Studies Of The New Soliton-like Solutions And Their Interactions In Metamaterials

Metamaterials(MMs) are a kind of artificial materials, which may have the negative permittivity and permeability at the same time, obtaining the negative refractive index by designing the structure and size of their micro-units. The artificial controllable electromagnetic properties provide much possibility to form the solitons in MMs.In this thesis, based on the model of normalized nonlinear Schrodinger equation which describes the ultrashort pulses transmission in MMs, we find two new types of bright- and dark-like soliton solutions with and without the self-steepening effect by ansatz method. And discuss the existence conditions and transmission properties of these solitons in MMs in details. Furthermore, we take the second type of bright- and dark-like solitons as examples to investigate their interactions in MMs by numerical method. The research results may provide some references for further studying the transmission of optical solitons in MMs.The main contents are as follows:(1) The research background and current status of MMs, optical solitons and the transmission of ultrashort pulses in nonlinear MMs are introduced.(2) Based on the model of normalized nonlinear Schrodinger equation describing ultrashort pulses transmission in MMs, two new types of bright- and dark-like solitons with and without self-steepening effect are obtained respectively by using ansatz method. And the existence conditions and transmission properties of these solitons are studied in detail. The results show,1) the first type of bright- and dark-like solitons can exist in the abnormal dispersion regime of positive refraction region of self-focusing and self-defocusing nonlinear MMs; the second type of bright-like soliton can exist in the abnormal dispersion regimes of positive and negative refraction regions of self-defocusing nonlinear MMs, and in the abnormal dispersion regime of positive refraction MMs with self-focusing nonlinearity; the second type of dark-like soliton can exist in the abnormal dispersion regimes of positive and negative refraction MMs with self-defocusing nonlinearity and in the abnormal dispersion regime of negative refraction MMs with self-focusing nonlinearity; 2) under the existence conditions deviation, the bright- and dark-like solitons can maintain their shape during transmission, deviation of existence conditions only slightly influences the velocity and frequency shift of solitons-like.(3) We take the second type of bright- and dark-like solitons as examples to discuss numerically the interactions of solitons-like in MMs. The results show,1) the interactions between both the bright-like solitons and between dark-like solitons behave repulsion each other, the interactions enhance with the initial separation decrease; 2) the interactions of the bright-like solitons in negative refraction region are weaker than those in positive refraction in self-defocusing MMs, the interactions of dark-like solitons in negative refraction region are also weaker than those in positive refraction in self-focusing MMs; 3) the interactions of the dark-like solitons are weaker than the bright-like solitons. In conclusion, the dark-like solitons in negative refraction region of MMs are more appropriate as the information carrier than the corresponding bright-like solitons.