Field enhancement of epsilon-near-zero modes in realistic ultrathin absorbing films

Using electrodynamical description of the average power absorbed by a conducting film, we present an expression for the electric-field intensity enhancement (FIE) due to epsilon-near-zero (ENZ) polariton modes. We show that FIE reaches a limit in ultrathin ENZ films inverse of second power of ENZ losses. This is illustrated in an exemplary series of aluminum-doped zinc oxide nanolayers grown by atomic layer deposition. Only in a case of unrealistic lossless ENZ films, FIE follows the inverse second power of film thickness predicted by S. Campione, et al. [Phys. Rev. B, vol. 91, no. 12, art. 121408, 2015]. We also predict that FIE could reach values of 100,000 in ultrathin polar semiconductor films. This work is important for establishing the limits of plasmonic field enhancement and the development of near zero refractive index photonics, nonlinear optics, thermal, and quantum optics in the ENZ regime.