Wigner delay times of Frozen Mode Regime in the presence of weak disorder

Our ability to control wave transport via dispersion management is one of the greatest achievements of the last thirty years. It offers us the possibility to reduce a wave’s group velocity, thereby enhancing wave-matter interaction. One way to achieve this slow wave propagation is through stationary inflection point (SIP) singularities where the relation between frequency and the wavenumber can be approximated as (w-w₀) ~ (k-k₀)³. When an infinite periodic system is studied in the scattering scenario, the SIP gives rise to the so-called frozen mode regime (FMR). We investigate the stability of this FMR in the presence of (weak) disorder and derive scaling expressions (both with respect to the size of the sample and frequency detuning) of Wigner delay time, which provide a measure of time that a particle spends inside the scattering domain.