Breakdown of effective-medium theory in dielectric composites containing epsilon-near-zero constituents

Dielectric composites are believed to tightly obey the effective-medium theory (EMT) when their dimensions are much smaller compared to the wavelength inside them. It is naturally expected that when the refractive indices of a part of the constituent materials approach zero, the validity of the EMT is further strengthened. Here, we demonstrate that the EMT breaks down in deep-subwavelength dielectric composites containing homogeneous epsilon-near-zero (ENZ) constituents, which is contrary to the above intuitive picture, as validated by both the Bloch-wave analysis and numerical simulations. This breakdown of EMT originates in the presence of strong evanescent waves emerging on the interfaces between the constituent materials, which stem from the extreme mismatch of energy-flux distributions between them. The energy flux within such composites is highly nonuniform: significantly enhanced in the ENZ constituents and largely depressed in other normal constituents. When such composites are illuminated by planar waves with uniform energy-flux distributions, evanescent waves for redistributing flux into the ENZ constituents are generated on the internal interfaces of the composites, and lead to properties beyond the prediction of traditional EMT. Our work unveils the mechanism of EMT breakdown in dielectric composites with constituents of near-zero permittivity.