Frequency-tunable quartic soliton in nonlinear negative-index metamaterials

Abstract

An exact quartic soliton solution along with its constraint conditions in metamaterials (MMs) is presented on the basis of the nonlinear Schrödinger 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 pure-quartic 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.