  Periodic structures with Bloch dispersion relation supporting a stationary
inflection point (SIP) can display a unique scattering feature, the frozen mode
regime (FMR). The FMR is much more robust than common cavity resonances; it is
much less sensitive to the boundary conditions, structural imperfections, and
losses. Using perturbation theory, we analyze the FMR in the realistic case of
a finite fragment of a periodic structure. We show that in close proximity of
SIP frequency, the character of the FMR is qualitatively different from the
known case of a semi-infinite structure.
