Beam focusing in metamaterials with electric and magnetic nonlinearities

Based on the Drude mode, beam focusing in metamaterials with both electric and magnetic nonlinearities are investigated, both analytically and numerically. The results show that beam focusing occurs not only in self-focusing nonlinear materials (positive-index region), but also in self-defocusing nonlinear material (negative-index region). In addition, the self-focusing effect is stronger when the plasma frequency of the material shifts closer to the central frequency of the beam. In particular, when the signs for electric and magnetic susceptibilities are different, the sign of nonlinearity for metamaterials can be engineered by varying the relative magnitude between electric and the magnetic plasma frequencies. This provides us an alternative approach to manipulate beam propagation at wi