Frozen Mode Regime in Finite Periodic Structures

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.