Slowdown of group velocity in periodic waveguides

TL;DR

This paper derives asymptotic formulas for the group velocity in one-dimensional periodic waveguides, revealing conditions for frequency-independent slowdown unrelated to resonance phenomena.

Contribution

It provides new asymptotic expressions for group velocity in periodic media, highlighting frequency-independent slowdown effects based on material parameters.

Findings

Minimum group velocity occurs at equal volume fractions of components.

Group velocity slowdown is frequency-independent in the asymptotic regimes.

Leading terms of group velocity do not depend on frequency.

Abstract

We consider the propagation of acoustic, electromagnetic and elastic waves in a one-dimensional periodic two-component material. Accurate asymptotic formulas are provided for the group velocity as a function of the material parameters when the concentration of scatterers is small or the characteristic impedances of the two media differ substantially. In the latter case, it is shown that the minimum group velocity occurs when the volume fractions of the components of the material are equal. In both asymptotic cases we show that the leading terms of the group velocity do not depend on frequency. Thus slowdown is frequency-independent and is not related to the resonance phenomena.