Collapse of Optical Wave Controlled by Anomalous Nonlinear Diffraction in Metamaterials

In this paper, we put forward a novel method for the management of optical collapse through controlling anomalous nonlinear diffraction (NLD) originating from the vectoral effect in metamaterials with simultaneous cubic electric and magnetic nonlinearity, particularly focusing on the unusual behaviors different from those in ordinary positive-index materials. First, NLD in metamaterials can be positive or negative, which makes it possible for us to offer greatly enhanced design freedom to manipulate the behavior of optical collapse at will. Then, it is further demonstrated that the negative NLD can arrest the catastrophic self-focusing of optical wave; however, the positive NLD will lead to the acceleration of its occurrence, as opposed to the case in ordinary positive-index materials. Our analysis is performed by directly numerically solving the nonlinear Schrödinger equation, as well as by using the modulation theory, both showing consistent results. These findings show that NLD in metamaterials can provide a more powerful tool in controlling the collapse of optical wave when compared with the corresponding case in ordinary positive-index materials.