Frozen Mode Regime in Finite Periodic Structures

TL;DR

This paper investigates the frozen mode regime in finite periodic structures with stationary inflection points, revealing its robustness and unique behavior near the SIP frequency through perturbation analysis.

Contribution

It provides a detailed perturbation theory analysis of the frozen mode regime in finite structures, highlighting differences from semi-infinite cases.

Findings

FMR is robust against boundary conditions and imperfections

FMR behavior differs significantly in finite vs. semi-infinite structures near SIP

Perturbation theory effectively describes FMR in finite periodic structures

Abstract

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.