Figure of merit for design of ε-near-zero metamaterials with enhanced Kerrtype nonlinearities

Metamaterials are artificial media designed to display properies going beyond those of ordinary materials. Particularly interesting are ε-near-zero (ENZ) media with real part of the permittivity going to zero in a certain spectral range. Examples of ENZ metamaterials are metal dielectric multilayers, which allow to tune the position of the ENZ wavelength depending on their composition and which have been found to have enhanced Kerr-type nonlinearities, i.e. nonlinear absorption and nonlinear refraction. In this work we define a figure of merit for the design of multilayer metamaterials with strong Kerr-type nonlinearities and compare our predictions with both simulations and experimental results