Scaling theory of absorption in the frozen mode regime

A stationary inflection point (SIP) of the Bloch dispersion relation of a periodic system is a prominent example of an exceptional point degeneracy (EPD) where three Bloch eigenmodes coalesce. The scattering problem for a bounded photonic structure supporting a SIP features the frozen mode regime (FMR), where the incident wave is converted into the "frozen mode" with vanishing group velocity and diverging amplitude. We analyze the effect of losses and disorder on the FMR and develop a scaling formalism for the absorbance in the FMR that takes into consideration losses, disorder, and system size. The signatures of the 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 localization length.