Nonlinear Surface Polaritons In Indefinite Media

In the recent years, surface polaritons, which propagate along the interfacebetween two media and decay in the transverse directions, have drawn considerableattention in novel metamaterial with simultaneous negative permittivity and negativepermeability. The unique properties of metamaterial such as negative refraction andnegative phase velocity, enriched the field of research on electromagnetic wavepropagation, leading to novel phenomenons which are different with the case inconventional media.The nonlinear surface polaritons in metamaterial may have robust propertiescompared with linear regime. After the realization of nonlinear metamaterial in2003, study of nonlinear surface polaritons has been a more interesting topic. In asingle interface configuration, the negative refractive metamaterial can supportnonlinear surface wave for both self-focusing and self-defocusing nonlinearity. Thenonlinear surface polaritons can also exist in nonlinear waveguide structures.A slabwaveguide with a negative refractive matamaterials core surrounded by a claddingwith Kerr nonlinearity was shown to support unusual types of modes which do notexist in conventional waveguides. It was also shown that the nonlinear negativerefractive waveguide can propagate bright and dark soliton-like nonlinear guidedmodes-nonlinear surface waves.Usually, the works discussed above assumed the negative refractivemetamaterials is isotropic. Nevertheless, the metamaterials fabricated in experimentare intrinsically anisotropic on account of the orientations of the rings and rods inspace. Indefinite metamaterial, one of the anisotropic metamaterials, in which not allthe principal components of the electric permittivity and magnetic permeabilitytensors have the same sign, can offer four different types of dispersion relationsand therefore owns much more peculiar electromagnetic properties. The existence conditions of linear surface polaritons have been studied at a single interfacebetween an indefinite media and a conventional media.The waveguide with anindefinite media core can support both fast wave guided modes and the slow wavesurface polaritons. Xu et. al. have also investigated the nonlinear surface polaritonsat a single interface between an anisotropic Kerr-type indefinite metamaterials and alinear conventional media.In this paper, we make theoretical investigation of nonlinear surface polaritonslocalized at the single interface separating a nonlinear conventional dielectric mediaand a linear indefinite media,the result are as follows:1．Based on the continuity of the fields at the interface, we derive the dispersionrelation of the nonlinear surface waves. According to the classification of thefrequency,we discuss the existence of the nonlinear surface polaritons. And finnallywe find that the surface effect of beam is very different with the propagation(transmission) effect in indefinite media. The always cut-off media can support thenonlinear surface polaritons but the never cut-off media can not support thenonlinear surface polaritons.2．In the first type of always cut-off media, there exist a singular frequency ofthe nonlinear surface polaritons at which the group velocity has a sudden transition，which has potential application in group velocity controlling.