Soft surfaces and enhanced nonlinearity enabled via epsilon-near-zero media doped with zero-area perfect electric conductor inclusions

Introducing a dielectric inclusion inside an epsilon-near-zero (ENZ) host has been shown to dramatically affect the effective permeability of the host for a TM-polarized incident wave, a concept coined as photonic doping [Science 355, 1058 (2017)]. Here, we theoretically study the prospect of doping the ENZ host with infinitesimally thin perfect electric conductor (PEC) inclusions, which we call 'zero-area' PEC dopants. First, we theoretically demonstrate that zero-area PEC dopants enable the design of soft surfaces with an arbitrary cross-sectional geometry. Second, we illustrate the possibility of engineering the PEC dopants with the goal of transforming the electric field distribution inside the ENZ while maintaining a spatially invariant magnetic field. We exploit this property to enhance the effective nonlinearity of the ENZ host.