Nonlinear beams and active controllable field concentrator with isotropic metamaterials

The idea of nonlinear field concentrator, inspired by papers on “linear black hall” and transformational optics [13] was originally proposed in the series of our conference papers [5-8]. We emphasize an importance of the strong nonlinearity, not considered in the resent papers [9, 10], where, in fact, only weak (Kerr-type) nonlinearity was included without any saturation. Namely, inclusion of strong (non-Kerr) saturable nonlinearity becomes very important in the “regime of superfocusing”. Such a regime occurs during consequent linear and nonlinear focusing in the layered cylindrical structure, respectively in the external cylinder, where dielectric constant increases towards the center of the system and in the internal cylindrical region with nonlinear permittivity, linear part of which remains constant in space (and permittivity depends only on field intensity distribution). When amplitude exceeds some threshold value, the tendency to strongly nonlinear focusing, actually, “hot spot” formation, is observed. The new step done in the present paper is the demonstration of effective nonlinear controllability of the proposed [5-8] nonlinear effect. Namely, we have shown that the state of isotropic nonlinear field concentrator can be pushed into a regime of strongly nonlinear focusing, when two incident beams are used and an amplitude of one of these beams is gradually increased. Therefore we propose a possibility of a control of focusing of one (“signal”) beam by means of amplitude of another (controlling”) beam in a nonlinear field concentrator. In spite of a fact that of our evaluations are done for optic regime, a possibility of similar nonlinear signal processing is expected in wide range of frequencies, “from acoustic to optics”. We demonstrate only a general idea of “beam-beam control”, while more detail description of this new proposition will be a subject of another paper. Systems under consideration could be used for creation of antenna with strongly nonlinear focusing, achieving strongly nonlinear effects such as higher harmonic generation etc.