Using basic considerations on the average power absorbed in ultra-thin conducting films, we derive a closed-form expression for the average electric- field intensity enhancement (FIE) due to epsilon-near-zero (ENZ) polariton modes. We show that FIE in ENZ media with realistic losses reaches a maximum value in the limit of ultra-small film thickness. The maximum value is reciprocal to the second power of ENZ losses. This is illustrated in an exemplary series of aluminum-doped zinc oxide nanolayers of varying thickness grown by atomic layer deposition technique. The limiting behavior of FIE is shown in exact cases of the perfect absorption, normal incidence, and in a case of ultra- thin lossless ENZ films. Only in the case of lossless ENZ films FIE is inversely proportional to the second power of film thickness as it was predicted by S. Campione, et al. [Phys. Rev. B 91, 121408(R) (2015)]. We also show that FIE could achieve values as high as 100,000 in ultra-thin polar semiconductor films, which have losses as small as 0.02 close to the longitudinal optic (LO) phonon frequency.
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Field enhancement of epsilon-near-zero modes in realistic ultrathin absorbing films
Abstract 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.
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- Award ID(s):
- 2113010
- PAR ID:
- 10443275
- Date Published:
- Journal Name:
- Nanophotonics
- Volume:
- 12
- Issue:
- 14
- ISSN:
- 2192-8606
- Page Range / eLocation ID:
- 2913 to 2920
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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