The Transmission Of A New Type Of Solitary Waves And Higher-order Solitons In Metamaterials

Metamaterials(MMs) is a new type of artificial materials with dispersive dielectric permittivity ε and magnetic permeability μ. By designing the structure and size of the mediums, one can achieve either positive or negative dielectric permittivity and magnetic permeability, then realize a positive or negative refractive index. To date, a number of linear and nonlinear MMs have been studied in theory and experiment over a range of frequencies from microwave to optical region. With the emergence of nonlinear optical MMs, the propagation of ultrashort laser pulses in such particular mediums has aroused great interest as a new research focus.In this paper, based on the equation describing the propagation of ultrashort pulses in MMs, the transmission of a new type of combined solitary waves and higher-order solitons in MMs is investigated.The combined solitary wave solutions are obtained, then the transmission characteristics is analytically and numerically analyzed in detail. Furthermore, we numerically study the transmission of higher-order solitons under higher-order effects and carry out a detailed analysis of the transmission stability of bright2-soliton, bright3-soliton, dark2-soliton, and dark3-soliton in MMs. The obtained results may provide some references for further studies of the existence and transmission of higher-order bright solitons, dark solitons and combined solitary waves in MMs.The main contents are as follow:(1) We outline the background and status of MMs and introduce the theory and research progress of the transmission of ultrashort pulses in MMs.(2) Based on the nonlinear Schrodinger equation describing the propagation of ultrashort pulses in MMs, we obtain a new type of solitary wave solutions and the corresponding existence conditions by a trigonometric function expansion method, then analytically and numerically analyze the transmission characteristics in MMs. The results show that bright and dark solitary waves may combine together under certain conditions, representing brightlike and darklike solitary waves, and the darklike solitary waves are more stable than the brightlike ones in MMs.(3) Based on the higher order nonlinear Schrodinger equation describing the propagation of ultrashort pulses in MMs, the transmission characteristics of higher-order bright and dark solitons in MMs under the influence of higher-order effects is studied numerically. Numerical simulations show that third-order dispersion and self-steepening effects lead to the split and radiation of higher-order solitons damaging the periodical evolutions of higher-order bright solitons, and result in asymmetry split of higher-order dark solitons. The higher the order of the solitons is, the stronger the influence of these effects is. Due to the controllable dispersion and nonlinearity of MMs, it is easy to obtain the stable transmission of bright2-soliton, dark2-soliton and dark3-soliton in MMs by adjusting the coefficients of third-order dispersion and self-steepening effects.