Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction

We study one- and two-dimensional transmission of electro-magnetic waves through a finite slab of a dielectric material with negative refraction. In the case when the dielectric slab possesses an intensity-dependent nonlinear response, we observe the nonlinearity-induced wave transmission through an opaque slab accompanied by the generation of spatiotemporal solitons. We solve this problem numerically, by employing the finite-difference time-domain simulations, for the parameters of microstructured materials with the negative refractive index in the microwave region, but our results can be useful for a design of nonlinear metamaterials with the left-handed properties in other frequency range.