Study Of The Formation And Propagation Of Ultrashort Electromagnetic Solitons In Metamaterials

Metamaterials (MMs), with particular and abundant linear and nonlinear electromagnetic properties, contain vast solitary phenomena; at the same time, their electromagnetic properties, which can be artificially tuned at will, offer conditions and measures for forwardly manipulating solitons. Based on studying and summarizing predecessors's research works, this paper searches the exact solitary solutions of ultra-short electromagnetic pulses propagation equation in nonlinear metamaterials by using the mature method to solve nonlinear evolution equations. Combining with the special properties of metamaterial, the formation of solitons and the condition and properties of steady propagation are analyzed, which has theory and fact meanings to enrich and develop soliton physics, develop relative photon devices and optical-controlled optical technologies based on metamaterials. The main research results are as following:Firstly, from the Maxwell equation, the nonlinear Schr?dinger equation of propagation of ultrashort electromagnetism pulse in nonlinear metamaticals is particularly derived; combining with the special properties of metamaterials, the properties of each coefficients of nonlinear Schr?dinger equation and the influence of them to the propagation of ultra-short pulses are analyzed.Secondly, exact solitary solutions of nonlinear Schr?dinger equation are solved in the case of different parameters by using an extended Tanh-Function method. Then each effect, especially, the influence of higher-order dispersion effect, the controlled self-steepening (SS) effect and second-order nonlinear dispersion (SOND) to the formation and propagation of solitons are analyzed. The results indicate: third-order dispersion (TOD) can make the soliton center move, thereinto, the positive and negative TOD respectively makes the soliton center move to the trailing or leading side of soliton; The negative SS effect MMs peculiarly possess makes the soliton center move to the leading side of soliton, opposite to that in ordinary material in which the SS effect is always positive; Most importantly, due to the role of the SOND, solitons can be formed in the absence of linear dispersion, or even in the case of anomalous linear group-velocity dispersion.