the generic, non-resonant case when the quadratically growing mode is excited; and the resonant case, when a defect-guided frozen mode is resonantly excited. This joint work with Aaron Welters.