Transmission Properties Of Exact Bright-like And Dark-like Solitons In Metamaterials

Metamaterial(MM) is a new type of artificial composite materials. Different from ordinary medium, MMs have dispersive dielectric permittivity and dispersive magnetic permeability, and may possess negative index by engineering the structure and size of materials and present the unique properties that ordinary media couldn’t have. In recent years, most researchers both at home and abroad study the MMs with linearity and nonlinearity at microwave and light wave bands. With the development of nonlinear MMs, the nonlinear transmission of ultrashort pulses in MMs has attracted widespread interest as a new research hotspot.In this dissertation, based on the generalized nonlinear Schrodinger equation which describes the propagation of ultrashort pulses in MMs, two sets of the exact bright-like and dark-like soliton solutions are obtained by ansatz method, and the existence conditions and the transmission properties of such soliton solutions are analyzed in detail. In addition, we numerically investigate the transmission stabilities of these bright-like and dark-like solitons. These research results may provide some references in developing and enriching soliton theory and manufacturing the related devices in MMs.The main contents are as follows:(1) Introduce the background and research progress of MMs, and outline the status of transmission of ultrashort pulses and optical solitons in nonlinear MMs.(2) Based on the generalized nonlinear Schrodinger equation which describes the propagation of ultrashort pulses in MMs, we obtain a new type of bright-like and dark-like solitons by ansatz method, and analyze the corresponding existence conditions and transmission properties in detail. The results show that there exist the bright-like and the dark-like solitons when self-steepening coefficient is zero. Different from the counterparts in ordinary media, the bright-like solitons can exist in the anomalous dispersion regime of self-defocusing MMs; the dark-like solitons can exist in the anomalous dispersion regime of self-focusing MMs. Moreover, we numerically investigate the transmission stabilities of the bright-like and the dark-like solitons under the disturbed existence conditions.(3) Furthermore, a new set of bright-like and dark-like soliton solutions with influence of self-steepening effect in MMs are obtained by assuming a new ansatz. Different from the existence conditions of the solutions listed in (2), self-steepening effect, group velocity dispersion and pseudo five-order nonlinear effect must reach mutual balance in this situation. Moreover, such bright-like and dark-like solitons can only exist in the positive refraction region of self-focusing and self-defocusing MMs. Through numerical analysis of transmission stabilities of these solitons, we find that both the bright-like and dark-like solitons may propagate stably under small disturbed balance condition; while the dark-like soliton has better stability than the bright-like soliton under the initial pulse width fluctuation and white noise perturbation. These results imply that the dark-like soliton is more appropriate for the information carrier compared with the bright-like soliton.