Frequency-tunable quartic soliton in nonlinear negative-index metamaterials

An exact quartic soliton solution along with its constraint conditions in metamaterials (MMs) is presented on the basis of the nonlinear Schro center dot dinger equation (NLSE) with second-, third- and fourth-order diffraction. Through analyzing the parameter relations based on the Drude model, it is demonstrated that the quartic soliton can only exist in the negative-index region (NIR) of self-focusing nonlinear MMs. With insight into the underlying parameter relations of quartic soliton, it is found that by selecting suitable frequency of incident wave, the quartic soliton in negative-index MMs (NIMs) exhibits frequency tunability or frequency stability. Particularly, the quartic solitons with different frequencies can propagate in an identical velocity, which provides a theoretical basis for realizing frequency division multiplexing (FDM) technology in nonlinear MMs. Different from purequartic soliton (PQS) in ordinary materials exhibiting oscillatory decaying tails in spatial domain and a flat top in frequency domain on logarithmic scale, the quartic soliton reported here possesses triangular distributions in both spatial and frequency domains. The presented results contribute to a fundamental theoretical support for future application of quartic soliton and are beneficial for exploring new solitary waves in MMs.