Two-peaked and flat-top perfect bright solitons in nonlinear metamaterials with epsilon near zero

We investigate analytically transverse-magnetic spatial bright solitons, as exact solutions of Maxwell's equations, propagating through nonlinear metamaterials whose linear dielectric permittivity is very close to zero and whose effective nonlinear Kerr parameters can be tailored to achieve values not available in standard materials. Exploiting the fact that, in the medium considered, linear and nonlinear polarization can be comparable at feasible and realistic optical intensities, we identify two self-trapping mechanisms able to support two-peaked and flat-top solitons, respectively. Specifically, these two mechanisms are based on the occurrence of critical points at which the effective nonlinear permittivity vanishes, the two mechanisms differing in the way the compensation between linear and nonlinear polarization is achieved through the nonstandard values of the nonlinear parameters.