Scaling theory of absorption in frozen mode regime

William Tuxbury

An exceptional point degeneracy (EPD) in the transfer matrix spectrum of a periodic system, leads to the formation of a stationary inflection point in its Bloch dispersion relation. Its presence ensures that the associated scattering set-up supports a Frozen Mode Regime (FMR) corresponding to slow light. We analyze the consequences of losses, disorder and nonlinearity in the formation of the FMR and develop a scaling formalism for the absorbance in the FMR that takes into consideration these parameters with respect to system size. The signatures of EPD appear as an abrupt growth of absorbance for system sizes greater than a characteristic length that follows a parallel resistance law involving the absorption length and the Anderson or nonlinear localization lengths, respectively.